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...shown that by sufficiently dense sampling in phase space the corresponding functions will span a frame for the Hilbert space. ...y is the derivation of atomic decompositions for Banach spaces. One of the key steps is to define the voice transform for distributions in a natural way. ...

...ef>[http://cosmology.lbl.gov/talks/Heitmann_08.pdf Dark Matter Halos, Mass Functions, and Cosmology: a Theorist’s View]</ref>) of a certain mass within a given increases with time. Such functions had previously been noted by Schechter ...

{{Short description|Password-based key derivation function}} ...proceeds in this fashion, using a progressively modified state to hash the key and replace bits of state, until all subkeys have been set. ...

{{Short description|Key derivative function}} ...hashing|password hashing scheme]] (PHS) that can also function as a [[key derivation function]] (KDF). It gained recognition during the [[Password Hashing Compe ...

...sasco, Lorenzo |author3=Lawrence, Neil D. |title=Kernels for Vector-Valued Functions: A Review|eprint=1106.6251 |date=June 2011|class=stat.ML}}</ref> The main assumption in the regularization perspective is that the set of functions <math>\mathcal{F}</math> is assumed to belong to a reproducing kernel Hilbe ...

...mming with Computable Functions'' or ''Programming language for Computable Functions''.</ref> was a stage in the evolution of lambda calculus into modern functi ...] essentially implement a let expression, to implement restricted scope of functions, in block structures.{{citation needed|date=January 2020}} ...

...random generator]] (PRG), but the two concepts are not identical. Both are functions that take as input a small, uniformly random seed and produce a longer outp ...d''(''n''), ''m''(''n'') a family Ext&nbsp;=&nbsp;{Ext_''n''} of functions ...

==Background and derivation== Ignoring the details of the matrix elements, the key consequences are that the effective mass varies with the smallest bandgap a ...

== Physical derivation == This derivation is from <ref name="foog">{{cite web |title=Lecture Notes by Jeremy Quastel ...

...such codes do not exist if the family of "[[Tampering (crime)|tampering]] functions" F is completely unrestricted, they are known to exist for many broad tampe ...Cryptology – EUROCRYPT 2014 |chapter=Efficient Non-malleable Codes and Key-Derivation for Poly-size Tampering Circuits |volume= 8441|pages=111–128|url=http://inf ...

...016214506000000186|s2cid=13712496}}</ref> In parametric modeling, variance functions take on a parametric form and explicitly describe the relationship between ...on.<ref>{{cite journal|first=R.W.M.|last=Wedderburn|title=Quasi-likelihood functions, generalized linear models, and the Gauss–Newton Method|journal=Biometrika| ...

...uids through porous mediums, ''J. Appl. Phys.'', 1(5), 318–333.</ref> The key difference being that the dependent variable is the position of the wetting ==Derivation== ...

== Derivation of the First DCA Pattern == |title=Empirical orthogonal functions and related techniques in atmospheric science: A review ...

...zer|perceptual quantizer]] (PQ) or [[hybrid log–gamma]] (HLG) nonlinearity functions, but is most commonly associated with the PQ function (which was also devel ==Derivation== ...

...ation, however, has increased dissipated power per unit area and made it a key limiting factor in [[integrated circuits|integrated circuit]] performance. Function <math>\overline{\Theta}</math> is expanded in terms of cosine functions for the <math>x</math> and <math>y</math> variables and in terms of hyperbo ...

...|first=Marcos |date=23 July 2024 |title=Quantum Spin Chains and Symmetric Functions |arxiv=2404.04322 }}</ref> The other key component to understanding the QET mechanism is [[Quantum fluctuation|vacuu ...

...ert space.<ref>{{harvb|Koopman|1931}}</ref> According to this formulation, functions representing physical observables become vectors, with an inner product def ===Derivation starting from the Liouville equation=== ...

...mation function. The agents do not see or know about these transformation functions. Then there appears no rational basis for preferring one function over ano The [[principle of indifference]] has played a key role in probability theory. It says that if N statements are symmetric so t ...

...tions]] associated to these stochastic particles. It is best known for its derivation of the [[Schrödinger equation]] as the [[Kolmogorov equations|Kolmogorov eq ...zation or stochasticization.{{sfn|Nelson|2014}} As the theory allows for a derivation of the Schrödinger equation, it has given rise to the stochastic interpreta ...

...r global interoperability of contact tracing and exposure alerting apps, a key aspect of achieving widespread adoption.<ref name="initial-commit">{{Cite w ...}}</ref>{{Rp|line. 13}} Then, using the RAK an initial ''temporary contact key'' (TCK) is generated using the algorithm <math> ...