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Proceedings – Mathematical Sciences

• BIJAN KUMAR PATEL PRASANTA KUMAR RAY MANASI K SAHUKAR

• FAHIMEH KHOSH-AHANG SOMAYEH MORADI

• He Xin

Abstract

We prove that the projectivization of the tangent bundle of a nonsingular toric variety is Frobenius split.

• AMIT SAMANTA SANTANU SARKAR

• A K AGARWAL MEGHA GOYAL

• XIAOJUAN DUAN

Abstract

In this paper, we explicitly construct some rotationally symmetricextremal (pseudo-)KÄahler metrics of non-constant scalar curvature, which de-pend on some parameters, on some line bundles over projective spaces. We alsodiscuss the phase change phenomenon caused by the variation of parameters.

• Alternating groups as a quotient of $PSL(2, \mathbb{Z}[i])$

Qaiser Mushtaq Awais Yousaf

Abstract

In this study, we developed an algorithm to find the homomorphisms of the Picard group 𝑃𝑆𝐿(2,𝑍[𝑖]) into a finite group 𝐺. This algorithm is helpful to find a homomorphism (if it is possible) of the Picard group to any finite group of order less than 15! because of the limitations of the Gap and computer memory. Therefore, we obtain only five alternating groups 𝐴𝑛, where 𝑛 = 5, 6, 9, 13 and 14 as a quotient of Picard group. In order to extend the degree of the alternating groups, we use coset diagrams as a tool . In the end, we prove our main result with the help of three diagrams which are used as building blocks and proved that, for 𝑛 ≡ 1; 5; 6(mod 8), all but finitely many alternating groups An can be obtained as the quotients of the Picard group 𝑃𝑆𝐿(2,𝑍[𝑖]). A code in Groups Algorithms Programming (GAP) is developed to perform the calculation.

• Global Weighted Estimates for Second-Order Nondivergence Elliptic and Parabolic Equations

Fengping Yao

Abstract

In this paper we obtain the global weighted 𝐿𝑝 estimates for second-order nondivergence elliptic and parabolic equations with small BMO coefficients in the whole space. As a corollary we obtain 𝐿𝑝-type regularity estimates for such equations.

• SAYANI BERA KAUSHAL VERMA

Abstract

The goal of this article is two fold. First, using transcendental shift{like automorphisms of Ck; k \geq 3 we construct two examples of non{degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck; k \geq 3 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of Dixon{Esterle in C2: The second example shows the existence of a Fatou{Bieberbach domain in Ck; k\geq3 that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and Rosay{Rudin. In the second part we compute the order and type of entire mappings that parametrize one dimensional unstable manifolds for shift{like polynomial automorphisms and show how they can be used to prove a Yoccoz type inequality for this class of automorphisms.

• M AFKHAMI A ERFANIAN K KHASHYARMANESH N VAEZ MOOSAVI

Abstract

Let R be a commutative ring with a nonzero identity element. For a natural number n, we associate a simple graph, denoted by \gamma^n_R, with R^n\{0}as the vertex set and two distinct vertices X and Y in Rn being adjacent if andonly if there exists an n \times n lower triangular matrix A over R whose entrieson the main diagonal are nonzero and one of the entries on the main diagonalis regular such that X^T AY = 0 or Y^T AX = 0, where, for a matrix B, B^T isthe matrix transpose of B. If n = 1, then \gamma^n_R is isomorphic to the zero divisor graph \gamma(R), and so \gamma^n_R is a generalization of \gamma(R) which is called a generalized zero divisor graph of R. In this paper, we study some basic properties of \gamma^n_R. We also determine all isomorphic classes of finite commutative rings whose generalized zero divisor graphs have genus at most three.

• M H Heydari M R Hooshmandasl C Cattani

Abstract

In this paper, an efficient and accurate computational method based on the Chebyshev wavelets (CWs) together with spectral Galerkin method is proposed for solving a class of nonlinear multi-order fractional differential equations (NMFDEs). To do this, a new operational matrix of fractional order integration in the Riemann-Liouville sense for the CWs is derived. Hat functions (HFs) and the collocation method are employed to derive a general procedure for forming this matrix. By using the CWs and their operational matrix of fractional order integration and Galerkin method, the problems under consideration are transformed into corresponding nonlinear systems of algebraic equations, which can be simply solved. Moreover, a new technique for computing nonlinear terms in such problems is presented. Convergence of the CWs expansion in one dimension is investigated. Furthermore, the efficiency and accuracy of the proposed method are shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As a useful application, the proposed method is applied to obtain an approximate solution for the fractional order Van der Pol oscillator (VPO) equation.

• Cross-product of bessel functions: monotonicity patterns and functional inequalities

Árpád Baricz Saminathan Ponnusamy Sanjeev Singh

Abstract

In this paper we study the Dini functions and the cross-product of Bessel functions. Moreover, we are interested on the monotonicity patterns for the cross-product of Bessel and modified Bessel functions. In addition, we deduce Redheffer-type inequalities, and the interlacing property of the zeros of Dini functions and the cross-product of Bessel and modified Bessel functions. Bounds for logarithmic derivatives of these functions are also derived. The key tools in our proofs are some recently developed infinite product representations for Dini functions and cross-product of Bessel functions.

• Positive solutions with single and multi-peak for semilinear elliptic equations with nonlinear boundary condition in the half-space

Li Wang Peihao Zhao

Abstract

We consider the existence of single and multi-peak solutions of the following nonlinear elliptic Neumann problem

$\begin{cases} - \Delta u + \lambda^2 u= Q (x) |u|^{p-2}u & ~\text{in}\quad \mathbb{R}_+^N,\\ \hspace{1.7cm}\frac{\partial u}{\partial n} = f(x, u) & ~\text{on}\quad \partial \mathbb{R}_+^N \end{cases}$

where $\lambda$ is a large number, $p \in \left(2, \frac{2N}{N-2} \right)$ for $N \geq 3, f(x, u)$ is subcritical about $u$ and $Q$ is positive and has some non-degenerate critical points in $\mathbb{R}^{N}_{+}$ . For $\lambda$ large, we can get solutions which have peaks near the non-degenerate critical points of $Q$.

• INDIRA MISHRA MADHUKANT SHARMA

Abstract

In this paper, we establish the approximate controllability results for a non-autonomous functional differential equation using the theory of linearevolution system, Schauder fixed point theorem, and by making use of resolventoperators. The obtained results in the paper, improve the existing ones in thisdirection, up to the considerable extent. An example is also given to illustratethe abstract results

• M AFKHAMI K HAMIDIZADEH K KHASHYARMANESH

Abstract

Let R be a commutative ring with nonzero identity, L_n(R) be the set of all lower triangular n \times n matrices, and U be a triangular subset of R_n i.e. the product of any lower triangular matrix with the transpose of any element of U, belongs to U. The graph GT^n_U (R^n) is a simple graph whose vertices consists of all elements of R^n, and two distinct vertices (x_1; : : : ; x_n) and(y1; : : : ; y_n) are adjacent if and only if (x1 + y1; : : : ; x_n + y_n) \in U. The graph GT^n_U (Rn) is a generalization for total graphs. In this paper, we investigate the basic properties of GT^n_U (Rn). Moreover, we study the planarity of the graphs GT^n_U (U), GT^n_U (Rn\ U) and GT^n_U (R^n).

• MOHAMMAD ASHRAF VINCENZO DE FILIPPIS

Abstract

Let R be a prime ring, Z(R) its center, C its extended centroid,L a Lie ideal of R, F a generalized skew derivation associated with a skewderivation d and automorphism α. Assume that there exist t ≥ 1 and m, n ≥ 0fixed integers such that vu = umF(uv)tun for all u, v 2 L. Then it is shownthat either L is central or char(R) = 2, R ⊆M2(C), the ring of 2×2 matricesover C, L is commutative and u2 2 Z(R), for all u 2 L. In particular, ifL = [R,R], then R is commutative.

• Farzali Izadi Rasool Naghdali Forooshani Amaneh Amiryousefi Varnousfaderani

Abstract

In this paper we examine a class of fourth power Diophantine equa-tions of the form x4 + kx2y2 + y4 = z2 and ax4 + by4 = cz2, in the GaussianIntegers, where a and b are prime integers.

• Davood Bakhshesh Mohammad Farshi Mohammad Reza Hooshmandasl

Abstract

Let $G = (V, E)$ be a graph. A subset $S \subseteq V$ is a $k$-dominating set ofG if each vertex in $V - S$ is adjacent to at least $k$ vertices in $S$. The $k$-domination number of $G$ is the cardinality of the smallest $k$-dominatingset of $G$. In this paper, we shall prove that the 2-domination number of generalized Petersen graphs $P(5k+1, 2)$ and $P(5k+2, 2)$, for $k > 0$,is $4k + 2$ and $4k + 3$, respectively. This proves two conjectures dueto Yi-Jie Cheng (PhD thesis, National Chiao Tung University, 2013). Moreover, we determine the exact 2-domination number of generalized Petersen graphs $P(2k, k)$ and $P(5k+4, 3)$. Furthermore, we give a good lower and upper bounds on the 2-domination number of generalized Petersen graphs $P(5k + 1, 3)$, $P(5k + 2, 3)$ and $P(5k + 3, 3)$.

• AZANDARYANI M MIRZAEE FEREYDOONI A

Abstract

In this paper we introduce pair frames in Hilbert C*−modules and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also obtain the necessary and sufficient conditions for a standard Bessel sequence to construct a pair frame and we get the necessary and sufficient conditions for a Hilbert C*−module to admit a pair frame with a symbol and two standard Bessel sequences. Moreover by generalizing some of the results obtained for Bessel multipliers in Hilbert C*−modules to pair frames andconsidering the stability of pair frames under invertible operators, we constructnew pair frames and we show that pair frames are stable under small perturbations.

• Bahmann Yousefi Fatemeh Zangeneh

• Seon-Hong Kim Sung Yoon Kim Tae Hyung Kim Sangheon Lee

• NAZIM AGAYEV CESIM CELIK TAHIRE OZEN

Abstract

Let R be a ring with identity. A module M_R is called an r-semisimple module if for any right ideal I of R, MI is a direct summand of M_R which is a generalization of semisimple and second modules. We investigate when an r-semisimple ring is semisimple and prove that a ring R with the number of nonzero proper ideals

\leq 4 and J(R) = 0 is r-semisimple. Moreover, we prove that R is an r-semisimple ring if and only if it is a direct sum of simple rings and we investigate the structure of module whenever R is an r-semisimple ring.

• Saminathan Ponnusamy Jinjing Qiao Xiantao Wang

Abstract

The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family BH(λ) of uniformly locally univalent harmonic mappings. Finally, we show that the subclass of k-quasiconformal harmonic mappings in BH(λ) and the class BH(λ) are contained in the Hardy space of a specific exponent depending on the λ, respectively, and we also discuss the growth of coefficients for harmonic mappings in BH(λ).

• CRISTINA B CORCINO ROBERTO B CORCINO ISTVAN MEZO JOSE L RAMIREZ

Abstract

In the present article we study three families of polynomials associated withthe r-Whitney numbers of the second kind. They are the $r$-Dowling polynomials, $r$-Whitney-Fubini polynomials and the $r$-Eulerian-Fubini polynomials. Then we derive several combinatorial results by using algebraic arguments (Rota's method), combinatorial arguments (set partitions) and asymptotic methods.

• VIVEK V RANE

• NianLiang Wang

• MARYAM AL-TOWAILB OURIMI NABIL

• Mo Chen

• R DAHER S EL OUADIH

Abstract

New estimates are proved for the Helgason Fourier transform in thespace $L^2(X)$ on certain classes of functions characterized by the spherical modulus of continuity.

• Mehdi Baghalaghdam Farzali Izadi

• SHIVAM ARORA KRISHNENDU GONGOPADHYAY

• FATMA CALISKAN

Abstract

In this paper, we prove that some power series with rational coeffcients take either values of rational numbers or transcendental numbers for the arguments from the set of Liouville numbers under certain conditions in the field of complex numbers. We then apply this result to an algebraic number field. In addition, we establish the $p$-adic analogues of these results and show that these results have analogues inthe field of $p$-adic numbers.

• Cesar E Torres Ledesma

Abstract

In this article we consider the following fractional Hamiltonian systems$_{t}D^{\alpha}_{\infty}(_{-\infty}D^{\alpha}_{t}u) +\lambdaL(t)u = \nablaW(t, u), t\in\mathbb{R}$,where $\alpha \in (1/2, 1), \lambda > 0$ is a parameter, $L \in C(\mathbb{R}, \mathbb{R}^{n\times n})$ and $W \in C^{1}(\mathbb {R}\times\mathbb{R}^n, \mathbb{R})$. Unlike most other papers on this problem, we require that $L(t)$ is a positive semi-definite symmetric matrix for all $t \in\mathbb{R}$, that is, $L(t) \equiv 0$ isallowed to occur in some finite interval $\mathbb{I}$ of $\mathbb{R}$. Under some mild assumptions on $W$, we establish the existence of nontrivial weak solution, which vanish on $\mathbb{R} \backslash \mathbb{I}$ as $\lambda\rightarrow\infty$, and converge to $\tilde{u}$ in $H^{\infty}(\mathbb{R})$; here $\tilde{u} \in E^{\infty}_{0}$ is nontrivialweak solution of the Dirichlet BVP for fractional Hamiltonian systems on the finite interval $\mathbb{I}$. Furthermore we give a multiplicity results for (0.1).

• DHIRENDRA BAHUGUNA ANUPAM SHARMA

Abstract

In this paper, we establish some weak and strong convergence theorems for a new iterative algorithm under some suitable conditions to approximate the common fixed point of three infinite families of multi-valued generalized non expansive mappings in a uniformly convex Banach spaces. Our results generalize and improve several previously known results of theexisting literature.

• Shan CHANG Hang LIU

• RAVI S KULKARNI JAGMOHAN TANTI

• ASGHAR RAHIMI NILOUFAR SEDDIGHI

Abstract

In this article, we present a constructive method for computingthe frame coefficients of finite wavelet frames over prime fieldsusing tools from computational harmonic analysis and group theory.

• SUMANA HATUI

• Shusuke Otabe

Abstract

In our previous paper, we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed field of characteristic 0 with genus g > 1, Nori fundamental group acts faithfully on the unipotent fundamental group of its universal covering. However, it was not mentioned about any explicit module structure. In this paper, we prove that the Chevalley-Weil formula gives a description of it

• STEPHAN BAIER ANISH GHOSH

• Mi-mi Zhang

• S BANERJEE

• MASOUD GHORAISHI KARIM SAMEI

• Nandini Nilakantan Anurag Singh

• M N N NAMBOODIRI S PRAMOD P SHANKAR AK VIJAYARAJAN

• K ALI AKBAR V KANNAN

• Zhengxing Li

• Chan-Gyun Kim Eun Kyoung Lee

• M NAJAFI TAVANI

Abstract

Let $A$ and $B$ be two Banach function algebras and $p$ a two variable polynomial $p(z, w) = zw + az + bw + c$, $(a, b, c \in\mathbb{C})$. We characterize the general form of a surjection $T : A \rightarrow B$ which satisfies $Ran_{\pi}(p(T f, T g)) \cap Ran_{\pi}(p( f, g)) \neq\emptyset, ( f, g \in A and c \neq ab)$, where $Ran_{\pi}( f )$ is the peripheral range of $f$ .

• MAHUYA DATTA SAUVIK MUKHERJEE

• ABHISHEK JUYAL SHIV DATT KUMAR

• SURATNO BASU SARBESWAR PAL

Abstract

Let $X$ be a smooth projective hyperelliptic curve of arbitrary genus $g$. Inthis short article we will classify the rank 2 stable vector bundles with parabolic structure along a reduced divisor of degree 4.

• Ahmad Erfanian Masoumeh Ganjali

Abstract

The aim of this paper is to state some results on an $\alpha$-nilpotent group, which was recently introduced by Barzegar and the first author, for any fixed automorphism $\alpha$ of a group $G$. We define an identity nilpotent group and classify all finitely generated identity nilpotent groups. Moreover, we prove a theorem on a generalization of the converse of the known Schur’s theorem. In the last section of the paper, we study absolute normal sub-groups of a finite group.

• TARUN KUMAR CHAKRA TARAKANTA NAYAK KEDARNATH SENAPATI

• Jinshan Zhang

• BAPPADITYA BHOWMIK GOUTAM SATPATI

• Binod Kumar Sahoo Bikramaditya Sahu

• VIVEK V RANE

• SURJEET KOUR

• QAISER MUSHTAQ ABDUL RAZAQ AWAIS YOUSAF

• WALTER CARBALLOSA AMAURIS DE LA CRUZ JOSE M RODRIGUEZ

• Dheer Noal Sunil Desai Kamal Lochan Patra

• VICHIAN LAOHAKOSOL WUTTICHAI SURIYACHAROEN

• SP Murugan S Sundar

• PRIYADWIP DAS BASUDEB DHARA SUKHENDU KAR

• # Proceedings – Mathematical Sciences

Current Issue
Volume 127 | Issue 5
November 2017

• # Proceedings – Mathematical Sciences | News

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