In the present paper, we study large values of Dirichlet $L$- functions inside the critical strip. For every $1/2<σ<1$, we show that for $q$ sufficiently large, there exists a non-principal character $χ$ modulo $q$ and a constant $c(σ)>0$ such tha...
This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results of some sp...
Reverse Hölder inequalities for a class of functions on a probability space constitute an important tool in Analysis in Probability. After revisiting how a (modified) log-Sobolev inequality can be used to derive reverse Hölder inequalities for the...
Creating user defined functions (UDFs) is a powerful method to improve the quality of computer applications, in particular spreadsheets. However, the only direct way to use UDFs in spreadsheets is to switch from the functional and declarative style o...
The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In this pa...
Dec 20, 2023 · The Startup class you are using supports In-Process Functions. MSDOC states that isolated functions contain a Program.cs file which provides complete access to the Host instance for …
We present B and R-band luminosity functions (LF) for a sample of 25 nearby groups of galaxies. We find that the LFs of the groups with low X-ray luminosity (L_X < 10^{41.7} erg/s) are significantly different from those of the X-ray brighter groups...
Nov 25, 2015 · Sharply-peaked and broad functions Ask Question Asked 14 years, 6 months ago Modified 10 years, 3 months ago
Development of modern integrated circuit technologies makes it feasible to develop cheaper, faster and smaller special purpose signal processing function circuits. Digital Signal processing functions are generally implemented either on ASICs with inf...
Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix into a func...
Influence functions are commonly used to attribute model behavior to training documents. We explore the reverse: crafting training data that induces model behavior. Our framework, Infusion, uses scalable influence-function approximations to compute s...
We study a question posed by Stephen Simons in his 2008 monograph involving "bigger conjugate" (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and adva...
The one loop 3-point vertex functions of QCD in the maximal abelian gauge (MAG) are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum (MOM) schemes which are defined by the trivale...
In this work, we presented a study regarding two important aspects of evolving feature-based game evaluation functions: the choice of genome representation and the choice of opponent used to test the model. We compared three representations. One simp...
Nov 25, 2015 · Sharply-peaked and broad functions Ask Question Asked 14 years, 6 months ago Modified 10 years, 3 months ago
In this paper, we explicitly compute two kinds of algebraic Belyi functions on Bring's curve. One is related to a congruence subgroup of ${\rm SL}_2(\mathbb{Z})$ and the other is related to a congruence subgroup of the triangle group $Δ(2,4,5)\subse...
Aug 19, 2023 · Discover the types of airplanes and their functions. Let's explore various civilian aircraft: commercial airliners, private jets, propeller planes, and more.
not strict is called non-strict. A strict programming language is one in which user-defined functions are always strict. Intuitively, non-strict functions
A strict programming language is a programming language that only allows strict functions (functions whose parameters must be evaluated completely before
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2kπ}{M}$ for some integer $M$. Firstly, w...
We study existence and uniqueness of Green functions for the Cheeger $Q$-Laplacian in metric measure spaces that are Ahlfors $Q$-regular and support a $Q$-Poincaré inequality with $Q>1$. We prove uniqueness of Green functions both in the case of rel...
As in the paper [G. Groenewald, M.A. Kaashoek, A.C.M. Ran, Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28 (2017) 694--710] our aim is to obtain ex...
Inspired by the paper of Groenewald, Kaashoek and Ran (Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28, (2017), 649-710), we present an operator-th...
Use of polynomial indicator functions to enumerate fractional factorial designs with given properties is first introduced by Fontana, Pistone and Rogantin (2000) for two-level factors, and generalized by Aoki (2019) for multi-level factors. In this p...
A polynomial indicator function of designs is first introduced by Fontana {\it et al}. (2000) for two-level cases. They give the structure of the indicator functions, especially the relation to the orthogonality of designs. These results are generali...
We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. As an application of these integral representations, we obtain a simple conceptual proof of a family of identities for J...
A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the Askey--Wilson p...
The HST's WFPC2 has several advantages over ground--based observations for the study of globular cluster luminosity functions (GCLFs) and distance determination. Here we present WFPC2 data on the globular clusters associated with NGC 5846. This gia...
The membership of some galaxies in the nearby (d ~ 12 Mpc) Coma I cloud is uncertain. Here we present globular cluster luminosity functions (GCLFs) from the HST for two bright ellipticals which may belong to this group. After fitting the GCLF, we f...
Mar 26, 2025 · This article covers the anatomy of the tooth, including structure, parts, types, functions, and clinical aspects. Learn more about this topic at Kenhub!
Jul 23, 2025 · There are different integration formulas for different functions. Below we will discuss the integration of different functions in depth and get complete knowledge about the integration formulas.
Maximally-localized Wannier functions (MLWFs) are widely employed as an essential tool for calculating the physical properties of materials due to their localized nature and computational efficiency. Projectability-disentangled Wannier functions (PDW...
Aug 19, 2023 · Discover the types of airplanes and their functions. Let's explore various civilian aircraft: commercial airliners, private jets, propeller planes, and more.
We give a very short proof of the fact that the number of $(a,b)$-parking functions of length $n$ equals $a(a+bn)^{n-1}$. This was first proved in 2003 by Kung and Yan, via a very long and torturous route, as a corollary of a more general result. Thi...
An efficient method of computing power expansions of algebraic functions is the method of Kung and Traub and is based on exact arithmetic. This paper shows a numeric approach is both feasible and accurate while also introducing a performance improvem...
Is there a way to add a sidebar that allows me to use an AI API (e.g. Gemini, GPT5, etc) to chat with the content of the page, similar to how the Dia browser functions?...
We present a theory of expected utility with state-dependent linear utility functions for monetary returns, that incorporates the possibility of loss-aversion. Our results relate to first order stochastic dominance, mean-preserving spread, increasing...
We consider secure computation of randomized functions between two users, where both the users (Alice and Bob) have inputs, Alice sends a message to Bob over a rate-limited, noise-free link, and then Bob produces the output. We study two cases: (i) w...
This paper focuses on the problem of evolving Boolean functions of odd sizes with high nonlinearity, a property of cryptographic relevance. Despite its simple formulation, this problem turns out to be remarkably difficult. We perform a systematic eva...
Nov 3, 2023 · Overview of the types, characteristics and functions of the epithelial tissue giving many examples with diagrams. Learn this topic now at Kenhub!