Let p be a prime not dividing the integer n. By an Ihara result, we mean existence of a cokernel torsion-free injection from a full lattice in the space of p-old modular forms into a full lattice in the space of all modular forms of level pn. In this paper, we will prove an Ihara result in the number field case, for Siegel modular forms. The case of elliptic modular forms is discussed in Ihara (Discrete

The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter bounds the path cover number which is the minimum number of vertex-disjoint-induced paths that cover all the vertices of graph. In this paper, we investigate these two parameters and present an infinite number of graphs with the large difference between these two parameters and an infinite number of graphs

In this paper, we propose a new customized proximal point algorithm for linearly constrained convex optimization problem, and further extend the proposed method to separable convex optimization problem. Unlike the existing customized proximal point algorithms, the proposed algorithms do not involve relaxation step, but still ensure the convergence. We obtain the particular iteration schemes and the

A path cover of a graph G is a spanning subgraph of G consisting of vertex disjoint paths; a minimum path cover of G is a path cover of G consisting of minimum number of paths; a path cover number of G, denoted by p(G), is the number of paths in a minimum path cover of G, i.e., \(p(G)=\min \{|{\mathcal {P}}|:\)\({\mathcal {P}}\) is a path cover of \(G\}.\) A graph G is quasi-claw-free if for any two

In this paper, we study the numerical radius parallelism for bounded linear operators on a Hilbert space \(\big ({\mathscr {H}}, \langle \cdot ,\cdot \rangle \big )\). More precisely, we consider bounded linear operators T and S which satisfy \(\omega (T + \lambda S) = \omega (T)+\omega (S)\) for some complex unit \(\lambda \), and is denoted by \(T \parallel _{\omega } S\). We show that \(T \parallel

This paper is concerned with bistable wave fronts in a class of nonlocal reaction diffusion model for a single species with stage structure and distributed maturation delay. By choosing the strong and weak kernel functions to transform system with delays to a two- or three-dimensional system without any delays, the existence of traveling wave fronts is established by abstract results. Then we prove

This paper introduces a noninstantaneous impulsive Lasota–Wazewska model with pure delay. We establish existence and uniqueness of positive almost periodic solutions and show any solution converges exponentially to this positive almost periodic solution. An example is given to illustrate our theoretical results.

In this paper, by using the notion of convolution types we introduce symmetric and non-symmetric convolution type \(\hbox {C}^*\)-algebras. It is shown that any (exact) convolution type induces a (an exact) functor on the category of \(\hbox {C}^*\)-algebras. In particular, any group induces a convolution type and a functor on the category of \(\hbox {C}^*\)-algebras. It is also shown that discrete

In this paper, we use the Gauss–Jacobi quadrature formula to get an approximate solution for a finite part singular integral equation. The zeros of Jacobi polynomials and Jacobi functions of the second kind are used to construct a square system of algebraic equations which yield an interpolating function for the regular part of the solution of the singular integral equation. In a special case, another

Abaffy, Broyden and Spediacto (ABS) introduced a class of the so-called ABS methods to solve systems of linear equations. The ABS approach was specialized to solve linear Diophantine systems by Esmaeili, Mahdavi-Amiri and Spedicato. The method was extended to systems of certain linear inequalities to provide all solutions. Here, we mainly focus on the theoretical research into rank reduction processes

Assume that G is a finite non-Dedekind p-group, where p is an odd prime. Passman introduced the following concept: we say that \(H_{1}

Let R be a commutative Noetherian ring and M, N be two finitely generated R-modules. In this note, we prove the cofiniteness of generalized local cohomology modules \(H^{i}_{I}(M,N)\) with respect to I for all \(i

Galois has completed a programme started by Al Khwarizmi 1000 years before.

Let \({\mathcal {R}}\) be a 2-torsion-free commutative ring with unity, X a locally finite pre-ordered set with a finite number of connected components and \(I(X,{\mathcal {R}})\) the incidence algebra of X over \({\mathcal {R}}\). In this paper, we give a sufficient and necessary condition for a commuting map on \(I(X,{\mathcal {R}})\) to be proper.

In this letter, we propose a continuous-time dynamics for social network that represents patterns of both amity and enmity through directed signed graphs. The introduction of discrepancies between true and perceived sentiments gives rise to a non-autonomous system and distinguishes itself from the prior models. We show that for almost all initial configurations, the system will evolve into at most

Let G be a finite group and H a subgroup of G. We say that H: is generalized S-quasinormal in G if \(H=\left\langle A,B\right\rangle \) for some modular subgroup A and S-quasinormal subgroup B of G; m-S-complemented in G if there are a generalized S-quasinormal subgroup S and a subgroup T of G such that \(G=HT\) and \(H\cap T\le S\le H\). In this paper, we study finite groups with given systems of

Ideal convergence in a topological space is induced by changing the definition of the convergence of sequences on the space by an ideal. Let \({\mathcal {I}}\subseteq 2^{\mathbb {N}}\) be an ideal. A sequence \((x_{n}:n\in {\mathbb {N}})\) in a topological space X is said to be \(\mathcal I\)-convergent to a point \(x\in X\) provided for any neighborhood U of x in X, we have the set \(\{n\)\(\in {\mathbb

As usual, the ring of continuous real-valued functions on a completely regular frame L is denoted by \(\mathcal {R}L\). It is well known that an ideal Q in \(\mathcal {R}L\) is a z-ideal if and only if \(\sqrt{Q}\) is a z-ideal in which case \(Q=\sqrt{Q}\). We show the same fact in d-ideal context and then it turns out that the sum of a primary ideal and a z-ideal (d-ideal) in \(\mathcal {R}L\) which

Let \({\mathbf {M}}_{n,m}\) be the set of all n-by-m real matrices and let the relation \(\prec \) on \({\mathbf {M}}_{n,m}\) be the multivariate majorization. A linear mapping \(\Phi \!:{\mathbf {M}}_{n,m}\longrightarrow {\mathbf {M}}_{n,m}\) is said to be a linear preserver of multivariate majorization if \(\Phi (X)\prec \Phi (Y)\) whenever \(X\prec Y\). Also, \(\Phi \) is said to be a local linear

A space X is said to be cellular-Lindelöf if, for every family \(\mathcal U\) of disjoint non-empty open sets of X, there is a Lindelöf subspace \(L\subset X\), such that \(U\cap L \not = \emptyset \) for every \(U\in \mathcal U\). This class of spaces was introduced by Bella and Spadaro in 2007. In this paper, our main result is to show that the Pixley–Roy space \(\mathcal F[X]\) is cellular-Lindelöf