a natural chemical which controls a specific body function is called a ( n )
hormone
171947
Hormone A hormone (from the Greek participle “”, "to set in motion, urge on") is any member of a class of signaling molecules produced by glands in multicellular organisms that are transported by the circulatory system to target distant organs to regulate physiology and behavior. Hormones have diverse chemical structures, mainly of 3 classes: eicosanoids, steroids, and amino acid/protein derivatives (amines, peptides, and proteins). The glands that secrete hormones comprise the endocrine signaling system. The term hormone is sometimes extended to include chemicals produced by cells that affect the same cell (autocrine or intracrine signalling) or nearby cells (paracrine signalling).
Hormone
10765388
Pretzel syndrome Pretzel syndrome is a rare disorder characterized by skeletal deformity, malformation of the brain (with accompanying seizures), electrolyte imbalances, and variable malformations of the heart and other organs. It is a single gene disorder but it is complex in its mechanics. The defective gene is called LYK5. It has a complicated function that is only partly understood. The LYK5 gene product is part of a chemical “relay” or “messaging” system that controls the growth and function of many cells in the body. In Pretzel syndrome, part of the LYK5 gene is missing, which leads to a complete loss
Pretzel syndrome
10765390
many affected children. Pretzel syndrome Pretzel syndrome is a rare disorder characterized by skeletal deformity, malformation of the brain (with accompanying seizures), electrolyte imbalances, and variable malformations of the heart and other organs. It is a single gene disorder but it is complex in its mechanics. The defective gene is called LYK5. It has a complicated function that is only partly understood. The LYK5 gene product is part of a chemical “relay” or “messaging” system that controls the growth and function of many cells in the body. In Pretzel syndrome, part of the LYK5 gene is missing, which leads to
Pretzel syndrome
18474349
a highly conserved N-glycosylation site. The attached sugar moieties modulate the binding to specific immunoreceptors, thereby modifying the whole antibody function. Smith et al. demonstrate the application of the aldehyde tag as a chemical conjugation site for glycans. The aldehyde tag sequence was incooperated into the Fc construct and introduced into CHO (Chinese hamster ovary) cells. As controls, gene constructs were used in which the cysteine residue was mutated to an alanine. After expression, the Fc proteins were purified using a protein A/G agarose column. The conversion in CHO cells of cystein to formylglycine was examined using aminooxy AlexaFluor 488
Aldehyde tag
9305183
Thus, for all "n" and for any "n"-length sequence of natural numbers formula_1, there exists an appropriate natural number "a", called the Gödel number of the sequence such that formula_7. Our specific solution will depend on a pairing function—there are several ways to implement the pairing function, so one method must be selected. Now, we can abstract from the details of the implementation of the pairing function. We need only to know its “interface”: let formula_8, "K", and "L" denote the pairing function and its two projection functions, respectively, satisying specification We shall not discuss and formalize the axiom for
Gödel numbering for sequences
3605302
Constructible function In complexity theory, a time-constructible function is a function "f" from natural numbers to natural numbers with the property that "f"("n") can be constructed from "n" by a Turing machine in the time of order "f"("n"). The purpose of such a definition is to exclude functions that do not provide an upper bound on the runtime of some Turing machine. There are two different definitions of a time-constructible function. In the first definition, a function "f" is called time-constructible if there exists a positive integer "n" and Turing machine "M" which, given a string 1 consisting of "n"
Constructible function
9077871
"S" formula_1 "S" → formula_2 which assigns a natural number called "arity" to every function or relation symbol. A function or relation symbol is called "n"-ary if its arity is "n". A nullary ("0"-ary) function symbol is called a "constant symbol". A signature with no function symbols is called a relational signature, and a signature with no relation symbols is called an algebraic signature. A finite signature is a signature such that "S" and "S" are finite. More generally, the cardinality of a signature σ = ("S", "S", ar) is defined as |σ| = |"S"| + |"S"|. The language of
Signature (logic)
334836
the "n"th prime are all primitive recursive. So are many approximations to real-valued functions. In fact, it is difficult to devise a total recursive function that is "not" primitive recursive, although some are known (see the section on Limitations below). The set of primitive recursive functions is known as PR in computational complexity theory. The primitive recursive functions are among the number-theoretic functions, which are functions from the natural numbers (nonnegative integers) {0, 1, 2, ...} to the natural numbers. These functions take "n" arguments for some natural number "n" and are called "n"-ary. The basic primitive recursive functions are
Primitive recursive function
16617181
activities, such as flight, are possible. Insect behavior involves inefficient muscle operation which produces excess heat and establishes the thermal range in which specific muscles best function. The high metabolic cost of insect flight muscles means that great amounts of chemical energy are utilized by these specific muscles. However, only a very small percentage of this energy translates into actual mechanical work or wing movement. Thus, the rest of this chemical energy is transformed into heat that in turn produces body temperatures significantly greater than those of the ambient. These high temperatures at which flight muscles work impose a constraint
Insect thermoregulation
330693
specific cellular signaling or metabolic pathways by affecting sites directly on cell-surface receptors (which modulate and mediate cellular signaling pathways controlling cellular function). A chemical has, from the pharmacological point-of-view, various properties. Pharmacokinetics describes the effect of the body on the chemical (e.g. half-life and volume of distribution), and pharmacodynamics describes the chemical's effect on the body (desired or toxic). When describing the pharmacokinetic properties of the chemical that is the active ingredient or active pharmaceutical ingredient (API), pharmacologists are often interested in "L-ADME": Medication is said to have a narrow or wide "therapeutic index" or "therapeutic window". This describes
Pharmacology
17668052
of the protein. The R domain contains specific allosteric cGMP binding site that controls the enzymes function. This specific binding site consists of subdomain GAF (cGMP-specific cGMP-stimulated PDE, adenylate cyclase, and FhlA) which is located in the N-terminal section of the specific proteins. The allosteric binding site GAF consists of GAFa and GAFb where GAFa has a higher binding affinity. The importance and functional role of the two homologous binding sites are unknown. Conformational change occurs when cGMP binds to the allosteric site that exposes serine and permits phosphorylation. The results for the phosphorylation of serine leads to increased cGMP
Discovery and development of phosphodiesterase 5 inhibitors
1784724
and magnesium. All of the remaining elements in a human body are called "trace elements". The trace elements that have a specific biochemical function in the human body are sulfur, iron, chlorine, cobalt, copper, zinc, manganese, molybdenum, iodine and selenium. Most chemical elements that are ingested by organisms are in the form of simple compounds. Plants absorb dissolved elements in soils, which are subsequently ingested by the herbivores and omnivores that eat them, and the elements move up the food chain. Larger organisms may also consume soil (geophagia) or use mineral resources, such as salt licks, to obtain limited minerals
Mineral (nutrient)
4861149
soil conditioner. Vermicompost is especially easy. The byproduct is also an excellent source of nutrients for an organic garden. Differing approaches to pest control are equally notable. In chemical horticulture, a specific insecticide may be applied to quickly kill off a particular insect pest. Chemical controls can dramatically reduce pest populations in the short term, yet by unavoidably killing (or starving) natural control insects and animals, cause an increase in the pest population in the long term, thereby creating an ever-increasing problem. Repeated use of insecticides and herbicides also encourages rapid natural selection of resistant insects, plants and other organisms,
Organic horticulture
2149587
Successor function In mathematics, the successor function or successor operation is a primitive recursive function "S" such that "S"("n") = "n"+1 for each natural number "n". For example, "S"(1) = 2 and "S"(2) = 3. Successor operations are also known as zeration in the context of a zeroth hyperoperation: H("a", "b") = 1 + "b". In this context, the extension of zeration is addition, which is defined as repeated succession. The successor function is used in the Peano axioms which define the natural numbers. As such, it is not defined by addition, but rather is used to define all natural
Successor function
6514394
N-Methyltryptamine "N"-Methyltryptamine (NMT) is a member of the substituted tryptamine chemical class and a natural product which is biosynthesized in the human body from tryptamine by certain N-methyltransferase enzymes, such as indolethylamine "N"-methyltransferase. It is a common component in human urine. NMT is an alkaloid derived from -tryptophan that has been found in the bark, shoots and leaves of several plant genera, including "Virola", "Acacia", "Mimosa", and "Desmanthus"—often together with the related compounds "N","N"-dimethyltryptamine (DMT) and 5-methoxy-"N","N"-dimethyltryptamine (5-MeO-DMT). Orally administered NMT appears to produce no psychoactive effects, likely as a result of extensive first-pass metabolism. However, it may become active
N-Methyltryptamine
6514395
upon combination with a MAO inhibitor (MAOI). By vaporization NMT shows activity at 50–100 mg, with a duration of 45–70 minutes; duration of visual effects 15–30 seconds. Effects are primarily non-visual. N-Methyltryptamine "N"-Methyltryptamine (NMT) is a member of the substituted tryptamine chemical class and a natural product which is biosynthesized in the human body from tryptamine by certain N-methyltransferase enzymes, such as indolethylamine "N"-methyltransferase. It is a common component in human urine. NMT is an alkaloid derived from -tryptophan that has been found in the bark, shoots and leaves of several plant genera, including "Virola", "Acacia", "Mimosa", and "Desmanthus"—often together
N-Methyltryptamine
15770958
have near 100% natural abundance, while C and N have low natural abundances. For these latter two nuclei, there is the capability of isotopically enriching desired atoms within the molecules, either uniformly or in a site-specific manner. Nucleotides uniformly enriched in C and/or N can be obtained through biochemical methods, by performing polymerase chain reaction using dNTPs or NTPs derived from bacteria grown in an isotopically enriched environment. Site-specific isotope enrichment must be done through chemical synthesis of the labeled nucleoside phosphoramidite monomer and of the full strand; however these are difficult and expensive to synthesize. Because nucleic acids have
Nuclear magnetic resonance spectroscopy of nucleic acids
36149
integers. "θ"("x") and "ψ"("x"), the Chebyshev functions, are defined as sums of the natural logarithms of the primes not exceeding "x". The Chebyshev function "ψ"("x") is the summation function of the von Mangoldt function just below. Λ("n"), the von Mangoldt function, is 0 unless the argument is a prime power, in which case it is the natural log of the prime: "p"("n"), the partition function, is the number of ways of representing "n" as a sum of positive integers, where two representations with the same summands in a different order are not counted as being different: λ("n"), the Carmichael function,
Arithmetic function
721310
is that block-scope variables can be declared not only within the body of the block, but also within the control statement, if any. This is analogous to function parameters, which are declared in the function declaration (before the block of the function body starts), and in scope for the whole function body. This is primarily used in for loops, which have an initialization statement separate from the loop condition, unlike while loops, and is a common idiom. Block scope can be used for shadowing. In this example, inside the block the auxiliary variable could also have been called n, shadowing
Scope (computer science)
2272493
first second and higher order derivatives, such as its internal energy, entropy, and specific heat. Because of the relationship between the free energy and the cumulant generating function, all these quantities are related to cumulants e.g. the energy and specific heat are given by and formula_70 symbolizes the second cumulant of the energy. Other free energy is often also a function of other variables such as the magnetic field or chemical potential formula_33, e.g. where "N" is the number of particles and formula_73 is the grand potential. Again the close relationship between the definition of the free energy and the
Cumulant
586824
of an action on an ecosystem, so that natural balances are not upset. New pesticides are being developed, including biological and botanical derivatives and alternatives that are thought to reduce health and environmental risks. In addition, applicators are being encouraged to consider alternative controls and adopt methods that reduce the use of chemical pesticides. Pesticides can be created that are targeted to a specific pest's lifecycle, which can be environmentally more friendly. For example, potato cyst nematodes emerge from their protective cysts in response to a chemical excreted by potatoes; they feed on the potatoes and damage the crop. A
Pesticide
15263551
function enjoys high efficiency comparable to the NTRU scheme formula_75 evaluation time and storage cost). Subsequently, Lyubashevsky and Micciancio and independently Peikert and Rosen showed how to modify Micciancio’s function to construct an efficient and provably secure collision resistant hash function. For this, they introduced the more general class of "ideal lattices", which correspond to ideals in polynomial rings formula_76. The collision resistance relies on the hardness of the restriction of Poly(n)-SVP to "ideal lattices" (called "Poly(n)"-Ideal-SVP). The average-case collision-finding problem is a natural computational problem called Ideal-SIS, which has been shown to be as hard as the worst-case instances
Ideal lattice cryptography
3917138
called "available PV work", formula_4 is called "entropic loss" or "heat loss" and the final term is called "available chemical energy." Other thermodynamic potentials may be used to replace internal energy so long as proper care is taken in recognizing which natural variables correspond to which potential. For the recommended nomenclature of these potentials, see (Alberty, 2001). Equation (2) is useful for processes where system volume, entropy, and number of moles of various components change because internal energy is also a function of these variables and no others. An alternative definition of internal energy does not separate available chemical potential
Exergy
341851
exist. Given a set "X", an element "a" of "X" and a function formula_7, the theorem states that there is a unique function formula_8 (where formula_4 denotes the set of natural numbers including zero) such that for any natural number "n". Take two functions formula_8 and formula_13 such that: where "a" is an element of "X". It can be proved by mathematical induction that formula_18 for all natural numbers "n": By induction, formula_18 for all formula_25. A common method of simplification is to divide a problem into subproblems of the same type. As a computer programming technique, this is called
Recursion
383714
Sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called "elements", or "terms"). The number of elements (possibly infinite) is called the "length" of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and order matters. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a sequence of finite length "n"). The position of
Sequence
10050395
Anderson's theorem In mathematics, Anderson's theorem is a result in real analysis and geometry which says that the integral of an integrable, symmetric, unimodal, non-negative function "f" over an "n"-dimensional convex body "K" does not decrease if "K" is translated inwards towards the origin. This is a natural statement, since the graph of "f" can be thought of as a hill with a single peak over the origin; however, for "n" ≥ 2, the proof is not entirely obvious, as there may be points "x" of the body "K" where the value "f"("x") is larger than at the corresponding translate
Anderson's theorem
1301844
only enough water for normal plant function is the best way to ensure disease pressure is reduced as much as possible. Despite the fact that the above cultural controls cannot completely control Microdochium Patch, when they are all used to reduce disease pressure, they can have a noticeable impact and will help to reduce the amount of chemical control that is required. Chemical controls (i.e. the use of fungicides) to specifically control turf grass diseases have been around since 1891. Over the years better controls have been developed, all of which tend to be less toxic to animals and the
Fusarium patch
12642131
the only important thermodynamic control variable is the ratio of chemical potential to temperature "µ"/("kT"). The exponential of this ratio, "z" = exp("µ"/("kT")) is called the activity and larger values correspond roughly to denser configurations. For a triangular lattice with "N" sites, the grand partition function is where "g"("n", "N") is the number of ways of placing "n" particles on distinct lattice sites such that no 2 are adjacent. The function κ is defined by so that log(κ) is the free energy per unit site. Solving the hard hexagon model means (roughly) finding an exact expression for κ as a
Hard hexagon model
159728
brain, the spiritual soul was in the heart, and the appetitive soul was in the liver. Galen was the first scientist and philosopher to assign specific parts of the soul to locations in the body because of his extensive background in medicine. This idea is now referred to as localization of function. Galen's assignments were revolutionary for the time period, which set the precedent for future localization theories. Galen believed each part of this tripartite soul controlled specific functions within the body and that the soul, as a whole, contributed to the health of the body, strengthening the "natural functioning
Galen
338352
systems are independent to each other, which allows activation of certain parts of the body, while others remain rested. Primarily using the neurotransmitter acetylcholine (ACh) as a mediator, the parasympathetic system allows the body to function in a “rest and digest” state. Consequently, when the parasympathetic system dominates the body, there are increases in salivation and activities in digestion, while heart rate and other sympathetic response decrease. Unlike the sympathetic system, humans have some voluntary controls in the parasympathetic system. The most prominent examples of this control are urination and defecation. Diseases of the peripheral nervous system can be specific
Peripheral nervous system
6572383
N-Acetylglutamic acid N"-Acetylglutamic acid (also referred to as N"-Acetylglutamate, abbreviated NAG, chemical formula CHNO) is biosynthesized from glutamate and acetylornithine by ornithine acetyltransferase, and from glutamic acid and acetyl-CoA by the enzyme "N"-acetylglutamate synthase. The reverse reaction, hydrolysis of the acetyl group, is catalyzed by a specific hydrolase. It is the first intermediate involved in the biosynthesis of arginine in prokaryotes and simple eukaryotes and a regulator in the process known as the urea cycle that converts toxic ammonia to urea for excretion from the body in vertebrates. N-Acetylglutamic acid is an extracellular metabolite isolated from the prokaryote Rhizobium trifolii
N-Acetylglutamic acid
497371
biogenic amines present in the body to produce MAOIs related to tetrahydroisoquinoline and β-carboline. Tobacco smokers may also experience more powerful effects with psilocybin, because tobacco smoke exposure decreases the activity of MAO in the brain and peripheral organs. Psilocybin ("O"-phosphoryl-4-hydroxy-"N,N"-dimethyltryptamine, 4-PO-Psilocin, or 4-PO-HO-DMT) is a prodrug that is converted into the pharmacologically active compound psilocin in the body by a dephosphorylation reaction. This chemical reaction takes place under strongly acidic conditions, or under physiological conditions in the body, through the action of enzymes called alkaline phosphatases. Psilocybin is a tryptamine compound with a chemical structure containing an indole ring
Psilocybin
11360060
is a predicate over the natural numbers, it is expressed as: That is, if "P" is decidable, and it cannot be false for every natural number "n", then it is true for some "n". (In general, a predicate "P" over some domain is called "decidable" if for every "x" in the domain, either "P"("x") is true, or "P"("x") is not true, which is not always the case constructively.) It is equivalent in the language of arithmetic to: for formula_3 a total recursive function on the natural numbers. It is equivalent, in the language of real analysis, to the following principles:
Markov's principle
13374311
0→0 are called "functions" and objects that take inputs of type other than 0 are called "functionals". For any two types σ and τ, the type σ×τ represents an ordered pair, the first element of which has type σ and the second element of which has type τ. For example, consider the functional "A" takes as inputs a function "f" from N to N, and a natural number "n", and returns "f"("n"). Then "A" has type (0 × (0→0))→0. This type can also be written as 0→(0→0)→0, by Currying. The set of (pure) "finite types" is the smallest collection of
Primitive recursive functional
7545165
Multiplicity function for N noninteracting spins The multiplicity function for a two state paramagnet, W(n,N), is the number of spin states such that n of the N spins point in the z-direction. This function is given by the combinatoric function C(N,n). That is: formula_1 It is primarily used in introductory statistical mechanics and thermodynamics textbooks to explain the microscopic definition of entropy to students. If the spins are non-interacting, then the multiplicity function counts the number of states which have the same energy in an external magnetic field. By definition, the entropy S is then given by the natural logarithm
Multiplicity function for N noninteracting spins
3605306
that must determine in "O"("f"("n")) time whether an algorithm has taken more than "f"("n") steps. This is, of course, impossible without being able to calculate "f"("n") in that time. Such results are typically true for all natural functions "f" but not necessarily true for artificially constructed "f". To formulate them precisely, it is necessary to have a precise definition for "a natural function f" for which the theorem is true. Time-constructible functions are often used to provide such definition. Space-constructible functions are used similarly, for example in the space hierarchy theorem. Constructible function In complexity theory, a time-constructible function is
Constructible function
9305181
we want to handle sequences of different length, we can store length data as a surplus member, or as the other member of an ordered pair by using a pairing function. We expect that there is an effective way for this information retrieval process in form of an appropriate total recursive function. We want to find a totally recursive function "f" with the property that for all "n" and for any "n"-length sequence of natural numbers formula_1, there exists an appropriate natural number "a", called the Gödel number of the sequence, such that for all "i" where formula_2, formula_3. There
Gödel numbering for sequences
2091587
The concept should not be confused with that of a bounded operator. An important special case is a bounded sequence, where "X" is taken to be the set N of natural numbers. Thus a sequence "f" = ("a", "a", "a", ...) is bounded if there exists a real number "M" such that for every natural number "n". The set of all bounded sequences, equipped with a vector space structure, forms a sequence space. This definition can be extended to functions taking values in a metric space "Y". Such a function "f" defined on some set "X" is called bounded if
Bounded function
8229753
function φ("n") is the number of positive integers less than "n" and coprime to "n". Ramanujan defines a generalization of it, if is the prime factorization of "n", and "s" is a complex number, let so that "φ"("n") = "φ"("n") is Euler's function. He proves that and uses this to show that Letting "s" = 1, Note that the constant is the inverse of the one in the formula for σ("n"). Von Mangoldt's function unless "n" = "p" is a power of a prime number, in which case it is the natural logarithm log "p". For all "n" > 0,
Ramanujan's sum
3605303
ones, stops after exactly "f"("n") steps for all "n" ≥ "n". In the second definition, a function "f" is called time-constructible if there exists a Turing machine "M" which, given a string 1, outputs the binary representation of "f"("n") in "O"("f"("n")) time (a unary representation may be used instead, since the two can be interconverted in "O"("f"("n")) time). There is also a notion of a fully time-constructible function. A function "f" is called fully time-constructible if there exists a Turing machine "M" which, given a string 1 consisting of "n" ones, stops after exactly "f"("n") steps. This definition is slightly
Constructible function
10162682
as realizers for formulas in Heyting arithmetic. The following clauses are used to define a relation ""n" realizes "A"" between natural numbers "n" and formulas "A" in the language of Heyting arithmetic. A few pieces of notation are required: first, an ordered pair ("n","m") is treated as a single number using a fixed effective pairing function; second, for each natural number "n", φ is the computable function with index "n". With this definition, the following theorem is obtained: On the other hand, there are formulas that are realized but which are not provable in HA, a fact first established by
Realizability
6473750
less susceptible to normal turnover thus enhancing the presence of these abnormal bonds on various molecules. Importantly, alagebrium does not disrupt the natural carbohydrate modification to proteins, intra-molecular crosslinking or peptide bonds that are responsible for maintaining the normal integrity of the collagen chain. Thus, normal structure and function is preserved while abnormal crosslinking is reduced. Although alagebrium may break some important AGE crosslinks, there is no evidence that it is effective against the most prevalent crosslink: glucosepane. The chemical name for alagebrium is 4,5-dimethyl-3-(2-oxo-2-phenylethyl)thiazolium chloride; it has also been called dimethyl-3-N-phenacylthiazolium chloride. Alteon said that it had selected ALT-711
Alagebrium
10055604
or equal to 1), or zero of the Riemann zeta function "ζ"(.). The line formula_7 is a natural boundary as the singularities cluster near all points of this line. If one defines a sequence then The prime zeta function is related to Artin's constant by where "L" is the "n"th Lucas number. Specific values are: The integral over the prime zeta function is usually anchored at infinity, because the pole at formula_11 prohibits defining a nice lower bound at some finite integer without entering a discussion on branch cuts in the complex plane: The noteworthy values are again those where
Prime zeta function
12378346
gas constant, 8.314 J/(mol K), and "T" is the temperature. Written this way, it is sometimes called the "chemist's version", since it emphasizes the number of molecules "n". It can also be written as where formula_3 is the specific gas constant for a particular gas, in units J/(kg K), and ρ = m/V is density. This notation is the "gas dynamicist's" version, which is more practical in modeling of gas flows involving acceleration without chemical reactions. The ideal gas law does not make an assumption about the specific heat of a gas. In the most general case, the specific heat
Gas
8229750
"m" > 0, "m" = lcm("m", "m"). Then Ramanujan's sums satisfy an orthogonality property: Let "n", "k" > 0. Then known as the Brauer - Rademacher identity. If "n" > 0 and "a" is any integer, we also have due to Cohen. If "f"("n") is an arithmetic function (i.e. a complex-valued function of the integers or natural numbers), then a convergent infinite series of the form: or of the form: where the , is called a Ramanujan expansion of "f"("n"). Ramanujan found expansions of some of the well-known functions of number theory. All of these results are proved in an
Ramanujan's sum
2492578
Axiom of countable choice The axiom of countable choice or axiom of denumerable choice, denoted AC, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function. I.e., given a function "A" with domain N (where N denotes the set of natural numbers) such that "A"("n") is a non-empty set for every "n" ∈ N, then there exists a function "f" with domain N such that "f"("n") ∈ "A"("n") for every "n" ∈ N. The axiom of countable choice (AC) is strictly weaker than the axiom of dependent choice (DC), which
Axiom of countable choice
2492574
Axiom of countable choice The axiom of countable choice or axiom of denumerable choice, denoted AC, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function. I.e., given a function "A" with domain N (where N denotes the set of natural numbers) such that "A"("n") is a non-empty set for every "n" ∈ N, then there exists a function "f" with domain N such that "f"("n") ∈ "A"("n") for every "n" ∈ N. The axiom of countable choice (AC) is strictly weaker than the axiom of dependent choice (DC), which
Axiom of countable choice
2149590
hyperoperations. It is also one of the primitive functions used in the characterization of computability by recursive functions. Successor function In mathematics, the successor function or successor operation is a primitive recursive function "S" such that "S"("n") = "n"+1 for each natural number "n". For example, "S"(1) = 2 and "S"(2) = 3. Successor operations are also known as zeration in the context of a zeroth hyperoperation: H("a", "b") = 1 + "b". In this context, the extension of zeration is addition, which is defined as repeated succession. The successor function is used in the Peano axioms which define the
Successor function
9770587
product x. There is a specific threshold for each regulatory interaction, so if x regulates n elements, it will have up to n different thresholds. For the logical sum, there is a procedure that assigns a specific weight to each term in the logical relation. According to the scale of thresholds of the corresponding variable, the weighted algebraic sum is then discretized, so an n-valued variable is associated with an n-valued function. After discretization the integers of certain weights or sums of weights are called logical parameters. Generalized Kinetic Logic, although maintaining the analytic simplicity of the naive description, has
Kinetic logic
4944625
Superabundant number In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number "n" is called superabundant precisely when, for all "m" < "n" where "σ" denotes the sum-of-divisors function (i.e., the sum of all positive divisors of "n", including "n" itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... . For example, the number 5 is not a superabundant number because for 1, 2, 3, 4, and 5, the sigma is 1, 3, 4, 7, 6, and 7/4 > 6/5. Superabundant numbers
Superabundant number
3422299
Periodic sequence In mathematics, a periodic sequence (sometimes called a cycle) is a sequence for which the same terms are repeated over and over: The number "p" of repeated terms is called the period (period). A periodic sequence is a sequence "a", "a", "a", ... satisfying for all values of "n". If we regard a sequence as a function whose domain is the set of natural numbers, then a periodic sequence is simply a special type of periodic function. The sequence of digits in the decimal expansion of 1/7 is periodic with period 6: More generally, the sequence of digits
Periodic sequence
10579076
reject the crossing partitions and count only the noncrossing partitions, we may use the Catalan numbers to count the non-crossing partitions of all n elements of the set, formula_6. To count the non-crossing partitions in which the set is partitioned in exactly k blocks, we use the Narayana number formula_7. The generating function of the Narayana numbers is Narayana number In combinatorics, the Narayana numbers "N"("n", "k"), "n" = 1, 2, 3 ..., 1 ≤ "k" ≤ "n", form a triangular array of natural numbers, called Narayana triangle, that occur in various counting problems. They are named after Canadian mathematician
Narayana number
14741259
(IDE). Following are the IDEs which support Processing.js: There exists an integration of the Processing.js library and a Javascript application framework for iPhone, called iProcessing. Processing.js syntax is almost identical to that of the Processing language, in that a codice_1 function is used to define general visualization properties like canvas size, frame rate and other variables, and a codice_2 function controls the behavior of each frame in the animation. The Processing.js library can be included in head section of a web page as a single JavaScript file: A codice_3 element is declared inside the body, with a codice_4 attribute, specifying
Processing.js
4075548
C we have fixed all type variables to the type constant codice_1. In languages supporting anonymous functions, we can pass such a function as an argument to a higher-order function: In a language which does not support anonymous functions, we have to bind it to a name instead: Once we have anonymous or nested functions, it becomes natural for them to refer to variables outside of their body (called "non-local variables"): If functions are represented with bare function pointers, we can not know anymore how the value that is outside of the function's body should be passed to it, and
First-class function
4231481
Operators taking 0 arguments are considered constants, and one constructs their term-language by these simple constructs. This rewrite theory specifies all the natural numbers. The sort saying is introduced, that there exists a sort called Nat (short for natural numbers), and below is the specification of how these terms are constructed. The operator s in Example 1 is the successor function representing the next natural number in the sequence of natural numbers i.e. s(N) := N + 1. s(0) is meant to represent the natural number 1 and so on. 0 is a constant, it takes no input parameter(s) but
Maude system
5730814
and the microchip which is precious and can act as a natural filter. Fissell and his team have designed each pore (of the filter) to perform a specific function or task. The microchips will also act as a platform for which living kidney cells will reside and grow on and around the filters with the goal of imitating the natural functions of the kidney. The bio-hybrid device will not be in reach of the body’s immune response which allows it to be protected against being rejected by the patient's body. The device will be designed to be small enough to
Artificial kidney
5856662
"n", ..., "n". The natural variable which we have is the amplitude with which a particular wavefunction of the basic set participates in the actual wavefunction of the system. Let us denote the square of this amplitude by "p"("n", "n", ..., "n"). The goal is to turn this quantity "p" into the classical density function in phase space. We have to verify that "p" goes over into the density function in the classical limit, and that it has ergodic properties. After checking that "p"("n", "n", ..., "n") is a constant of motion, an ergodic assumption for the probabilities "p"("n", "n",
Von Neumann entropy
4153275
the same species, communication molecules that attract and activate symbiotic organisms, agents that solubilize and transport nutrients (siderophores etc.), and competitive weapons (repellants, venoms, toxins etc.) that are used against competitors, prey, and predators. For many other secondary metabolites, the function is unknown. One hypothesis is that they confer a competitive advantage to the organism that produces them. An alternative view is that, in analogy to the immune system, these secondary metabolites have no specific function, but having the machinery in place to produce these diverse chemical structures is important and a few secondary metabolites are therefore produced and selected
Natural product
1758614
to all real values of "n". Let "f"("x") be a function defined for "x" > 0. Form the definite integral from 0 to "x". Call this Repeating this process gives and this can be extended arbitrarily. The Cauchy formula for repeated integration, namely leads in a straightforward way to a generalization for real "n". Using the gamma function to remove the discrete nature of the factorial function gives us a natural candidate for fractional applications of the integral operator. This is in fact a well-defined operator. It is straightforward to show that the "J" operator satisfies This relationship is called
Fractional calculus
10297555
and are able to be used as a control method. Spanish varieties are most susceptible, Virginia varieties are intermediates, and runner varieties are partially resistant. Very specific chemical controls are used to prevent yield loss, and are required in a very narrow, specific time period in order to be most effective. To be most successful, spray chemical controls as soon as the onset of symptom development. Fungicide application is recommended on a 14-day set calendar schedule, or according to weather based leaf spot advisory. In fields that utilize crop rotation, fungicides should be sprayed during the early pod stage (R3),
Mycosphaerella berkeleyi
1719790
function, Fermi energy, and Fermi level. For example, n-type silicon has a higher internal chemical potential of electrons than p-type silicon. In a p–n junction diode at equilibrium the chemical potential ("internal" chemical potential) varies from the p-type to the n-type side, while the total chemical potential (electrochemical potential, or, Fermi level) is constant throughout the diode. As described above, when describing chemical potential, one has to say "relative to what". In the case of electrons in semiconductors, internal chemical potential is often specified relative to some convenient point in the band structure, e.g., to the bottom of the conduction
Chemical potential
318759
interactions between proteins are reversible, and depend heavily on the availability of different groups of partner proteins to form aggregates that are capable to carry out discrete sets of function, study of the interactions between specific proteins is a key to understand important aspects of cellular function, and ultimately the properties that distinguish particular cell types. The best-known role of proteins in the cell is as enzymes, which catalyse chemical reactions. Enzymes are usually highly specific and accelerate only one or a few chemical reactions. Enzymes carry out most of the reactions involved in metabolism, as well as manipulating DNA
Protein
10209727
for computing "S"("n"). The Kempner function is also sometimes called the Smarandache function following Florentin Smarandache's rediscovery of the function in 1980. Since "n" divides "n"!, "S"("n") is always at most "n". A number "n" greater than 4 is a prime number if and only if "S"("n") = "n". That is, the numbers "n" for which "S"("n") is as large as possible relative to "n" are the primes. In the other direction, the numbers for which "S"("n") is as small as possible are the factorials: "S"("k"!) = "k", for all "k" ≥ 1. "S"("n") is the smallest possible degree of
Kempner function
5197899
from the idea that these may be viewed as a Cartesian product of types. Pi-types can also be understood as models of universal quantifiers. For example, if we write formula_12 for "n"-tuples of real numbers, then formula_13 would be the type of a function which, given a natural number "n", returns a tuple of real numbers of size "n". The usual function space arises as a special case when the range type does not actually depend on the input. E.g. formula_14 is the type of functions from natural numbers to the real numbers, which is written as formula_15 in typed
Dependent type
12742772
through signals. Many different types of neurons can be identified based on their function, such as sensory neurons or motor neurons. Each responds to specific stimuli and sends respective and appropriate chemical signals to other neurons. The basic structure of a neuron is shown here on the right and consists of a nucleus that contains genetic information; the cell body, or the soma, which is equipped with dendritic branches that mostly receive the incoming inputs from other neurons; a long, thin axon that bears axon terminals which carry the output information to other neurons. The dendrites and axons are interfaced
Activity-dependent plasticity
14108130
as recognizing body parts; in naming objects; in understanding numbers; or in understanding geographic and/or spatial location. It applies to both sides of a person, even though a lesion in only one side of the parietal lobe – the dominant one – causes it. He argues that amorphosynthesis, on the other hand, is usually caused by a lesion in the non-dominant parieto-occipital lobe and results in lack of awareness on the opposite side of the body. Before Denny-Brown, researchers such as Lange, Dide, Lenz, and McFie and associates proposed that the brain's right hemisphere controls a specific function in spatial
Amorphosynthesis
17818610
conserved, tissue-specific or inducible, which reflects plasticity and regulatory function. Furthermore, expression of TRBU1, which is mostly expressed in the brain, goes up due to fear conditioning. In addition, expression of the ncRNAs needed to guide RNA-dependent PUS enzymes also goes up in response to fear. There are three major techniques for the site-specific mapping of pseudouridine in RNA, called Pseudo-seq, Ψ-seq and PSI-seq. All these methods are based on the unique reaction between pseudouridine and N-cyclohexyl-N'-(2-morpholinoethyl)carbodiimide metho-p-toluenesulfonate (CMCT). The RNA to be analyzed is fragmented and incubated with CMCT. Even if CMCT can form covalent bonds with U, G
Epitranscriptome
13368944
genetic code is possible: That is the BB’s can be recalled by the PCR-amplified genetic code, and the library compounds can be regenerated. This, in turn, enables the principle of Darwinian natural selection and evolution to be applied to small molecule selection in direct analogy to biological display systems; through rounds of selection, amplification and translation. In order to apply combinatorial chemistry for the synthesis of DNA-encoded chemical libraries, a Split-&-Pool approach was pursued. Initially a set of unique DNA-oligonucleotides (n) each containing a specific coding sequence is chemically conjugated to a corresponding set of small organic molecules.Consequently, the oligonucleotide-conjugate
DNA-encoded chemical library
12841190
N-acyl phosphatidylethanolamine-specific phospholipase D N-acyl phosphatidylethanolamine phospholipase D (NAPE-PLD) is an enzyme that catalyzes the release of N-acylethanolamine (NAE) from N-acyl-phosphatidylethanolamine (NAPE). This is a major part of the process that converts ordinary lipids into chemical signals like anandamide and oleoylethanolamine. In humans, the NAPE-PLD protein is encoded by the "NAPEPLD" gene. NAPE-PLD is an enzyme activity - a phospholipase, acting on phospholipids found in the cell membrane. It is not homology but the chemical outcome of its activity that classes it as phospholipase D. The enzymatic activity was discovered and characterized in a series of experiments culminating in the
N-acyl phosphatidylethanolamine-specific phospholipase D
10187156
distinct chemical signatures in the thalamus, midbrain and pons must function for a subject to be in a sufficient state of brain arousal to experience anything at all. These nuclei therefore belong to the enabling factors for consciousness. Conversely it is likely that the specific content of any particular conscious sensation is mediated by particular neurons in the cortex and their associated satellite structures, including the amygdala, thalamus, claustrum and the basal ganglia. The following is a very brief account of some contributions to the mind–body problem. The Buddha (480–400 B.C.E), founder of Buddhism, described the mind and the body
Mind–body problem
179569
etc., with mostly sequential numbers. For such data, a function that extracts the numeric part "k" of the file name and returns "k" mod "n" would be nearly optimal. Needless to say, a function that is exceptionally good for a specific kind of data may have dismal performance on data with different distribution. In some applications, such as substring search, one must compute a hash function "h" for every "k"-character substring of a given "n"-character string "t"; where "k" is a fixed integer, and "n" is greater than "k". The straightforward solution, which is to extract every such substring "s"
Hash function
15086439
Quasisymmetric function In algebra and in particular in algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn a subring of the formal power series ring with a countable number of variables. This ring generalizes the ring of symmetric functions. This ring can be realized as a specific limit of the rings of quasisymmetric polynomials in "n" variables, as "n" goes to infinity. This ring serves as universal structure in which relations between quasisymmetric polynomials can be expressed in a way independent of the number "n" of variables (but its elements are
Quasisymmetric function
418542
2.88 × 10. The Riemann hypothesis has been verified for the first 10 trillion zeroes of the zeta function. Neither of these statements is considered proved. Such evidence does not constitute proof. For example, the Mertens conjecture is a statement about natural numbers that is now known to be false, but no explicit counterexample (i.e., a natural number "n" for which the Mertens function "M"("n") equals or exceeds the square root of "n") is known: all numbers less than 10 have the Mertens property, and the smallest number that does not have this property is only known to be less
Theorem
334846
sequence of numbers can be encoded by a single number. Such a number can therefore represent the primitive recursive function until a given n. Let "h" be a 1-ary primitive recursion function defined by: where C is a constant and "g" is an already defined function. Using Gödel's β function, for any sequence of natural numbers (k, k, …, k), there are natural numbers b and c such that, for every i ≤ n, β(b, c, i) = k. We may thus use the following formula to define "h"; more precisely, "m"="h"("n") is a shorthand for the following: and the
Primitive recursive function
1400648
that a series of terms can be said to be the generator of its sequence of term coefficients. The "ordinary generating function" of a sequence "a" is When the term "generating function" is used without qualification, it is usually taken to mean an ordinary generating function. If "a" is the probability mass function of a discrete random variable, then its ordinary generating function is called a probability-generating function. The ordinary generating function can be generalized to arrays with multiple indices. For example, the ordinary generating function of a two-dimensional array "a" (where "n" and "m" are natural numbers) is The
Generating function
2131017
Multiply perfect number In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number "k", a number "n" is called "k"-perfect (or "k"-fold perfect) if and only if the sum of all positive divisors of "n" (the divisor function, "σ"("n")) is equal to "kn"; a number is thus perfect if and only if it is 2-perfect. A number that is "k"-perfect for a certain "k" is called a multiply perfect number. As of 2014, "k"-perfect numbers are known for each value of "k" up to 11.
Multiply perfect number
4153287
amines etc.) often have very specific interactions with a macromolecular target in the body (e.g. α-bungarotoxin from cobras). As with plant feeding deterrents, this biological activity is attributed to natural selection, organisms capable of killing or paralyzing their prey and/or defending themselves against predators being more likely to survive and reproduce. Because of these specific chemical-target interactions, venom constituents have proved important tools for studying receptors, ion channels, and enzymes. In some cases, they have also served as leads in the development of novel drugs. For example, teprotide, a peptide isolated from the venom of the Brazilian pit viper "Bothrops
Natural product
13872333
logical paradox comes in large part from the so-called "vicious circle principle", that no propositional function can be defined prior to specifying the function's scope of application. In other words, before a function can be defined, one must first specify exactly those objects to which the function will apply (the function's domain). For example, before defining that the predicate "is a prime number", one first needs to define the collection of objects that might possibly satisfy the predicate, namely the set, N, of natural numbers. It functions as a formal definition of the function of meta-communication in communication. Ivan Pavlov
Meta-communication
12299151
Normal order of an arithmetic function In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate values. Let "f" be a function on the natural numbers. We say that "g" is a normal order of "f" if for every "ε" > 0, the inequalities hold for "almost all" "n": that is, if the proportion of "n" ≤ "x" for which this does not hold tends to 0 as "x" tends to infinity. It is conventional to assume that the approximating function "g" is continuous and monotone.
Normal order of an arithmetic function
12299150
Normal order of an arithmetic function In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate values. Let "f" be a function on the natural numbers. We say that "g" is a normal order of "f" if for every "ε" > 0, the inequalities hold for "almost all" "n": that is, if the proportion of "n" ≤ "x" for which this does not hold tends to 0 as "x" tends to infinity. It is conventional to assume that the approximating function "g" is continuous and monotone.
Normal order of an arithmetic function
16934320
by the electron number density formula_7, is a function of "μ", the internal chemical potential. The exact functional form depends on the system. For example, for a three-dimensional Fermi gas, a noninteracting electron gas, at absolute zero temperature, the relation is formula_8. Proof: Including spin degeneracy, (in this context—i.e., absolute zero—the internal chemical potential is more commonly called the Fermi energy). As another example, for an n-type semiconductor at low to moderate electron concentration, formula_10. The main assumption in the Thomas–Fermi model is that there is an internal chemical potential at each point r that depends "only" on the electron
Thomas–Fermi screening
18883643
the situation. They suggested that information entropy ("H") is a function of the number of alternatives ("n") in a choice task, H = log("n" + 1); and that reaction time (RT) of a human operator is a linear function of the entropy: RT = a + bH. This is known as the Hick-Hyman law for choice response time. Pointing at stationary targets such as buttons, windows, images, menu items, and controls on computer displays is commonplace and has a well-established modeling tool for analysis - Fitt's law (Fitts, 1954) - which states that the time to make an aimed movement
Human performance modeling
5983885
In this representation, object level variables do not appear explicitly. The constant codice_1 takes an expression (that is being bound) and a meta-level function codice_2 → codice_2 (the body of the let). This function is the "higher-order" part: an expression with a free variable is represented as an expression with "holes" that are filled in by the meta-level function when applied. As a concrete example, we would construct the object level expression (assuming the natural constructors for numbers and addition) using the HOAS signature above as where codice_9 is Twelf's syntax for the function formula_1. This specific representation has advantages
Higher-order abstract syntax
10748326
connection between the proofs lies in the fact that Hermite already mentions that if "f" is a polynomial function and then from which it follows that Bourbaki's proof is outlined as an exercise in his calculus treatise. For each natural number "b" and each non-negative integer "n", define Since "A"("b") is the integral of a function which defined on [0,] that takes the value 0 on 0 and on and which is greater than 0 otherwise, "A"("b") > 0. Besides, for each natural number "b", "A"("b") < 1 if "n" is large enough, because and therefore On the other hand,
Proof that π is irrational
36157
0 if "x" is not an integer. Here "convolution" does not mean "Dirichlet convolution" but instead refers to the formula for the coefficients of the product of two power series: The sequence formula_82 is called the convolution or the Cauchy product of the sequences "a" and "b". <br>See Eisenstein series for a discussion of the series and functional identities involved in these formulas. Since σ("n") (for natural number "k") and τ("n") are integers, the above formulas can be used to prove congruences for the functions. See Ramanujan tau function for some examples. Extend the domain of the partition function by
Arithmetic function
18182846
as models of Peano axioms, that is, triples ("N",0,"S") where "N" is a set, 0 an element of "N", and "S" (called the successor function) a map of "N" to itself (satisfying appropriate conditions). In the first implementation "S"("n") = "n" ∪ ; in the second implementation "S"("n") = . As emphasized in Benacerraf's identification problem, the two implementations differ in their answer to the question whether 0 ∈ 2; however, this is not a legitimate question about natural numbers (since the relation ∈ is not stipulated by the relevant signature(s), see the next section). Similarly, different but isomorphic implementations
Equivalent definitions of mathematical structures
10971832
as a mechanical and chemical stress sensor. The specific function of this protein has not yet been determined; however, studies indicate that the function may involve a role in signal transduction and growth control. Recent studies indicate that TRPA1 is activated by a number of reactive (allyl isothiocyanate, cinnamaldehyde, farnesyl thiosalicylic acid, formalin, hydrogen peroxide, 4-hydroxynonenal, acrolein, and tear gases) and non-reactive compounds (nicotine, PF-4840154) and considered as a "chemosensor" in the body.. TRPA1 is co-expressed with TRPV1 on nociceptive primary afferent C-fibers in humans. This sub-population of peripheral C-fibers is considered important sensors of nociception in humans and their
TRPA1
42760
transformation can also be interpreted as a single linear transformation from the tensor product formula_9 to "Z". The concept of binary function generalises to "ternary" (or "3-ary") "function", "quaternary" (or "4-ary") "function", or more generally to "n-ary function" for any natural number "n". A "0-ary function" to "Z" is simply given by an element of "Z". One can also define an "A-ary function" where "A" is any set; there is one input for each element of "A". In category theory, "n"-ary functions generalise to "n"-ary morphisms in a multicategory. The interpretation of an "n"-ary morphism as an ordinary morphisms whose
Binary function
14160464
the Sciences of Body and Mind". ‍‍Ethologists‍‍ study behavior using two general methods: naturalistic observation and laboratory experimentation. Ethologist's insistence on observing organisms in their natural environment differentiates ethology from related disciplines such as evolutionary psychology and sociobiology, and their naturalistic observation "ranks as one of their main contributions to psychology" (Miller, 2001). Naturalistic Observation Ethologist believe that in order to study species-specific behaviors, a species must be observed in its natural environment. One can only understand the function of a behavior by seeing how it specifically fits into the ‍‍species‍‍ natural environment in order to fulfill a specific need.
Human ethology
241944
as argument and returns the "n"-th composition of "f", i.e. the function "f" composed with itself "n" times. This is denoted "f" and is in fact the "n"-th power of "f" (considered as an operator); "f" is defined to be the identity function. Such repeated compositions (of a single function "f") obey the laws of exponents, which is why these numerals can be used for arithmetic. (In Church's original lambda calculus, the formal parameter of a lambda expression was required to occur at least once in the function body, which made the above definition of 0 impossible.) One way of
Lambda calculus
9329440
for making a protein that is essential for normal mitochondrial function. Through a series of chemical reactions, mitochondria use oxygen and simple sugars to create adenosine triphosphate (ATP), the cell's main energy source. The MT-ATP6 protein forms one part (subunit) of an enzyme called ATP synthase, which is responsible for the last step in ATP production. Mutations in the "MT-ATP6" gene alter the structure or function of ATP synthase, reducing the ability of mitochondria to make ATP. It remains unclear how this disruption in mitochondrial energy production leads to muscle weakness, vision loss, and the other specific features of NARP.
Neuropathy, ataxia, and retinitis pigmentosa
15162094
Receptor proteins have specific sites into which certain other proteins, called ligands, fit like keys into locks. Together, ligands and their receptors trigger signals that affect cell development and function. Megalin has many ligands involved in various body processes, including the absorption of vitamins A and D, immune functioning, stress response, and the transport of fats in the bloodstream. Megalin is embedded in the membrane of cells that line the surfaces and cavities of the body (epithelial cells). The receptor helps move its ligands from the cell surface into the cell (endocytosis). It is active in the development and function
Donnai–Barrow syndrome
10530746
the ways in which one neuron communicates with another through synaptic connections and the process called synaptic transmission". Neurons have a specialized structure for their function, they "are different from most other cells in the body in that they are polarized and have distinct morphological regions, each with specific functions". The two important regions of a neuron are the dendrite and the axon. "Dendrites are the region where one neuron receives connections from other neurons. The cell body or soma contains the nucleus and the other organelles necessary for cellular function. The axon is a key component of nerve cells
GENESIS (software)
22421
"A" be a set, and apply the axiom of regularity to {"A"}, which is a set by the axiom of pairing. We see that there must be an element of {"A"} which is disjoint from {"A"}. Since the only element of {"A"} is "A", it must be that "A" is disjoint from {"A"}. So, since "A" ∈ {"A"}, we cannot have "A" ∈ "A" (by the definition of disjoint). Suppose, to the contrary, that there is a function, "f", on the natural numbers with "f"("n"+1) an element of "f"("n") for each "n". Define "S" = {"f"("n"): "n" a natural number},
Axiom of regularity
3917148
find the maximum theoretical work of. By using the following equations, one can calculate the chemical exergy of the substance in a given system. Below, Equation 8 uses the Gibbs function of the applicable element or compound to calculate the chemical exergy. Equation 9 is similar but uses standard molar chemical exergy, which scientists have determined based on several criteria, including the ambient temperature and pressure that a system is being analyzed and the concentration of the most common components. These values can be found in thermodynamic books or in online tables. formula_12 where: formula_13 Gibbs function of the specific
Exergy
2328001
Isothiocyanate Isothiocyanate is the chemical group –N=C=S, formed by substituting the oxygen in the isocyanate group with a sulfur. Many natural isothiocyanates from plants are produced by enzymatic conversion of metabolites called glucosinolates. These natural isothiocyanates, such as allyl isothiocyanate, are also known as mustard oils. An artificial isothiocyanate, phenyl isothiocyanate, is used for amino acid sequencing in the Edman degradation. The general method for the formation of isothiocyanates proceeds through the reaction between a primary amine (e.g. aniline) and carbon disulfide in aqueous ammonia. This results in precipitation of the ammonium dithiocarbamate salt, which is then treated with lead
Isothiocyanate
6440480
physical treatments and not chemical modifications. These include blending, cleaning, extrusion, freezing, drying, etc. A specific ingredient can be called "natural" if it didn't go through any processing except for the listed ones. The whole food can be called "natural" if the food is not a blend of foods (even if they are all natural), has no added ingredients, and underwent only the specified processes. In the United States, there are laws/regulations and agencies to protect the consumer when purchasing food products, specifically dedicated to the packaging and labeling. Some laws and organizations include the Nutrition and Labeling Education Act,
Natural foods
2131784
Almost perfect number In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number "n" such that the sum of all divisors of "n" (the sum-of-divisors function "σ"("n")) is equal to 2"n" − 1, the sum of all proper divisors of "n", "s"("n") = "σ"("n") − "n", then being equal to "n" − 1. The only known almost perfect numbers are powers of 2 with non-negative exponents . Therefore the only known odd almost perfect number is 2 = 1, and the only known even almost perfect numbers are those of the
Almost perfect number
5775213
can be in one of several power-performance states. These states are implementation-dependent. Though, P0 is always the highest-performance state; with P1 to P"n" being successively lower-performance states, up to an implementation-specific limit of "n" no greater than 16. P-states have become known as SpeedStep in Intel processors, as PowerNow! or Cool'n'Quiet in AMD processors, and as PowerSaver in VIA processors. ACPI-compliant systems interact with hardware through either a "Function Fixed Hardware (FFH) Interface", or a platform-independent hardware programming model which relies on platform-specific ACPI Machine Language (AML) provided by the original equipment manufacturer (OEM). Function Fixed Hardware interfaces are platform-specific
Advanced Configuration and Power Interface
3083803
Serine proteases are inhibited by a diverse group of inhibitors, including synthetic chemical inhibitors for research or therapeutic purposes, and also natural proteinaceous inhibitors. One family of natural inhibitors called "serpins" (abbreviated from serine protease inhibitors) can form a covalent bond with the serine protease, inhibiting its function. The best-studied "serpins" are antithrombin and alpha 1-antitrypsin, studied for their role in coagulation/thrombosis and emphysema/A1AT, respectively. Artificial irreversible small molecule inhibitors include AEBSF and PMSF. A family of arthropod serine peptidase inhibitors, called pacifastin, has been identified in locusts and crayfish, and may function in the arthropod immune system. Mutations may
Serine protease
9082740
all" and "there exists". The equality symbol is sometimes treated as a non-logical symbol and sometimes treated as a symbol of logic. If it is treated as a logical symbol, then any interpretation will be required to interpret the equality sign using true equality; if interpreted as a non-logical symbol, it may be interpreted by an arbitrary equivalence relation. A "signature" is a set of non-logical constants together with additional information identifying each symbol as either a constant symbol, or a function symbol of a specific arity "n" (a natural number), or a relation symbol of a specific arity. The
Non-logical symbol