In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving...
Dec 21, 2023 · Neurons are categorized into different types based on their unique morphologies and functions. This article will focus on the structure and physiology of a typical multipolar neuron, the …
"1-out-of-N" FEC code. For the first layer the orthogonal functions are (co)sine functions, with 32 different frequencies (tones). At a given time only
In this paper, using $p$-adic analysis and $p$-adic L-functions, we show how to extend classical congruences (due to Wilson, Gauss, Dirichlet, Jacobi, Wolstenholme, Glaisher, Morley, Lemher and other people) to modulo $p^k$ for any $k>0$....
We obtain an explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations. We have another integral expression different from that of Miyazaki [7]....
Oct 26, 2010 · An interesting fact is that most (i.e. a co-meager set of) continuous functions are nowhere differentiable. The proof is a consequence of the Baire Category theorem and can be found (as an …
Jun 2, 2024 · since PHP 7.4 => operator is also used for the arrow functions, a more concise syntax for anonymous functions. since PHP 8.0 => operator is also used to define hands in the match expression
We introduce an automorphism $\mathcal{S}$ of the space $C(\mathbb{Z}_p,\mathbb{C}_p)$ of continuous functions $\mathbb{Z}_p \rightarrow \mathbb{C}_p$ and show that it can be used to give an alternative construction of the $p$-adic incomplete $Γ$-fu...
In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems
We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and...
An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the $L^2$ norms of the gradients of the functions, where the magnitude o...
The generalized hypergeometric function $_qF_p$ is a power series in which the ratio of successive terms is a rational function of the summation index. The Gaussian hypergeometric functions $_2F_1$ and $_3F_2$ are most common special cases of the g...
We establish a theory of NC functions on a class of von Neumann algebras with a particular direct sum property, e.g. $B(\mathcal{H})$. In contrast to the theory's origins, we do not rely on appealing to results from the matricial case. We prove that...
1 贝塞尔方程 显然，这是一个二阶齐次线性常微分方程，其解为： 其中， 为阶数， 为第一类贝塞尔函数 (Bessel functions of the first kind)， 为第二类贝塞尔函数 (Bessel functions of the second kind)，有的 …
We interpret a fuzzy set as a random availability function and provide sufficient conditions under which a preference relation over the set of all random availability functions can be represented by a utility function....
1 贝塞尔方程 显然，这是一个二阶齐次线性常微分方程，其解为： 其中， 为阶数， 为第一类贝塞尔函数 (Bessel functions of the first kind)， 为第二类贝塞尔函数 (Bessel functions of the second kind)，有的 …
Dec 21, 2023 · The endocrine system uses chemical messengers called hormones to regulate a range of bodily functions through the release of hormones.
1 贝塞尔方程 显然，这是一个二阶齐次线性常微分方程，其解为： 其中， 为阶数， 为第一类贝塞尔函数 (Bessel functions of the first kind)， 为第二类贝塞尔函数 (Bessel functions of the second kind)，有的 …
We improve well-known results concerning normal families and shared values of meromorphic functions in the plane. In particular, we obtain two corollaries concerning meromorphic functions $f \colon {\mathbb C} \to {\widehat{\mathbb C}}$: i) If $f$ sh...
We study automorphisms and invariants for the algebra $\mathbb{O}$ of octonions and octonionic slice regular functions $f:\mathbb{O} \to \mathbb{O}$....