Iranian Journal of Mathematical Sciences and Informatics
Volume:17 Issue: 1, May 2022

Frames play significant role in various areas of science and engineering. Motivated by the work of Chander Shekhar, S. K. Kaushik and Abas Askarizadeh, Mohammad Ali Dehghan, we introduce the concepts of K-frames for B(H, K) and we establish some result. Also, we consider the relationships between K-Frames and K-Operator Frames for B(H).

In this paper we find all solutions of four kinds of the Diophantine equations x 2 ± Vtxy − y 2 ± x = 0 and x 2 ± Vtxy − y 2 ± y = 0, for an odd number t, and, x 2 ± Vtxy + y 2 − x = 0 and x 2 ± Vtxy + y 2 − y = 0, for an even number t, where Vn is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al [14]. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings as a subclass. The existence and convergence of coincidence-best and coincidence quasi-best proximity points in the setting of convex metric spaces are investigated.

In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left k-radicals Λ(a) = {x ∈ S | a l −→∞ x} induced by the transitive closure l −→∞ of the relation l −→ which induce the equivalence relation λ. Again non-transitivity of l −→ yields an expanding family { l −→n} of binary relations which associate subsets Λn(a) for all a ∈ S, which again induces an equivalence relation λn. We also define λ(λn)-simple semirings, and characterize the semirings which are distributive lattices of λ(λn)-simple semirings.

We firstly establish an identity for n time differentiable mappings Then, a new inequality for n times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose nth derivatives are of bounded variation are obtained.

The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factorizations by using the null space generators of some special nested submatrices of a matrix textit{A}.

This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stability and Hyers-Ulam-Rassias stability results. There are some primary lemmas, inequalities and relevant assumptions that helps in our stability results.

For a Tychonoff space X, we denote by Cp(X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. We study a functional characterization of the covering property of Hurewicz.

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n, r)-arc in PG(2, q) is denoted by mr(2, q). In this paper we present a new (184, 12)-arc in PG(2, 17), a new (244, 14)-arc and a new (267, 15)-arc in PG(2, 19).

This paper establishes a study on some important latest innovations in the uniqueness of solution for Caputo fractional Volterra-Fredholm integro-differential equations. To apply this, the study uses Banach contraction  principle and Bihari's inequality.  A wider applicability of these techniques are based on their reliability and reduction in the size of the mathematical work.

Let G be a finite group and cd∗ (G) be the set of nonlinear irreducible character degrees of G. Suppose that ρ(G) denotes the set of primes dividing some element of cd∗ (G). The bipartite divisor graph for the set of character degrees which is denoted by B(G), is a bipartite graph whose vertices are the disjoint union of ρ(G) and cd∗ (G), and a vertex p ∈ ρ(G) is connected to a vertex a ∈ cd∗ (G) if and only if p|a. In this paper, we investigate the structure of a group G whose graph B(G) has five vertices. Especially we show that all these groups are solvable.

A µ-way G-trade (µ ≥ 2) consists of µ disjoint decompositions of some simple (underlying) graph H into copies of a graph G. The number of copies of the graph G in each of the decompositions is the volume of the G-trade and denoted by s. In this paper, we determine all values s for which there exists a µ-way K1,m-trade of volume s for underlying graph H = K2m,2m and H = K2m.

In this paper we study translation surfaces with the nondegenerate third fundamental form in Lorentz- Minkowski space L 3 . As a result, we classify translation surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form III on the surface.

Let R be a commutative ring with identity. A proper submodule N of an R-module M is an n-submodule if rm ∈ N (r ∈ R, m ∈ M) with r /∈ p AnnR(M), then m ∈ N. A number of results concerning n-submodules are given. For example, we give other characterizations of n-submodules. Also various properties of n-submodules are considered.

In this work, we tried to find the inverse coefficient in the Euler problem with over determination conditions. It showed the existence, stability of the solution by iteration method and linearization method was used for this problem in numerical part. Also two examples are presented with figures.

The purpose of the present paper is to introduce a class Dn Σ;δC0(α) of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

In this paper, as a main result for Morrey spaces, we prove that the set Mp q (Rn)\ S q<r≤p Mp r (Rn) is spaceable in Mp q (Rn), where 0 < q < p < ∞.

This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given products are proposed.

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numerical method based on Taylor series expansion and Haar wavelets is presented for solving coupled system of nonlinear partial differential equations. Efficiency and accuracy of the proposed method is depicted by comparing with classical methods.