bluuebunny/crossref_metadata_2025 huggingface dataset:
Sums of fractional parts and sum of restricted divisors of a number
Authors: Jakimczuk Rafael
Published: September 2022

Let us consider a strictly increasing sequence of positive integers an such that A(x) is the distribution function of the sequence. That is, A(x)=∑ an≤ x 1. We study the sum ∑ an≤ x ans{x / an} and apply this formula in the study of the sum of a-divisors of a number. The distribution functions A(x) considered are very general. The methods used are very elementary.
Characterizing finite Boolean rings by using finite chains of subrings
Authors: Jarboui Noomen , Dobbs David
Published: September 2022

Let R be a nonzero associative ring with identity. It is proved that R is a finite Boolean ring if (and only if) 1 is the only unit of R and there exists a finite maximal chain C each of whose n steps is a proper unital ring extension, R0:=F2 ⊂ ... ⊂ Rn=R, going from F2 to R. If these equivalent conditions hold and R has exactly n maximal ideals, then any such C has length n-1 and the number of unital subrings of R is Bn, the nth Bell number. It is also proved that if R has characteristic p for some prime number p, then R is isomorphic to a finite direct product of copies of Fp if (and only if) for some integer m ≥ 0, R has exactly m+1 maximal ideals and there exists a finite maximal chain of proper unital ring extensions, ℛ0:=Fp ⊂ ... ⊂ ℛm=R, going from Fp to R, such that ℛm-1 is a commutative ring and R is a unital ℛm-1-algebra. Additional characterizations, applications, examples and remarks are given.
On some congruences for (j,k)-regular overpartitions
Authors: Mahadeva Naika Megadahalli Sidda Naika , Thippeswamy Harishkumar , Veeranayaka Terakanambi Nagarajanayaka
Published: September 2022

Let pj,k(n) denote the number of (j, k)-regular overpartitions of n in which none of the parts congruent to j (mod k). In this paper, we obtained infinitely many families of congruences modulo powers of 2 for p3,6(n), p5, 10(n) and p9, 18(n). For example, for all n ≥ 0 and α, β ≥ 0, p9, 18(34α+1 ∙ 52β+1(24 (5n+i)+23)) ≡ 0 (mod 64) where i=0, 1, 2, 4.
Properties of a subclass of harmonic mappings with restricted analytic part
Authors: Varma S.Sunil , Rosy Thomas
Published: September 2022

In this article, a new subclass of harmonic mappings with restricted analytic part is introduced. Coefficient bounds, Fekete-Szego inequality and integral representation for functions in this subclass are established. Further closure of this class under convex combination is proved. Finally we obtain an upper bound for the Bloch's constant for functions in this class.
Some remarks of analytic functions concerned with Jack's lemma
Authors: Örnek Bülent Nafi , Atli Gizem
Published: September 2022

In this paper, we give estimates of the Schwarz lemma in a novel class M(b) of analytical functions in the unit disc. The sharpness of some of the presented in equalities has also been shown.
Statistical convergence of sequences of subspaces
Authors: Nuray Fatih
Published: September 2022

In this study, we will give the deinition of statistical convergence of a sequences of subspaces of a k-dimensional inner product space and examine some inclusion relations.
Anti-invariant submanifolds of a normal paracontact metric manifold
Authors: Dirik Süleyman , Atceken Mehmet , Yildirim Ümit
Published: September 2022

In this paper, anti-invariant submanifolds of a normal paracontact metric manifold are studied and characterizing the submanifold with respect to covariant derivative of the second fundamental form of anti-invariant submanifold. Furthermore, some special cases are also discussed and we give a non-trivial example which satisfies the statements of theorems.
Continuity of the spectrum and Weyl type theorems for extension of 2-isometric operators
Authors: Prasad T , Mary Thampi Sandra
Published: September 2022

In this paper, we show that the spectrum, Weyl spectrum, and Browder spectrum are continuous on the set of all 2-quasi-2-isometric operators. Further, we show that k-quasi-2-isometric operator satisfies Bishop's property β. Moreover, we prove Weyl type theorems for f(dTS), where dTS denote the generalized derivation or the elementary operator with k-quasi-2-isometric operator entries T and S* and f ∈ H(σ(dTS)), the set of analytic functions which are defined on an open neighborhood of σ(dTS).
Geometric Brownian motion and a new approach to the spread of Covid-19 in Italy
Authors: Fabiano Nicola , Radenovic Stojan
Published: September 2022

Starting from the problem of the asymmetry of the curve, a new model is adoptedfor the spread of Covid-19. The pandemic waves are modelled from a geometric Brownian motion, leading to a lognormal distribution. The infection waves are described correctly by the model and the asymmetry problem is solved. The diffusion model of the geometric Brownian motion is able to reproduce correctly the first two Covid--19 waves, and possibly show signs of a starting third wave.
A note on time series differencing
Authors: Kamalov Firuz
Published: September 2022

Differencing is one of the key tools time series analysis. It is commonly used to obtain stationary time series. In this note, we show that the nth difference of a weakly stationary time series is weakly stationary. Similarly we prove that the nth difference of a strictly stationary time series is strictly stationary. We also consider the effect of differencing on the time series autocovariance.
Sequences related to the e number and Bernoulli numbers
Authors: Jakimczuk Rafael
Published: September 2022

We study some sequences related to the e number and the Bernoulli numbers.
Cohomology ring of the finite split metacyclic group
Authors: Hamraoui Hinda , Deblij Ahmed
Published: September 2022

Let G be the finite split metacyclic group of presentation G=. Huebschmann computed the integral cohomology ring of a large class of metacyclic groups using the mechanism of homological perturbation theory and determined the generators of the subring of even degree classes of any metacyclic group by means of the Chern classes of some of its representations. The purpose of this article is to investigate H∗(G; ℤ) by localization methods. It also aims to determine explicit representations of G whose Chern classes generate H∗(G; ℤ) by induction techniques.
The union of two graphs associated with the set of all non-zero annihilating ideals of a commutative ring
Authors: Visweswaran Subramanian , Patel Hiren
Published: September 2022

The rings considered in this article are commutative with identity which are not integral domains. Let R be a ring. Let A(R) denote the set of all annihilating ideals of R and let us denote A(R) \ {(0)} by A(R)∗. With R, in this article we associate an undirected graph denoted by G(R) whose vertex set is A(R)∗ and distinct vertices I and J are adjacent in G(R) if and only if either IJ ≠ (0) or I+J ∉ A(R). If R is reduced, then in Section 2, we prove that G(R) is connected and determine the diameter and radius of G(R). If R is not reduced, then in Section 3, we answer when G(R) is connected and determine the diameter and radius of G(R) when G(R) is connected.
Pseudo almost automorphic solutions to non autonomous third order differential equation with multiple deviating arguments
Authors: Amdouni Manel , Cherif Farouk
Published: September 2022

The pseudo almost automorphic solutions of non-autonomous third-order differential equation with multiple delays is investigated. By some sufficient conditions, we obtain the uniformly bounded of the solutions. Moreover, by Banach fixed point theorem we obtain the existence and uniqueness of the solutions. In addition, by suitable Laypunov functions, we give the globally exponential stability of the pseudo almost automorphic solutions. Finally, a numerical example is given to illustrate our results.
On a (k,mu)-paracontact manifold satisfying some conditions on the projective curvature tensor
Authors: Uygun Pakize , Atçeken Mehmet
Published: September 2022

In the present paper, we study the curvature tensors of (k,mu)-paracontact manifold satisfying the conditions P(ξ ,Y)Z=0, P(ξ ,Y)P=0, P(ξ ,Y)S =0 and (ξ,Y)R=0. According these cases, (k,μ)-paracontact manifolds have been characterized. We obtain the necessary and sufficient conditions of a (k,μ)-paracontact manifold to be η-Einsteins.
Fekete-Szego estimates and second Hankel determinant for a generalized subfamily of analytic functions defined by q-differential operator
Authors: Lasode Ayotunde , Opoola Timothy
Published: September 2022

In this paper, we considered a family of analytic and univalent functions having positive real parts in the unit disk and defined by a q-difference operator. The coefficients, the Fekete-Szego estimates and the second Hankel determinants were established for the family of functions. Our family of functions generalized some earlier known ones and by varying some parameters, our results also generalized some known ones.
Three-dimensional para-Kenmotsu manifolds admitting eta-Ricci solitons
Authors: Mondal Ashis
Published: September 2022

In the present paper we study η-Ricci solitons on three-dimensional para-Kenmotsu manifolds with the curvature condition R.Q=0. Also we study conformal flat, projectively flat and concircularly flat η-Ricci soliton on a three-dimensional para-Kenmotsu manifold. Finally, we construct an example of a three-dimensional para-Kenmotsu manifold which admits η-Ricci solitons.
Refinement of the upper bound of the radius of a circular integral points set
Authors: Undrakh Batzorig , Bat-Ochir Ganbileg
Published: September 2022

Let n be a product of the prime numbers whose positive integer powers are of the form a2+Db2 where D> 4 is a square-free number and a, b are positive integers. For n≤ 3072, we obtained a refinement of the upper bound of the radius of a circular points set which was previously given in Tables 1 and 2 of Ganbileg's paper. In order to prove this, we showed that there are points on the circle with the radius R=n √D/2D such that mutual distances between these points are all integers. Consequently, if n is a product of the prime numbers whose squares are of the form a2+Db2, then we showed that there are τ(n) points on the circle with the radius R=n √D/2D such that mutual distances between these points are all integer numbers, where τ(n) is the number of all positive divisors of n.
Abelian subgroup of O_4(Q) related to Ryser's conjecture
Authors: Gallardo Luis
Published: September 2022

We characterize the group generated by the 4 × 4 circulant Hadamard matrices divided by 2.
Existence and uniqueness of renormalized solutions to nonlinear multivalued parabolic problem with homogeneous Dirichlet boundary conditions involving variable exponent
Authors: Kyelem Bila Adolphe , Zongo Arouna Ouedraogo , Zongo Frederic
Published: September 2022

In this paper, we prove the existence and the uniqueness of renormalized solution to a nonlinear multivalued parabolic problem β(u)t - div a(x,∇ u) ∋ f , with homogeneous Dirichlet boundary conditions and L1-data. The functional setting involves Lebesgue and Sobolev spaces with variable exponent. Some a-priori estimates are used to obtain our results.
A collapsing sandpile problem with nonlocal boundary condition
Authors: Traore Urbain , Nassouri Estelle
Published: September 2022

In this work, we continue our study on the sandpile model proposed by Igbida. We are particularly interested in the study of avalanches that occur on the surface of a pile of sand following a drying out. The main novelty here is that we do a theoretical and numerical analysis in the case of local and non-local boundaries conditions. We also present some results of numerical simulations in 2D.
Common multiples of paths and stars with complete graphs
Authors: Thankachan Reji , Chandran Saritha
Published: September 2022

A graph G is a common multiple of two graphs H1 and H2 if there exists a decomposition of G into edge-disjoint copies of H1 and also a decomposition of G into edge-disjoint copies of H2. If G is a common multiple of H1 and H2 and G has q edges, then we call G a (q, H1, H2) graph. Our paper deals with the following question: ''Given two graphs H1 and H2, for which values of q does there exist a (q, H1, H2) graph?'' when H1 is either a path or a star with 3 or 4 edges and H2 is a complete graph.
Solution of fractional kinetic equation for Hadamard type fractional integral via Mellin transform
Authors: Ahmed Wagdi F. S. , Salamooni Ahmad Y. A. , Pawar Dnyaneshwar D.
Published: September 2022

The aim of this paper is to introduce the generalized form of the fractional kinetic equation including Hadamard type fractional integral. We also present the solution of Kinetic equation including Hadamard type fractional integral with the help of generalized k-Wright function and Mellin transform. We also present the solution of Kinetic equation including Hadamard type fractional integral with the help of generalized Multindex Bessel Function and Mellin transform.
Contact CR-submanifolds of trans-Sasakian manifolds with respect to quarter symmetric non-metric connection
Authors: Karmakar Payel , Arindam Bhattacharyya
Published: September 2022

The present paper deals with the study of contact CR-submanifolds of trans-Sasakian manifolds with respect to quarter symmetric non-metric connection. We investigate totally geodesic leaves and integrability of the distributions and also study the totally umbilical contact CR-submanifolds of trans-Sasakian manifolds. At last we give an example to verify a relation.
Hill restricted four-body problem with variable mass
Authors: A. Ansari Abdullah
Published: September 2022

The presentation of the paper consists the extended version of the Hill restricted three-body problem i.e. the Hill restricted four-body problem where the mass of the fourth smallest body is supposed to variable with time and also suppose that the other three massive bodies are remain fixed at the apices of an equilateral triangle. After shifting the origin and using the various transformations, we determine the equations of motion and quasi-Jacobi integral for this model. The properties like the equilibrium points and stability are performed analytically.
On minimal ring extensions of finite rings
Authors: Dobbs David
Published: September 2022

Two conditions, (i) and (ii), are defined, that may hold for a given (unital) ring extension R ⊂ S of (unital, associative, not necessarily commutative) finite rings. It is shown that if S is commutative, then ``"either (i) or (ii)” is a necessary and sufficient condition for R ⊂ S to be a minimal ring extension; and that for such extensions, (i) and (ii) are logically independent. For extensions with S (finite and) noncommutative, "either (i) or (ii)” is neither necessary nor sufficient for R ⊂ S to be a minimal ring extension; and for such minimal ring extensions, (i) and (ii) are logically independent. Next, let R ⊂ Sj be minimal ring extensions with Sj  (finite and) commutative (for j=1,2) and R local. Then: S1 and S2 are the same type (that is, ramified, decomposed or inert) of minimal extension of R ↔ |Z(S_1)|=|Z(S_2)| ↔ |U(S_1)|=|U(S_2)|.
On the equation Π_P Φ_3(P) = Π_P P^2 over F_2[x]
Authors: Gallardo Luis
Published: September 2022

We work a polynomial variant of an arithmetic problem solved by Steuerwald in 1937. More precisely, we prove, under a mild condition, that the equation on the title, has no solutions A := ΠP P2  ∈ F2[x], with irreducible P, and ω(A) < 16. Unconditionally, we prove that deg(P) ≥ 40. This improves on known results.
Maximum likelihood estimation in the generalized extreme value regression model for binary data
Authors: Fatimata Lo , Ba Demba Bocar , Aba Diop
Published: September 2022

Generalized extreme value regression model is widely used when the dependent variable Y represents a rare event. The quantile function of the GEV distribution is used as link function to investigate the relationship between the binary outcome Y and a set of potential predictors X. In this article we develop a maximum likelihood estimation procedure int he generalized extreme value regression model. We establish the asymptotic properties (existence, consistency and asymptotic normality) of the proposed maximum likelihood estimator.
The common fixed points in a bipolar metric space
Authors: Murthy Penumarthy Parvateesam , Mitrovic Zoran , Dhuri Chandra Prakash , Radenovic Stojan
Published: September 2022

The purpose of this paper is to obtain a new fixed point theorem in the bipolar metric spaces. The contraction used in our theorem is the extension of Boyd-Wong-type contraction in bipolar metric spaces.
Exact Solutions of non-Newtonian Fluid of Rotating MHD Flows Through Porous Media with Hall Effect by Complex Variable Technique
Authors: Prajapati Mantu , Kumar Manoj , Sil Sayantan
Published: September 2022

In this paper steady, two dimensional, incompressible, electrically conducting, MHD fluid through porous media in a rotating reference frame with Hall effect under the presence of magnetic field is considered. The magnetic field is applied along the z-axis. Using complex variable technique the governing equations are recast in solvable form. Exact solutions are obtained for straight parallel flows.
Rationalization of Toeplitz-Hankel operators
Authors: Verma Ruchika
Published: September 2022

In this paper, we introduce and study the rationalization of all kinds of Toeplitz and Hankel operators on the space L2(T), T being the unit circle.
Explicit representations of some generalized and mixed relatives of the Bessel functions
Authors: Qureshi Mohammad Idris , Ali Mahvish
Published: September 2022

Special functions can be defined in different ways such as Rodrigue's formulae, generating functions, summation formulae, integral representations et cetera, but it is usually shown to be expressible as a series, because this is frequently the most practical way to obtain numerical values for the functions. In this paper, the explicit representations of certain mixed special functions related to the Bessel functions are obtained. A Laurent type hypergeometric generating relation is derived using series rearrangement technique. Some special cases are obtained as generating function of the known mixed type relatives of the Bessel functions. Finally explicit forms of these mixed type special functions are obtained as applications.
On the extended graph associated with the set of all non-zero annihilating ideals of a commutative ring
Authors: Patel Hiren D.
Published: September 2022

Let Rbe a commutative ring with non-zero identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r∈R\{0} such that Ir=(0). Let A(R) denote the set of all annihilating ideals of R and A (R)*=A(R)\{0}. In this article, we introduce a new graph associated with R denoted by H(R) whose vertex set is A(R)* and two distinct vertices I, J are adjacent in this graph if and only if IJ=(0) or I+J ∈ A(R). The aim of this article is to study the interplay between the ring-theoretic properties of a ring R and the graph-theoretic properties of H(R). For such a ring R, we prove that H(R) is connected and find its diameter. Moreover, we determine girth of H(R). Furthermore, we provide some sufficient conditions under which H(R) is a complete graph.
Some observations on numbers in short intervals
Authors: Jakimczuk Rafael
Published: September 2022

We obtain some results about the primes and the prime factorizations of the positive integers in the interval (x, x+xθ], where 0<θ<1. We also obtain some results about the primes and the prime factorizations of the positive integers in the interval (x, x+f(x)], where f(x) is a function of slow increase. For instance, f(x)=logαx, where α>0.
Some results about weakly S-primary ideals of a commutative ring
Authors: Massaoud Essebti , Gouaid Badreddine
Published: September 2022

Let R be a commutative ring with identity and S ⊊ R a multiplicative subset. We define a proper ideal P of R disjoint from S to be weakly S-primary if there exists an s ∈ S such that for all a, b ∈ R if 0≠ ab ∈ P then sa ∈ P or sb ∈ √P. We show that weakly S-primary ideals enjoy analogs of many properties of weakly primary ideals and we study the form of weakly S-primary ideals of the amalgamation of A with B along an ideal J with respect to f (denoted by A ⋈fJ). Weakly S-primary ideals of the trivial ring extension are also characterized.
Invariance of convex sets: An alternative proof and application to Black-Scholes operator
Authors: Hilmi Chakir , Sani Ahmed , Elmourchid Samir
Published: September 2022

An alternative proof of invariance of convex sets by the solution of non autonomous Cauchy problem is given. The proof is based on the recent integral approximation of time dependent operators A(t) acting on Hilbert space when they are associated with smooth sesquilinear forms a(t,.,.) defined on common dense domain and the known Chernoff Product Formula. An application to positivity of Black-Scholes operator is given.
Existence and uniqueness of renormalized solution to multivalued homogeneous Neumann problem with L1-data
Authors: Ouedraogo Arouna , Valea Tiyamba
Published: September 2022

In this paper, we discuss the existence and uniqueness of renormalized solution to nonlinear multivalued elliptic problem  β(u)-div a(x, Du) ∈ f with homogeneous Neumann boundary conditions and L1 -data. The functional setting involves Lebesgue and Sobolev spaces with variable exponent. Some a-priori estimates are used to obtain our results.
Weighted parametric divergence models for discrete probability distributions
Authors: Sarangal Mukesh , Parkash Om
Published: September 2022

In the literature of information measures, it is well acknowledged phenomenon that distance models in probability spaces discover incredible applications in a diversity of disciplines related with science and technology. The significance of these models after attaching weights to the occurring events cannot be disregarded. The present communication is a footstep in the construction of such divergence models. We have developed two new weighted parametric divergence models for the discrete probability distributions and proved their legitimacy after studying their indispensable properties.
Certain cubic reduction formulas involving hypergeometric functions
Authors: Malik Shakir Hussain , Qureshi Mohammad Idris
Published: September 2022

In this paper, we obtain a new general double infinite series identity (in terms of the sum of three infinite series) involving the bounded sequence of arbitrary complex numbers using Saalschutz summation theorem for terminating Clausen series. As application of our double series identity, we establish two cubic reduction formulas for Srivastava-Daoust double hypergeometric functions in terms of generalized hypergeometric function with suitable convergence conditions. By the theory of analytic continuation, our cubic reduction formula is also valid in -211/25≤R(z)≤3/4 when F(z)=0, using Mathematica software.
On almost ∗-Ricci soliton
Authors: Kundu Satyabrota , Halder S. , De K.
Published: September 2022

Abstract. In the present paper, we prove three fundamental results concerning almost ∗-Ricci soliton in the framework of para-Sasakian manifold. The paper is organised as follows:• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is Jacobi along Reeb vector field ξ, then g becomes a ∗-Ricci soliton.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V as infinitesimal paracontact transformation, then V is killing and g is η-Einstein.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is collinear with the Reeb vector field ξ, then λ = 0, V is strict and g is η-Einstein.
Domination and dominator coloring of neighborhood corona of certain graphs
Authors: Krishnamurthy K. Sathish Kumar , David N. Gnanamalar , Subramanian K.G.
Published: September 2022

A dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph dominates every vertex of some color class. The dominator chromatic number of G is the minimum number of color classes in a dominator coloring of G. When operation on graphs is performed on classes of graphs result from the new class of graphs are obtained. The neighborhood corona is one such operation on graphs, having interesting applications as well. In this paper we study this operation on certain graph classes and discuss the bounds in terms of domination number and dominator chromatic number.
Some curvature characterizations on Kenmotsu metric spaces
Authors: Uygun Pakize , Dirik Suleyman , Atceken Mehmet
Published: September 2022

The purpose of this study is to characterize Kenmotsu manifolds that satisfy specific curvature conditions. We give the Kenmotsu manifold curvature tensors satisfying the conditions RW5 = 0, RW7 = 0, RW9 = 0 and φ-RW0* = 0. Also we consider a W0*-flat and a φ-W0*-flat Kenmotsu metric manifolds. As a result, M is an η-Einstein Kenmotsu metric manifold.
Special case of Fermat's Theorem
Authors: Gallardo Luis
Published: September 2022

We prove under a mild condition that the only rationals x, y with x ≥ 0, y≥ 0 and x+y=N(k), for some k ∈ Q*, and xp+yp=1 are x=0, y=1 and x=1, y=0. Here, we let N denote the norm from Q(ωp) to Q for p an odd prime number.
The logarithm of the least prime factor
Authors: Jakimczuk Rafael
Published: September 2022

Let p(n) be the least prime factor of the positive integer n. In this note we prove the equation ∑i-2n log p(i) = o(n log n).
Global attractivity and existence of weighted pseudo almost automorphic solution for GHNNS with delays and variable coefficients
Authors: Cherif F. , Nahia Z. Ben
Published: September 2022

In this paper, we shall explain a new result concerning weighted pseudo almost automorphic solutions of Hopfield neural network with time-varying delay and variable coefficients. Precisely, we shall prove existence and the global attractivity of the unique weighted pseudo almost automorphic solution of the considered model. Then, by employing suitable analytic techniques, global attractivity of the unique weighted pseudo almost automorphic solution is established. Lastly, an example is provided to demonstrate the validity of the results proposed.
A note on some recent best proximity point results for non-self mappings
Authors: Kadelburg Zoran , Radenovic Stojan
Published: September 2022

In this note, we show how an easy lemma, proved recently by Abkar and Gabeleh, can be applied to obtain Geraghty-type results for best proximity points. In particular, we obtain improvements of some recent best proximity point results and show by an example that these improvements are proper.
On a half-discrete reverse Hilbert-type inequality
Authors: Yang Bicheng
Published: September 2022

By using the weight functions and the techniques of real analysis, a half-discrete reverse Hilbert-type inequality with the best constant factor is given. A best extension with a parameter λ and the equivalent forms are also considered.
Fixed point results to tvs-cone b-metric spaces
Authors: Popovic Branislav , Radenovic Stojan , Shukla Satish
Published: September 2022

In this paper we introduce the concept of tvs-cone b-metric space over solid cone. Our results improve, generalize, extend, unify, enrich and complement recent fixed point results established by H. Huang and S. Xu, M. P. Stanic et al., A. S. Cvetkovic et. al. and M. H. Shah et al. The examples are given to illustrate the usability of our results.
A common fixed point result for (mu, psi)-weakly contractive mappings
Authors: Chandok Sumit
Published: September 2022

A common fixed point result satisfying a (μ ψ)-weak contract condition for single-valued mappings in the framework of metric spaces is derived. The results presented in the paper generalize and extend several well-known results in the literature.
On some projectively flat (alpha, beta)-metrics
Authors: Yadav Ravindra , Shanker Gauree
Published: September 2022

The (α β)-metric is a Finsler metric which is constructed from a Riemannian metric α and a differential 1-form β. We consider the projective flatness of Finsler spaces with some (α, β)-metrics. The purpose of the present paper is to find the conditions for a Finsler space with L = (α2 ∕ (α - β)) + β and L = α + (βn+1 ∕ αn).
On generalized weakly GP-contractive mappings in ordered GP-metric spaces
Authors: Parvaneh Vahid , Roshan Jamal Rezaei , Kadelburg Zoran
Published: September 2022

The aim of this paper is to present some fixed and common fixed point results for generalized weakly G-contractive mappings in the context of ordered GP-metric spaces. We also provide examples to illustrate the results presented herein. As an application of our results, periodic points of weakly G-contractive mappings are obtained.
Matrix equations with diagonalizable coefficients
Authors: Gil Michael
Published: September 2022

Let A and A' be diagonalizable matrices. The paper deals with the equation
∑j=0m1 ∑k=0m2 cjk AjX(A')k = M
where X should be found, cjk are numbers and M is a given matrix. A solution of this equation is represented as a function of two non-commuting matrices. We establish a norm estimate for a function of A and A' defined on their spectra. That estimate gives us a norm estimate for X. In addition, we suggest a new bound for the similarity condition number of a diagonalizable matrix.
Amalgamated algebra extensions defined by von Neumann regular and SFT conditions
Authors: Mahdou Najib , Louartiti Khalid
Published: September 2022

Let f: A → B be a ring homomorphism and let J be an ideal of B. In this paper, we characterize R ⋈f J to be both von Neumann regular ring and an SFT ring. Our results generate new and original examples which enrich the current literature with new families of von Neumann regular rings and SFT rings.
Gonality of curves and extensions of the base field
Authors: Ballico Eduardo
Published: September 2022

Let K be a perfect field and C a geometrically connected smooth curve of genus g ≥ 2 defined over K. Here we gives some upper bounds for the K-gonality γK(C) of C in terms of the gonality d of CK. In some cases, this is obtained giving an upper bound for g, sometimes g ≤ (5d2 ∕ 8) + 1, sometimes g ≤ (d-2)2 ∕ 2.
Transfer of Prufer-like conditions
Authors: Bakkari Chahrazade
Published: September 2022

This paper deals with five extensions of the Prufer domain concept to commutative rings with zero divisors. We investigate the stability of these Prufer-like conditions under localization and homomorphic image. Our results generate new and original examples of Prufer-like rings.
On Galois matrix rings of a ring
Authors: Szeto George , Jiang Xiaolong
Published: September 2022

Let R be a ring with 1, Mn(R) the ring of n × n-matrices over R for an integer n, and G an inner automorphism group of Mn(R) of order n2 induced by {Ui ∈ Mn(R), i = 1, ... , n2}. Then the Galois matrix ring Mn(R) over R with inner Galois group G is characterized in terms of {Ui} and the trace of G.
A systematic ladder-operator approach to orthogonal polynomials
Authors: Robin William
Published: September 2022

An elementary and systematic approach to the problem of factorizing classes of second-order linear homogeneous equations, with corresponding classes of orthogonal polynomials as their solutions, is developed. The factorized formats lead to ladder-operator representations of the solution of each class of second-order linear homogeneous equation and present a different (more straightforward and explicit) resolution of the mathematical problem leading to the factorization approach of, in particular, Jafarizadeh and Fakhri [3, 4]. The main solution process involves solving coupled Riccati equations along with a third `consistency' equation directly, to find, without further assumption, all of the components of each factorization representation. As a bonus, one of the assumptions of the original Jafarizadeh and Fakhri approach is eliminated. In some cases, a basic technique of Cotfas [1, 2] is also invoked to produce simplified derivations. The main results are presented in tabular form and a brief discussion of previous/other approaches given.
Best L_p-approximation of analytic functions and generalized (alpha, alpha)-growth
Authors: Kumar Devendra , Harfaoui Mohammed
Published: September 2022

The aim of this paper is the characterization of the generalized order and generalized type of analytic functions of several complex variables in the open set
ΩR = {z ∈ ℂn; exp VE(z) < R }
in terms of the best polynomial approximation on a compact set E in Lp-norm and the coefficients of the development with respect to the extremal polynomial according to the set
Ωr = {z ∈ ℂn; exp VE(z) ≤ r}, 1 < r < R,
where
VE = sup { (1 ∕ d) ln | Pd|, Pd a polynomial of degree ≤ d, |Pd|E ≤ 1}
is the Siciak extremal function of a L-regular compact E which defined the pluri-complex Green function with a pole at infinity.
Fuzzy H-weak contractions and fixed point theorems in fuzzy metric spaces
Authors: Shukla Satish
Published: September 2022

The purpose of this paper is to introduce the notion of a fuzzy ℋ-weak contraction and prove a fixed point theorem for fuzzy ℋ-weak contractions without exploiting the notion of continuity in M-complete fuzzy metric spaces. Examples are given to show that our result is a proper extension of some known results in the literature.
Submanifolds of some indefinite contact and paracontact manifolds
Authors: Bhattacharyya Arindam , Laha Barnali , Das Bandana
Published: September 2022

The purpose of the present paper is to study some types of submanifolds of indefinite contact and paracontact manifolds and a few properties of contact CR-submanifolds of an indefinite Sasakian manifold, indefinite Kenmotsu manifold, indefinite trans-Sasakian manifold and ε-paracontact Sasakian manifold.
A simple proof that the square-free numbers have density 6/(pi^2)
Authors: Jakimczuk Rafael
Published: September 2022

In this note we give a simple proof of the well-known result that the square-free numbers have density 6 ∕ π2.
On a new fractional complex system
Authors: Ibrahim Rabha W.
Published: September 2022

In this work, we suggest a new fractional complex system (three and five equations) of type Newton-Leipnik systems. The fractional calculus are taken in sense of the Caputo derivatives. The stability and stabilization of such a system are studied. The technique based on stability theory of fractional-order systems. Numerical solutions are imposed. Moreover, conditions of unique solution are illustrated.
Jordan higher derivations revisited
Authors: Xiao Zhankui , Xu Shafeng
Published: September 2022

In this note, we consider the question of when a Jordan higher derivation of an arbitrary ring degenerates to a higher derivation. Furthermore, several applications to specific rings or algebras are presented.
Matched pairs in abelian groupoids
Authors: Amini Massoud , Myrnouri Hassan
Published: September 2022

We use a canonical matched pair in an abelian groupoid to decompose it as a semidirect product. We use this decomposition to study the corresponding full C∗-algebra.
Rough convergence of double sequences
Authors: Dundar Erdinc , Cakan Celal
Published: September 2022

In this paper, we introduce the notion of rough convergence and the set of rough limit points of a double sequence and obtained two rough convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of cluster points and the set of rough limit points of a double sequence.
Numbers with n different prime factors in their prime factorization
Authors: Jakimczuk Rafael
Published: September 2022

In this note we give a simple proof of the well-known result that the numbers with a fixed number of different prime factors in their prime factorization have density zero.
Growth rates of Wronskians generated by complex valued functions
Authors: Datta Sanjib Kumar , Biswas Tanmay , Ali Sultan
Published: September 2022

In the paper we establish some new results depending on the comparative growth properties of composite entire or meromorphic functions using generalized L∗-order of Wronskians generated by one of the factors.
Prolate spheroidal wavelets and multidimensional chromatic series expansions
Authors: Kumar Devendra
Published: September 2022

Chromatic series were originally introduced for bandlimited functions. The nth chromatic derivative of an analytic function is a linear combination of kth ordinary derivatives with 0 ≤ k ≤ n, where the coefficients of linear combination are based on a suitable system of orthogonal polynomials. Chromatic derivative and series expansions of bandlimited functions have been used as a replacement for Taylor's series and they have been shown to be more useful in practical signal processing applications than Taylor series. In this paper we have shown that the theory can be extended to prolate spheroidal wavelet series that than combine chromatic series with sampling series in higher dimensions. The multidimensional case has much reacher structure than in the univariate case and will find more applications in image processing and analysis.
Approximate fixed point theorems in generalized metric spaces
Authors: George Sherly , Pulickakunnel Shalini
Published: September 2022

In this paper, we prove approximate fixed point theorems for various types of contraction mappings in the framework of generalized metric spaces by introducing the concept of T-asymptotically regular mapping. Our results in this paper extends and improves upon, among others, the corresponding results of Berinde and Prasad et al.
New sharp Jordan type inequalities and their applications
Authors: Yang Zhen-Hang
Published: September 2022

In this paper, we prove that for x ∈ (0, π ∕ 2)
(cos p0 x)1 ∕ p0 < (sin x ∕ x) < (cos (x ∕ 3 ))3
with the best constants p0 ≈ 0.34731 and 1 ∕ 3. Moreover, for x ∈ (0, c) ⊆ (0, π ∕ 2) the double inequality
βp (c)(cos px)1 ∕ p < (sin x ∕ x) < (cos px)1 ∕ p
holds if p ∈ (0, 1 ∕ 3], where βp (c) = c-1 (cos pc)-1 ∕ p and 1 are the best possible. Its reverse one holds if p ∈ [1∕ 2, 1). As applications, some precise estimates for sine integral and Catalan constant are given.
Existence and exponential stability of Stepanov-like almost automorphic mild solutions for semilinear evolution equations
Authors: Cao Junfei , Huang Xianyong , Tong Qian
Published: September 2022

This work is concerned with the existence and exponential stability of Stepanov-like almost automorphic mild solutions for the following semilinear evolution equations
x'(t) = Ax(t) + F(t, x(t)),     t ∈ ℝ,
where A is the infinitesimal generator of a C0-semigroup of bounded linear operator on a Banach space X and F: ℝ × X → X is a Stepanov-like almost automorphic function in t uniformly with respect to the second argument x. By applying the Banach contraction mapping principle (when F satisfies Lipschitz type conditions), and the Schauder's fixed point theorem (when F does not necessarily satisfy Lipschitz type conditions), we obtain the existence and exponential stability of Stepanov-like almost automorphic mild solutions for the semilinear evolution equations. Moreover, as application, two examples are given to illustrate our abstract results.
Presic-Maia type theorems in ordered metric spaces
Authors: Shukla Satish , Radenovic Stojan
Published: September 2022

The purpose of this paper is to prove some fixed point theorems in ordered metric spaces with two comparable metrics. Our results generalize and unify the fixed point theorems of Presic, Maia and some recent results from ordered metric spaces, into product spaces when underlying space is ordered. An iterative method for constructing the fixed points is also provided.
Identity on theta-centralizers in semiprime rings
Authors: Muthana Najat Mohammed
Published: September 2022

Let m and n be fixed integers with m ≥ 1, n ≥ 1 and let R be a (m + n +2)!-torsion free semiprime ring with the identity element suppose there exists an additive mapping T: R → R such that T(xm+n+1) = θ(xm) T(x) θ(xn) holds for all x ∈ R where θ is an automorphisms of R. In this case T is a centralizer.
Covering cover pebbling number for square of a path
Authors: Lourdusamy A. , Mathivanan T.
Published: September 2022

Let G be a connected graph. Let p be the number of pebbles distributed on the vertices of G. A pebbling move is defined by removing two pebbles from one vertex and put a pebble on an adjacent vertex. The covering cover pebbling number, σ(G), is the least p such that after a sequence of pebbling moves, the set of vertices should form a covering for G from every configuration of p pebbles on the vertices of G. In this paper, we determine the covering cover pebbling number for square of a path.
Some properties on certain new subclasses of analytic functions
Authors: Feng Jianzhong , Li Xiaofei
Published: September 2022

In this article, we define two new subclasses of univalent and analytic functions in the open disc U = {z : |z| < 1}. For functions belonging to these classes, we determine coefficient inequalities, inclusion relation and convolution property.
On the fine spectrum of generalized third order difference operator Delta_{vuw} on the Banach space c_0
Authors: Vandanjav Adiyasuren , Undrakh Batzorig
Published: September 2022

In this paper we examine the fine spectrum of Δvuw operator in Banach space c0.
Third Hankel determinant for alpha-starlike functions
Authors: Shanmugam G. , Stephen B. Adolf , Babalola K. O.
Published: September 2022

In this paper we investigate the third Hankel determinant, H3(1), for normalized univalent functions f(z) = z + a2 z2 + ... belonging to the class of α-starlike functions denoted by Mα. This class includes two important subclasses of the family of univalent functions - starlike and convex functions denoted by S∗ and C. Our results therefore includes the special cases of the third Hankel determinants for the two classes of functions.
Postulation in project spaces of a union of a low dimensional scheme and general rational curves or general unions of lines
Authors: Ballico Eduardo
Published: September 2022

Let Y ⊂ ℙr, r ≥ 3, be a scheme with dim(Y) ≤ r - 2. We prove the existence of an integer d0 such that for all d ≥ d0 a general union X of Y and either a general degree d rational curve or (if r ≠ 3) d lines has maximal rank, i.e. for each t ∈ ℕ X gives the expected number of conditions to the set of all degree t hypersurfaces of ℙr. We also consider unions of Y and a general curve with a prescribed genus and high degree.
Construction of semi-free S^3 actions on homotopy sphere with untwisted fixed point set
Authors: Kaddoura Issam
Published: September 2022

In his paper "Surgery and the theory of differentiable transformation groups", William Browder developed surgery techniques to study semi-free actions of S1 on homotopy spheres, under the additional assumption that the fixed point set is a homotopy sphere. He used this surgery to show how to construct such actions. In this paper, I discuss a similar theory about semi-free actions of S3 on homotopy spheres. An open problem is raised at the end of the paper.
On Galois matrix extensions of high order
Authors: Szeto George , Jiang Xiaolong
Published: September 2022

Let R be a commutative ring with 1 and A a central R-Galois algebra with an inner Galois group G of order n for some integer n. Let Mm(R) be the ring of m × m-matrices over R for an integer m. Then Mm(R) is also a central Galois R-algebra with an inner Galois group for each m = n(2i) where i is a non-negative integer. In particular, 2 is invertible in R if and only if Mm(R) is a central Galois R-algebra with an inner Galois group for each m = 2(2i) where i is a non-negative integer.
On modulus of noncompact convexity for a strictly minimalizable measure of noncompactness
Authors: Rekic-Vukovic Amra , Okicic Nermin , Arandjelovic Ivan
Published: September 2022

In this paper we consider modulus of noncompact convexity ΔX,φ associated with the strictly minimalizable measure of noncompactness φ. We also give some its properties and show its continuity on the interval [0, φ(BX)).
On a certain class of harmonic univalent functions defined by fractional calculus
Authors: Porwal Saurabh , Kanaujia Alka
Published: September 2022

The purpose of the present paper is to study a new subclass of harmonic univalent functions by using fractional calculus operator. We obtain coefficient conditions, extreme points, distortion bounds and radius of convexity for this class. We also show that the class studied in this paper is closed under convolution and convex combination and discuss a class preserving integral operator. The results obtained for this class reduce to the corresponding results for several known classes in the literature are briefly indicated.
The uniqueness of coupled fixed point for weakly C-contractive mappings in partial metric spaces
Authors: Alsulami Saud M.
Published: September 2022

We extend the concept of weakly C contractive mappings to the context of partial metric spaces. Also, we prove that every weakly C-contractive mapping in partial metric space has a unique coupled fixed point. Our result generalizes several well-known existing results in the literature.
Hilbert space frames, Riesz bases and tensor sums
Authors: Panayappan S.
Published: September 2022

In this article we study Riesz bases and frames using tensor sum of linear operators on Hilbert spaces. Moreover, we develope a theory for Riesz bases in tensor product of Hilbert spaces and discuss their properties.
Postulations in projective spaces of unions of a fixed schemes and several high degree general curves
Authors: Ballico Eduardo
Published: September 2022

Fix a subscheme Z ⊂ ℙr, r ≥ 5, with dim(Z) ≤ r - 5 and an integer g ≥ 0. We prove the existence of an integer Δ (depending only on r, g and the Hilbert polynomial of Z) with the following property. Fix positive integers c > 0, di > 0, 0 ≤ gi ≤ g, 1 ≤ i ≤ c, with ∑i di ≥ Δ; if gi > 0, then assume, say, di ≥ r + rgi ∕ 2. Let X ⊂ ℙr be a general union of c disjoint curves X1, ... , Xc with deg(Xi) = di and pa(Xi) = gi. Then Z ∪ X has maximal rank, i.e. its Hilbert function is the expected one.
On the numerical solution of fractional-order Fredholm-Volterra integro-differential and multi-fractional order integro-differential equations
Authors: Nasiri Tayebeh , Aminataei Azim
Published: September 2022

In this work, we have applied the homotopy perturbation method (HPM) and variational iteration method (VIM) for solving fractional Fredholm and Volterra integrodifferential equation. Further, we have shown that multi-fractional order integrodifferential equation is a special case of fractional Fredholm and Volterra integrodifferential equation. For this, the fractional derivatives are described in the Caputo sense. Some numerical experiments are solved by using the aforesaid methods wherein the high accuracy and efficiency of both methods are observed.
Gorenstein X-Flat dimension and Tate homology
Authors: Selvaraj C. , Umamaheswaran A.
Published: September 2022

In this paper, we study a Gorenstein X-flat dimension and investigate Tate homology Xtor of modules of finite Gorenstein X-flat dimension. We prove that if R is a right GXF-closed ring and M a R-module admitting a Tate X-flat resolution, and if N is a left R-module admitting a Tate X-flat resolution TN, then for any i ∈ ℤ, XtoriR (M, N) ≅ Hi(M ⊗R TN).
Sinclair's Theorem for spectrally bounded Jordan higher derivations
Authors: Hosseini Amin
Published: September 2022

In this article, we prove Sinclair's Theorem for spectrally bounded Jordan higher derivations on Banach algebras. Furthermore, it is proved that the image of a higher derivation , under certain conditions, is contained in the Jacobson radical.
Topological duals and Kothe Toeplitz duals of some double sequence spaces defined by a modulus function
Authors: Kilinc G.
Published: September 2022

In the present paper, topological duals and Kothe-Toeplitz Duals of some double sequence spaces defined by a modulus function are studied. Also, we investigate perfectness, normality and monotonicity of some vector valued modulus sequences.
Fuzzy bi-ideals and fuzzy quasi-ideals in ordered semirings
Authors: Mandal Debabrata
Published: September 2022

The notions of fuzzy bi-ideals and fuzzy quasi-ideals in ordered semirings are introduced and some of their characterizations are obtained through regularity criterion.