Forthcoming articles
Proceedings – Mathematical Sciences
PMSC-D-14-00152
The hypersurfaces in nearly Kaehler S3 \times S3
Biaogui Yang Qingqing Zhu
PMSC-D-14-00407
Hamiltonian Cycles in Polyhedral Maps
Dipendu Maity Ashish Kumar Upadhyay
We present a necessary and sufficient condition for existence of a contractible, non separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonianian cycle in equivelar triangulated maps. We also present two algorithms to construct such cycles whenever it exists where one of them is linear time and another is exponential time algorithm.
PMSC-D-15-00069
Homological Algebra in 𝑛-Abelian Categories
Deren Luo
In this paper, we study the homological theory in 𝑛-abelian categories. First, we prove some useful properties of 𝑛-abelian categories, such as $(n + 2) \times (n + 2)$-Lemma, 5-Lemma and 𝑛-Horseshoes Lemma. Secondly, we introduce the notions of right(left) 𝑛-derived functors of left(right) 𝑛-exact functors, 𝑛-(co)resolutions, and n-homological dimensions of 𝑛-abelian categories. For an 𝑛-exact sequence, we show that the long 𝑛-exact sequence theorem holds as a generalization of the classical long exact sequence theorem. As a generalization of Ext*(−,−), we study the n-derived functor nExt*(−,−) of hom-functor Hom(−,−). We give an isomorphism between the abelian group of equivalent classes of 𝑚-fold 𝑛-extensions nE^{𝑚}(𝐴,𝐵) of 𝐴,𝐵 and $\text{nExt}^{m}_{\mathcal{A}}(A,B)$ using 𝑛-Baer sum for $m, n \geq 1$.
PMSC-D-15-00090
On a Problem of Pillai with Fibonacci Numbers and Powers of 2
Mahadi Ddamulira Florian Luca Mihaja Rakotomalala
In this paper, we find all all integers c having at least two representations as a difference between a Fibonacci number and a power of 2.
Research Article
Positive Integer Solutions of Certain Diophantine Equations
BIJAN KUMAR PATEL PRASANTA KUMAR RAY MANASI K SAHUKAR
In this study, the Diophantine equations $x^{2}-32B_{n}xy-32y^{2} = \pm{32}^r, x^{4}-32B_{n}xy-32y^{2} = \pm{32}^r and x^{2}-32B_{n}xy-32y^4 = \pm{32}^r are considered and determine when these equations have positive integer solutions. Moreover, all positive integer solutions of these Diophantine equations in terms of balancing and Lucas-balancing numbers are also found out.
PMSC-D-15-00100
Involutions and trivolutions on second dual of algebras related to locally compact groups and topological semigroups
A Alinejad A Ghaffari
We investigate involutions and trivolutions in the second dual of algebras related to a locally compact topological semigroup and the Fourier algebra of a locally compact group. We prove, among the other things, that for a large class of topological semigroups namely, compactly cancellative foundation $\ast$-semigroup 𝑆 when it is infinite non-discrete cancellative, 𝑀_{𝑎}(𝑆)** does not admit an involution, and 𝑀_{𝑎}(𝑆)** has a trivolution with range 𝑀_{𝑎}(𝑆) if and only if 𝑆 is discrete. We also show that when 𝐺 is an amenable group, the second dual of the Fourier algebra of 𝐺 admits an involution extending one of the natural involutions of 𝐴(𝐺) if and only if 𝐺 is finite. However, 𝐴(𝐺)** always admits trivolution.
PMSC-D-15-00111
On the Strong Ergodic Theorem for Commutative Semigroup of Non-Lipschitzian Mappings in Multi-Banach Space
M Azhini H M Kenari R Saadati
Let 𝐶 be a bounded closed convex subset of a uniformly convex multi-Banach space 𝑋 and let $\mathfrak{J}_{j} = \{T_{j}(t) : t \in G\}$ be a commutative semigroup of asymptotically nonexpansive in the intermediate mapping from 𝐶 into itself. In this paper, we prove the strong mean ergodic convergence theorem for the almost-orbit of $\mathfrak{J}$. Our results extend and unify many previously known results especially [8].
PMSC-D-15-00125
ON BIGRADED REGULARITIES OF REES ALGEBRA
RAMAKRISHNA NANDURI
For any homogeneous ideal I in K[x1, . . . , xn] of analytic spread ℓ, we showthat for the Rees algebra R(I), regsyz (0,1)(R(I)) = regT (0,1)(R(I)). We compute a formula for the (0, 1)-regularity of R(I), which is a bigraded analog of Aramova-Herzog(2000) [AH00, Theorem 1.1] and R¨omer(2001)[R01, Theorem 2.2] to R(I). We show that if the defect sequence, ek := reg(Ik) − kρ(I), is weakly increasing for k ≥ regsyz (0,1)(R(I)),then reg(Ij) = jρ(I) + e for j ≥ regsyz (0,1)(R(I)) + ℓ, where ℓ = min{μ(J) | J ⊆ I a graded minimal reduction of I}. This is an improvement of R¨omer(2001) [R01, Corollary 5.9(i)].
PMSC-D-15-00130
Minimal surfaces in symmetric spaces with parallel second fundamental form
Xiaoxiang Jiao Mingyan Li
In this paper, we study geometry of isometric minimal immersions of Riemannian surfaces in a symmetric space by moving frames and prove that the Gaussian curvature must be constant if the immersion is of parallel second fundamental form. In particular, when the surface is $S^{2}$, we discuss the special case and obtain a necessary and sufficient condition such that its second fundamental form is parallel. We also consider isometric minimal two-spheres immersed in complex two-dimensional Kähler symmetric spaces with parallel second fundamental form, and prove that the immersion is totally geodesic with constant Kähler angle if it is neither holomorphic nor anti-holomorphic with Kähler angle $\alpha \neq 0$ (resp. $\alpha \neq \pi$) everywhere on $S^{2}$.
PMSC-D-15-00134
Spectral properties and stability of perturbed cartesian product
Prakash A Dabhi Savan K Patel
Let $\mathcal{A}$ and $\mathcal{B}$ be commutative Banach algebras, and let $T : \mathcal{B} \rightarrow \mathcal{A}$ be an algebra homomorphism with $||T|| \leq 1$. Then $T$ induces a Banach algebra product $\times _{T}$ perturbing the coordinatewise product on the Cartesian product space $\mathcal{A} × \mathcal{B}$. We show that the spectral properties like spectral extension property, unique uniform norm property, regularity, weak regularity as well as Ditkin’s condition are stable with respect to this product.
PMSC-D-15-00143
M-curves and symmetric product
INDRANIL BISWAS SHANE D’MELLO
Let (X , σ) be a geometrically irreducible smooth projective M-curve ofgenus g defined over the field of real numbers. We prove that the n–th symmetricproduct of (X , σ) is an M-variety for n = 2 , 3 and n ≥ 2g − 1.
PMSC-D-15-00149
Codismantlability and projective dimension of the Stanley-Reisner ring of special hypergraphs
Fahimeh Khosh Ahang Somayeh Moradi
In this paper firstly, we generalize the concept of codismantlable graphs to hypergraphs and show that some special vertex decomposable hypergraphs are codismantlable. Then we generalize the concept of bouquet in graphs to hypergraphs to extend some combinatorial invariants of graphs about disjointness of a set of bouquets. We use these invariants to characterize the projective dimension of Stanley-Reisner ring of special hypergraphs in some sense.
PMSC-D-15-00156
Twisting Formula of Epsilon Factors
Sazzad Ali Biswas
For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors. In this paper we give a generalized twisting formula of epsilon factors via local Jacobi sums.
PMSC-D-15-00157
Frobenius splitting of projective toric bundles
He Xin
We prove that the projectivization of the tangent bundle of a nonsingular toric variety is Frobenius split.
PMSC-D-15-00162
Properties of Singular Integral Operators 𝑆_{𝛼,𝛽}
Amit Samanta Santanu Sarkar
For $\alpha, \beta \in L^{\infty}(S^{1})$, the singular integral operator 𝑆_{𝛼,𝛽} on 𝐿^{2}(𝑆^{1}) is defined by $S_{\alpha, \beta}f := \alpha Pf + \beta Qf$, where 𝑃 denotes the orthogonal projection of 𝐿^{2}(𝑆^{1}) onto the Hardy space 𝐻^{2}(𝑆^{1}), and 𝑄 denotes the orthogonal projection onto $H^{2}(S^{1})^{\perp}$. In a recent paper Nakazi and Yamamoto have studied the normality and self-adjointness of 𝑆_{𝛼,𝛽}. This work has shown that 𝑆_{𝛼,𝛽} may have analogous properties to that of the Toeplitz operator. In this paper we study several other properties of 𝑆_{𝛼,𝛽}.
PMSC-D-15-00163
On 3-way combinatorial identities
A K Agarwal Megha Goyal
In this paper we provide combinatorial meanings to two generalized basic series with the aid of associated lattice paths. These results produce two new classes of infinite 3-way combinatorial identities. Five particular cases are also discussed. These particular cases provide new combinatorial versions of Göllnitz-Gordon identities and Göllnitz identity. Seven 𝑞-identities of Slater and five 𝑞-identities of Rogers are further explored using the same combinatorial object. These results extend the work of Goyal and Agarwal, Agarwal and Rana and Agarwal.
PMSC-D-15-00165
Sharp Trudinger-Moser type inequality invoking Hardy inequalities
MOHAMED KHALIL ZGHAL
We establish a sharp Trudinger-Moser type inequality invoking a Hardy inequality for any even dimension. This leads to a non compact Sobolev embedding in some Orlicz space. We also give a description of the lack of compactness of this embedding in the spirit of [8].
PMSC-D-15-00171
LIE $n$-DERIVATIONS ON $\mathcal{J}$ -SUBSPACE LATTICE ALGEBRAS
XIAOFEI QI
Let $\mathcal{L}$ be a $\mathcal{J}$ -subspace lattice on a Banach space $X$ over the real or complex field $\mathbb{F}$ with dim $X\geq3$ and let $n\geq2$ be an integer. Suppose that dim $K\neq2$ for every $K \in \mathcal{J (L)}$ and $L$ : Alg$\mathcal{L}$ → Alg$\mathcal{L}$ is a linear map.It is shown that $L$ satisfies $\sum^n_i=1 pn(A_1, . . . , A_i−1, L(A_i), A_i+1, . . . , A_n) = 0$ whenever $pn(A_1, A_2, . . . , A_n) = 0$ for $A_1, A_2, . . . , A_n \in Alg\mathcal{L}$ if and only if for each $K \in \mathcal{J (L)}$, there exists a bounded linear operator $T_K \in \mathcal{B}(K)$, a scalar $\lamda_K$ and a linear functional $h_K$ : $Alg\mathcal{L}$ → $\mathbb{F}$ such that $L(A)x$ =$(T_{K}A − AT_K + \lamda_{K}A + h_{K}(A)I)x$ for all $x \in K$ and all $A \in Alg\mathcal{L}$. Based on this result, a complete characterization of linear $n$-Lie derivations on Alg$\mathcal{L}$ is obtained.
PMSC-D-15-00190
On Some U(n)-Symmetric Extremal K"ahler metrics of Non-Constant Scalar Curvature
XIAOJUAN DUAN
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.
PMSC-D-15-00202
Alternating groups as a quotient of $PSL(2, \mathbb{Z}[i])$
Qaiser Mushtaq Awais Yousaf
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 𝐴_{𝑛}, 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.
PMSC-D-15-00239
ON A CONJECTURE ON LINEAR SYSTEMS
SONICA ANAND
In a remark to Green’s conjecture [4], Paranjape and Ramanan analyzed the vector bundle E which is the pullback by the canonical map of the universal quotient bundle T Pg−1 (−1) on Pg−1 [6] and stated a more general conjecture [5] and proved it for the curves with Clifford Index 1 (trigonal and plane quintics). In this paper, we state the conjecture for general linear systems and obtain results for the case of hyperelliptic curves.
PMSC-D-15-00241
Global Weighted Estimates for Second-Order Nondivergence Elliptic and Parabolic Equations
Fengping Yao
In this paper we obtain the global weighted 𝐿^{𝑝} estimates for second-order nondivergence elliptic and parabolic equations with small BMO coefficients in the whole space. As a corollary we obtain 𝐿^{𝑝}-type regularity estimates for such equations.
PMSC-D-15-00259
SOME ASPECTS OF SHIFT{LIKE AUTOMORPHISMS OF Ck
SAYANI BERA KAUSHAL VERMA
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.
PMSC-D-15-00261
New modular relations involving cubes of the G$\"{o}$llnitz-Gordon functions
Olivia XM Yao
Chen and Huang established some elegant modular relations for the G$\"{o}$llnitz-Gordon functions analogous to Ramanujan’s list of forty identities for the Rogers-Ramanujan functions. In this paper, we derive some new modular relations involving cubes of the G$\"{o}$llnitz-Gordon functions. Furthermore, we also provide new proofs of some modular relations for the G$\"{o}$llnitz-Gordon functions due to Gugg.
PMSC-D-15-00272
A GENERALIZATION OF ZERO DIVISOR GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
M AFKHAMI A ERFANIAN K KHASHYARMANESH N VAEZ MOOSAVI
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.
PMSC-D-15-00276
Schrödinger operators on a periodically broken zigzag carbon nanotube ^{∗}
Niikuni Hiroaki
In this paper, we study the spectra of Schrödinger operators on zigzag carbon nanotubes, which are broken by abrasion or in a process to refine. Throughout this paper, we assume that our carbon nanotubes are broken periodically and deal with one of those model. Making use of the Floquet–Bloch theory, we examine the spectra of the Schrödinger operators and compare the spectra of the broken case and the pure unbroken case.
PMSC-D-15-00288
M H Heydari M R Hooshmandasl C Cattani
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.
PMSC-D-15-00290
Cross-product of bessel functions: monotonicity patterns and functional inequalities^{∗}
Árpád Baricz Saminathan Ponnusamy Sanjeev Singh
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.
PMSC-D-15-00296
Positive solutions with single and multi-peak for semilinear elliptic equations with nonlinear boundary condition in the half-space
Li Wang Peihao Zhao
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 $Q$.
PMSC-D-15-00320
Closed subspaces and some basic topological properties of noncommutative Orlicz spaces^{✩}
Lining Jiang Zhenhua Ma
In this paper, we study the noncommutative Orlicz space $L_{\varphi}(\widetilde{\mathcal{M}}, \tau)$, which generalizes the concept of noncommutative $L^{p}$ space, where $\mathcal{M}$ is a von Neumann algebra, and $\varphi$ is an Orlicz function. As a modular space, the space $L_{\varphi}(\widetilde{\mathcal{M}}, \tau)$ possesses the Fatou property, and consequently, it is a Banach space. In addition, a new description of the subspace $E_{\varphi}(\widetilde{\mathcal{M}}, \tau) = \overline{\mathcal{M}\cap L_{\varphi}(\widetilde{\mathcal{M}},\tau)}$ in $L_{\varphi}(\widetilde{\mathcal{M}}, \tau)$, which is closed under the norm topology and dense under the measure topology, is given. Moreover, if the Orlicz function $\varphi$ the $\Delta_{2}$-condition, then $L_{\varphi}(\widetilde{\mathcal{M}}, \tau)$ is uniformly monotone, and convergence in the norm topology and measure topology coincide on the unit sphere. Hence, $E_{\varphi}(\widetilde{\mathcal{M}}, \tau) = L_{\varphi}(\widetilde{\mathcal{M}}, \tau)$ if $\varphi$ satisfies the $\Delta_{2}$-condition.
PMSC-D-15-00361
APPROXIMATE CONTROLLABILITY OF A NON-AUTONOMOUS DIFFERENTIAL EQUATION
INDIRA MISHRA MADHUKANT SHARMA
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
PMSC-D-15-00363
A GENERALIZATION OF TOTAL GRAPHS
M AFKHAMI K HAMIDIZADEH K KHASHYARMANESH
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).
PMSC-D-15-00378
ANALYZING THE WU METRIC ON A CLASS OF EGGS IN Cn – II
G P BALAKUMAR PRACHI MAHAJAN
PMSC-D-15-00380
A NOTE ON GENERALIZED SKEW DERIVATIONS ON LIE IDEALS
MOHAMMAD ASHRAF VINCENZO DE FILIPPIS
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.
PMSC-D-15-00388
Fourth Power Diophantine Equations in Gaussian Integers
Farzali Izadi Rasool Naghdali Forooshani Amaneh Amiryousefi Varnousfaderani
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.
Research Article
2-domination number of generalized Petersen graphs
Davood Bakhshesh Mohammad Farshi Mohammad Reza Hooshmandasl
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 $P(5k + 3, 3)$.
PMSC-D-15-00404
Pair frames in Hilbert C^*-modules.
AZANDARYANI M MIRZAEE FEREYDOONI A
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.
PMSC-D-16-00050
Root and Critical Point Behaviors of Certain Sums of Polynomials
Seon-Hong Kim Sung Yoon Kim Tae Hyung Kim Sangheon Lee
PMSC-D-16-00051
ON A GENERALIZATION OF SEMISIMPLE MODULES
NAZIM AGAYEV CESIM CELIK TAHIRE OZEN
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.
PMSC-D-16-00057
Uniformly locally univalent harmonic mappings
Saminathan Ponnusamy Jinjing Qiao Xiantao Wang
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).
PMSC-D-16-00058
On Coefficient Estimates of Negative Powers and Inverse Coefficients for Certain Starlike Functions
Md Firoz Ali A Vasudevarao
PMSC-D-16-00083
Some Polynomials Associated with the r-Whitney Numbers
CRISTINA B CORCINO ROBERTO B CORCINO ISTVAN MEZO JOSE L RAMIREZ
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.
PMSC-D-16-00084
On the number of special numbers
KEVSER AKTAS M RAM MURTY
For lack of a better word, a number is called special if it has mutually distinctexponents in its canonical prime factorizaton for all exponents. Let V (x) be the number of special numbers ≤ x. We will prove that there is a constant c > 1 such that V (x) ~cxlog x.We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.
PMSC-D-16-00097
SOME INEQUALITIES FOR THE BELL NUMBERS
FENG QI
In the paper, the author presents derivatives of the generatingfunctions for the Bell numbers by induction and by the Fa`a di Bruno formula,recovers an explicit formula for the Bell numbers in terms of the Stirlingnumbers of the second kind, finds the (logarithmically) absolute and completemonotonicity of the generating functions for the Bell numbers, and constructssome inequalities for the Bell numbers. From these inequalities, the authorderives the logarithmic convexity of the sequence of the Bell numbers.
Research Article
Character Average of Fourth Power of Dirichlet L-series at Unity
VIVEK V RANE
PMSC-D-16-00138
Arithmetical Fourier and Limit values of elliptic modular functions
NianLiang Wang
PMSC-D-16-00141
ANALYTIC SETS AND EXTENSION OF HOLOMORPHIC MAPS OF POSITIVE CODIMENSION
MARYAM AL-TOWAILB OURIMI NABIL
PMSC-D-16-00154
CONTRIBUTIONS TO A CONJECTURE OF MUELLER AND SCHMIDT ON THUE INEQUALITIES
N SARADHA DIVYUM SHARMA
PMSC-D-16-00160
SOME NEW ESTIMATES FOR THE HELGASON FOURIER TRANSFORM ON RANK 1 SYMMETRIC SPACES
R DAHER S EL OUADIH
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.
Research Article
A note on the high power Diophantine equations
Mehdi Baghalaghdam Farzali Izadi
PMSC-D-16-00188
$z$--CLASSES IN FINITE GROUPS OF CONJUGATE TYPE $(n, 1)$
SHIVAM ARORA KRISHNENDU GONGOPADHYAY
Research Article
Transcendence of some power series for liouville number arguments
FATMA CALISKAN
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.
Research Article
Cesar E Torres Ledesma
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).
PMSC-D-16-00256
MAXIMAL REGULARITY FOR NON-AUTONOMOUS STOCHASTIC EVOLUTION EQUATIONS IN UMD BANACH SPACES
Viet Ton Ta Atsushi Yagi Yoshitaka Yamamoto
A non-autonomous stochastic linear evolution equation in UMD Banach spaces of type 2 is considered. We construct unique strict solutions to the equation and show their maximal regularity. The abstract results are then applied to a stochastic partialdifferential equation.
PMSC-D-16-00259
ON CERTAIN GEODESIC CONJUGACIES OF FLAT CYLINDERS
C S ARAVINDA H A GURURAJA
We prove C^0-conjugacy rigidity of any Flat Cylinder among two different classes of metrics on the cylinder, namely among the class of rotationally symmetric metrics and among the class of metrics without conjugate points.
PMSC-D-16-00269
Some functional inequalities on non-reversible Finsler manifolds
Shin-ichi Ohta
We continue our study of geometric analysis on (possibly non-reversible) Finslermanifolds, based on the Bochner inequality established by the author and Sturm.Following the approach of the $\Gamma$-calculus `a la Bakry et al, we show the dimensional versions of the Poincar´e–Lichnerowicz inequality, the logarithmic Sobolev inequality, and the Sobolev inequality. In the reversible case, these inequalities were obtained by Cavalletti–Mondino in the framework of curvature-dimension condition by means of the localization method. We show that the same (sharp) estimates hold also for non-reversible metrics.
PMSC-D-16-00276
DHIRENDRA BAHUGUNA ANUPAM SHARMA
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.
Research Article
Augmentation Quotients for Real Representation Rings of Cyclic Groups
Shan CHANG Hang LIU
Research Article
On the Role of Associativity in Ramsey Algebras
Andrew Rajah Wen Chean Teh Zu Yao Teoh
It is known that semigroups are Ramsey algebras. This paper is an attempt to understand the role associativity plays in a binary system being a Ramsey algebra. Specifically, we show that the nonassociative Moufang loop of octonions is not a Ramsey algebra.
Research Article
On the partition dimension of two-component graphs
Debi Oktia Haryeni Edy Tri Baskoro Suhadi Wido Saputro Martin Baca Andrea Semanicova-Fenovcıkova
In this paper, we continue investigating the partition dimension for disconnected graphs. We determine the partition dimension for some classes of disconnected graphs $G$ consisting of two components. If $G = G_{1}\cup G_{2}$, then we give the bounds of the partition dimension of $G$ for $G_{1} = P_{n}$ or $G_{1} = C_{n}$ and also for $pd(G_{1}) = pd(G_{2})$.
PMSC-D-16-00311
Allowable graphs of the nonlinear Schr$\"{o}$dinger equation and their applications
NGUYEN BICH VAN
We construct the definition of allowable graphs of the nonlinear Schr$\"{o}$dinger equation of arbitrary degree and use it to verify the separation and irreducibility (over the ring of integers) of the characteristic polynomials of all the possible graphs giving 3-dimensional blocks of the normal form of the nonlinear Schr$\"{o}$dinger equation. The method is purely algebraic and the obtained results will be useful in further studies of the nonlinear Schr$\"{o}$dinger equation
Research Article
A CONSTRUCTIVE APPROACH TO THE FINITE WAVELET FRAMES OVER PRIME FIELDS
ASGHAR RAHIMI NILOUFAR SEDDIGHI
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.
PMSC-D-16-00323
A CHARACTERIZATION OF FINITE $p$-GROUPS BY THEIR SCHUR MULTIPLIER
SUMANA HATUI
PMSC-D-16-00337
The Fundamental Group and Extensions of Motives of Jacobians of Curves
Subham Sarkar Ramesh Sreekantan
In this paper we construct extensions of mixed Hodge structure coming from the mixed Hodge structure on the graded quotients of the group ring of the Fundamental group of a smooth projective pointed curve which correspond to the regulators of certain motivic cohomology cycles on the Jacobian of the curve essentially constructed by Bloch and Beilinson. This leads to a new iterated integral expression for the regulator. This is a generalisation of a theorem of Colombo [Col02] where she constructed the extension corresponding to Collino's cycles in the Jacobian of a hyperelliptic curve.
PMSC-D-16-00346
Semifinite Bundles and the Chevalley-Weil Formula
Shusuke Otabe
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
PMSC-D-16-00380
Comparison of graphs associated to a commutative Artinian ring
MASOUD GHORAISHI KARIM SAMEI
Research Article
polynomially peripheral range-preserving maps between Banach algebras
M NAJAFI TAVANI
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 $f$ .
PMSC-D-17-00027
HEISENBERG UNIQUENESS PAIRS CORRESPONDING TO FINITE NUMBER OF PARALLEL LINES
SAYAN BAGCHI
In this paper we study the Heisenberg uniqueness pairs correspondingto finite number of parallel lines $\Gamma$. We give a necessary condition and a sufficient condition for a subset $\Lambda$ of $\mathbb{R}^2$ so that ($\Gamma$, $\Lambda$) becomes a HUP.
Research Article
Moduli space of Parabolic vector bundles over hyperelliptic curves
SURATNO BASU SARBESWAR PAL
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.
Research Article
Nilpotent groups related to an automorphism
Ahmad Erfanian Masoumeh Ganjali
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.
Current Issue
Volume 127 | Issue 3
June 2017
© 2017 Indian Academy of Sciences, Bengaluru.