title: Hyksos

text: Josephus, and most of the writers of antiquity, associated the Hyksos with the Jews. Quoting from Manetho's "Aegyptiaca", Josephus states that when the Hyksos were expelled from Egypt, they founded Jerusalem ("Contra Apion" I.90). It is unclear if this is original to Manetho or Josephus's own addition, as Manetho does not mention "Jews" or "Hebrews" in his preserved account of the expulsion. Josephus's account of Manetho connects the expulsion of the Hyksos to another event two hundred years later, in which a group of lepers led by the priest Osarseph were expelled from Egypt to the abandoned Avaris. There they ally with the Hyksos and rule over Egypt for thirteen years before being driven out, during which time they oppress the Egyptians and destroy their temples. After the expulsion, Osarseph changes his name to Moses ("Contra Apion" I.227-250). Assmann argues that this second account is largely a mixture of the experiences of the later Amarna period with the Hyksos invasion, with Osarseph likely standing in for Akhenaten. The final mention of Osarseph, in which he changes his name to Moses, may be a later interpolation. The second account is sometimes held not to have been written by Manetho at all.


title: Hyksos

text: Over the years, especially in the early to mid 20th century, some scholars have suggested that seemingly authentic Egyptian elements in the Bible indicate the historical plausibility of the story of the Egyptian sojourn and exodus of the Israelites, including the story of Joseph, great grandson of Abraham. John Bright states that Egyptian and Biblical records both suggest that Semitic people maintained access to Egypt at all periods of Egypt's history, and he suggested that it is tempting to suppose that Joseph who, according to the Old Testament (Genesis 39:50), was in favour at the Egyptian court and held high administrative positions next to the ruler of the land, was associated to the Hyksos rule in Egypt during the Fifteenth Dynasty. Such a connection might have been facilitated by their shared Semitic ethnicity. He also wrote that there is no proof for these events. Howard Vos has suggested that the "coat of many colors" said to have been worn by Joseph could be similar to the colorful garments seen in in the tomb of Khnumhotep II.


title: Hyksos

text: Ronald B. Geobey notes a number of problems with identifying the narrative of Joseph with events either prior to or during the Hyksos' rule, such as the detail that the Egyptians abhorred Joseph's people ("shepherds"; Gen. 46:31) and numerous anachronisms. Manfred Bietak suggests that the story fits better with the ambience of the later Twentieth Dynasty of Egypt, in particular with the xenophobic policy of pharaoh Setnakhte (1189–1186 BC). And Donald Redford argues that "to read [the Joseph story] as history is quite wrongheaded," while Megan Bishop Moore and Brad E. Kelle note the lack of any extra-biblical evidence for the events of Genesis, including the Joseph story, or Exodus.


title: Hyksos

text: Scholars such as Jan Assmann and Redford have supported the notion that the story of the biblical exodus may have been wholly or partially inspired by the expulsion of the Hyksos. An identification with the Hyksos would only depart minimally from accepted biblical chronology, and their expulsion is the only known large-scale expulsion of Asiatics from Egypt. However, Bietak writes:


title: Hyksos

text: [T]he population under Hyksos rule was an urban society allied to trade and seafaring and, for a certain period, ruled Egypt (c. 1640–1530 BC). They experienced the glory of controlling the Delta and a part of the Nile valley for over 100 years. However, this is in no way in keeping with the tradition of the Israelites and their experience of oppression in Egypt. That is why an association of the Hyksos and their people with the Proto-Israelites should be dismissed.


title: Hyksos

text: Archaeological evidence suggests that the Israelites primarily emerged natively from Canaan. A number of scholars do not believe that the exodus has any historical basis at all, while only those on the fundamentalist fringes accept the entire biblical account "unless [it] can be absolutely disproved". The current consensus among archaeologists is that, if an Israelite exodus from Egypt occurred, it must have happened instead in the Nineteenth Dynasty of Egypt (13th century BC), given the first appearance of a distinctive Israelite culture in the archaeological record. The potential connection of the Hyksos to the exodus is no longer a central focus of scholarly study of the Hyksos, but this supposed connection to the Exodus has continued to inspire popular interest.


title: Hyksos

text: The Hyksos' rule continued to be condemned by New Kingdom pharaohs such as Hatshepsut, who, 80 years after their defeat, claimed to rebuild many shrines and temples which they had neglected.


title: Hyksos

text: Ramses II moved Egypt's capital to the Delta, building Pi-Ramesses on the site of Avaris, where he set up a stela marking the 400th anniversary of the cult of Set. Scholars used to suggest that this marked 400 years since the Hyksos had established their rule, however the lists of Ramesses' ancestors continued to omit the Hyksos and there is no evidence that they were honored during his reign. The Turin King List, which includes the Hyksos and all other disputed or disgraced former rulers of Egypt, appears to date from the reign of Ramesses or one of his successors. The Hyksos are marked as foreign kings via a throw-stick determinative rather than a divine determinative after their names, and the use of the title rather than the usual royal title. Kim Ryholt notes that these measures are unique to the Hyksos rulers and "may therefore have been a direct result of what seems to have been deliberate attempt to obliterate the memory of their kingship after their defeat."


title: Hyksos

text: It is "often accepted" that Egypt established an empire in Canaan at the end of the wars against the Hyksos. Campaigns against locations in Canaan and Syria were conducted by Ahmose I and Thutmose I at the beginning of the Eighteenth Dynasty, as recorded in the tombs of Ahmose, son of Ebana and Ahmose pen-Nekhebet; Thutmose I is also mentioned as having hunted elephants in Syria in inscriptions at the temple of Hatshepsut at Deir el-Bahari. Thutmose III is known to have campaigned widely, conquering the ""Shasu"" Bedouins of northern Canaan, and the land of Retjenu, as far as Syria and Mittani in numerous military campaigns circa 1450 BC. However, Felix Höflmayer argues that there is little evidence of other campaigns and that "there is no evidence that would suggest such a scenario" as an Egyptian empire during the Eighteenth Dynasty. As regards claims that the campaigns in the Near East were spurred on by Hyksos rule, Thomas Schneider argues that "the empire building started with a delay of two generations and seeing a direct nexus may be as much a historical fallacy as it would be to link the fall of the Soviet Union in 1989 to the end of the Second World War in 1945, two generations earlier."


title: Hyksos

text: The Nineteenth-Dynasty story "The Quarrel of Apophis and Seqenenre" claimed that the Hyksos worshiped no god but Set, making the conflict into one between Ra, the patron of Thebes, and Set as patron of Avaris. Furthermore, the battle with the Hyksos was interpreted in light of the mythical battle between the gods Horus and Set, transforming Set into an Asiatic deity while also allowing for the integration of Asiatics into Egyptian society.


title: Hyksos

text: Manetho's portrayal of the Hyksos, written nearly 1300 years after the end of Hyksos rule and found in Josephus, is even more negative than the New Kingdom sources. This account portrayed the Hyksos "as violent conquerors and oppressors of Egypt" has been highly influential for perceptions of the Hyksos until modern times. Marc van de Mieroop argues that Josephus's portrayal of the initial Hyksos invasion is no more trustworthy than his later claims that they were related to the Exodus, supposedly portrayed in Manetho as performed by a band of lepers.


title: Hyksos

text: The discovery of the Hyksos in the 19th century, and their study following the decipherment of ancient Egyptian scripts, led to various theories about their history, origin, ethnicity and appearance, often illustrated with picturesque and imaginative details.


title: Floor and ceiling functions

text: In mathematics and computer science, the floor function is the function that takes as input a real number , and gives as output the greatest integer less than or equal to , denoted or . Similarly, the ceiling function maps to the least integer greater than or equal to , denoted or .


title: Floor and ceiling functions

text: The integral part or integer part of , often denoted (and, historically, by a variety of other notations), is a synonym for the floor function. Some authors may define as if is nonnegative, and otherwise. For example, and . The operation of truncation generalizes this to a specified number of digits: truncation to zero significant digits is the same as the integer part.


title: Floor and ceiling functions

text: The "integral part" or "integer part" of a number ( in the original) was first defined in 1798 by Adrien-Marie Legendre in his proof of the Legendre's formula.


title: Floor and ceiling functions

text: Carl Friedrich Gauss introduced the square bracket notation in his third proof of quadratic reciprocity (1808). This remained the standard in mathematics until Kenneth E. Iverson introduced, in his 1962 book "A Programming Language", the names "floor" and "ceiling" and the corresponding notations and . Both notations are now used in mathematics, although Iverson's notation will be followed in this article.


title: Floor and ceiling functions

text: In some sources, boldface or double brackets are used for floor, and reversed brackets or for ceiling. Sometimes is taken to mean the round-toward-zero function.


title: Floor and ceiling functions

text: In the LaTeX typesetting system, these symbols can be specified with the codice_1 and codice_1 commands in math mode, and extended in size using codice_3 and codice_4 as needed.


title: Floor and ceiling functions

text: Given real numbers "x" and "y", integers "k", "m", "n" and the set of integers formula_1, floor and ceiling may be defined by the equations


title: Floor and ceiling functions

text: Since there is exactly one integer in a half-open interval of length one, for any real number "x", there are unique integers "m" and "n" satisfying the equation


title: Floor and ceiling functions

text: In the language of order theory, the floor function is a residuated mapping, that is, part of a Galois connection: it is the upper adjoint of the function that embeds the integers into the reals.


title: Floor and ceiling functions

text: The above are never true if "n" is not an integer; however, for every and , the following inequalities hold:


title: Floor and ceiling functions

text: and similarly for the ceiling and fractional part functions (still for positive and coprime "m" and "n"),


title: Floor and ceiling functions

text: None of the functions discussed in this article are continuous, but all are piecewise linear: the functions formula_39, formula_40, and formula_41 have discontinuities at the integers.


title: Floor and ceiling functions

text: Since none of the functions discussed in this article are continuous, none of them have a power series expansion. Since floor and ceiling are not periodic, they do not have uniformly convergent Fourier series expansions. The fractional part function has Fourier series expansion


title: Floor and ceiling functions

text: At points of discontinuity, a Fourier series converges to a value that is the average of its limits on the left and the right, unlike the floor, ceiling and fractional part functions: for "y" fixed and "x" a multiple of "y" the Fourier series given converges to "y"/2, rather than to "x" mod "y" = 0. At points of continuity the series converges to the true value.


title: Floor and ceiling functions

text: For an integer "x" and a positive integer "y", the modulo operation, denoted by "x" mod "y", gives the value of the remainder when "x" is divided by "y". This definition can be extended to real "x" and "y", "y" ≠ 0, by the formula


title: Floor and ceiling functions

text: Then it follows from the definition of floor function that this extended operation satisfies many natural properties. Notably, "x" mod "y" is always between 0 and "y", i.e.,


title: Floor and ceiling functions

text: There are formulas that use floor to express the quadratic character of small numbers mod odd primes "p":


title: Floor and ceiling functions

text: For an arbitrary real number formula_58, rounding formula_58 to the nearest integer with tie breaking towards positive infinity is given by formula_60; rounding towards negative infinity is given as formula_61.


title: Floor and ceiling functions

text: If tie-breaking is away from 0, then the rounding function is formula_62 (see sign function), and rounding towards even can be expressed with the more cumbersome formula_63, which is the above expression for rounding towards positive infinity formula_64 minus an integrality indicator for formula_65.


title: Floor and ceiling functions

text: Let "n" be a positive integer and "p" a positive prime number. The exponent of the highest power of "p" that divides "n"! is given by a version of Legendre's formula


title: Floor and ceiling functions

text: where formula_70 is the way of writing "n" in base "p". This is a finite sum, since the floors are zero when "p" > "n".


title: Floor and ceiling functions

text: The Beatty sequence shows how every positive irrational number gives rise to a partition of the natural numbers into two sequences via the floor function.


title: Floor and ceiling functions

text: There are formulas for Euler's constant γ = 0.57721 56649 ... that involve the floor and ceiling, e.g.


title: Floor and ceiling functions

text: The fractional part function also shows up in integral representations of the Riemann zeta function. It is straightforward to prove (using integration by parts) that if formula_74 is any function with a continuous derivative in the closed interval ["a", "b"],


title: Floor and ceiling functions

text: Letting formula_76 for real part of "s" greater than 1 and letting "a" and "b" be integers, and letting "b" approach infinity gives


title: Floor and ceiling functions

text: This formula is valid for all "s" with real part greater than −1, (except "s" = 1, where there is a pole) and combined with the Fourier expansion for {"x"} can be used to extend the zeta function to the entire complex plane and to prove its functional equation.


title: Floor and ceiling functions

text: In 1947 van der Pol used this representation to construct an analogue computer for finding roots of the zeta function.


title: Floor and ceiling functions

text: The floor function appears in several formulas characterizing prime numbers. For example, since formula_79 is equal to 1 if "m" divides "n", and to 0 otherwise, it follows that a positive integer "n" is a prime if and only if


title: Floor and ceiling functions

text: One may also give formulas for producing the prime numbers. For example, let "p" be the "n"-th prime, and for any integer "r" > 1, define the real number "α" by the sum


title: Floor and ceiling functions

text: Let ("x") be the number of primes less than or equal to "x". It is a straightforward deduction from Wilson's theorem that


title: Floor and ceiling functions

text: In most programming languages, the simplest method to convert a floating point number to an integer does not do floor or ceiling, but truncation. The reason for this is historical, as the first machines used ones' complement and truncation was simpler to implement (floor is simpler in two's complement). FORTRAN was defined to require this behavior and thus almost all processors implement conversion this way. Some consider this to be an unfortunate historical design decision that has led to bugs handling negative offsets and graphics on the negative side of the origin.


title: Floor and ceiling functions

text: A bit-wise right-shift of a signed integer formula_58 by formula_89 is the same as formula_90. Division by a power of 2 is often written as a right-shift, not for optimization as might be assumed, but because the floor of negative results is required. Assuming such shifts are "premature optimization" and replacing them with division can break software.


title: Floor and ceiling functions

text: Many programming languages (including C, C++, C#, Java, PHP, R, and Python) provide standard functions for floor and ceiling, usually called codice_5 and codice_6, or less commonly codice_7. The language APL uses codice_8 for floor. The J Programming Language, a follow-on to APL that is designed to use standard keyboard symbols, uses codice_9 for floor and codice_10 for ceiling.


title: Floor and ceiling functions

text: In Microsoft Excel the floor function is implemented as codice_12 (which rounds down rather than toward zero). The command codice_13 in earlier versions would round toward zero, effectively the opposite of what "int" and "floor" do in other languages. Since 2010 codice_13 has been fixed to round down, with extra arguments that can reproduce previous behavior. The OpenDocument file format, as used by OpenOffice.org, Libreoffice and others, uses the same function names; codice_12 does floor and codice_13 has a third argument that can make it round toward zero.


title: Orthogonal matrix

text: In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors.


title: Orthogonal matrix

text: This leads to the equivalent characterization: a matrix is orthogonal if its transpose is equal to its inverse:


title: Orthogonal matrix

text: An orthogonal matrix is necessarily invertible (with inverse ), unitary (), where is the Hermitian adjoint (conjugate transpose) of , and therefore normal () over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix preserves the inner product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation, reflection or rotoreflection. In other words, it is a unitary transformation.


title: Orthogonal matrix

text: The set of orthogonal matrices, under multiplication, forms the group , known as the orthogonal group. The subgroup consisting of orthogonal matrices with determinant +1 is called the special orthogonal group, and each of its elements is a special orthogonal matrix. As a linear transformation, every special orthogonal matrix acts as a rotation.


title: Orthogonal matrix

text: An orthogonal matrix is the real specialization of a unitary matrix, and thus always a normal matrix. Although we consider only real matrices here, the definition can be used for matrices with entries from any field. However, orthogonal matrices arise naturally from dot products, and for matrices of complex numbers that leads instead to the unitary requirement. Orthogonal matrices preserve the dot product, so, for vectors and in an -dimensional real Euclidean space


title: Orthogonal matrix

text: where is an orthogonal matrix. To see the inner product connection, consider a vector in an -dimensional real Euclidean space. Written with respect to an orthonormal basis, the squared length of is . If a linear transformation, in matrix form , preserves vector lengths, then


title: Orthogonal matrix

text: Thus finite-dimensional linear isometries—rotations, reflections, and their combinations—produce orthogonal matrices. The converse is also true: orthogonal matrices imply orthogonal transformations. However, linear algebra includes orthogonal transformations between spaces which may be neither finite-dimensional nor of the same dimension, and these have no orthogonal matrix equivalent.


title: Orthogonal matrix

text: Orthogonal matrices are important for a number of reasons, both theoretical and practical. The orthogonal matrices form a group under matrix multiplication, the orthogonal group denoted by , which—with its subgroups—is widely used in mathematics and the physical sciences. For example, the point group of a molecule is a subgroup of O(3). Because floating point versions of orthogonal matrices have advantageous properties, they are key to many algorithms in numerical linear algebra, such as decomposition. As another example, with appropriate normalization the discrete cosine transform (used in MP3 compression) is represented by an orthogonal matrix.


title: Orthogonal matrix

text: The simplest orthogonal matrices are the matrices [1] and [−1], which we can interpret as the identity and a reflection of the real line across the origin.


title: Orthogonal matrix

text: In consideration of the first equation, without loss of generality let , ; then either , or , . We can interpret the first case as a rotation by (where is the identity), and the second as a reflection across a line at an angle of .


title: Orthogonal matrix

text: The special case of the reflection matrix with generates a reflection about the line at 45° given by and therefore exchanges and ; it is a permutation matrix, with a single 1 in each column and row (and otherwise 0):


title: Orthogonal matrix

text: A reflection is its own inverse, which implies that a reflection matrix is symmetric (equal to its transpose) as well as orthogonal. The product of two rotation matrices is a rotation matrix, and the product of two reflection matrices is also a rotation matrix.


title: Orthogonal matrix

text: Regardless of the dimension, it is always possible to classify orthogonal matrices as purely rotational or not, but for matrices and larger the non-rotational matrices can be more complicated than reflections. For example,


title: Orthogonal matrix

text: Rotations become more complicated in higher dimensions; they can no longer be completely characterized by one angle, and may affect more than one planar subspace. It is common to describe a rotation matrix in terms of an axis and angle, but this only works in three dimensions. Above three dimensions two or more angles are needed, each associated with a plane of rotation.


title: Orthogonal matrix

text: However, we have elementary building blocks for permutations, reflections, and rotations that apply in general.


title: Orthogonal matrix

text: The most elementary permutation is a transposition, obtained from the identity matrix by exchanging two rows. Any permutation matrix can be constructed as a product of no more than transpositions.


title: Orthogonal matrix

text: Here the numerator is a symmetric matrix while the denominator is a number, the squared magnitude of . This is a reflection in the hyperplane perpendicular to (negating any vector component parallel to ). If is a unit vector, then suffices. A Householder reflection is typically used to simultaneously zero the lower part of a column. Any orthogonal matrix of size can be constructed as a product of at most such reflections.


title: Orthogonal matrix

text: A Givens rotation acts on a two-dimensional (planar) subspace spanned by two coordinate axes, rotating by a chosen angle. It is typically used to zero a single subdiagonal entry. Any rotation matrix of size can be constructed as a product of at most such rotations. In the case of matrices, three such rotations suffice; and by fixing the sequence we can thus describe all rotation matrices (though not uniquely) in terms of the three angles used, often called Euler angles.


title: Orthogonal matrix

text: A Jacobi rotation has the same form as a Givens rotation, but is used to zero both off-diagonal entries of a symmetric submatrix.


title: Orthogonal matrix

text: A real square matrix is orthogonal if and only if its columns form an orthonormal basis of the Euclidean space with the ordinary Euclidean dot product, which is the case if and only if its rows form an orthonormal basis of . It might be tempting to suppose a matrix with orthogonal (not orthonormal) columns would be called an orthogonal matrix, but such matrices have no special interest and no special name; they only satisfy , with a diagonal matrix.


title: Orthogonal matrix

text: The determinant of any orthogonal matrix is +1 or −1. This follows from basic facts about determinants, as follows:


title: Orthogonal matrix

text: The converse is not true; having a determinant of ±1 is no guarantee of orthogonality, even with orthogonal columns, as shown by the following counterexample.


title: Orthogonal matrix

text: With permutation matrices the determinant matches the signature, being +1 or −1 as the parity of the permutation is even or odd, for the determinant is an alternating function of the rows.


title: Orthogonal matrix

text: Stronger than the determinant restriction is the fact that an orthogonal matrix can always be diagonalized over the complex numbers to exhibit a full set of eigenvalues, all of which must have (complex) modulus 1.


title: Orthogonal matrix

text: The inverse of every orthogonal matrix is again orthogonal, as is the matrix product of two orthogonal matrices. In fact, the set of all orthogonal matrices satisfies all the axioms of a group. It is a compact Lie group of dimension , called the orthogonal group and denoted by .


title: Orthogonal matrix

text: The orthogonal matrices whose determinant is +1 form a path-connected normal subgroup of of index 2, the special orthogonal group of rotations. The quotient group is isomorphic to , with the projection map choosing [+1] or [−1] according to the determinant. Orthogonal matrices with determinant −1 do not include the identity, and so do not form a subgroup but only a coset; it is also (separately) connected. Thus each orthogonal group falls into two pieces; and because the projection map splits, is a semidirect product of by . In practical terms, a comparable statement is that any orthogonal matrix can be produced by taking a rotation matrix and possibly negating one of its columns, as we saw with matrices. If is odd, then the semidirect product is in fact a direct product, and any orthogonal matrix can be produced by taking a rotation matrix and possibly negating all of its columns. This follows from the property of determinants that negating a column negates the determinant, and thus negating an odd (but not even) number of columns negates the determinant.


title: Orthogonal matrix

text: Now consider orthogonal matrices with bottom right entry equal to 1. The remainder of the last column (and last row) must be zeros, and the product of any two such matrices has the same form. The rest of the matrix is an orthogonal matrix; thus is a subgroup of (and of all higher groups).


title: Orthogonal matrix

text: Since an elementary reflection in the form of a Householder matrix can reduce any orthogonal matrix to this constrained form, a series of such reflections can bring any orthogonal matrix to the identity; thus an orthogonal group is a reflection group. The last column can be fixed to any unit vector, and each choice gives a different copy of in ; in this way is a bundle over the unit sphere with fiber .


title: Orthogonal matrix

text: Similarly, is a subgroup of ; and any special orthogonal matrix can be generated by Givens plane rotations using an analogous procedure. The bundle structure persists: . A single rotation can produce a zero in the first row of the last column, and series of rotations will zero all but the last row of the last column of an rotation matrix. Since the planes are fixed, each rotation has only one degree of freedom, its angle. By induction, therefore has


title: Orthogonal matrix

text: Permutation matrices are simpler still; they form, not a Lie group, but only a finite group, the order symmetric group . By the same kind of argument, is a subgroup of . The even permutations produce the subgroup of permutation matrices of determinant +1, the order alternating group.


title: Orthogonal matrix

text: More broadly, the effect of any orthogonal matrix separates into independent actions on orthogonal two-dimensional subspaces. That is, if is special orthogonal then one can always find an orthogonal matrix , a (rotational) change of basis, that brings into block diagonal form:


title: Orthogonal matrix

text: where the matrices are rotation matrices, and with the remaining entries zero. Exceptionally, a rotation block may be diagonal, . Thus, negating one column if necessary, and noting that a reflection diagonalizes to a +1 and −1, any orthogonal matrix can be brought to the form


title: Orthogonal matrix

text: The matrices give conjugate pairs of eigenvalues lying on the unit circle in the complex plane; so this decomposition confirms that all eigenvalues have absolute value 1. If is odd, there is at least one real eigenvalue, +1 or −1; for a rotation, the eigenvector associated with +1 is the rotation axis.


title: Orthogonal matrix

text: Suppose the entries of are differentiable functions of , and that gives . Differentiating the orthogonality condition


title: Orthogonal matrix

text: In Lie group terms, this means that the Lie algebra of an orthogonal matrix group consists of skew-symmetric matrices. Going the other direction, the matrix exponential of any skew-symmetric matrix is an orthogonal matrix (in fact, special orthogonal).


title: Orthogonal matrix

text: For example, the three-dimensional object physics calls angular velocity is a differential rotation, thus a vector in the Lie algebra formula_24 tangent to . Given , with being a unit vector, the correct skew-symmetric matrix form of is


title: Orthogonal matrix

text: Numerical analysis takes advantage of many of the properties of orthogonal matrices for numerical linear algebra, and they arise naturally. For example, it is often desirable to compute an orthonormal basis for a space, or an orthogonal change of bases; both take the form of orthogonal matrices. Having determinant ±1 and all eigenvalues of magnitude 1 is of great benefit for numeric stability. One implication is that the condition number is 1 (which is the minimum), so errors are not magnified when multiplying with an orthogonal matrix. Many algorithms use orthogonal matrices like Householder reflections and Givens rotations for this reason. It is also helpful that, not only is an orthogonal matrix invertible, but its inverse is available essentially free, by exchanging indices.


title: Orthogonal matrix

text: Permutations are essential to the success of many algorithms, including the workhorse Gaussian elimination with partial pivoting (where permutations do the pivoting). However, they rarely appear explicitly as matrices; their special form allows more efficient representation, such as a list of indices.


title: Orthogonal matrix

text: Likewise, algorithms using Householder and Givens matrices typically use specialized methods of multiplication and storage. For example, a Givens rotation affects only two rows of a matrix it multiplies, changing a full multiplication of order to a much more efficient order . When uses of these reflections and rotations introduce zeros in a matrix, the space vacated is enough to store sufficient data to reproduce the transform, and to do so robustly. (Following , we do "not" store a rotation angle, which is both expensive and badly behaved.)


title: Orthogonal matrix

text: Consider an overdetermined system of linear equations, as might occur with repeated measurements of a physical phenomenon to compensate for experimental errors. Write , where is , .


title: Orthogonal matrix

text: The linear least squares problem is to find the that minimizes , which is equivalent to projecting to the subspace spanned by the columns of . Assuming the columns of (and hence ) are independent, the projection solution is found from . Now is square () and invertible, and also equal to . But the lower rows of zeros in are superfluous in the product, which is thus already in lower-triangular upper-triangular factored form, as in Gaussian elimination (Cholesky decomposition). Here orthogonality is important not only for reducing to , but also for allowing solution without magnifying numerical problems.


title: Orthogonal matrix

text: In the case of a linear system which is underdetermined, or an otherwise non-invertible matrix, singular value decomposition (SVD) is equally useful. With factored as , a satisfactory solution uses the Moore-Penrose pseudoinverse, , where merely replaces each non-zero diagonal entry with its reciprocal. Set to .


title: Orthogonal matrix

text: The case of a square invertible matrix also holds interest. Suppose, for example, that is a rotation matrix which has been computed as the composition of numerous twists and turns. Floating point does not match the mathematical ideal of real numbers, so has gradually lost its true orthogonality. A Gram–Schmidt process could orthogonalize the columns, but it is not the most reliable, nor the most efficient, nor the most invariant method. The polar decomposition factors a matrix into a pair, one of which is the unique "closest" orthogonal matrix to the given matrix, or one of the closest if the given matrix is singular. (Closeness can be measured by any matrix norm invariant under an orthogonal change of basis, such as the spectral norm or the Frobenius norm.) For a near-orthogonal matrix, rapid convergence to the orthogonal factor can be achieved by a "Newton's method" approach due to (1990), repeatedly averaging the matrix with its inverse transpose. has published an accelerated method with a convenient convergence test.


title: Orthogonal matrix

text: For example, consider a non-orthogonal matrix for which the simple averaging algorithm takes seven steps


title: Orthogonal matrix

text: Gram-Schmidt yields an inferior solution, shown by a Frobenius distance of 8.28659 instead of the minimum 8.12404.


title: Orthogonal matrix

text: Some numerical applications, such as Monte Carlo methods and exploration of high-dimensional data spaces, require generation of uniformly distributed random orthogonal matrices. In this context, "uniform" is defined in terms of Haar measure, which essentially requires that the distribution not change if multiplied by any freely chosen orthogonal matrix. Orthogonalizing matrices with independent uniformly distributed random entries does not result in uniformly distributed orthogonal matrices, but the decomposition of independent normally distributed random entries does, as long as the diagonal of contains only positive entries . replaced this with a more efficient idea that later generalized as the "subgroup algorithm" (in which form it works just as well for permutations and rotations). To generate an orthogonal matrix, take an one and a uniformly distributed unit vector of dimension . Construct a Householder reflection from the vector, then apply it to the smaller matrix (embedded in the larger size with a 1 at the bottom right corner).


title: Orthogonal matrix

text: The problem of finding the orthogonal matrix nearest a given matrix is related to the Orthogonal Procrustes problem. There are several different ways to get the unique solution, the simplest of which is taking the singular value decomposition of and replacing the singular values with ones. Another method expresses the explicitly but requires the use of a matrix square root:


title: Orthogonal matrix

text: This may be combined with the Babylonian method for extracting the square root of a matrix to give a recurrence which converges to an orthogonal matrix quadratically:


title: Orthogonal matrix

text: Using a first-order approximation of the inverse and the same initialization results in the modified iteration:


title: Orthogonal matrix

text: A subtle technical problem afflicts some uses of orthogonal matrices. Not only are the group components with determinant +1 and −1 not connected to each other, even the +1 component, , is not simply connected (except for SO(1), which is trivial). Thus it is sometimes advantageous, or even necessary, to work with a covering group of SO("n"), the spin group, . Likewise, has covering groups, the pin groups, Pin("n"). For , is simply connected and thus the universal covering group for . By far the most famous example of a spin group is , which is nothing but , or the group of unit quaternions.


title: Orthogonal matrix

text: The Pin and Spin groups are found within Clifford algebras, which themselves can be built from orthogonal matrices.


title: Orthogonal matrix

text: If is not a square matrix, then the conditions and are not equivalent. The condition says that the columns of "Q" are orthonormal. This can only happen if is an matrix with (due to linear dependence). Similarly, says that the rows of are orthonormal, which requires .


title: Orthogonal matrix

text: There is no standard terminology for these matrices. They are variously called "semi-orthogonal matrices", "orthonormal matrices", "orthogonal matrices", and sometimes simply "matrices with orthonormal rows/columns".


title: Orthogonal matrix

text: For the case , matrices with orthonormal columns may be referred to as orthogonal k-frames and they are elements of the Stiefel manifold.


title: Naturalization

text: Naturalization (or naturalisation) is the legal act or process by which a non-citizen of a country may acquire citizenship or nationality of that country. It may be done automatically by a statute, i.e., without any effort on the part of the individual, or it may involve an application or a motion and approval by legal authorities. The rules of naturalization vary from country to country but typically include a promise to obey and uphold that country's laws and taking and subscribing to an oath of allegiance, and may specify other requirements such as a minimum legal residency and adequate knowledge of the national dominant language or culture. To counter multiple citizenship, some countries require that applicants for naturalization renounce any other citizenship that they currently hold, but whether this renunciation actually causes loss of original citizenship, as seen by the host country and by the original country, will depend on the laws of the countries involved.


title: Naturalization

text: The massive increase in population flux due to globalization and the sharp increase in the numbers of refugees following World War I created many stateless persons, people who were not citizens of any state. In some rare cases, laws for mass naturalization were passed. As naturalization laws had been designed to cater for the relatively few people who had voluntarily moved from one country to another (expatriates), many western democracies were not ready to naturalize large numbers of people. This included the massive influx of stateless people which followed massive denationalizations and the expulsion of ethnic minorities from newly created nation states in the first part of the 20th century.


title: Naturalization

text: Since World War II, the increase in international migrations created a new category of migrants, most of them economic migrants. For economic, political, humanitarian and pragmatic reasons, many states passed laws allowing a person to acquire their citizenship after birth, such as by marriage to a national – "jus matrimonii" – or by having ancestors who are nationals of that country, in order to reduce the scope of this category. However, in some countries this system still maintains a large part of the immigrant population in an illegal status, albeit with some massive regularizations. Examples include Spain under José Luis Rodríguez Zapatero's government, and Italy under Silvio Berlusconi's government.


title: Naturalization

text: The following list is a brief summary of the duration of legal residence before a national of a foreign state, without any cultural, historical, or marriage ties or connections to the state in question, can request citizenship under that state's naturalization laws.


title: Naturalization

text: The "Australian Citizenship Act 1973" ended the preferential treatment for British subjects from 1 December 1973. People who became permanent residents from 1 July 2007 must have been lawfully resident in Australia for four years before applying for citizenship by conferral. Those who were present in Australia as permanent residents before 1 July 2007 remain subject to the previous residence requirement (in force since 1984, e.g. resident for 2 years).


title: Naturalization

text: The People's Republic of China gives citizenship to people with one or two parents with Chinese nationality who have not taken residence in other countries. The country also gives citizenship to people born on its territory to stateless people who have settled there. Furthermore, individuals may apply for nationality if they have a near relative with Chinese nationality, if they have settled in China, or if they present another legitimate reason. In practice, few people gain Chinese citizenship; as of 2010, China had only 1,448 naturalised Chinese in total.


title: Naturalization

text: The naturalization process starts with a written application. Applicants must submit three copies, written with a ball-point or fountain pen, to national authorities, and to provincial authorities in the Ministry of Public Security and the Public Security Bureau. Applicants must also submit original copies of a foreign passport, a residence permit, a permanent residence permit, and four two-and-a-half inch long pictures. According to the conditions outlined in the Nationality Law of the People's Republic of China, authorities may also require "any other material that the authority believes are related to the nationality application".


title: Naturalization

text: People who fulfil all of the following criteria can obtain French citizenship through naturalisation:


title: Naturalization

text: People who fulfil all of the following criteria can obtain German citizenship through naturalisation:


title: Naturalization

text: The dependent minor children of an applicant for naturalisation may also themselves become naturalised German citizens.


title: Naturalization

text: The fee for standard naturalisation is €255, while it is €51 per dependent minor child naturalised along with their parent. The fee may be waived in cases of extreme hardship or public interest.


title: Naturalization

text: People who naturalise as German citizens must usually give up their previous nationality, as German law takes a restrictive approach to multiple citizenship. Exceptions are made for EU and Swiss citizens (provided that the law of their country of origin does not prohibit the acquisition of another citizenship) and citizens of countries where renouncing one's citizenship is too difficult or humiliating (e.g. Afghanistan), prohibitively expensive (e.g. the United States) or legally impossible (e.g. Argentina).


title: Naturalization

text: The Indian citizenship and nationality law and the Constitution of India provides single citizenship for the entire country. The provisions relating to citizenship at the commencement of the Constitution are contained in Articles 5 to 11 in Part II of the Constitution of India. Relevant Indian legislation is the Citizenship Act 1955, which has been amended by the Citizenship (Amendment) Act 1986, the Citizenship (Amendment) Act 1992, the Citizenship (Amendment) Act 2003, and Citizenship (Amendment) Ordinance 2005. The Citizenship (Amendment) Act 2003 received the assent of the President of India on 7 January 2004 and came into force on 3 December 2004. The Citizenship (Amendment) Ordinance 2005 was promulgated by the President of India and came into force on 28 June 2005.


title: Naturalization

text: Following these reforms, Indian nationality law largely follows the "jus sanguinis" (citizenship by right of blood) as opposed to the "jus soli" (citizenship by right of birth within the territory).


title: Naturalization

text: In 2019, a Citizenship Amendment Act was passed by the Parliament of India. This Act aims at fast tracking citizenship for illegal immigrants of Hindu, Sikh, Buddhist, Jain, Parsi or Christian faiths who have entered India on or before 31 December 2014 from the neighbouring countries of Pakistan, Afghanistan and Bangladesh.


title: Naturalization

text: Indonesian nationality is regulated by Law No. 12/2006 (UU No. 12 Tahun 2006). The Indonesian nationality law is based on jus sanguinis and jus soli. The Indonesian nationality law does not recognize dual citizenship except for people under the age of 18 (limited double citizenship principle). After reaching 18 years of age individuals are forced to choose one citizenship (single citizenship principle).


title: Naturalization

text: Israel's Declaration of Independence was made on 14 May 1948, the day before the British Mandate was due to expire as a result of the United Nations Partition Plan. The Israeli parliament created two laws regarding immigration, citizenship and naturalization: the Law of Return and the Israeli citizenship law. The Law of Return, enacted on July 15, 1950, gives Jews living anywhere in the world the right to immigrate to Israel. This right to immigrate did not and still does not grant citizenship. In fact, for four years after Israel gained independence, there were no Israeli citizens.


title: Naturalization

text: On July 14, 1952, the Israeli parliament enacted the Israeli Nationality Law. The Nationality Law naturalized all citizens of Mandated Palestine, the inhabitants of Israel on July 15, 1952, and those who had legally resided in Israel between May 14, 1948, and July 14, 1952. The law further clarified that naturalization was available to immigrants who had arrived before Israel's creation, immigrants who arrived after statehood was granted, and those who did not come to Israel as immigrants but have since expressed desire to settle in Israel, with restriction. Naturalization applicants must also meet the following requirements: be over 18 years of age, have resided in Israel for three out of the five preceding years, have settled or intend to settle permanently in Israel, have some knowledge of Hebrew, and have renounced prior nationality or demonstrated ability to renounce nationality after becoming a citizen of Israel.


title: Naturalization

text: Because of Israel's relatively new and culturally mixed identity, Israel does not grant citizenship to people born on Israeli soil. Instead, the government chose to enact a jus sanguinis system, with the naturalization restrictions listed above. There is currently no legislation on second-generation immigrants (those born in Israel to immigrant parents). Furthermore, foreign spouses can apply for citizenship through the Minister of the Interior, but have a variety of restrictions and are not guaranteed citizenship.


title: Naturalization

text: People who fulfil all of the following criteria can obtain Luxembourg citizenship through naturalisation:


title: Naturalization

text: Naturalisation in Malaysia is guided by the 1964 Malaysian Constitution. According to the law, those who want to be the country citizen should live in the country for a period of 10–12 years. The would-be-citizens are required to speak the Malay language as well submitting the identity cards of two Malaysians who recommend the applicant for citizenship. As the Government of Malaysia does not recognise dual citizenship, those who seek naturalisation are needed to reside permanently in the country and renouncing their former country citizenship.


title: Naturalization

text: Commonwealth Act No. 473, the Revised Naturalization Law, approved June 17, 1939, provided that people having certain specified qualifications may become a citizen of the Philippines by naturalization. Republic Act No. 9139, approved June 8, 2001, provided that aliens under the age of 18 who were born in the Philippines, who have resided in the Philippines since birth, and who possess other specified qualifications may be granted Philippines citizenship by administrative proceeding subject to certain requirements.


title: Naturalization

text: Naturalization in Russia is guided by articles 13 and 14 of the federal law "About Citizenship of Russian Federation" passed on May 31, 2002. Citizenship of Russia can be obtained in general or simplified order. To become a citizen in general order, one must be 18 years of age or older, continuously live in Russia as a permanent resident for at least five years (this term is limited to one year for valued specialists, political asylum seekers and refugees), have legal means of existence, promise to obey the laws and Constitution of Russia and be fluent in the Russian language.


title: Naturalization

text: There is also a possibility to naturalize in a simplified order, in which certain requirements will be waived. Eligible for that are people, at least one parent of whom is a Russian citizen living on Russian territory; people, who lived on the territories of the former Soviet republics but never obtained citizenships of those nations after they gained independence; people, who were born on the territory of RSFSR and formerly held Soviet citizenship; people married to Russian citizens for at least 3 years; people, who served in Russian Armed Forces under contract for at least 3 years; parents of mentally incapacitated children over 18 who are Russian citizens; participants of the State Program for Assisting Compatriots Residing Abroad; and some other categories.


title: Naturalization

text: People who fulfill all of the following criteria can obtain Spanish citizenship through naturalisation


title: Naturalization

text: People who naturalise as Spanish citizens must usually give up their previous nationality, as Spanish law takes a restrictive approach to multiple citizenship.


title: Naturalization

text: Chapter 2 of the South African Citizenship Act, enacted on October 6, 1995, defines who is considered a naturalized citizen at the time of the act and also outlines the naturalization process for future immigrants.


title: Naturalization

text: Any person who immediately prior to the commencement of the act had been a South African citizen via naturalization, had been deemed to be a South African citizen by registration, or had been a citizen via naturalization of any of the former states now composing South Africa is now considered to be a naturalized citizen of South Africa.


title: Naturalization

text: Those wishing to apply for naturalization in the future must apply to the Minister of Home Affairs and must meet a slew of requirements. First, naturalization applicants must be over the age of 18 and must have been a permanent resident of South Africa for five years prior to application (prior to 2010, the permanent residence requirement was one year prior to application and for four out of the eight years prior to application). Applicants must also demonstrate good character and knowledge of the basic responsibilities and privileges of a South African citizen. The ability to communicate in one of the official languages of South Africa is also required. Applicants must show the intention to reside in South Africa after naturalization, and they are required to make a declaration of allegiance. The Constitution of South Africa states that national legislation must provide for the acquisition, loss and restoration of citizenship.


title: Naturalization

text: Being a naturalized South African citizen is a privilege, not a right. Even after meeting all the requirements and going through the naturalization process, the minister holds the right to deny citizenship. Foreign spouses of South African citizens can apply for naturalization after two years of marriage, but is subject to potential denial of the minister. The minister can also grant citizenship to minors, if their parent applies for them.


title: Naturalization

text: The minister also holds the power to revoke naturalization at any time for specific reasons listed in the Act. Reasons for revoking the naturalization certificate include marrying someone who is a citizen of another country and holding citizenship in another country, or applying for citizenship of another country without prior authorization for retention of citizenship. If a permanent resident is denied naturalization, he or she must wait at least one year before reapplying.


title: Naturalization

text: There has always been a distinction in the law of England and Wales between the subjects of the monarch and aliens: the monarch's subjects owed the monarch allegiance, and included those born in his or her dominions (natural-born subjects) and those who later gave him or her their allegiance (naturalised subjects). Today, the requirements for naturalisation as a citizen of the United Kingdom depend on whether or not one is the spouse or civil partner of a citizen. An applicant who is a spouse or civil partner of a British citizen must:


title: Naturalization

text: Persons who are not US citizens may receive citizenship through the process of naturalization, following the Congressional requirements in the Immigration and Nationality Act (INA). Naturalized citizens have the same rights has those who acquired citizenship at birth.


title: Naturalization

text: The Naturalization Act of 1795 set the initial rules on naturalization: "free, White persons" who had been resident for five years or more. An 1862 law allowed honorably discharged Army veterans of any war to petition for naturalization after only one year of residence in the United States. An 1894 law extended the same privilege to honorably discharged five-year veterans of the Navy or Marine Corps. Laws enacted in 1919, 1926, 1940, and 1952 continued preferential treatment provisions for veterans.


title: Naturalization

text: Following the Spanish–American War in 1898, Philippine citizens were classified as US nationals, and the 1917 Jones–Shafroth Act granted US citizenship to natives of Puerto Rico. But the 1934 Tydings–McDuffie Act reclassified Filipinos as aliens, and set a quota of 50 immigrants per year, and otherwise applying the Immigration Act of 1924 to them.


title: Naturalization

text: The Magnuson Act repealed the Chinese Exclusion Act. During the 1940s, 100 annual immigrants from British India and the Philippines were allowed. The War Brides Act of 1945 permitted soldiers to bring back their foreign wives and established precedent in naturalization through marriage. The Immigration Act of 1965 finally allowed people from all nations to be given equal access to immigration and naturalization.


title: Naturalization

text: Illegal immigration became a major issue in the United States at the end of the 20th century. The Immigration Reform and Control Act of 1986, while tightening border controls, also provided the opportunity of naturalization for illegal aliens who had been in the country for at least four years. Today, lawful permanent residents of the United States are eligible to apply for US citizenship after five years, unless they continue to be married to a US citizen, in which case they can apply after only three years of permanent residency.


title: Naturalization

text: The Child Citizenship Act of 2000 streamlined the naturalization process for children adopted internationally. A child under age 18 who is adopted by at least one US citizen parent, and is in the custody of the citizen parent(s), is now automatically naturalized once admitted to the United States as an immigrant or when legally adopted in the United States, depending on the visa under which the child was admitted to the United States. The Act also provides that the non-citizen minor child of a newly naturalized US citizen, whether by birth or adoption, also automatically receives US citizenship.


title: Naturalization

text: A few rare mass naturalization processes have been implemented by nation states. In 1891, Brazil granted naturalization to all aliens living in the country. In 1922, Greece massively naturalized all the Greek refugees coming from Turkey. The second massive naturalization process was in favor of Armenian refugees coming from Turkey, who went to Syria, Lebanon or other former Ottoman countries. Reciprocally, Turkey massively naturalized the refugees of Turkish descent or other ethnic backgrounds in Muslim creed from these countries during a redemption process.


title: Naturalization

text: Canada instituted a mass naturalization by Act of Parliament with the enactment of the Canadian Citizenship Act 1946.


title: Naturalization

text: After annexation of the territories east of the Curzon line by the Soviet Union in 1945, Soviets naturalized "en masse" all the inhabitants of those territories—including ethnic Poles, as well as its other citizens who had been deported into the Soviet Union, mainly to Kazakhstan. Those people were forcibly naturalized as Soviet citizens. Later on, Germany granted to the ethnic German population in Russia and Kazakhstan full citizenship rights. Poland has a limited repatriation program in place.


title: Naturalization

text: The most recent massive naturalization case resulted from the Argentine economic crisis in the beginning of the 21st century. Existing or slightly updated right of return laws in Spain and Italy allowed many of their diasporic descendants to obtain—in many cases to regain—naturalization in virtue of "jus sanguinis", as in the Greek case. Hence, many Argentines acquired European nationality.


title: Naturalization

text: Since the Fourteenth Amendment to the United States Constitution grants citizenship only to those "born or naturalized in the United States, and subject to the jurisdiction thereof", and the original United States Constitution only grants Congress the power of naturalization, it could be argued that all acts of Congress that expand the right of citizenship are cases of mass naturalization. This includes the acts that extended U.S. citizenship to citizens of Puerto Rico, the United States Virgin Islands, Guam, and the Northern Mariana Islands, as well as the Indian Citizenship Act of 1924 which made all Native Americans citizens (most of them were previously excluded under the "jurisdiction" clause of the 14th Amendment).


title: Naturalization

text: In the eastern Malaysian state of Sabah, mass naturalisation also happened during the administration of United Sabah National Organisation (USNO) and Sabah People's United Front (BERJAYA's) Muslim-dominated political parties to increase the Muslim population in the territory by naturalising immigrants and refugees from the mainly-Muslim dominated areas of Mindanao and Sulu Archipelago of the Philippines and Sulawesi of Indonesia.


title: Naturalization

text: The mass naturalization of native people in occupied territories is illegal under the laws of war (Hague and Geneva Conventions). However, there have been many instances of such illegal mass naturalizations in the 20th century.


title: 2018 Hawaii false missile alert

text: On the morning of Saturday, January 13, 2018, a ballistic missile alert was accidentally issued via the Emergency Alert System and Wireless Emergency Alert System over television, radio and cellphones in the U.S. state of Hawaii. The alert stated that there was an incoming ballistic missile threat inbound to Hawaii, advised residents to seek shelter, before it concluded: "This is not a drill". The message was sent at 8:07 a.m. local time. Civil defense outdoor warning sirens were not authorized by the state.


title: 2018 Hawaii false missile alert

text: Thirty-eight minutes and 13 seconds later, state officials blamed a miscommunication during a drill at the Hawaii Emergency Management Agency for the first message. Governor David Ige publicly apologized for the erroneous alert. The Federal Communications Commission and the Hawaii House of Representatives launched investigations into the incident, leading to the resignation of the state's emergency management administrator.


title: 2018 Hawaii false missile alert

text: Escalating tensions between North Korea and the United States, including threats by both countries that they could use nuclear weapons against one another, prompted a heightened state of readiness in Hawaii. North Korea had conducted several intercontinental ballistic missile tests over the past year, most recently in November 2017, enhancing its strike capabilities. It is possible that North Korea may have the capability to deliver nuclear missiles to Hawaii. Hawaii is located roughly from North Korea, and a missile launched from North Korea would leave approximately 12 to 15 minutes of warning time.


title: 2018 Hawaii false missile alert

text: Hawaii officials had been working for some time to refresh the state's emergency plans in case of a nuclear attack from North Korea. An October 2017 email from the University of Hawaii to students with the subject line "In the event of a nuclear attack", containing instructions from the Hawaii Emergency Management Agency on how to react in case of a nuclear attack, caused controversy; a university spokesman ultimately apologized for "any needless concern it may have caused". Testing of the civil defense warning sirens and attack drills were also conducted in the state on the first business day of the month beginning in December 2017. On December 1, 2017, a nuclear threat siren was tested in Hawaii for the first time in more than 30 years, the first of what state officials said would be monthly drills. At 11:45 a.m. on January 2, 2018, the state conducted its monthly test of the civil defense outdoor warning siren system including the sounding of a one-minute Attention Alert Signal (Steady Tone) followed by a one-minute Attack Warning Signal (Wailing Tone). There was no exercise or drill accompanying the test. Prior to January 13, 2018, 26 drills had been conducted. Vern Miyagi, the administrator of the Hawaii Emergency Management Agency, explained that state leaders "couldn't ignore these constant threats and missile tests from North Korea" and felt the need to prepare residents for the possibility of an attack. Officials also outlined what would happen if an emergency alert were sent: a push alert to smartphones and a message interrupting television and radio broadcasts.


title: 2018 Hawaii false missile alert

text: Earlier in January 2018, U.S. Federal Communications Commission chairman Ajit Pai said the commission planned to vote to overhaul the wireless emergency alert system. The proposed reforms include providing more detailed information in alerts and confining emergency notifications to a more specific geographic area. Pai said he hoped the reforms, which would take effect if approved by the FCC, would lead to greater use of the alert system in local emergency situations and prompt people to take alerts they receive more seriously.


title: 2018 Hawaii false missile alert

text: The alert was sent at 8:07 a.m. Hawaii–Aleutian Standard Time. People in Hawaii reported seeing the alert on their smartphones. Many screenshots of the push alert were shared on social media platforms, such as Twitter. The alert read, in all capital letters:


title: 2018 Hawaii false missile alert

text: Local television broadcasts, including a college basketball game between Florida and Ole Miss being shown on CBS affiliate KGMB and a Premier League match between Tottenham Hotspur and Everton on NBC affiliate KHNL were also interrupted by a similar alert message, broadcast as a Civil Danger Warning. The alert message on television broadcasts took the form of both an audio message and a scrolling banner. It stated in part:


title: 2018 Hawaii false missile alert

text: The U.S. Pacific Command has detected a missile threat to Hawaii. A missile may impact on land or sea within minutes. THIS IS NOT A DRILL. If you are indoors, stay indoors. If you are outdoors, seek immediate shelter in a building. Remain indoors well away from windows. If you are driving, pull safely to the side of the road and seek shelter in a building or lay on the floor. We will announce when the threat has ended. THIS IS NOT A DRILL. Take immediate action measures.


title: 2018 Hawaii false missile alert

text: An alert message also interrupted radio broadcasts in the state. In Lihue, a resident reported hearing a message on the radio advising of "an incoming missile warning for the islands of Kauai and Hawaii".


title: 2018 Hawaii false missile alert

text: Culpability for the false alert was attributed to an employee at the Hawaii Emergency Management Agency, who officials said was a 10-year agency veteran who had previously exhibited behavior that had troubled coworkers, according to "The Washington Post". Vern Miyagi, then-administrator of HI-EMA, said the alert had been inadvertently triggered by the employee as he was working at the Diamond Head Crater headquarters during a shift change. During the shift change, a supervisor ran an unscheduled drill in which he contacted emergency management workers in the guise of an officer from U.S. Pacific Command, according to state officials. The supervisor deviated from the script, officials said, erroneously stating at one point, "This is not a drill", although he reportedly did state before and after the message, "Exercise, exercise, exercise", agency code to indicate a test rather than an actual emergency.


title: 2018 Hawaii false missile alert

text: Officials said that upon hearing the supervisor's statement, the employee, who had "confused real-life events and drills" at least twice before believed there was an actual emergency, and he later attested to this in a written statement. In an interview with "NBC News", the employee shared that he was, "100 percent sure that it was the right decision and that it was real". The man went on to state that he is not to blame for the incident, that overall it was a system failure, and that he did exactly what he was trained to do. He clicked the button to send out an actual notification on Hawaii's emergency alert interface during what was intended to be a test of the state's ballistic missile preparations computer program and then clicked through a second screen, which had been intended as a safeguard, to confirm. An agency spokesman told "The Washington Post" that the employee was prompted to choose between the options "test missile alert" and "missile alert", had selected the latter, initiating the alert sent out across the state. The employee later claimed to the Associated Press that he had not heard the "exercise" part of the phone call because a co-worker had placed it on speakerphone partway into the message, and as a result, he had been "100 percent sure" the attack was real. State officials said five other workers were present at the agency at the time and all of them recognized the phone call as an impromptu drill. Since this incident, the employee responsible has received numerous death threats and has expressed on multiple occasions his apologies.


title: 2018 Hawaii false missile alert

text: By 8:10 a.m. HST, three minutes after the first alert, Hawaii National Guard Adjutant General Arthur "Joe" Logan had contacted U.S. Pacific Command and confirmed there had been no missile launch. At that time, the Honolulu Police Department was notified that the alert had been a false alarm. Officials used the State Warning Point system at 8:13 a.m. to cancel the alert, preventing it from being sent out to any phones that had not already received it, such as those that were switched off or did not have reception. The employee who originally sent out the erroneous notification did not respond when directed to cancel the alert, according to state officials. He later said he felt like he had been dealt a "body blow" upon realizing the supposed attack had been a drill, the Associated Press reported. Another unidentified worker grabbed the employee's computer mouse and canceled the alert when the first employee failed to respond.


title: 2018 Hawaii false missile alert

text: Official messages refuting the emergency alert were not sent out until 8:20 a.m., according to the timeline released by officials after the incident. Hawaii Emergency Management Agency accounts on Facebook and Twitter posted messages at that time urging people to disregard the erroneous alert. Minutes later, Governor David Ige retweeted the HI-EMA message on Twitter and posted a similar message on Facebook to notify followers that the alert had been canceled. Ige later said the delay was caused in part by the fact he did not know his Twitter login information. An email from the state was also sent at about 8:25 a.m. advising that the initial alert was not correct, the "Honolulu Star-Advertiser" reported.


title: 2018 Hawaii false missile alert

text: Electronic highway signs were also used to spread the word that the alert had been issued "in error" and that there was no threat to Hawaii.


title: 2018 Hawaii false missile alert

text: At 8:45 a.m. HST, 38 minutes after the initial alert was sent to smartphones in Hawaii, a second emergency alert was sent, which stated:


title: 2018 Hawaii false missile alert

text: The second alert was sent "well after everyone from Hawaii's congressional delegation to the U.S. Pacific Command had assured the world on Twitter that it was a false alarm", "Pacific Business News" remarked.


title: 2018 Hawaii false missile alert

text: Governor David Ige explained at a news conference that afternoon that officials "had to initiate a manual process" and obtain authorization from the Federal Emergency Management Agency in order to send the second alert because there was no automated way to countermand the first alert. Those procedures accounted for the delay more than 30 minutes after officials had confirmed internally that the alert was inaccurate, according to officials.


title: 2018 Hawaii false missile alert

text: During the 38 minutes between the first and second alerts, Hawaii's siren warning system—which had been tested as part of a missile preparedness exercise the previous month for the first time since the Cold War—was not formally activated. Had a missile truly been launched, the Hawaii push alert should have been followed up with another set of alarms with sirens, which did not happen, as observed by some residents. Nevertheless, officials stated that some sirens did appear to go off in some communities, with some residents reporting sirens activated on Oahu a few minutes after the push notification. Little to no activity was reported at military bases in the state. Some commercial flights were reportedly delayed for a short time, although the Hawaii Department of Transportation said there were no widespread impacts at the state's airports and harbors.


title: 2018 Hawaii false missile alert

text: Disruptions were reported across the state. "Honolulu Civil Beat" reported that motorists parked inside the Interstate H-3 tunnel on the island of Oahu for shelter. Hawaii News Now reported that alarms sounded at Aloha Gymfest, an international gymnastics meet in Kailua, sending hundreds of people running for cover. Students at the University of Hawaii at Manoa reportedly headed for marked fallout shelters on campus but, finding them locked, ended up taking shelter in nearby classrooms instead. Officials at the Sony Open PGA Tour golf tournament on Oahu ordered an evacuation of the media center, while staff members sought cover in the kitchen and players' locker room. Tourists at Kualoa Ranch in Kaneohe were taken up to Battery Cooper Bunker by staff, a concrete bunker built in the mountains during WW2 as part of former Kualoa Airfield, and told to shelter there. Congresswoman Colleen Hanabusa later said her husband had been driving on a Honolulu-area freeway and saw cars speeding at up to after the alert was sent out. Many Hawaii residents and visitors sought shelter or rushed through emergency preparations where they were. Some discounted the alarm when they realized that they heard no sirens, and that they personally saw no immediate coverage on television or local radio. Others were in areas where sirens did go off; in addition, some television stations did broadcast the alert.


title: 2018 Hawaii false missile alert

text: The incident also created a strain on Hawaii's telephone system. Civil Defense offices in Hawaii were inundated with calls from frightened citizens asking for advice or more information, the "New Zealand Herald" reported. Many calls to 911 would not go through. Many wireless data services were likewise initially jammed, leaving many unable to access the Internet to confirm whether the alarm was real. Some residents called friends or family members to say goodbye. Others remained where they were, as with Mark Gardner, who, believing that escape was impossible, recorded a final message to his family in anticipation of the missile striking its target.


title: 2018 Hawaii false missile alert

text: U.S. Defense Secretary James Mattis reported that the false alert did not appear to have prompted any sort of reaction from the North Korean government.


title: 2018 Hawaii false missile alert

text: One man suffered a heart attack minutes after saying what he thought were his last goodbyes to his children following the initial alert, though he survived the heart attack.


title: 2018 Hawaii false missile alert

text: The event was examined in an academic article by Richard Ling and Brett Oppegaard. The analysis interviewed 418 people and showed how information (and false information) can propagate quickly in society.


title: 2018 Hawaii false missile alert

text: Fear and panic quickly spread through the locals and tourists of Hawaii. Many Twitter posts and screenshots of text messages shared on social media in the immediate wake of the first alert conveyed confusion, alarm, and fear among those who received the warning. With very little warning and instructions, many people were unsure of what to do. This later became a major criticism of the Hawaii Emergency Management Agency and is a key issue they are working on to improve, which will ensure that people can receive more accurate information in the case of a real emergency.


title: 2018 Hawaii false missile alert

text: Members of Hawaii's congressional delegation also took to Twitter to dispel the false alarm. Congresswoman Tulsi Gabbard tweeted at 8:19 a.m. HST, about 12 minutes after the initial alert was sent, stating in all capitals that the message was a "false alarm" and that she had confirmed with officials that there was no incoming ballistic missile toward Hawaii. The next day, she told CNN that the incident highlighted the need for President Donald Trump to negotiate with North Korean leader Kim Jong-un to resolve nuclear tensions between the United States and North Korea, and she called for those responsible for the erroneous alert in Hawaii "to be held accountable". Congresswoman Colleen Hanabusa, a 2018 candidate for governor, tweeted that the "panic and fear created by this false alarm was very dangerous". In further comments, Hanabusa panned the delay between the two emergency alerts, suggesting it should not have taken 38 minutes for the second message to be sent. Senator Mazie Hirono tweeted that officials "need to get to the bottom of what happened and make sure it never happens again". In his own tweets immediately after the incident, Senator Brian Schatz repeated that the first alert had been a false alarm. He described the erroneous alert message as "totally inexcusable", adding: "The whole state was terrified. There needs to be tough and quick accountability and a fixed process."


title: 2018 Hawaii false missile alert

text: Commander David Benham, a spokesman for U.S. Pacific Command, confirmed to media that there was no imminent missile threat to Hawaii. A spokesman for North American Aerospace Defense Command (NORAD) stated that "NORAD did not see anything that indicated any sort of threat to Hawaii" and said NORAD and U.S. Northern Command were still verifying what had happened. President Trump had also been under fire by critics for his "lack of response" some said. A White House official said the alert had been part of "a state exercise" and President Trump was briefed on the situation. Trump ordered National Security Advisor H.R. McMaster to take charge of the administration's response to the incident. About the incident, Trump said, "They made a mistake."


title: 2018 Hawaii false missile alert

text: U.S. Homeland Security Secretary Kirstjen Nielsen said the incident was "unfortunate" and officials were working to prevent a similar false alert from being issued in the future. Speaking on Fox News the next day, she said people "can trust government systems" and should pay attention to any alerts they receive from authorities in the future, in spite of the January 13 incident in Hawaii.


title: 2018 Hawaii false missile alert

text: Ajit Pai, chairman of the U.S. Federal Communications Commission, announced the commission would launch a full investigation into the false alert. He blamed Hawaii's government for not having "reasonable safeguards or process controls in place to prevent the transmission of a false alert", later stating that other agencies should "learn from these mistakes".


title: 2018 Hawaii false missile alert

text: Congresswoman Tulsi Gabbard stated in an interview after the second emergency alert was sent that the incident was "a taste of the stark reality of what we face here of a potential nuclear strike on Hawaii", referring to the possibility of a North Korean attack. She and former Secretary of Defense William J. Perry both said the false alert highlighted the possibility of an "accidental nuclear war", in which a technical or human error leads to the use of nuclear weapons due to a misunderstanding or misinterpretation.


title: 2018 Hawaii false missile alert

text: Honolulu Mayor Kirk Caldwell also tweeted that the message had been a false alarm, saying the message had been sent in error before the second alert was sent out by the Hawaii Emergency Management Agency.


title: 2018 Hawaii false missile alert

text: HI-EMA administrator Vern Miyagi took responsibility for the incident, ultimately resigning over it. Miyagi described the initial warning as a "mistake", saying it "should have been caught" before the alert was sent out. HI-EMA officials, including Miyagi, said there was no evidence that the agency's systems had been hacked to send the false emergency message.


title: 2018 Hawaii false missile alert

text: Miyagi apologized for the false alert, as did Governor David Ige, who called the incident "unfortunate and regrettable". They said officials would review the state's procedures to prevent it from happening again. Ige said:


title: 2018 Hawaii false missile alert

text: I know first-hand how today's false alarm affected all of us here in Hawaii, and I am sorry for the pain and confusion it caused. I, too, am extremely upset about this and am doing everything I can do to immediately improve our emergency management systems, procedures and staffing.


title: 2018 Hawaii false missile alert

text: Hawaii Senate Majority Leader J. Kalani English said he was "outraged" by the error, which caused unnecessary "panic and pandemonium" throughout the state. Hawaii House of Representatives Speaker Scott K. Saiki announced the House would investigate the incident:


title: 2018 Hawaii false missile alert

text: This system we have been told to rely upon failed and failed miserably today. I am deeply troubled by this misstep that could have had dire consequences. Measures must be taken to avoid further incidents that caused wholesale alarm and chaos today. Clearly, government agencies are not prepared and lack the capacity to deal with emergency situations. Apparently, the wrong button was pushed and it took over 30 minutes for a correction to be announced. Parents and children panicked during those 30 minutes. The Hawaii House of Representatives will immediately investigate what happened and there be consequences. This cannot happen again.


title: 2018 Hawaii false missile alert

text: The deputy adjutant of the Hawaii National Guard said that notwithstanding the erroneous alert, people should continue to follow instructions and take shelter if another alert is sent in the future.


title: 2018 Hawaii false missile alert

text: State officials held a news conference in the afternoon of January 13 to address the incident. State officials placed former Hawaii Army National Guard commander Bruce E. Oliveira in charge of internally investigating the events that resulted in the false alert being sent out. In his report, published January 30, Oliveira faulted "insufficient management controls, poor computer software design, and human factors" for the incident.


title: 2018 Hawaii false missile alert

text: Officials did not name the employee responsible for the error. Hawaii Emergency Management Agency head Vern Miyagi initially declined to say whether the employee, who he said felt "terrible" about the false alert, would face discipline. An agency spokesman said January 14 the employee had been "temporarily reassigned" to a position that did not allow him access to the emergency warning system, pending the result of the internal investigation. The employee was ultimately fired on January 26, following findings in Oliveira's investigation regarding his work history, with NBC News reporting that the employee had "a history of confusing drill and real-world events". A second employee, who was also not identified and whose role in the incident was not disclosed, was suspended without pay. Toby Clairmont, HI-EMA's executive officer, announced January 20 he planned to retire by the end of the year.


title: 2018 Hawaii false missile alert

text: The Federal Communications Commission also announced that it would conduct a full investigation into the incident. On January 25, an FCC official announced that the former employee responsible for sending the false report was refusing to cooperate with the FCC probe of the incident. The FCC report, released January 30, faulted the state for failing to quickly notify the public and not having safeguards in place sufficient to prevent the error. FCC Chairman Ajit Pai stated:


title: 2018 Hawaii false missile alert

text: Every state and local government that originates alerts needs to learn from these mistakes. Each should make sure they have adequate safeguards in place.… The public needs to be able to trust that when the government issues an alert it is indeed a credible alert.


title: 2018 Hawaii false missile alert

text: Miyagi resigned as HI-EMA administrator the same day the state and federal reports were released. Clairmont announced his resignation a day later.


title: 2018 Hawaii false missile alert

text: Then-administrator Vern Miyagi said the Hawaii Emergency Management Agency suspended tests while assessing what had happened following the incident. He also announced the agency immediately changed its procedures to require two people, instead of just one, to send out both test alerts and actual alerts. HI-EMA employees will be "counseled and drilled so this never happens again", Miyagi said January 14.


title: 2018 Hawaii false missile alert

text: Governor David Ige announced January 15 that he was appointing Brigadier General Kenneth Hara, Hawaii's deputy adjutant general, to oversee a review of the state's emergency management systems and procedures and implement reforms. The agency also moved quickly to implement a cancellation command that officials said can be triggered within seconds of an erroneous alert being sent out, which it reportedly lacked before the January 13 incident. The Hawaii emergency alert interface screen was updated with a "BMD False Alarm" selection the same day, addressing a system deficiency that made it difficult for the state to countermand an alert sent in error.


title: 2018 Hawaii false missile alert

text: HI-EMA reported that some of its employees received death threats after the false alert incident. In a rare public address, Ige called the threats "completely unacceptable" and said he was "ultimately responsible" for the error.


title: 2018 Hawaii false missile alert

text: Although Governor Ige's office issued on February 27, 2018, a "Siren and Emergency Alert System Test" for March 1, 2018, the state of Hawaii did not test the nuclear warning siren in March and dropped its monthly test of the nuclear warning siren beginning on March 1, 2018.


title: 2018 Hawaii false missile alert

text: In July 2018, the FCC issued a report and order which makes changes to EAS regulations to "improve the integrity, efficacy, and reliability" of the system and "minimize the potential for false alerts". The changes require EAS participants to configure their hardware to "reject Common Alerting Protocol-based alerts that contain an invalid digital signature and legacy (over-the-air)-based alerts whose expiration time falls outside of specific time limits", and report any false alarms to the FCC. The commission also implemented procedures for authorizing voluntary participation in "live code" tests—public exercises that simulate an actual emergency in order to "promote greater proficiency" in the system by EAS operators and participants. These changes were the result of recommendations from the FCC's report on the Hawaii incident.


title: 2018 Hawaii false missile alert

text: North Korea's "Rodong Sinmun", the Workers' Party of Korea newspaper, described the false alarm as a "tragicomedy".


title: 2018 Hawaii false missile alert

text: An official with the Division of Homeland Security & Emergency Management in the U.S. state of Alaska, also within the theoretical range of North Korean nuclear missiles, said his department encourages Alaskans to shelter in place rather than trying to get elsewhere if there is an attack, as many people in Hawaii did after the false alert was issued.


title: 2018 Hawaii false missile alert

text: U.S. Senator Brian Schatz, one of Hawaii's two members of the United States Senate, introduced federal legislation that would prohibit state and local agencies from notifying the public of a missile launch, placing the responsibility on federal authorities to make that determination. In July 2018, Schatz also introduced the Reliable Emergency Alert Distribution Improvement (READI) Act, which proposed that a reporting system be established for false alarms, that FEMA establish best practices on use of emergency alerts and preventing dissemination of false alarms, and that State Emergency Communications Committees (SECCs) be required to update their procedures on a periodic basis. The act also proposed user-visible changes to EAS behavior, including requiring that users be prevented from opting out of wireless alerts originating from FEMA, mandating repetition of EAS broadcasts for active FEMA or presidential alerts, and compelling the FCC to investigate the feasibility of delivering emergency alerts via over-the-top streaming media services. The bill passed in the Senate but failed in the House of Representatives.


title: Roshan Mathew

text: Roshan Mathew (born 22 March 1992) is an Indian actor who works predominantly in Malayalam films and Hindi, Tamil & Telugu films. He began his career with numerous theatre productions based in Chennai and Mumbai. These include "The Glass Menagerie" directed by Rajit Kapoor and "07/07/07" directed by Faezeh Jalali.


title: Roshan Mathew

text: Roshan had his first major role in the 2016 film "Puthiya Niyamam" and his career progressed with supporting roles in "Aanandam" (2016), "Koode" (2018), and "Moothon" (2019). For the latter two, he won two SIIMA Awards. He gained wider attention for his leading roles in the dramas "Kappela" (2020) and "C U Soon" (2021). Mathew has also appeared in the Hindi films "Choked" (2020) and "Darlings" (2022).


title: Roshan Mathew

text: Roshan hails from Changanassery, Kottayam in the Indian state of Kerala.He belongs to A Syro Malabar Catholic family. His father Mathew Joseph is a bank manager in Canara Bank and his mother Regina Augustine is a retired PWD engineer. He studied in Kendriya Vidyalaya, Kottayam. After enrolling in School of Engineering, CUSAT in Kochi he dropped out after one year to study B.Sc Physics in Madras Christian College in Chennai. During his second year in college he developed an interest in acting, and after graduation joined the Drama School Mumbai.


title: Roshan Mathew

text: Roshan had been active on stage since school, but his first opportunity to work in professional theatre came when the Chennai-based theatre company "Stagefright Productions" came to Madras Christian College to audition actors for their production of "Dirty Dancing" in August 2010. Roshan bagged the role of "Neal Kellerman", and the production went on stage at The Museum Theatre, Chennai in February 2011. He almost instantly fell in love with theatre, and went on to work with all the prominent Chennai-based companies in plays such as "Kamala, Leap, The Uprising, Tughlaq," and "Murder Me Always". He was also part of "The Little Theatre"’s Christmas Pantomime in 2013.


title: Roshan Mathew

text: In Madras Christian College, Roshan along with his friends started a theatre group called "Theatre No. 59" which staged many plays in different colleges in the state. Their production of Alfred Hitchcock/Patrick Hamilton’s "Rope" was widely appreciated, and their revival of Jean-Paul Sartre’s "No Exit" won Roshan the award for Best Director at a national level student theatre festival in 2013.


title: Roshan Mathew

text: After moving to Bombay in 2014, Roshan was part of The Drama School Mumbai’s adaptation of Eugene Shwartz's "The Dragon" in 2016. After school, he went to join Faezeh Jalali's widely acclaimed production "07/07/07". He then appeared in "Given" directed by Padma Damodaran and written by Shivam Sharma, and Rajit Kapoor's adaptation of "The Glass Menagerie". He has also directed an original play in Kochi called "A Very Normal Family" with a new team of artists based in the city.


title: Roshan Mathew

text: He made his screen acting debut in a web series "Tanlines". He made his film debut in 2016 in "Puthiya Niyamam" directed by A. K. Sajan, followed by a small role in "Adi Kapyare Kootamani". It was Ganesh Raj's Aanandam (2016) that put Roshan on the map. The coming-of-age movie opened to packed houses and was one of the biggest successes of the year in Malayalam. In 2018, he essayed a role in "Koode" directed by Anjali Menon. His other notable performances came in "Thottappan" (2019) alongside Vinayakan, in "Viswasapoorvam Mansoor" (2017), and "Orayiram Kinakkalal" (2018). In 2019, he shot to fame by playing Ameer opposite Nivin Pauly in Geetu Mohandas's film "Moothon". His upcoming films are "Varthamanam", directed by Sidhartha Siva along with Parvathy, his debut Tamil film "Cobra" directed by R Ajay Gnanamuthu alongside Vikram (actor). His recently released film is Netflix's Choked directed by Anurag Kashyap alongside Saiyami Kher, Kappela where he played the lead role alongside Anna Benand Sreenath Bhasi which gained positive reviews and also C U Soon alongside Fahadh Faasil. His performance in the latest malayalam movie Kuruthi alongside Prithviraj Sukumaran also garnered much attention.


title: Nikhil Nanda

text: Nikhil Nanda is an Indian businessman. Part of the Nanda family, Kapoor family and Bachchan Family, he is the chairman and managing director of Escorts Limited, an engineering company founded in 1944 by his paternal grandfather, Har Prasad Nanda.


title: Nikhil Nanda

text: Nikhil Nanda was born on 18 March 1974 in New Delhi, Delhi, India to a Punjabi Hindu family. His father, Rajan Nanda from Fazilka, was an industrialist and the chairman and managing director of Escorts Group, while his mother, Ritu Nanda, worked as an insurance agent for Life Insurance Corporation of India. His maternal grandfather was actor-director Raj Kapoor and his great-grandfather, Prithviraj Kapoor, was an actor. Actors Rishi Kapoor, Randhir Kapoor and Rajiv Kapoor are his maternal uncles, while actresses Neetu Singh and Babita Kapoor are his aunts by marriage. Actors Karisma Kapoor, Kareena Kapoor, Ranbir Kapoor, Armaan Jain and Aadar Jain are his maternal first cousins.


title: Nikhil Nanda

text: Nanda attended the Doon School in Dehradun, and went on to study business management at Wharton School of the University of Pennsylvania, where he majored in finance and marketing.


title: Nikhil Nanda

text: Nanda served as Chief Operating Officer from October 2005, then as Joint Managing Director of Escorts Limited from September 2007 when he became managing director of Escorts Limited in September 2013. He was appointed Chairman on 7 August 2018 after the death of his father. He was one of five Indians selected as the Global Leaders of Tomorrow by the World Economic Forum in Geneva, in 2001.


title: Nikhil Nanda

text: Nanda married Shweta Bachchan, daughter of film actors Amitabh Bachchan and Jaya Bachchan, on 16 February 1997. They have two children named Navya Naveli Nanda and Agastya Nanda.


title: Daikon

text: Daikon (Japanese for 'big root') or mooli, "Raphanus sativus" var. "longipinnatus," is a mild-flavored winter radish usually characterized by fast-growing leaves and a long, white, root. Originally native to continental East Asia, daikon is harvested and consumed throughout the region, as well as in South Asia, and is available internationally. In some locations, daikon is planted for its ability to break up compacted soils and recover nutrients, but is not harvested.


title: Daikon

text: In culinary contexts, daikon (from ) or are the most common names in all forms of English. Historical ties to South Asia permit "mooli" (from its Hindi/Punjabi name and also in Urdu) as a general synonym in English. The generic terms white radish, winter radish, Oriental radish, long white radish, and other terms are also used. Other synonyms usually vary by region or describe regional varieties of the vegetable. When it is necessary to distinguish the usual Japanese form from others, it is sometimes known as Japanese radish.


title: Daikon

text: The vegetable's Mandarin names are still uncommon in English; in most forms of Chinese cuisine, it is usually known as "báiluóbo" (Chinese white radish), although in Cantonese and Malaysian cuisine, it is encountered as "lobak" or "lo pak", which are Cantonese pronunciations of the general Chinese term for "radish" or "carrot" (蘿蔔). In the cuisines of Hokkien and Teochew dialect-speaking areas such as Singapore, Thailand and Taiwan, it is also known as "chai tow" or "chai tau" (菜頭). In any of these, it may also simply be referred to as "radish", with the regional variety implied by context. In English-speaking countries, it is also sometimes marketed as icicle radish.


title: Daikon

text: In mainland China and Singapore, the calque white carrot or misnomer "carrot" is sometimes used, owing to the similarity of the vegetables' names in Mandarin and Hokkien. This variant inspired the title for a popular guidebook on Singaporean street food, "There's No Carrot in Carrot Cake", which refers to "chai tow kway", a kind of cake made from daikon.


title: Daikon

text: In North America, it is primarily grown not for food, but as a fallow crop, with the roots left unharvested to prevent soil compaction; the leaves (if harvested) are used as animal fodder. The official general name used by the United States Department of Agriculture is oilseed radish, but this is only used in non-culinary contexts. Other English terms employed when daikon is being used as animal feed or as a soil ripper are "forage radish", "fodder radish", and "tillage radish".


title: Daikon

text: A number of nonwhite varieties occur. The Cantonese "lobak", "lo pak", etc. sometimes refer to the usual Chinese form, but is also applied to a form of daikon with light green coloration of the top area of the root around the leaves. The Korean radish, also called "mu", has similar pale green shade halfway down from the top, and are generally shorter, stouter, and sturdier, with denser flesh and softer leaves. Both are often spicier than the long white radishes.


title: Daikon

text: The heirloom watermelon radish is another Chinese variety of daikon with a dull green exterior, but a bright rose or fuchsia-colored center. Its Chinese name "xīnlǐměi luóbó") is sometimes irregularly romanized as the "shinrimei" radish and sometimes translated as the "beauty heart", "beautiful heart inside", or "roseheart" radish.


title: Daikon

text: The Chinese and Indian varieties tolerate higher temperatures than the Japanese one. These varieties also grow well at lower elevations in East Africa. If moisture is abundant, it can grow quickly; otherwise, the flesh becomes overly tough and pungent. The variety "Long White Icicle" is available as seed in Britain, and will grow very successfully in Southern England, producing roots resembling a parsnip by midsummer in good garden soil in an average year.


title: Daikon

text: The roots can be stored for some weeks without the leaves if lifted and kept in a cool, dry place. If left in the ground, the texture tends to become woody, but the storage life of untreated whole roots is not long.


title: Daikon

text: Certain varieties of daikon can be grown as a winter cover crop and green manure. These varieties are often named "tillage radish" because the plant grows a huge, penetrating root which effectively performs deep cultivation. The roots bring nutrients lower in the soil profile up into the higher reaches, and are good nutrient scavengers, so they are good partners with legumes instead of grasses; if harsh winters occur, the root will decompose while in the soil, releasing early nitrogen stores in the spring.


title: Daikon

text: In Japan, many types of pickles are made with daikon roots, including "takuan" and "bettarazuke". Daikon roots can be served raw, in salads, or as "sashimi"'s , which is prepared by meticulous . is frequently used as a garnish, often mixed into various dippings such as "ponzu", a soy sauce and citrus juice condiment. The pink spicy is daikon grated with chili pepper. Simmered dishes are also popular such as "oden". Daikon that has been shredded and dried (a common method of preserving food in Japan) is called . Daikon radish sprouts () are used raw for salad or garnishing "sashimi". Daikon leaves are frequently eaten as a green vegetable. They are thorny when raw, so softening methods such as pickling and stir frying are common. The daikon leaf is one of the Festival of Seven Herbs, where it is called "suzushiro".