جستجوی مقالات مرتبط با کلیدواژه « rank » در نشریات گروه « ریاضی »

‎The minimum edge dominating energy‎, ‎denoted by $EE_{F}(G)$‎, ‎is the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of graph $G$‎. ‎In this paper‎, ‎we give some bounds and sharp bounds of $EE_{F}(G)$ in terms of matching number‎, ‎the number of positive eigenvalues of the minimum edge dominating matrix‎, ‎and the rank of $G$‎.

A finite group G is said to be (l,m, n)-generated, if it is a quotient group of the triangle group T(l,m, n) = ⟨x, y, z| x l =y m = z n= xyz = 1⟩. In [J. Moori, (p, q, r)-generations for the Janko groups J1 and J2, Nova J. Algebra and Geometry, 2 (1993), no. 3, 277-285], Moori posed the question of finding all the (p,q,r) triples, where p, q and r are prime numbers, such that a non-abelian finite simple group G is (p,q,r)-generated. Also for a finite simple group G and a conjugacy class X of G, the rank of X in G is defined to be the minimal number of elements of X generating G. In this paper we investigate these two generational problems for the group PSL(3,7), where we will determine the (p,q,r)-generations and the ranks of the classes of PSL(3,7). We approach these kind of generations using the structure constant method. GAP [The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.9.3; 2018. (http://www.gap-system.org)] is used in our computations.

In the preprint of ``Pseudo-Gorenstein and Level Hibi Rings,'' Ene, Herzog, Hibi, and Saeedi Madani assert (Theorem 4.3) that for a regular planar lattice $L$ with poset of join-irreducibles $P$, the following are equivalent:(1) $L$ is level;(2) for all $x,yin P$ such that $ylessdot x$, $height_{hat P}(x)+depth_{hat P}(y)lerank(hat P)+1$;(3) for all $x,yin P$ such that $ylessdot x$, either $depth(y)=depth(x)+1$ or $height(x)=height(y)+1$.They added, ``Computational evidence leads us to conjecture that the equivalent conditions given in Theorem 4.3 do hold for any planar lattice (without any regularity assumption).''Ene {sl et al.} prove the equivalence of (2) and (3) for a regular simple planar lattice, and write, ``One may wonder whether the regularity condition ... is really needed.''We show one cannot drop the regularity condition. Ene {sl et al.} say that ``we expect'' (2) to imply (1) for any finite distributive lattice $L$.We provide a counter-example.

Differential equations can be used to examine patrials of higher rank with varying coefficients in various regions of the Cartesian coordinate plane. Meanwhile, the researchers and scientists have N. Rajabov, A.S. Star and F.A. Nasim Adeeb Haneen, and others. As a result, while the coefficients of partial differential equations differ from those of partial differential equations, this research examined the partial differential equation based on its rank (fourth rank). Conditions are established for the production of their coefficients within the context of that equation. In multiple different scenarios involving these coefficients, a single solution for that partial differential equation. These circumstances were summed up in five theories.

If Gis a finite group and X a conjugacy class of‎ ‎elements of G‎, ‎then we define \rank(G:X) to be the minimum‎ ‎number of elements of X generating G‎. ‎In the present article‎, ‎we‎ ‎determine the ranks for the Fischer's simple group Fi′24‎ ‎and the baby monster group B.

ýLet G be a finite group and X be a conjugacy class of G. Theý ýrank of X in G, denoted by rank(G:X), is defined toý ýbe the minimal number of elements of X generating G. In thisý ýpaper we establish the ranks of all the conjugacy classes ofý ýelements for simple alternating group A10 using the structureý ýconstants method and other results established iný ý[A.B.Mý. ýBasheer and Jý. ýMooriý, ýOn the ranks of the alternating group Aný, ýBullý. ýMalaysý. ýMathý. ýSciý. ýSoc..

ýA rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operationsý. ýMoreoverý, ýby using this equality and Theorems 8 and 10 in [Chen Mý. ýand et alý. ýOn the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applicationsý, ýThe Scientific World Journal 2014 (2014)ý, ýArticle ID 702413ý, ý7 pagesý.]ý, ýsome other rank equalities for tripotent matrices are givený. ýFurthermoreý, ýwe obtain several rank equalities related to some special types of matricesý, ýsome of which are available in the literatureý, ýfrom the results establishedý.

M24 is the largest Mathieu sporadic simple group of order 244823040=210⋅33⋅5⋅7⋅11⋅23 and contains all the other Mathieu sporadic simple groups as subgroups. The object in this paper is to study the ranks of M24 with respect to the conjugacy classes of all its nonidentity elements.

Let E be an elliptic curve over Q with the given Weierstrass equation y 2 =x 3 欟 . If D is a squarefree integer, then let E (D) denote the D -quadratic twist of E that is given by E (D) :y 2 =x 3 2 x 3 . Let E (D) (Q) be the group of Q -rational points of E (D) . It is conjectured by J. Silverman that there are infinitely many primes p for whichE (p) (Q) has positive rank, and there are infinitely many primes q for which E (q) (Q) has rank 0 . In this paper, assuming the parity conjecture, we show that for infinitely many primes p , the elliptic curve E (p) n :y 2 =x 3 −np 2 x has odd rank and for infinitely many primes p , E (p) n (Q) has even rank, where n is a positive integer that can be written as biquadrates sums in two different ways, i.e., n=u 4 4 =r 4 4 , where u,v,r,s are positive integers such that gcd(u,v)=gcd(r,s)=1 . More precisely, we prove that: if n can be written in two different ways as biquartic sums and p is prime, then under the assumption of the parity conjecture E (p) n (Q) has odd rank (and so a positive rank) as long as n is odd and p≡5,7(mod8) or n is even and p≡1(mod4) .
In the end, we also compute the ranks of some specific values of n and p explicitly.

The triple factorization of a group G has been studied recently showing that G=ABA for some proper subgroups A and B of G, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups D2n and PSL(2,2n) for their triple factorizations by finding certain suitable maximal subgroups, which these subgroups are define with original generators of these groups. The related rank-two coset geometries motivate us to define the rank-two coset geometry graphs which could be of intrinsic tool on the study of triple factorization of non-abelian groups.

In this article, we construct families of elliptic curves arising from the Heron triangles and Diophantine triples with the Mordell-Weil torsion subgroup of Z/2Z × Z/2Z. These families have ranks at least 2 and 3, respectively, and contain particular examples with rank equal to 7.

In this paper, we study the extremal ranks and inertias of the Hermitian matrix expression $$ f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is Hermitian, $*$ denotes the conjugate transpose, $X$ and $Y$ satisfy the following consistent system of matrix equations $A_{3}Y=C_{3}, A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As consequences, we get the necessary and sufficient conditions for the above expression $f(X,Y)$ to be (semi) positive, (semi) negative. The relations between the Hermitian part of the solution to the matrix equation $A_{3}Y=C_{3}$ and the Hermitian solution to the system of matrix equations $A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2}$ are also characterized. Moreover, we give the necessary and sufficient conditions for the solvability to the following system of matrix equations $A_{3}Y=C_{3},A_{1}X=C_{1},XB_{1}=D_{1}, A_{2}XA_{2}^{*}=C_{2},X=X^{*}, B_{4}Y+(B_{4}Y)^{*}+A_{4}XA_{4}^{*}=C_{4} $ and provide an expression of the general solution to this system when it is solvable.

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semilinear transformations and matrices, and we prove a result which is closely related to the well-known Jordan-Chevalley decomposition of an element.

Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some conditions in this paper.