Bulletin of The Iranian Mathematical Society最新文献

The quantum injectivity problem classifies frames which are injective with respect to self-adjoint Hilbert-Schmidt operators. In this paper, we aim to analyze quantum injective frames in terms of the excess of frame elements in (mathbb {R}^n). Especially, we investigate the connection between the injectivity, full spark and phase retrieval frames. In addition, we detect injective (alternate) dual frames and show that the family of quantum injective dual frames is open and dense in the set of all dual frames. Finally, the stability of quantum injective frames will be addressed.

In this paper, we investigate some new truncated second main theorems by using the Jackson ( p )-Casorati determinant, where the truncated counting functions are assigned varying weights. We specifically concentrate on the Jackson difference operator applied to zero-order holomorphic mappings intersecting a finite set of slowly moving targets in ( mathbb {P}^n(mathbb {C}) ). As an application, we prove a uniqueness theorem of meromorphic functions sharing some small functions with the Jackson-type counting functions.

Various extensions of DMP-inverses have been proposed recently. Expressions involving G-Drazin inverses and the Moore–Penrose are known as GDMP-inverses. To generalize the definition of the GDMP inverse for square matrices, we firstly present and study the strong weighted G-Drazin inverse for bounded linear operators between two Hilbert spaces. We introduce the strong weighted GDMP inverse and its dual for operators by employing the strong weighted G-Drazin inverse and the Moore-Penrose inverse. Different properties, characterizations and representations for two new inverses are proved. Applying the strong weighted GDMP inverse, we define the strong weighted GDMP partial order.

It has been shown in Yang and Tian (Acta Math Sci 42B(3):847–864, 2022) that the function (xmapsto -frac{d}{dx}log {big [(1-x)^p{{,mathrm{{mathcal {K}}},}}(sqrt{x})big ]}) is absolutely monotonic on (0, 1) if and only if (pge 1/4), where ({{,mathrm{{mathcal {K}}},}}(r)) is the complete elliptic integral of the first kind defined on (0, 1). This result, in this paper, will be extended to the Gaussian hypergeometric function, more precisely, the absolutely monotonic properties of (xmapsto log {big [(1-x)^s{_2F_1}(a,b;c;x)big ]}) will be studied. As applications, several inequalities involving the ratio of Gaussian hypergeometric function and the generalized Grötzch ring function are established.

In this paper, we mainly focus on how to use Hom-partial actions to construct a new monoidal Hom–Hopf algebra. For this, we first introduce the notions of partial Hom–Smash products and partial Hom–Smash coproducts. Then, partial matched Hom-pairs are established to construct monoidal Hom–Hopf algebras, as application, some concrete examples are elaborated.

In this research, we extend three attractive iterative methods—conjugate gradient, conjugate residual, and minimal residual—to solve large sparse symmetric multilinear system (mathcal {A}textbf{x}^{m-1}=textbf{b}). We prove that the developed iterative methods converge under some appropriate conditions. As an application, we applied the proposed methods for solving the Klein–Gordon equation with Dirichlet boundary condition. Also, comparing these iterative methods to some new preconditioned splitting methods shows that, applying new methods for solving symmetric tensor equation (mathcal {A}textbf{x}^{m-1}=textbf{b}), in which the coefficient tensor is an (mathcal {M})-tensor, are more efficient. Numerical results demonstrate that our methods are feasible and effective for solving this type of tensor equations. Finally, some concluding remarks are given.

The common divisor graph, (Gamma (X)), is a graph that has been defined on a set of positive integers X. Some properties of this graph have been studied in the cases when either X is the set of character degrees or the set of conjugacy class sizes of a group. This paper deals with several properties of a particular case of the common divisor graph, (Gamma (Z)), when Z is a multiset of positive integers that admits a decomposition (Z=XY), where (XY={ xy | xin X, yin Y }) and (1in X) and (1 in Y). Our results can be applied for the graphs associated to character degrees and conjugacy classes of the direct product of two finite groups.

Let ((mathcal {L}, mathcal {A})) be a bi-complete duality pair. We consider when the relative Gorenstein modules with respect to such a duality pair coincide with the classical homological modules. As applications, we characterize (weak) global dimension via such a duality pair, characterize strongly CM-freeness of flat-typed ((mathcal {L}, mathcal {A}))-Gorenstein rings and obtain the compactly-generatedness of some relative derived categories. Applying the results into frequent duality pairs, our results unify the corresponding results for Gorenstein AC-modules and Ding modules.

In this paper, we give the complete classification of 5-dimensional complex solvable symmetric Leibniz algebras.

Let ((N_{n})_{nge 0}) be Narayana’s cows sequence given by a recurrence relation ( N_{n+3}=N_{n+2}+N_n ) for all ( nge 0 ), with initial conditions ( N_0=0 ), and ( N_1= N_2=1 ). In this paper, we find all members in Narayana’s cows sequence that are palindromic concatenations of two distinct repdigits. Our proofs use techniques on Diophantine approximation which include the theory of linear forms in logarithms of algebraic numbers and Baker’s reduction method. We show that 595 is the only member in Narayana’s cow sequence that is a palindromic concatenation of two distinct repdigits in base 10.