scholarly journals Some equalities on q-gamma and q-digamma functions

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 2947-2954
Author(s):  
İnci Ege ◽  
Emrah Yıldırım
Keyword(s):  
Negative Integer ◽  
Neutrix Limit

In this paper, we give some equalities on q-gamma and q-digamma functions for negative integer values of x by aid of using the concepts of neutrix and neutrix limit.

scholarly journals A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases

2021 ◽  
Vol 96 ◽  
pp. 545-558
Author(s):  
Paulo Roberto Prezotti Filho ◽  
Valderio Anselmo Reisen ◽  
Pascal Bondon ◽  
Márton Ispány ◽  
Milena Machado Melo ◽  
...  
Keyword(s):  
Time Series ◽  
Statistical Model ◽  
Respiratory Diseases ◽  
Negative Integer

Analytical method for optimum non‐negative integer bit allocation

2016 ◽  
Vol 10 (8) ◽  
pp. 936-946 ◽  
Author(s):  
Mahdi Hatam ◽  
Mohammad Ali Masnadi‐Shirazi
Keyword(s):  
Analytical Method ◽  
Negative Integer ◽  
Bit Allocation

scholarly journals Reachability Relations and the Structure of Transitive Digraphs

10.37236/115 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Norbert Seifter ◽  
Vladimir I. Trofimov
Keyword(s):  
Positive Integer ◽  
Negative Integer ◽  
Equivalence Relations ◽  
Basic Relation ◽  
Factor Graphs ◽  
Locally Finite ◽  
General Properties

In this paper we investigate reachability relations on the vertices of digraphs. If $W$ is a walk in a digraph $D$, then the height of $W$ is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed opposite to their orientation. Two vertices $u,v\in V(D)$ are $R_{a,b}$-related if there exists a walk of height $0$ between $u$ and $v$ such that the height of every subwalk of $W$, starting at $u$, is contained in the interval $[a,b]$, where $a$ ia a non-positive integer or $a=-\infty$ and $b$ is a non-negative integer or $b=\infty$. Of course the relations $R_{a,b}$ are equivalence relations on $V(D)$. Factorising digraphs by $R_{a,\infty}$ and $R_{-\infty,b}$, respectively, we can only obtain a few different digraphs. Depending upon these factor graphs with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ it is possible to define five different "basic relation-properties" for $R_{-\infty,b}$ and $R_{a,\infty}$, respectively. Besides proving general properties of the relations $R_{a,b}$, we investigate the question which of the "basic relation-properties" with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ can occur simultaneously in locally finite connected transitive digraphs. Furthermore we investigate these properties for some particular subclasses of locally finite connected transitive digraphs such as Cayley digraphs, digraphs with one, with two or with infinitely many ends, digraphs containing or not containing certain directed subtrees, and highly arc transitive digraphs.

scholarly journals Higher Nash blowups

2007 ◽  
Vol 143 (6) ◽  
pp. 1493-1510 ◽  
Author(s):  
Takehiko Yasuda
Keyword(s):  
Algebraic Variety ◽  
Characteristic Zero ◽  
Negative Integer ◽  
Curve Singularity ◽  
Irreducible Curve ◽  
Numerical Monoid

AbstractFor each non-negative integer n we define the nth Nash blowup of an algebraic variety, and call them all higher Nash blowups. When n=1, it coincides with the classical Nash blowup. We study higher Nash blowups of curves in detail and prove that any curve in characteristic zero can be desingularized by its nth Nash blowup with n large enough. Moreover, we completely determine for which n the nth Nash blowup of an analytically irreducible curve singularity in characteristic zero is normal, in terms of the associated numerical monoid.

BASES FOR Sk(Γ1(4)) AND FORMULAS FOR EVEN POWERS OF THE JACOBI THETA FUNCTION

2013 ◽  
Vol 09 (08) ◽  
pp. 1973-1993 ◽  
Author(s):  
SHINJI FUKUHARA ◽  
YIFAN YANG
Keyword(s):  
Eisenstein Series ◽  
Theta Function ◽  
Congruence Subgroup ◽  
Negative Integer ◽  
Cusp Forms ◽  
Jacobi Theta Function

We find a basis for the space Sk(Γ1(4)) of cusp forms of weight k for the congruence subgroup Γ1(4) in terms of Eisenstein series. As an application, we obtain formulas for r2k(n), the number of ways to represent a non-negative integer n as sums of 2k integer squares.

scholarly journals Subgroups of infinite index in the modular group II

1981 ◽  
Vol 22 (1) ◽  
pp. 101-118 ◽  
Author(s):  
W. W. Stothers
Keyword(s):  
Modular Group ◽  
Negative Integer ◽  
Infinite Index ◽  
Group Ii

Let H be a subgroup of Γ, the modular group. Let h be the number of orbits of under the action of H. In each orbit, the stabilizers are H-conjugate. Let U be the mapping z↦z + 1. Each stabilizer is Γ-conjugate to 〈Uc〉 for some non-negative integer c. The integer c is the cusp-width of the orbit. Let h0 be the number of orbits with non-trivial stabilizer, i.e. with c>0. The sequence (c(1), …, c(h0)) of non-zero cuspwidths is the cusp-split of H. Clearly, h0<h, and h∞ = h−h0 is the number of orbits with trivial stabilizer.

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