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is equal to the area of a region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, with areas below the x-axis being subtracted.
The term "integral" may also refer to the notion of antiderivative, a function F whose derivative is the given function f. In this case it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals.
The principles of integration were formulated by Isaac Newton and Gottfried Leibniz in the late seventeenth century. Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if f is a continuous real-valued function defined on a closed interval [a, b], then, once an antiderivative F of f is known, the definite integral of f over that interval is given by
Integrals and derivatives became the basic tools of calculus, with numerous applications in science and engineering. A rigorous mathematical definition of the integral was given by Bernhard Riemann. It is based on a limiting procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs. Beginning in the nineteenth century, more sophisticated notions of integral began to appear, where the type of the function as well as the domain over which the integration is performed has been generalised. A line integral is defined for functions of two or three variables, and the interval of integration [a,b] is replaced by a certain curve connecting two points on the plane or in the space. In a surface integral, the curve is replaced by a piece of a surface in the three-dimensional space. Integrals of differential forms play a fundamental role in modern differential geometry. These generalizations of integral first arose from the needs of physics, and they play an important role in the formulation of many physical laws, notably those of electrodynamics. Modern concepts of integration are based on the abstract mathematical theory known as Lebesgue integration, developed by Henri Lebesgue.
The next major step in integral calculus came in the 11th century, when the Iraqi mathematician, Ibn al-Haytham (known as Alhazen in Europe), devised what is now known as "Alhazen's problem", which leads to an equation of the fourth degree, in his Book of Optics. While solving this problem, he performed an integration in order to find the volume of a paraboloid. Using mathematical induction, he was able to generalize his result for the integrals of polynomials up to the fourth degree. He thus came close to finding a general formula for the integrals of polynomials, but he was not concerned with any polynomials higher than the fourth degree. Some ideas of integral calculus are also found in the Siddhanta Shiromani, a 12th century astronomy text by Indian mathematician Bhāskara II.
The next significant advances in integral calculus did not begin to appear until the 16th century. At this time the work of Cavalieri with his method of indivisibles, and work by Fermat, began to lay the foundations of modern calculus. Further steps were made in the early 17th century by Barrow and Torricelli, who provided the first hints of a connection between integration and differentiation.
The modern notation for the indefinite integral was introduced by Gottfried Leibniz in 1675 (). He adapted the integral symbol, "∫", from an elongated letter "s", standing for summa (Latin for "sum" or "total"). The modern notation for the definite integral, with limits above and below the integral sign, was first used by Joseph Fourier in Mémoires of the French Academy around 1819–20, reprinted in his book of 1822 (). In so-called modern Arabic mathematical notation, which aims at pre-university levels of education in the Arab world and is written from right to left, an inverted integral symbol is used .
The simplest case, the integral of a real-valued function f of one real variable x on the interval [a, b], is denoted by
The ∫ sign, an elongated "s", represents integration; a and b are the lower limit and upper limit of integration, defining the domain of integration; f is the integrand, to be evaluated as x varies over the interval [a,b]; and dx is the variable of integration. In correct mathematical typography, the dx is separated from the integrand by a space (as shown). Some authors use an upright d (that is, instead of dx).
The variable of integration dx has different interpretations depending on the theory being used. For example, it can be seen as strictly a notation indicating that x is a dummy variable of integration, as a reflection of the weights in the Riemann sum, a measure (in Lebesgue integration and its extensions), an infinitesimal (in non-standard analysis) or as an independent mathematical quantity: a differential form. More complicated cases may vary the notation slightly.
To start off, consider the curve y = f(x) between x = 0 and x = 1, with f(x) = √x. We ask:
As a first approximation, look at the unit square given by the sides x = 0 to x = 1 and y = f(0) = 0 and y = f(1) = 1. Its area is exactly 1. As it is, the true value of the integral must be somewhat less. Decreasing the width of the approximation rectangles shall give a better result; so cross the interval in five steps, using the approximation points 0, 1⁄5, 2⁄5, and so on to 1. Fit a box for each step using the right end height of each curve piece, thus √1⁄5, √2⁄5, and so on to √1 = 1. Summing the areas of these rectangles, we get a better approximation for the sought integral, namely
Notice that we are taking a sum of finitely many function values of f, multiplied with the differences of two subsequent approximation points. We can easily see that the approximation is still too large. Using more steps produces a closer approximation, but will never be exact: replacing the 5 subintervals by twelve as depicted, we will get an approximate value for the area of 0.6203, which is too small. The key idea is the transition from adding finitely many differences of approximation points multiplied by their respective function values to using infinitely fine, or infinitesimal steps.
As for the actual calculation of integrals, the fundamental theorem of calculus, due to Newton and Leibniz, is the fundamental link between the operations of differentiating and integrating. Applied to the square root curve, f(x) = x1/2, it says to look at the antiderivative F(x) = 2⁄3x3/2, and simply take F(1) − F(0), where 0 and 1 are the boundaries of the interval [0,1]. (This is a case of a general rule, that for f(x) = xq, with q ≠ −1, the related function, the so-called antiderivative is F(x) = (xq+1)/(q + 1).) So the exact value of the area under the curve is computed formally as
The notation
Historically, after the failure of early efforts to rigorously interpret infinitesimals, Riemann formally defined integrals as a limit of weighted sums, so that the dx suggested the limit of a difference (namely, the interval width). Shortcomings of Riemann's dependence on intervals and continuity motivated newer definitions, especially the Lebesgue integral, which is founded on an ability to extend the idea of "measure" in much more flexible ways. Thus the notation
Differential geometry, with its "calculus on manifolds", gives the familiar notation yet another interpretation. Now f(x) and dx become a differential form, ω = f(x) dx, a new differential operator d, known as the exterior derivative appears, and the fundamental theorem becomes the more general Stokes' theorem,
More recently, infinitesimals have reappeared with rigor, through modern innovations such as non-standard analysis. Not only do these methods vindicate the intuitions of the pioneers, they also lead to new mathematics.
Although there are differences between these conceptions of integral, there is considerable overlap. Thus the area of the surface of the oval swimming pool can be handled as a geometric ellipse, as a sum of infinitesimals, as a Riemann integral, as a Lebesgue integral, or as a manifold with a differential form. The calculated result will be the same for all.
The Riemann integral is defined in terms of Riemann sums of functions with respect to tagged partitions of an interval. Let [a,b] be a closed interval of the real line; then a tagged partition of [a,b] is a finite sequence
This partitions the interval [a,b] into i sub-intervals [xi−1, xi], each of which is "tagged" with a distinguished point ti ∈ [xi−1, xi]. Let Δi = xi−xi−1 be the width of sub-interval i; then the mesh of such a tagged partition is the width of the largest sub-interval formed by the partition, maxi=1…n Δi. A Riemann sum of a function f with respect to such a tagged partition is defined as
The Riemann integral is not defined for a wide range of functions and situations of importance in applications (and of interest in theory). For example, the Riemann integral can easily integrate density to find the mass of a steel beam, but cannot accommodate a steel ball resting on it. This motivates other definitions, under which a broader assortment of functions is integrable . The Lebesgue integral, in particular, achieves great flexibility by directing attention to the weights in the weighted sum.
The definition of the Lebesgue integral thus begins with a measure, μ. In the simplest case, the Lebesgue measure μ(A) of an interval A = [a,b] is its width, b − a, so that the Lebesgue integral agrees with the (proper) Riemann integral when both exist. In more complicated cases, the sets being measured can be highly fragmented, with no continuity and no resemblance to intervals.
To exploit this flexibility, Lebesgue integrals reverse the approach to the weighted sum. As puts it, "To compute the Riemann integral of f, one partitions the domain [a,b] into subintervals", while in the Lebesgue integral, "one is in effect partitioning the range of f".
One common approach first defines the integral of the indicator function of a measurable set A by:
When the measure space on which the functions are defined is also a locally compact topological space (as is the case with the real numbers R), measures compatible with the topology in a suitable sense (Radon measures, of which the Lebesgue measure is an example) and integral with respect to them can be defined differently, starting from the integrals of continuous functions with compact support. More precisely, the compactly supported functions form a vector space that carries a natural topology, and a (Radon) measure can be defined as any continuous linear functional on this space; the value of a measure at a compactly supported function is then also by definition the integral of the function. One then proceeds to expand the measure (the integral) to more general functions by continuity, and defines the measure of a set as the integral of its indicator function. This is the approach taken by and a certain number of other authors. For details see Radon measures.
Linearity, together with some natural continuity properties and normalisation for a certain class of "simple" functions, may be used to give an alternative definition of the integral. This is the approach of Daniell for the case of real-valued functions on a set X, generalized by Nicolas Bourbaki to functions with values in a locally compact topological vector space. See for an axiomatic characterisation of the integral.
A number of general inequalities hold for Riemann-integrable functions defined on a closed and bounded interval [a, b] and can be generalized to other notions of integral (Lebesgue and Daniell).
(fg)(x)= f(x) g(x), ; f^2 (x) = (f(x))^2, ; |f| (x) = |f(x)|.,
In this section f is a real-valued Riemann-integrable function. The integral
The first convention is necessary in consideration of taking integrals over subintervals of [a, b]; the second says that an integral taken over a degenerate interval, or a point, should be zero. One reason for the first convention is that the integrability of f on an interval [a, b] implies that f is integrable on any subinterval [c, d], but in particular integrals have the property that:
Instead of viewing the above as conventions, one can also adopt the point of view that integration is performed on oriented manifolds only. If M is such an oriented m-dimensional manifold, and M' is the same manifold with opposed orientation and ω is an m-form, then one has (see below for integration of differential forms):
The fundamental theorem of calculus is the statement that differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieved. An important consequence, sometimes called the second fundamental theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated.
A "proper" Riemann integral assumes the integrand is defined and finite on a closed and bounded interval, bracketed by the limits of integration. An improper integral occurs when one or more of these conditions is not satisfied. In some cases such integrals may be defined by considering the limit of a sequence of proper Riemann integrals on progressively larger intervals.
If the interval is unbounded, for instance at its upper end, then the improper integral is the limit as that endpoint goes to infinity.
That is, the improper integral is the limit of proper integrals as one endpoint of the interval of integration approaches either a specified real number, or ∞, or −∞. In more complicated cases, limits are required at both endpoints, or at interior points.
Consider, for example, the function integrated from 0 to ∞ (shown right). At the lower bound, as x goes to 0 the function goes to ∞, and the upper bound is itself ∞, though the function goes to 0. Thus this is a doubly improper integral. Integrated, say, from 1 to 3, an ordinary Riemann sum suffices to produce a result of . To integrate from 1 to ∞, a Riemann sum is not possible. However, any finite upper bound, say t (with t > 1), gives a well-defined result, . This has a finite limit as t goes to infinity, namely . Similarly, the integral from 1⁄3 to 1 allows a Riemann sum as well, coincidentally again producing . Replacing 1⁄3 by an arbitrary positive value s (with s < 1) is equally safe, giving . This, too, has a finite limit as s goes to zero, namely . Combining the limits of the two fragments, the result of this improper integral is
It may also happen that an integrand is unbounded at an interior point, in which case the integral must be split at that point, and the limit integrals on both sides must exist and must be bounded. Thus
Integrals can be taken over regions other than intervals. In general, an integral over a set E of a function f is written:
Here x need not be a real number, but can be another suitable quantity, for instance, a vector in R3. Fubini's theorem shows that such integrals can be rewritten as an iterated integral. In other words, the integral can be calculated by integrating one coordinate at a time.
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function and the plane which contains its domain. (The same volume can be obtained via the triple integral — the integral of a function in three variables — of the constant function f(x, y, z) = 1 over the above-mentioned region between the surface and the plane.) If the number of variables is higher, then the integral represents a hypervolume, a volume of a solid of more than three dimensions that cannot be graphed.
For example, the volume of the parallelepiped of sides 4 × 6 × 5 may be obtained in two ways:
Because it is impossible to calculate the antiderivative of a function of more than one variable, indefinite multiple integrals do not exist, so such integrals are all definite.
The concept of an integral can be extended to more general domains of integration, such as curved lines and surfaces. Such integrals are known as line integrals and surface integrals respectively. These have important applications in physics, as when dealing with vector fields.
A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. Various different line integrals are in use. In the case of a closed curve it is also called a contour integral.
The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes the line integral from simpler integrals defined on intervals. Many simple formulas in physics have natural continuous analogs in terms of line integrals; for example, the fact that work is equal to force multiplied by distance may be expressed (in terms of vector quantities) as:
A surface integral is a definite integral taken over a surface (which may be a curved set in space); it can be thought of as the double integral analog of the line integral. The function to be integrated may be a scalar field or a vector field. The value of the surface integral is the sum of the field at all points on the surface. This can be achieved by splitting the surface into surface elements, which provide the partitioning for Riemann sums.
For an example of applications of surface integrals, consider a vector field v on a surface S; that is, for each point x in S, v(x) is a vector. Imagine that we have a fluid flowing through S, such that v(x) determines the velocity of the fluid at x. The flux is defined as the quantity of fluid flowing through S in unit amount of time. To find the flux, we need to take the dot product of v with the unit surface normal to S at each point, which will give us a scalar field, which we integrate over the surface:
A differential form is a mathematical concept in the fields of multivariable calculus, differential topology and tensors. The modern notation for the differential form, as well as the idea of the differential forms as being the wedge products of exterior derivatives forming an exterior algebra, was introduced by Élie Cartan.
We initially work in an open set in Rn. A 0-form is defined to be a smooth function f. When we integrate a function f over an m-dimensional subspace S of Rn, we write it as
(The superscripts are indices, not exponents.) We can consider dx1 through dxn to be formal objects themselves, rather than tags appended to make integrals look like Riemann sums. Alternatively, we can view them as covectors, and thus a measure of "density" (hence integrable in a general sense). We call the dx1, …,dxn basic 1-forms.
We define the wedge product, "∧", a bilinear "multiplication" operator on these elements, with the alternating property that
for all indices a. Note that alternation along with linearity implies dxb∧dxa = −dxa∧dxb. This also ensures that the result of the wedge product has an orientation.
We define the set of all these products to be basic 2-forms, and similarly we define the set of products of the form dxa∧dxb∧dxc to be basic 3-forms. A general k-form is then a weighted sum of basic k-forms, where the weights are the smooth functions f. Together these form a vector space with basic k-forms as the basis vectors, and 0-forms (smooth functions) as the field of scalars. The wedge product then extends to k-forms in the natural way. Over Rn at most n covectors can be linearly independent, thus a k-form with k > n will always be zero, by the alternating property.
In addition to the wedge product, there is also the exterior derivative operator d. This operator maps k-forms to (k+1)-forms. For a k-form ω = f dxa over Rn, we define the action of d by:
with extension to general k-forms occurring linearly.
This more general approach allows for a more natural coordinate-free approach to integration on manifolds. It also allows for a natural generalisation of the fundamental theorem of calculus, called Stokes' theorem, which we may state as
where ω is a general k-form, and ∂Ω denotes the boundary of the region Ω. Thus in the case that ω is a 0-form and Ω is a closed interval of the real line, this reduces to the fundamental theorem of calculus. In the case that ω is a 1-form and Ω is a 2-dimensional region in the plane, the theorem reduces to Green's theorem. Similarly, using 2-forms, and 3-forms and Hodge duality, we can arrive at Stokes' theorem and the divergence theorem. In this way we can see that differential forms provide a powerful unifying view of integration.
Note that the integral is not actually the antiderivative, but the fundamental theorem allows us to use antiderivatives to evaluate definite integrals.
The difficult step is often finding an antiderivative of f. It is rarely possible to glance at a function and write down its antiderivative. More often, it is necessary to use one of the many techniques that have been developed to evaluate integrals. Most of these techniques rewrite one integral as a different one which is hopefully more tractable. Techniques include:
Even if these techniques fail, it may still be possible to evaluate a given integral. Many nonelementary integrals can be expanded in a Taylor series and integrated term by term. Occasionally, the resulting infinite series can be summed analytically. The method of convolution using Meijer G-functions can also be used, assuming that the integrand can be written as a product of Meijer G-functions. There are also many less common ways of calculating definite integrals; for instance, Parseval's identity can be used to transform an integral over a rectangular region into an infinite sum. Occasionally, an integral can be evaluated by a trick; for an example of this, see Gaussian integral.
Computations of volumes of solids of revolution can usually be done with disk integration or shell integration.
Specific results which have been worked out by various techniques are collected in the list of integrals.
Many problems in mathematics, physics, and engineering involve integration where an explicit formula for the integral is desired. Extensive tables of integrals have been compiled and published over the years for this purpose. With the spread of computers, many professionals, educators, and students have turned to computer algebra systems that are specifically designed to perform difficult or tedious tasks, including integration. Symbolic integration presents a special challenge in the development of such systems.
A major mathematical difficulty in symbolic integration is that in many cases, a closed formula for the antiderivative of a rather simple-looking function does not exist. For instance, it is known that the antiderivatives of the functions exp (x2), xx and sin x /x cannot be expressed in the closed form involving only rational and exponential functions, logarithm, trigonometric and inverse trigonometric functions, and the operations of multiplication and composition; in other words, none of the three given functions is integrable in elementary functions. Differential Galois theory provides general criteria that allow one to determine whether the antiderivative of an elementary function is elementary. Unfortunately, it turns out that functions with closed expressions of antiderivatives are the exception rather than the rule. Consequently, computerized algebra systems have no hope of being able to find an antiderivative for a randomly constructed elementary function. On the positive side, if the 'building blocks' for antiderivatives are fixed in advance, it may be still be possible to decide whether the antiderivative of a given function can be expressed using these blocks and operations of multiplication and composition, and to find the symbolic answer whenever it exists. The Risch algorithm, implemented in Mathematica and other computer algebra systems, does just that for functions and antiderivatives built from rational functions, radicals, logarithm, and exponential functions.
Some special integrands occur often enough to warrant special study. In particular, it may be useful to have, in the set of antiderivatives, the special functions of physics (like the Legendre functions, the hypergeometric function, the Gamma function and so on). Extending the Risch-Norman algorithm so that it includes these functions is possible but challenging.
Most humans are not able to integrate such general formulae, so in a sense computers are more skilled at integrating highly complicated formulae. Very complex formulae are unlikely to have closed-form antiderivatives, so how much of an advantage this presents is a philosophical question that is open for debate.
The integrals encountered in a basic calculus course are deliberately chosen for simplicity; those found in real applications are not always so accommodating. Some integrals cannot be found exactly, some require special functions which themselves are a challenge to compute, and others are so complex that finding the exact answer is too slow. This motivates the study and application of numerical methods for approximating integrals, which today use floating point arithmetic on digital electronic computers. Many of the ideas arose much earlier, for hand calculations; but the speed of general-purpose computers like the ENIAC created a need for improvements.
The goals of numerical integration are accuracy, reliability, efficiency, and generality. Sophisticated methods can vastly outperform a naive method by all four measures (; ). Consider, for example, the integral
Using the left end of each piece, the rectangle method sums 16 function values and multiplies by the step width, h, here 0.25, to get an approximate value of 3.94325 for the integral. The accuracy is not impressive, but calculus formally uses pieces of infinitesimal width, so initially this may seem little cause for concern. Indeed, repeatedly doubling the number of steps eventually produces an approximation of 3.76001. However 218 pieces are required, a great computational expense for so little accuracy; and a reach for greater accuracy can force steps so small that arithmetic precision becomes an obstacle.
A better approach replaces the horizontal tops of the rectangles with slanted tops touching the function at the ends of each piece. This trapezium rule is almost as easy to calculate; it sums all 17 function values, but weights the first and last by one half, and again multiplies by the step width. This immediately improves the approximation to 3.76925, which is noticeably more accurate. Furthermore, only 210 pieces are needed to achieve 3.76000, substantially less computation than the rectangle method for comparable accuracy.
Romberg's method builds on the trapezoid method to great effect. First, the step lengths are halved incrementally, giving trapezoid approximations denoted by T(h0), T(h1), and so on, where hk+1 is half of hk. For each new step size, only half the new function values need to be computed; the others carry over from the previous size (as shown in the table above). But the really powerful idea is to interpolate a polynomial through the approximations, and extrapolate to T(0). With this method a numerically exact answer here requires only four pieces (five function values)! The Lagrange polynomial interpolating {hk,T(hk)}k=0…2 = {(4.00,6.128), (2.00,4.352), (1.00,3.908)} is 3.76+0.148h2, producing the extrapolated value 3.76 at h = 0.
Gaussian quadrature often requires noticeably less work for superior accuracy. In this example, it can compute the function values at just two x positions, ±2⁄√3, then double each value and sum to get the numerically exact answer. The explanation for this dramatic success lies in error analysis, and a little luck. An n-point Gaussian method is exact for polynomials of degree up to 2n−1. The function in this example is a degree 3 polynomial, plus a term that cancels because the chosen endpoints are symmetric around zero. (Cancellation also benefits the Romberg method.)
Shifting the range left a little, so the integral is from −2.25 to 1.75, removes the symmetry. Nevertheless, the trapezoid method is rather slow, the polynomial interpolation method of Romberg is acceptable, and the Gaussian method requires the least work — if the number of points is known in advance. As well, rational interpolation can use the same trapezoid evaluations as the Romberg method to greater effect.
|Rel. Err.
In practice, each method must use extra evaluations to ensure an error bound on an unknown function; this tends to offset some of the advantage of the pure Gaussian method, and motivates the popular Gauss–Kronrod quadrature formulas. Symmetry can still be exploited by splitting this integral into two ranges, from −2.25 to −1.75 (no symmetry), and from −1.75 to 1.75 (symmetry). More broadly, adaptive quadrature partitions a range into pieces based on function properties, so that data points are concentrated where they are needed most.
This brief introduction omits higher-dimensional integrals (for example, area and volume calculations), where alternatives such as Monte Carlo integration have great importance.
A calculus text is no substitute for numerical analysis, but the reverse is also true. Even the best adaptive numerical code sometimes requires a user to help with the more demanding integrals. For example, improper integrals may require a change of variable or methods that can avoid infinite function values; and known properties like symmetry and periodicity may provide critical leverage.
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Tintin is on the trail of a big story which leads him into a world of high adventure. When he and his friends find the directions to a sunken ship, they go off to find the treasure it contained and Tintin must face the notorious Red Rackham.
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From Staff Reports
MANTACHIE – The Mantachie Mustangs scored four runs in the first inning to spark themselves to a 6-2 win over East Webster Friday night in the Class 2A baseball playoffs.
The victory gives Mantachie a 1-0 lead in the best-of-three, third-round series.
"We didn't play bad, we just didn't play good enough to win," said East Webster head coach Wes Johnson. "But (today) is a new day. We can beat them twice."
On Friday, the Wolverines (19-7) found themselves unable to muster much offense.
Jamie McKee recorded a pair of doubles for East Webster while Hayden Hendrix and Austin Halford also had hits.
"(Mantachie's) pitcher did a good job of throwing strikes and didn't walk anyone," said Johnson.
Pitcher Ty Hendrix hurled a complete game for East Webster, but was saddled with the loss.
The Wolverines will attempt to even things up against the Mustangs today at 1 p.m. East Webster is hosting the game in Houston due to the storm damage on their campus in Cumberland.
If the Wolverines win today, the third game of the series will be played in Mantachie on Monday.
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Ken Block answers your questions
Mr Gymkhana sets the world to rights over a game of ping pong
Posted: 26 Mar 2013
You may be wondering why Ken Block is pictured above with two table tennis bats in his hand. Surely there should be shredded tyres and YouTube hits filling those mitts? Well, Kenny from the Block is a big fan of table tennis. Indeed, he's such a fan that he literally eats off a ping pong table at home. So before he was unveiling his new rallycross car to the public, we decided to challenge him to a game of Boris Johnson's favoured pastime: wiff-waff.
Apparently, in the past he's beaten opponents while holding an infant under one arm - a handicap we've yet to see in the Olympics. Still, TG.com decided to challenge him to a game and fire your questions (and some balls) his way.
He's answered everything: who his idols are, what his favourite car is and whether he'd like to fight giant ducks or midget horses. So click through and see Ken put the internet's questions to rights.
(And thank you all for your contributions, TopGear.commers)
AirMax: What is the most exciting production car you've ever driven?
It has to be the Ford F150 Raptor. It's so versatile for snow, on road, off-road - I just love it. I have one up in the mountains where I live and whenever it's snowing I go out and drift it around like my rally car. It's the best daily driver I've ever had.
I love to abuse cars and I can do it in that because the thing has four-wheel drive and very soft suspension. You can drive it like a rally car because when you brake, the weight transfers and it's a lot of fun to throw around. And don't think I'm saying that because I'm sponsored by Ford, it genuinely is one of the best cars I've ever driven.
rishmanVR6: Would you ever consider other forms of motorsport outside rally and Gymkhana?
I've had lots of offers to do different motorsports. The thing is I love that you can drive so aggressive in rally and Gymkhana, but it's still all about precision. There are other forms of precision from Formula One to off-road trucks, but Formula One to me is too precise, it's too much of the same thing over and over.
And then the flip side of that is something like the Baja 1000, but for that the suspension and everything has to be so soft to soak up all the bumps that you lose some of the precision. So, for me, stage rally and rallycross are a nice balance of being able to drive so aggressive but still be able to have the precision. I've had offers to do Le Mans 24 hours, Dakar and Baja 1000 - a huge range of things - but I can't get enough of what I'm doing as it is, so why try and diversify?
Gavinload: What is the best vintage rally car you have ever driven?
The '78 MKII Escort - it's so much fun. The way they handle and the sound they make is just amazing.
The_Stig_Farmer: What's it like seeing people parody your YouTube videos and painting their cars like yours?
I take it as a huge compliment. I'm continually blown away by how much people appreciate and like the things I do. I'm always very honored that people want to imitate either the graphics or videos that I do.
Rshohet: How did your rally career as a driver start and have you got any tips?
I think that the best thing to do is go to a rally school. You can waste a lot of time and money by driving cars around not knowing what you're doing. The best way to start is to let someone who has the experience teach you how to do it.
I've been to several rally schools, the main one being Team O'Neil in the States. That was the first place I ever went and I got a lot of knowledge out of them. Travis Pastrana had gone there and I thought it looked fun, so I wanted to try and drive a rally car. I absolutely loved it but also found that I had a pretty decent amount of talent inside the car and since then I've just been pushing to learn more and more.
Sayaraa: Please describe for me what the feeling is like when all four tyres of your car are in the air?
It's absolutely incredible. I've just done WRC Mexico which features BIG jumps. It's really enjoyable to take a WRC car and go flat out, sixth gear off a jump - it's amazing.
Morgan-rees: What gets you motivated before an event?
Well the main thing is that I absolutely doing all this stuff. So the idea of me being able to get in a car and be able to drive all these courses at a demo is just for fun. But at a competition, like X Games or WRC, the competitive side takes over and I just want to win.
Strokemymailbox: Is everything sideways for you? Crabs walk sideways, are they your favourite animal?
Errr no. I just leave going sideways to cars. My favourite animals aren't crabs, I own Siberian huskies as pets, so they're my favourite.
James Russell: Would you rather fight one horse-sized duck, or 100 duck-sized horses?
I would say the 100 duck-sized horses because you could sucker kick them.
John Catterson: Apart from the likes of Colin McRae, who inspired you to become a rally driver?
The biggest inspiration for me is Colin McRae. But besides that, I watched a lot of rally in the late '80s and early '90s but especially the Group B era. That was so awe-inspiring that it really caught my attention while in America and brought my attention to rally.
KeithLemon: Where did the idea behind Gymkhana come from?
The idea of Gymkhana actually came from the fact that we don't have tarmac rallies in our championship in America. I wanted to gain more experience sliding the car around on tarmac like I saw rally drivers in Europe do. It was a way to get more experience and expand my skill set. It just turned into making videos because there was a Gymkhana championship in southern California and I had built a car to specifically go and do it. But the guy that was organizing the championship quit, so I had an amazing car but nothing to do with it. So that's when I made my first video, which was at one of the facilities where I had done a Gymkhana event. I went back there and we filmed an event practice but we had no idea it was going to be as popular as it was.
Shazad M Ali: Do you believe Jeremy's theory that pulling on the handbrake will make women like him? Is this why you're constantly pulling it?
I've never thought of it that way. That's pretty good, though. It's a great theory but it was never my intention.
Marcel Dorrego: What is the most insane/scary/memorable drive you've ever had?
It has to be racing some of the roads and stages of the WRC event in New Zealand. The event and roads they build down there are cambered because they get so much rain and I've gone through corners there where I was actually laughing because it was so fun. I had such a big smile on my face I couldn't hold back the laughter... and that was at full speed in a WRC car. There's nothing else like it.
RolandRedTrousers: What do you think of the death of the Subaru STi and Impreza in the UK?
I think it's too bad what Subaru have done over the last couple of years with rally. Dropping out of the WRC, pulling their performance models and their support for rally around the world is just unfortunate. I had some great years rallying with them but it's just unfortunate that they can't do what they used to do.
Joe Coggings: What is the best moment of your career?
That's a really tough one but one of the most amazing moments of my racing career was racing against Colin McRae and pressuring him in to crashing. We were in a head-to-head competition at the X-Games and I was leading and he took on the extra pressure and crashed. He told me later that night that it was my pressure that caused him. And to be able to say you've pressured Colin McRae into crashing is just f*cking awesome. It's one of the biggest highlights of my life.
Kari Koskinen: What was the hardest thing to adapt to in the WRC?
The speed. I could drive the car quick right off the bat, but really the biggest problem was pace notes. A lot of these guys come from championships from around the world where there's a lot more pace note development and we don't have that sort of development in the States. Writing my own pace notes was a big skill that I had to learn quite quickly. I still struggle with it today as I'm just not at the level these other guys are as they've been doing it that much longer than me. Take Peter Solberg, I have 20 WRC events under my belt and he has something like 180. I have barely over ten per cent of what he has experience-wise. I can drive the car quite quickly down the stage but it's that whole package of stage notes and everything that truly makes a fast rally driver.
Istvan Siroki: How does it feel racing against yourself in the Dirt videogame series?
I absolutely love it. But hearing my voice is sometimes a bit scary. It genuinely freaks me out but to be able to have my car in a game is something I never thought would ever be possible. I get a good laugh each time I see it.
ButteryThunder: What do you see happening with Gymkhana as an entity in the future?
I started doing Gymkhana because I liked the competition side of it. It's great practice and going out and being able to compete against people like Tanner Foust and Travis Pastrana is great fun. And in the future I want the series side of it to grow and I want to compete in more events. We've got a big series starting here in Europe and there'll also be events in the States. It's really fun for me as it grows because it gives me more events to go and play at.
RolandRedTrousers: Are the Gymkhana 6 gears turning in your head right now?
Absolutely. Being able to play with cars like that is something you dream of as a kid. Now I get to come up with crazy ideas and then go out and do them means that I'm always coming up with different things. I've got long documents of random ideas at home and it's a lot of fun and a real creative outlet for marketing as well as combining it with what I do as a driver.


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Nov 13, 2007
What is a "Real" programming language? Or a "best" one?
While I consider RobotC indeed a tool quite well adapted to NXT programmers' needs, I rather disagree with some arguments of his (and left an according comment).
What do you think about his opinions on that subject? It's an interesting discussion that has been led many times already in the past (and will no doubt go on in the future) with a lot of aspects involved.
Leave comments there!
6 comments:
As I responded on GeekDad, I agree with many of your comments. My point is that almost any text-based language is a step up from NXT-G, but my preference for RobotC is all about the amazingly polished IDE/programming environment, not necessarily the C language itself.
- Nov 13, 2007, 8:55:00 PM
- RDewsbery said...
"If you're not a C programmer, don't worry--aside from a few grammatical conventions, it could be BASIC."
Except that I'm not a BASIC programmer either. Call me lazy, but I'm too old to struggle with too many new concepts and ways of doing things. Studless construction is a big enough wrench; requiring me to learn C, some derivative of C, BASIC or (frankly) anything else is a tall order.
There seems to be a big assumption in that article that everyone can - and should - be using a text-based programming language, and NXT-G is a "toy", unsuited to the task. Which is odd, because I was under the impression that the whole of the Mindstorms NXT kit was a big construction toy, suitable for making toy robots. the fact that you can take things further if you're experienced with programming is a big plus point, but I suspect that I'm actually part of the silent majority of users, who may never go much beyond either building basic robots or using the included NXT-G software.
Nope, I'll stick to NXT-G. I'm reasonably confident with features like datawires and variables it will far eclipse the (obvioulsy limited) software included with the old RCX anyway.
- Nov 13, 2007, 10:25:00 PM
- dickswan said...
There's lots of choices for NXT programming environments. See my article from Robot magazine at "http://www.botmag.com/articles/10-31-07_NXT.shtml" for a comparison.
I completely agree that there is not a single solution that will fit the needs of all individuals.
Dick Swan
- Nov 14, 2007, 2:30:00 PM
- Matthias Paul Scholz said...
Please see my according response at GeekDad.
By the way,I encourage everyone who has a comment on this topic to post it there, as I find it hard to follow a discussion scattered on two different blogs.
- Nov 14, 2007, 7:40:00 PM
- Joshua Heinzl said...
What advantage does RobotC have over RoboLab besides being text based? The firmware is the same...
- Nov 16, 2007, 8:03:00 PM
- Michael Aivaliotis said...
As a LabVIEW programmer, I can see how NXT-G may be frustrating. It's a stripped down version of LabVIEW. Let's not forget however that for kids, text based programming is not very exciting, to put it mildly. This is the real target for NXT-G. Sure, if you are older and are keen to try something else then more power to you.
- Nov 17, 2007, 8:28:00 PM


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Montreal Canadiens (14-9-2) at Washington Capitals (12-11-2), 5 p.m.
(SportsNetwork.com) - The Montreal Canadiens and Washington Capitals are headed in opposite directions. They meet for the second time in a week on Friday evening with a rematch in D.C.
The Canadiens have ripped off a season high-tying four straight victories, a span that includes a 3-2 victory in Washington on Nov. 22. That setback is part of a season-high four-game slide for the Capitals.
Montreal kept its winning streak intact on Wednesday with a 3-1 win over the Buffalo Sabres. David Desharnais had a goal and an assist, while Alex Galchenyuk and Brendan Gallagher also scored.
Desharnais has two goals and three assists over his past four games after going 13 in a row without a point.
"In the last two weeks he's playing well," Canadiens coach Michel Therrien said of Desharnais. "He's competing to the puck, he's working hard on both sides of the ice. It's not a coincidence that he's got success. He's working really hard."
Andrei Markov assisted on all three goals and P.K. Subban notched the 100th assist of his career on Desharnais' second-period goal. Carey Price stopped 24-of-25 shots faced in the win as the Habs moved to 6-1-1 in their last eight.
Peter Budaj is slated to get the start for Montreal tonight, with Price in line to start on Saturday against visiting Toronto. Budaj is 1-2-1 with a 2.73 goals against average in five games (4 starts) versus the Capitals, stopping 25-of-27 shots faced in last Friday's victory.
Desharnais, Travis Moen and Daniel Briere all scored for the Canadiens, while Alex Ovechkin scored both of the Capitals' goals and Michal Neuvirth made 28 saves in defeat.
Washington had won eight of its previous nine versus Montreal before that setback.
The Capitals were in a good position to snap their skid on Wednesday versus the Ottawa Senators, but struggled late in a 6-4 loss. Zack Smith netted the winner for the Sens with 2:23 to play.
Washington got first-period goals by Eric Fehr, Marcus Johansson and Brooks Laich, while John Carlson scored 62 seconds before Smith's go-ahead goal.
Braden Holtby gave up five goals on 40 shots faced.
"We had them. We were close to putting our stamp on it, but we let them back," Carlson said. "It's tough. We need wins right now and this is certainly one that we can look back on and make sure it doesn't happen again because it's not a good loss."
Holtby could start again tonight and has won all three of his previous starts versus the Canadiens while posting a 1.00 GAA and a shutout.


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Posts tagged as 'Blues'
Check out all of the posts tagged with 'Blues' below. If you still can't find what you are looking for, try searching using the form within the right side navigation of this page.
New Exhibition: Hatch Show Print - Nashville Calling
Thursday, 14th Nov 2013
London's CHELSEA Space Gallery has just opened a new exhibition dedicated to the American letterpress art of Hatch Show Print, based in Nashville, Tennessee. Established in 1879, well before TV advertising and the internet, Hatch Show Print used their bold letterpress designs to promote Country, Americana, Blues and Jazz musicians. Their bright and colourful artworks have featured the likes of Bessie Smith, Duke Ellington, Louis Armstrong and Hank Williams.
Though best known for their work with musicians, Hatch Show Print originally began by making posters for religious meetings, local businesses and political rallies. Nashville Calling features archive artefacts, photographs, film and many of the signature poster designs created by the company from the 1920s to the present day. The exhibition explores Hatch's unique history and positioning as an information network, universally respected art and design agency and cultural icon.
Nashville Calling will run until 14th December 2013, and will be accompanied by a series of talks, lectures and music events to celebrate Hatch Show Print and its history. As with each exhibition at the CHELSEA Space gallery, a new illustrated publication will accompany the show.


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text: Luxury west orientated, modern villa with beautiful sea and sunset views near the village of San Jose and west coast beaches. The house has been fully renovated in 2010 and boasts a large, light lounge with fireplace, dining room and a sleek kitchen. The beautiful master bedroom commands the entire upper floor with a glass fronted fireplace, sitting room and ensuite bathroom another 2 bedrooms and 2 bathrooms are on the lower floor and a small adjoining guest house with one bedroom and bathroom. An infinity swimming pool to the front of the lounge and numerous fruit trees and mediterranean plants in the garden along with an enchanting barbeque area with al-fresco dining area contribute to the feeling of wellbeing. The property is fully fenced and there is plenty of parking space .


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- algorithmic game theory (1)
- competitive analysis (1)
- delay management (1)
- mechanism design (1)
- online optimization (1)
- public transportation (1)
- selfish routing (1)
- Complexity and Approximability of the Maximum Flow Problem with Minimum Quantities (2012)
- We consider the maximum flow problem with minimum quantities (MFPMQ), which is a variant of the maximum flow problem where the flow on each arc in the network is restricted to be either zero or above a given lower bound (a minimum quantity), which may depend on the arc. This problem has recently been shown to be weakly NP-complete even on series-parallel graphs. In this paper, we provide further complexity and approximability results for MFPMQ and several special cases. We first show that it is strongly NP-hard to approximate MFPMQ on general graphs (and even bipartite graphs) within any positive factor. On series-parallel graphs, however, we present a pseudo-polynomial time dynamic programming algorithm for the problem. We then study the case that the minimum quantity is the same for each arc in the network and show that, under this restriction, the problem is still weakly NP-complete on general graphs, but can be solved in strongly polynomial time on series-parallel graphs. On general graphs, we present a \((2 - 1/\lambda) \)-approximation algorithm for this case, where \(\lambda\) denotes the common minimum quantity of all arcs.
- Truthful Mechanisms for Selfish Routing and Two-Parameter Agents (2009)
- We prove a general monotonicity result about Nash flows in directed networks and use it for the design of truthful mechanisms in the setting where each edge of the network is controlled by a different selfish agent, who incurs costs when her edge is used. The costs for each edge are assumed to be linear in the load on the edge. To compensate for these costs, the agents impose tolls for the usage of edges. When nonatomic selfish network users choose their paths through the network independently and each user tries to minimize a weighted sum of her latency and the toll she has to pay to the edges, a Nash flow is obtained. Our monotonicity result implies that the load on an edge in this setting can not increase when the toll on the edge is increased, so the assignment of load to the edges by a Nash flow yields a monotone algorithm. By a well-known result, the monotonicity of the algorithm then allows us to design truthful mechanisms based on the load assignment by Nash flows. Moreover, we consider a mechanism design setting with two-parameter agents, which is a generalization of the case of one-parameter agents considered in a seminal paper of Archer and Tardos. While the private data of an agent in the one-parameter case consists of a single nonnegative real number specifying the agent's cost per unit of load assigned to her, the private data of a two-parameter agent consists of a pair of nonnegative real numbers, where the first one specifies the cost of the agent per unit load as in the one-parameter case, and the second one specifies a fixed cost, which the agent incurs independently of the load assignment. We give a complete characterization of the set of output functions that can be turned into truthful mechanisms for two-parameter agents. Namely, we prove that an output function for the two-parameter setting can be turned into a truthful mechanism if and only if the load assigned to every agent is nonincreasing in the agent's bid for her per unit cost and, for almost all fixed bids for the agent's per unit cost, the load assigned to her is independent of the agent's bid for her fixed cost. When the load assigned to an agent is continuous in the agent's bid for her per unit cost, it must be completely independent of the agent's bid for her fixed cost. These results motivate our choice of linear cost functions without fixed costs for the edges in the selfish routing setting, but the results also seem to be interesting in the context of algorithmic mechanism design themselves.
- The Generalized Assignment Problem with Minimum Quantities (2012)
- We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (a minimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the most general version of the problem, we show that it does not admit a polynomial time approximation algorithm (unless P=NP), even for the case of a single bin. This motivates to study dual approximation algorithms that compute solutions violating the bin capacities and minimum quantities by a constant factor. When the number of bins is fixed and the minimum quantity of each bin is at least a factor \(\delta>1\) larger than the largest size of an item in the bin, we show how to obtain a polynomial time dual approximation algorithm that computes a solution violating the minimum quantities and bin capacities by at most a factor \(1-\frac{1}{\delta}\) and \(1+\frac{1}{\delta}\), respectively, and whose profit is at least as large as the profit of the best solution that satisfies the minimum quantities and bin capacities strictly. In particular, for \(\delta=2\), we obtain a polynomial time (1,2)-approximation algorithm.
- Online Delay Management (2010)
- We present extensions to the Online Delay Management Problem on a Single Train Line. While a train travels along the line, it learns at each station how many of the passengers wanting to board the train have a delay of delta. If the train does not wait for them, they get delayed even more since they have to wait for the next train. Otherwise, the train waits and those passengers who were on time are delayed by delta. The problem consists in deciding when to wait in order to minimize the total delay of all passengers on the train line. We provide an improved lower bound on the competitive ratio of any deterministic online algorithm solving the problem using game tree evaluation. For the extension of the original model to two possible passenger delays delta_1 and delta_2, we present a 3-competitive deterministic online algorithm. Moreover, we study an objective function modeling the refund system of the German national railway company, which pays passengers with a delay of at least Delta a part of their ticket price back. In this setting, the aim is to maximize the profit. We show that there cannot be a deterministic competitive online algorithm for this problem and present a 2-competitive randomized algorithm.


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Apple, the world's most valuable company, will be calculated in the Dow Jones Industrial Average index starting later this month, the Wall Street Journal reported on Friday. The move has been a long time coming, and was likely made possible by last year's 7-for-1 stock split which significantly reduced the per-share price of Apple, making it easier to fold into the price-weighted blue chip index. Apple will replace AT&T in the prestigious group of thirty major American companies. Apple is currently traded on the Nasdaq and shares were trading at $125.41 at the time of publication.
When I wrote about the decentralization movement a year back, one of the big pro-privacy hopes was Mailpile, which is ambitiously trying to build a user-friendly yet rock-solid encrypted webmail system with a hybrid desktop/in-browser approach. On Friday, Mailpile's Bjarni Rúnar Einarsson announced the rejection of the Mailpile beta, saying feedback had led the team to go back to the drawing board. One key issue was unsurprisingly related to making "all that crypto stuff completely seamless." Iceland-based Einarsson is taking a break to get married (mazel tov) and, with the back-end providing most of the problems, front-end designer Brennan Novak has "moved on to other things for now." Here's hoping Mailpile gets back on track when development resumes next month.
Facebook Pages may lose some of their likes soon. Thursday the company warned businesses it's removing likes from deactivated or memorialized accounts. The like dip would be more of an ego hit for companies than an actual hit on their Page's reach, since Facebook is only removing people who weren't around anyways. On the upside, Facebook points out that this "gives businesses up-to-date insights on the people who actively follow their Page."
Apple iPhone and iPad owners opting to use the official Gmail application have a compelling upgrade waiting for them notes The Verge. The newest version of Gmail for iOS takes advantage of Apple's willingness to let third-party apps share information and have actionable notifications. Gmail for iOS now lets you reply to incoming mail through notifications, for example, meaning you never have to leave the app you're in when replying. Messages showing on the lock screen can now be archived or deleted as well, making it quicker to manage email. Gmail can be added to the "share" menu in iOS 8 as well, so you can send images or documents outside of the Gmail app.


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French Wing Headboard
- No Longer Available -
Our winged headboard borrows its silhouette from a vintage French wing chair, originally designed to keep occupants cozy, warm and sheltered from drafts.
- Built with a sturdy kiln-dried hardwood frame and solid oak legs finished in weathered oak
- Water-resistant linen upholstery in flax
- Hand-hammered exposed brads reflect its artisan tailoring
- Designed for use with our Metal Bed Frame (sold separately)
- Designed for use with a mattress and box spring
- Assembly required
French Wing Headboard
- Twin Headboard: 48"W x 11"D x 49"H
- Twin Headboard Weight: 42 lbs.
- Full Headboard: 64"W x 11"D x 49"H
- Full Headboard Weight: 48 lbs.
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Oklahoma Sound Corporation Smart Cart Sound Full Podium
Oklahoma Sound Corporation Smart Cart Sound Full Podium
Weights & Dimensions
|Product Type: Full podium
|Style: Modern
|Solid Wood Construction: No
|Primary Material: Wood
|Number of Items Included: 1
|Scratch Resistant: Yes
|Powered: Yes
|Batteries Included: No
|Storage Included: Yes
|Shelves Included: Yes
|Drawers Included: No
|Doors Included: Yes
|Wheels Included: Yes
|Clock Included: No
|Reading Light Included: No
|Wireless: No
|Sound System Included: Yes
|Speakers Included: Yes
|Microphone Included: Yes
|Voltage: 117 Volts (V)
|Commercial Use: Yes
|Recycled Content: Yes
|Eco-Friendly: Yes
|Country of Manufacture: China
|Assembly Required: Yes
|Installation Required: No
|Additional Parts Required: No
|Product Warranty: 5 Years
|UL Listed: Yes
About the ManufacturerOklahoma Sound manufactures state of the art audio voice amplification technology integrated into the highest quality cabinetry in your choice of laminates and veneers.
Oklahoma Sound now offers a wired and wireless capability integrated into a multimedia amplifier system with options providing a solution to your every presentation requirement. Oklahoma Sound has many new designs, styles and unique ideas with a broad range of color selections.
Full multimedia capability, including power output selections from 20 - 50 watts, phantom power, switchable Dynamic/Condenser mic inputs, tape and CD, play and record capability - to name just a few are built in. Sound lecterns include AC plug and optional 12V battery capability where the lectern recharges the battery! And now out products carry the U.L. mark of safety.
OSC now offers wired and wireless capability, all built into each Sound Lectern, with a full choice of optional wireless microphones; Hand held, Tie clip or the NEW Headset style. Cabinetry is handcrafted and steel parts fabricated by American Craftsmen in our own factory.
Oklahoma Sound Corporation Smart Cart Sound Full Podium
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OUR SKU # OS1059Smart Cart Sound Full Podium is also sometimes listed under the following manufacturer numbers: SCLS-MO, SCLS-MY, SCLS-OK, SCLS-WT


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All new mini candy bar wrapper baby shower favors sticker labels. Our personalized mini candy bar wrapper sticker labels will be a hit at your next baby shower event. Each sheet of labels will complete 20 Hershey's® miniature candy bars. What a super fun way to add that extra special personalized touch to your party.1 sheet of 20 sticker labels.
Each sticker is 1 3/8" x 2 5/8"
We provide the personalized stickers.
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These stickers are designed to fit Hershey's® brand miniature candy bars.
Some assembly is required. Photo instructions are included.
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Supreme Court won't hear German home-school case
Associated Press | posted Mar 3rd - 8:04am
The Supreme Court has declined to hear an appeal from a German family seeking asylum in the United States because their home country does not allow home-schooling.
High court to look at inmate's right to grow beard
Associated Press | posted Mar 3rd - 7:59am
The Supreme Court has agreed to decide whether an Arkansas prison inmate must be allowed to grow a short beard in accordance with his religious beliefs.
Justices decline to re-enter immigration debate
Associated Press | posted Mar 3rd - 7:50am
The Supreme Court has ended two local governments' efforts to prevent some immigrants from renting apartments.
Teeth-whitening challenge gets high court review
Associated Press | posted Mar 3rd - 7:38am
The Supreme Court will examine the North Carolina dental regulatory board's claim that only dentists should be allowed to whiten teeth.
High court looks at death row inmate's IQ scores
Mark Sherman, Associated Press | posted Mar 3rd - 1:32am
The Supreme Court is hearing an appeal from a Florida death row inmate who claims he is protected from execution because he is mentally disabled.
YouTube video purports to show high court action
Associated Press | posted Feb 27th - 3:51pm
A protest group has posted what appears to be the first video of the Supreme Court taken inside the courtroom with the court in session.
Supreme Court seems divided in climate case
Mark Sherman, Associated Press | posted Feb 24th - 1:43pm
The Supreme Court appeared divided on Monday over the sole Obama administration program already in place to limit power plant and factory emissions of gases blamed for global warming.
High court won't block Va. capital murder retrial
Associated Press | posted Feb 24th - 7:47am
The Supreme Court will not block Virginia from retrying an accused drug dealer, whose earlier capital murder conviction was set aside because of misconduct by prosecutors.
High court rejects NRA appeals
Jesse J. Holland, Associated Press | posted Feb 24th - 7:44am
The Supreme Court has turned away appeals from the National Rifle Association which complained about resistance by governments and judges to the high court's recent seminal rulings declaring that Americans have a constitutional right to own a gun.
A changing judicial landscape for gay rights
Mark Sherman, Associated Press | posted Feb 14th - 4:10pm
The overturning of Virginia's gay marriage ban places the legal fight over same-sex unions increasingly in the hands of federal appeals courts shaped by President Barack Obama's two election victories.
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997 St. Sebastian WayAugusta, GA 30912706-721-6597
1446 Harper StreetAugusta, GA 30912706-721-5437 (KIDS)
1003 Chafee Ave.Augusta, GA 30912 706-721-2426
1447 Harper StreetAugusta, GA 30912-5536706-721-CARE (2273)
1120 15th StreetAugusta, GA 30912706-721-2273 (CARE)
1411 Laney Walker Blvd.Augusta, GA 30912706-721-6744
1430 John Wesley Gilbert DriveAugusta, GA 30912706-721-2696
821 St. Sebastian WayAugusta, GA 30912706-721-2971
1220 West Wheeler PkwyAugusta, GA 30909
6135 Roosevelt Highway Warm Springs, GA 31830
GRU includes nine colleges and schools and is Georgia's only public academic health center.
Dr. Azziz also serves as Chairman of the Boards of the GR Health System and the GR Medical Center, responsible for the coordination and alignment of the entire clinical enterprise; and is Professor of Obstetrics, Gynecology, and Medicine at Georgia Regents Medical Center.
Georgia Regents Health System includes:
Medical College of Georgia, (the 13th oldest and 10th largest medical school in the nation)
College of Dental Medicine, (the only one in Georgia and one of the largest in the country)
College of Nursing, (awarding the highest number of graduate degrees in nursing in the state)
College of Allied Health Sciences
The Graduate School
Since assuming his leadership role, Dr. Azziz has focused on advancing the university's education, research, and clinical programs; re-energizing philanthropy; and expanding GRU's state, national and global reach. He has strengthened the university's commitment to civic and scholarly engagement, embraced sustainability, and fostered collaborative partnerships both within and outside the university community.
In previous positions, Dr. Azziz served as a transformational leader of multiple institutions, including the Cedars-Sinai Medical Center; the University of California, Los Angeles (UCLA); and University of Alabama at Birmingham. In addition to maintaining a nationally recognized clinical practice, Dr. Azziz led institution-wide initiatives to measure and improve faculty productivity, new faculty development and retention, and academic excellence. He is an internationally recognized clinical translational researcher, developing an important research program into androgen-excess disorders in women, which has been funded by the NIH since 1988.
A native of Uruguay and an accomplished artist, Dr. Azziz brings a global and creative spirit to his leadership of Georgia Regents University. He and his wife, Cindy, are enjoying life in the South with their children, Ashlee, Jonathon, and Mallory, and their dog, Arlo..
Buckley, Chairman of the Physicians Practice Group Board of Trustees, served as Chairman of the GHSU Department of Psychiatry and Health Behavior before being named Dean of the Medical College of Georgia in 2011. He also serves as a Professor of Radiology, Psychiatry/Health Behavior, Pharmacology/Toxicology and Graduate Studies. He has extensively researched and treated schizophrenia and schizoaffective disorders. He earned his medical degree from the University College of Dublin.
In February 2013, Doug Duncan was elected by Governor Nathan Deal to serve as Vice Chairman of the State Workforce Investment Board. He received his bachelor of business administration degree from GRU Summerville Campus, 1985. Mr. Duncan was former President and CEO of Golf Augusta Pro Shops and currently serves on the GRHealth System Planning and Development Committee. He previously served on the ASU Foundation Board of Trustees.
Fran Forehand serves as Vice President of Georgia Power's East Region, where she leads the company's operations for 155,000 customers in a 13-county area that includes Augusta, Thomson and Waynesboro. In this role, Forehand is responsible for delivery, engineering, customer service, sales, economic and community development, and external affairs activities.
Forehand was named to her current position in April 2014. Before then, she served as Georgia Power's Metro North Region Manager, where she led the company's service to 327,000 customers in Gwinnett, Forsyth, north Fulton and north DeKalb counties. She began her Southern Company career at Alabama Power in 1991 as an engineering co-op student and came to Georgia Power in 1996, where she has served in various transmission leadership roles and as land acquisition manager, with responsibility for securing property rights for the placement of distribution, transmission and generation facilities statewide.
Forehand earned a bachelor's degree in electrical engineering from the University of Alabama and an MBA in finance from Augusta State University.
Kurt is an Audit Partner and the chair of the firm's Public Company (SEC) Practice Group. Kurt has over 29 years of experience in the accounting industry. Prior to joining HA&W, Kurt was with BDO Seidman where he served as the managing partner of the firm's assurance and accounting practice. He specializes in providing accounting and auditing services to publicly-traded and privately owned businesses in a variety of industries, including manufacturing, technology (hardware and software), medical equipment, healthcare and life sciences, pharmaceutical, telecommunications, distribution, real estate and aviation/airline clients.
He was Mayor of the city of Thomson from 1979 to 2007. An active member of the American Cancer Society, he has been the Co-chair of the McDuffie County Relay for Life since 1998. He serves as a member of the Board of Trustees of Wesleyan College, the Board of Directors of the CSRA Community Foundation, the McDuffie Museum Board and the Camellia Partners for Economic and Historic Preservation.
Dr. Mercer received her medical degree from the Medical College of Georgia and completed her residency in OB/GYN at Emory University School of Medicine. She is a member of the Planning and Development Committee for the Medical College of Georgia in Athens, and serves on the Board of Directors for the Athens Specialty Group.
Mr. Nixon is a Past President of the Independent Insurance Agents of Augusta and of Georgia. He has held leadership positions with the Georgia-Carolina Council of the Boy Scouts of America, Augusta Museum of History, Augusta Rowing Club, Augusta Opera and Porter Fleming Foundation. He is a Trustee of the Academy of Richmond County and is Co-founder of the Westobou Festival, LLC.
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Georgia Regents Medical Center 1120 15th Street Augusta, GA 30912-5563
Affiliated with Georgia Regents University


text:
Michigan: A Right-to-Work State?
Labor never ruled Michigan as such. It may have been home to the best and biggest American union, the United Auto Workers, but even at the height of their power, the UAW could seldom elect its candidates to Detroit city government. Still, the UAW dominated the state's Democratic Party and much of state politics for decades—at least, until the auto industry radically downsized.
Just how downsized union power has become is apparent from the decision of the state's Republican governor, Rick Snyder, to support a right-to-work bill that began speeding its way through the state's lame-duck GOP-controlled legislature on Thursday. Should the bill become law—and given Republican control of state government, it's hard to envision how it won't—Michigan would join historically more conservative Indiana as the second state from the industrial Midwest to move to right-to-work status. Until last year, when Indiana enacted its statute, right-to-work states were confined to the South, the Plains states and the Mountain West—states devoid of a major union presence. That such laws are now coming to the industrial Midwest is just more evidence of the continual weakening of industrial unions—the unions that have taken the most direct hit from offshoring and mechanization.
But why enact such laws when most unions are no longer big enough to take any bite out of company profits? In fact, the pressure for such laws isn't coming from companies like Ford or GM, which can how hire new union workers for half of what they pay their more veteran workers. It's purely political. Weakened though they be in the economic arena, unions still punch well above their weight at election time. That's one reason why President Obama carried every state in the industrial Midwest save (almost) perpetually Republican Indiana.
And if anyone doubts that politics lies behind the Michigan Republicans' decision to enact a right-to-work bill, consider one of the bill's particulars: the only unions it exempts from the bill's coverage, the Wall Street Journal is reporting, are police and firefighter unions. Snyder said that the GOP had carved out that exception because their jobs needed protection from labor strife.
Think about that for a moment. The effect of the Republicans' exemption would be to ensure police and firefighters have the strongest unions in the state, the ones most capable of taking job actions when they sought to better their pay and working conditions. Elsewhere across the U.S. today, states and cities are trying to scale back pensions and other benefits of their employees, and police and firefighters are often targeted because their pay and benefits exceed those of other public workers. Moreover, historically, governors and mayors have been wary of the power of such unions—Republican governors and mayors in particular. Massachusetts Gov. Calvin Coolidge first came to the nation's attention by breaking a Boston police strike in 1919—"There is no right to strike against the public safety," he proclaimed. It was his strikebreaking that won him a place on the 1920 Republican ticket.
Now, however, Snyder, like Wisconsin Gov. Scott Walker, has created a police-and-firefighter carve out. The reason is purely political—in Michigan, as in Wisconsin, the police and firefighter unions often support Republicans for state and local office, and Republicans want to make sure that they'll continue to do so with undiminished clout. The carve-out, said Michigan House Democratic leader Tim Greimel, "makes it very clear that this is not about sound economic policy. It's motivated by a desire to punish supporters of the Democratic Party."
And so it is.
Fri, 2012-12-07 12:11
It's ok for Obama to cater to the "hispanic" community by buying their votes through a temporary amnesty, vowing destruction to business and the rich, Obamacare (forced through a Dem controlled administration) and the like, but, the republicans do something similar and the left cries foul.
Can you say hypocrite?
Fri, 2012-12-07 19:56
The Democrats never tried to DENY the ability of non-Hispanic voters to raise money for politics, nor did they target the higher wages that non-Hispanics statistically receive compared to Hispanics (if there is such an advantage). The Republicans are WRITING INTO LAW conditions that will LOWER WAGES for workers that currently have union protection, REDUCE their health care support, REMOVE protection from unsafe working conditions, and STARVE THE UNIONS of funds to administer themselves (and more importantly, to donate to Democrats) by denying VOLUNTARY payroll deductions. By the way, for those who say that "union bosses" (as opposed to business LEADERS?) control "political slush funds", the fact is that IN ADDITION to union dues, unions are required to solicit VOLUNTARY EXTRA DONATIONS for money that can be used politically. Check with any local office of any union to verify this.
As a Southerner, I have always worked in RTWFL states (except for one 3-month assignment in California in the 1970's), and if I had not been in engineering with a college degree, would have been working low wage jobs my entire career. Except for one summer job in college, in a defense plant, and my last three full-time working years working for a large company with a nationwide union tradition, I never belonged to a union, and for more than half my career, I did not work for a company that HAD unions for other departments than mine. I have seen how workers in RTWFL states live, and I would not want to spread those conditions to others.
Remember, you cannot make a nation MORE prosperous by making a larger percentage of its people LESS prosperous.
Capt. Gene
Mon, 2012-12-10 12:21
Fri, 2012-12-07 14:28
Ultimately Michigan felt it had to do something to make the state more competitive. With Indiana's recent decision to become a RTW state, there was pressure for Michigan to be more business friendly. We had already seen companies leave Michigan for Indiana (http://bit.ly/THATfV).
Mon, 2012-12-10 15:10
Your article presents no evidence in support of your claim.
Did you make up your claim that "We had already seen companies leave Michigan for Indiana" or do you actually have a source?
Incidentally, we have seen jobs leave Michigan for RTW states for decades. Last I checked, Michigan didn't want to become Mississippi or Alabama. What do you believe has changed?
Sat, 2012-12-08 19:15
Sun, 2012-12-09 17:06
No right-to-work state has excellent schools. Mostly they attract polluting businesses and low wage workers. It is a race to the bottom. Michigan has proven the willingness to go to the bottom with Gov. Snyder who prefers the tyrant model to democracy. Michigan voted him in and they either respond or live with the results.
Sun, 2012-12-09 17:29
Are you talking about the excellent schools in New York and Illinois and California, all strong Democratic states that never allow teachers to be fired even if they announce to their class that since they can't be fired they intend to ignore the ungrateful little student in their classes and just read novels during teaching time. (Actual Example by the way: See the film "Waiting for Superman" about the problems in today's educational system. This is NOT a right-wing movie -- it is intensely caring about the children, often blacks, who get ghastly educations).
Mon, 2012-12-10 10:25
I am talking about Wisconsin that has a stellar educational system being destroyed by the right-wing Koch Brother fan Scott Walker. I live in Sacramento where Kevin Johnson is married to the Charter School maven who made "Waiting for Superman". If you have no commitment to public schools, think cherry-picking students is the way to go and hiring teachers with a commitment to the school profit, that school is for you. CA education was trashed by Prop. 13, another right-wing boondoggle for the sponsor, Howard Jarvis.
Capt. Gene
Mon, 2012-12-10 12:28
Mon, 2012-12-10 15:26
As someone in SoCal for 20+ years, you haven't a clue.
This state has seen fit to raid money. Prop 13 for taxes only meant that taxes went up ~2% per year. AGAIN, even including great appreciation in housing value, once an older home is sold, it is taxed at the new purchase price. So, if someone buys a home back in the 1980's for 50K and is taxed on that home while they raise their kids (i.e., paying for schools and teachers, etc.,) and then in the boom of 2000's sold it for 350K, the new homeowners are paying a tax bill at the new value of 350K. WTF is wrong with that? Under the old scenario, as that house appreciated, though the original owners did not recieve any money from that appreciation, the tax guy said "doesn't matter. We're going to tax you as the appreciation goes up." WTF??
So the schools weren't trashed by Prop 13.
Second, when the state initiated the lottery, all proceeds were to go to education. You can thank the D's who have controlled the state for years that there's no money.
Third, with 10% of the nations population, we have 1/3 of the country's welfare recipients. Why? Because let's all sing kumbaya and let everyone in no matter what. We have over 1/3 of Latino and black kids dropping out of school. Great teachers? Nope. Just a social policy of "passing" kids so their self-esteem won't get hurt. Nevermind that they haven't learned anything.
Now we learn after that great tax increase from November that November state receipts are 10% below what they were estimated to be. But Moonbat Brown had some folks from Stanford, in sociology and some other make believe background, do a study in which they said millionaires and billionaires wouldn't leave because "they don't want to pull their kids from their friends in school and they like to network here." Facebook anyone?
And speaking of Facebook, the D's made their budget last year with the premise of people cashing in their Facebook stock to the tune of $1B to help fill in the deficit. Yeah, great investors these D state legislaturers.
So the mayor of Sacratmento is married to the producer of a conservative movie and that's a response? Gor every Koch brother, there's a Soros. As for "Cherry picking" who the heck do you think would leave inner city schools on a voucher program? WASP kids? NEWSFLASH !! The ones who could leave have already left. Why not give the inner-city kid the same chance with state money rather than plowing it back into a failed system? And it's the D's who say the R's are leaving in fantasy land.
If my kid's teacher can't hold a job because of accountability, then he/she should be fired. It's not that hard. i remember sitting in classrooms of 5 across and 5 or 6 deep. The problem is teacher's are more focuse on "what" they think students should know instead of teaching. My Two Dads. Che Guevarra. the Evil Koch Brothers. Ed Asner's Cal Teacher Ass asinine rich cartoon video. That's the reason Johnny can't read. It's not because the Koch Brothers, Adelson or anyone else contributes to politicians. Ever wonder why teachers and politicians send their kids to private schools? BECAUSE THEY KNOW !!!
Give me your address and I'll send you a quarter to buy a clue.
Mister Obvious
Sun, 2012-12-09 17:38
More Liberal slipshod journalism.
Firefighters and Police are exempt from Michigan's RTW law because they are prohibited from striking and must submit to binding arbitration for all disputes.
It isn't a matter of politics or endorsement. It is a matter of practicality with highly skilled professions having high turnover and low longevity.
Mon, 2012-12-10 15:16
You are aware that Michigan prohibits public employees, including school teachers, from striking, aren't you?
So it's your belief that all civil service unions should be exempt from the law?
Sun, 2012-12-09 18:16
But why enact such laws when most unions are no longer big enough to take any bite out of company profits?
Because they take a bit out of employees' paychecks. Workers are FORCED to join a union against their will, then FORCED to pay dues to the Democratic Party. If you want to grouse about the politics of this issue, there it is.
The effect of the Republicans' exemption would be to ensure police and firefighters have the strongest unions in the state, the ones most capable of taking job actions when they sought to better their pay and working conditions.
That's nonsense. Public employees can't take "job actions" in Michigan. State law prohibits them from striking. You know very well that if those unions were included in the right-to-work law, you would still oppose it as "political."
Let police or firefighter just try striking, and perhaps they'll get a dose of PATCO medicine. Sooner or later, one way or another, they'll be broken too, just as the rest of the public-sector unions are being busted now. And it's high time!
Mon, 2012-12-10 15:21
Prior to Reagan, union support for the parties was roughly equal. You may find it confounding, but most others can figure out why decades of concerted Republican attacks on organized labor have resulted in a shift of union money away from the party that is actively working against the interests of organize labor. Meanwhile, as you should know, despite the history to which Myerson points, Republicans are exempting police and firefighters from their present union-bashing efforts and, lo and behold... those unions largely support Republican candidates.
If it's a horror that "Workers are FORCED to join a union against their will, then FORCED to pay dues to the [Republican] Party", why do you suppose Republican politicians want to continue to inflict that horror on on policemen and firemen?
Mon, 2012-12-10 15:37
Majority of Firefighters and Police unions do not support R politicians. It is typically state by state. In Cali, it's the D's. Probably in Tennessee, it's the R's.
However, there are pockets in every state. Take Cali. 1/3 of it is conservative. Does that mean that the 1/3 of Firefighters who are R's should have to pay dues to support D politicians? At the end of the day, very little dues money is used for strike fund, none of it is used for pensions, and most goes to political campaigns and unions stewards (management) pockets.
Ever wonder why D's and allies were against letting younger workers put their some of their SS contributions into the market? Yet, where does CalPers, UAW and the like put their money for pensions? It sure isn't under the mattress.
Sun, 2012-12-09 18:17
Sun, 2012-12-09 20:34
"No right-to-work state has excellent schools. Mostly they attract polluting businesses and low wage workers. It is a race to the bottom."
Wow and the great state of Michigan and the wonderful city of Detroit are at the top of the heap. Get real. Public unions are responsible for the destruction of this once great country.
Sun, 2012-12-09 22:30
one thing is for certain. if you want hyper partisan rhetoric, of a not very intelligent type, look no further than harold meyerson. here or in the feckless Wapo, meyerson is the kind of myopic "progressive" that makes a thinking man cringe. we have to "protect" workers by forcing them to join and pay for organizations that they don't want to join. we have to force them to accept the "protection" of unions, meyerson, you hack? that sounds like mob brooklyn more than anything fair/noble. you're a joke, man....
Mon, 2012-12-10 01:30
Mon, 2012-12-10 15:25
A comment that would be more interesting if it were true.
Ann Arbor has a vibrant economy, due in no small part to its highly educated workforce, good schools, good amenities.... And it attracts good jobs.
Flint has a struggling economy, due in no small part to its poorly educated workforce, bad schools, poor amenities.... And it has become a staging ground for non-unionized call centers, paying low wages.
What type of jobs might theoretically be drawn to Michigan by union-busting? The type exemplified by Flint and its call centers.
Mon, 2012-12-10 01:37
Until now, Unions could count on the state or employer to extract dues from their members, now unions must collect that money themselves. If that shift criples unions ability to collect, maybe they should demonstrate a little more accountability to their members instead of funneling billions to the Democratic party.
Mon, 2012-12-10 03:20
The new rtw law does not hinder collective bargaining. The Unions are also free to ask workers to join. The only difference is workers don't HAVE TO JOIN. If there is an advantage they will. People don't like to HAVE TO support the Democratic Party. And that is where a lot of the money goes to. ( And, of course, to pay hefty salaries to the Union bosses.)
Gov Snyder was not going to push the issue, but they tried put a proposal to a vote to CHANGE Michigan's Constitution to ENSURE union participation.It would have hampered our Congress' ability to pass laws, and negated some already passed. That is why Snyder will sign the bill.
Mon, 2012-12-10 15:28
From day one the entire purpose of "right to work" laws has been to hinder collective bargaining - and it has worked. Nobody with a whit of knowledge on the subject, including the Republicans who are working so hard to undermine labor organization, would suggest otherwise.
You are aware that states have legislatures, and that Congress is a federal institution, aren't you? Alas, I suspect not...
You need to be logged in to comment.
(If there's one thing we know about comment trolls, it's that they're lazy)


text:
Jack Kirby was the man. Do you understand this? Stan Lee gets all the credit these days for being the face of Marvel Comics and it has more to do with his flamboyant personality than his ability to craft interesting character and stories. Without Jack Kirby, Stan Lee's ideas were common comic book dreck. I'm often dismissive of comic book artists because I'm a writer and I can get over bad art in a comic if the writing is good. My opinion is that most comic artists are interchangable whores and that anyone could have drawn Sandman or Watchmen and the overall effect of the end product would have been the same. This is, of course, extremely prejudicial and short sighted. The art of Matt Wagner, Mike Mignola and James O'Barr are as instrumental to their comics' success as their stories. It's part of their signature, but when you came up in the age of Rob Liefeld's inexplicable success or the rise of Image Comics, can you blame me? For years, the work coming out of Image, which was a signature of 90's comics, was dumb, poorly considered bullshit.
But I digress. Rant off. Jack Kirby was awesome, ya herd?
Kirby split from the comic book world in the 70's after his work-for-hire status with Marvel and DC left him high and dry while the parent companies forged marketing empires based on his hard work and ideas. He would create these awesome characters and teams who would evolve into Saturday morning dynamos, with comics, TV shows and cartoons, toys, bedsheets, etc. – Whatever you could put The Thing's face on, they did and Kirby didn't see a dime of it. He wound up in the offices of Ruby Spears, an animation house in the 70's that split from Hanna-Barbera. In the 80's, Ruby Spears was behind some of the most asinine cartoons you can think of like the one with the anthropomorphic Rubik's Cube and Turbo Teen, about a kid who turns into a car when he's hot. They also did that stupid Rambo cartoon. You know, the cartoon based on the movie about the guy who tears people's throats out with his bare hands. Yeah. That one. Rambo and Santa Claus are tight, according to the world of Ruby Spears. I'll cut them some slack, though. By 1985, the Saturday morning well had pretty much run dry and everyone in the creative department was probably coked up into orbit anyway. Here's the thing, Kirby's most comfortble, prolific period was spent in the offices of Ruby Spears. There he churned out, according to The New York Times, 600 production boards of stuff that was mostly left on the drawing boards and then summarily packed away in boxes. No one knew what to do with the stuff but Ruby Spears liked what he did and treated him fairly, something that Marvel and DC couldn't be bothered with. After all, Kirby leaving didn't mean much to them, they still had Jim Steranko and Steve Ditko to buttfuck all the way to the bank. King Kirby has been in the headlines a lot, lately, too. After a precedent set by Jerry Siegel and Joe Shuster winning back the ownership of Superman after decades and following Disney's acquisition of Marvel, the family Kirby ambushed the fuck out of the comic industry and demanded their birthright, contesting the ownership of Kirby characters that both DC and Marvel have licenses for. Now there's this. Here's hoping the legacy of the man who made modern comics what they are today, as well as being the model illustrator for comic artists everywhere, gets his due and comes back to the fore.
Ruby Spears has finally pulled the lid off these unused properties and in this age of rampant comic book marketing has plans to develop as many of these unused designs and concepts into whatever they can make them into. Aided by the mighty Sid and Marty Kroft of, well, just about every wacked out Saturday morning show to feature anyone in a crazy-ass foam rubber costume (and by that I mean H.R. Pufnstuff, Sigmund The Seamonster, etc. – Check Tank Riot's awesome Krofts episode) they hope to find the next big superhero property somewhere in there. With the many hundreds of concept to choose from, there must be something they can use. Check out the gallery below for an idea of some of the things that Ruby Spears has unearthed. I would totally watch Warriors of Illusion.
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