• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Theophilus Agama

In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem of counting the number of complete subsets of any given set. That is, given any interval of integers ℌ ≔ [1, N] and letting $${\cal C}(N)$$ denotes the complete

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Absos Ali Shaikh, Pinaki Ranjan Ghosh

The present paper deals with a study of curves on a smooth surface whose position vector always lies in the tangent plane of the surface and it is proved that such curves remain invariant under isometry of surfaces. It is also shown that length of the position vector, tangential component of the position vector and geodesic curvature of a curve on a surface whose position vector always lies in the

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Theophilus Agama

In this paper we introduce the prime index function $$\iota \left( n \right) = {\left( { - 1} \right)^{\pi \left( n \right)}},$$ where π(n) is the prime counting function. We study some elementary properties and theories associated with the partial sums of this function given by $$\xi \left( x \right): = \sum\limits_{n \le x} {\iota \left( n \right).}$$

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06

In this paper, we consider a class of fractional Sturm-Liouville problems, in which the second order derivative is replaced by the Caputo fractional derivative. The Laplace transform method is applied to obtain algebraic equations. Then, the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems are obtained numerically. We provide a convergence analysis for given method. Finally

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Amit Kumar Singh

We study the splitting of the pullback of the tangent bundle Tℙ3 on an elliptic curve under the morphism given by a line bundle of degree less or equal to 5.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Yufeng Yu

Using a different method — the sphere method, which is based on the technique of changing the integral on a plane into the integral on a hemisphere, we give some concise inverse formulas of the Radon transforms of functions with support in a cone with vertex at the origin and flare angle less than π/2, or with compact support. These formulas are easy for the computer to operate and thus can be applied

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Gamaliel Cerda-Morales

In this paper, in considering aspects of the geometric mean sequence, offers new results connecting generalized Tribonacci and third-order Horadam numbers which are established and then proved independently.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Shaoyong Zhang, Zhaohui Gu, Yongjin Li

Let λ be a reflexive Banach sequence lattice and X be a Banach lattice. In this paper, we show that the positive injective tensor product $$\lambda {\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\smile}}\over \otimes } _{\left| \varepsilon \right|}}X$$ is a Grothendieck space if and only if X is a Grothendieck space and every positive linear operator from λ* to X** is compact.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Ushangi Goginava

In this paper we study the a. e. exponential strong (C, 1, 0) summability of of the 2-dimensional trigonometric Fourier series of the functions belonging to L (log+L)2.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Yuemei Mao, Xiaojian Ma

Let $$\mathfrak{F}$$ denote a class of groups. A maximal subgroup M of G is called $$\mathfrak{F}$$-abnormal provided G/MG ∉ $$\mathfrak{F}$$. We say that (K, H) is an $$\mathfrak{F}$$-abnormal pair of G provided K is a maximal $$\mathfrak{F}$$-abnormal subgroup of H. Let Σ = {G0 ≤ G1 ≤ G2 ≤ … ≤ Gn} be a subgroup series of G. A subgroup H of G is said to be Σ-$$\mathfrak{F}$$-embedded in G if H either

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Sh. Shahriyari, H. Zahmatkesh, S. Shakeri

Using the method of sub-super solutions and comparison principle, we study the existence of positive solutions for a class of quasilinear elliptic systems with sign-changing weights involving nonlocal operator.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Shekhar Singh Negi, Syed Abbas, Muslim Malik

In this paper, we establish the existence of periodic solution of a delayed predator-prey model with M -predators and N -preys over the time scales. We derive sufficient conditions for the existence of a periodic solution with the help of continuation theorem of coincidence degree theory. At the end, we give an example with numerical simulations to illustrate our analytical findings.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06

In this paper we discuss a new approach to discuss Stokes flow past porous bodies of arbitrary shape using the Darcy  model and Saffman  boundary conditions.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Animesh Bhandari, Saikat Mukherjee

This paper introduces the concept of atomic subspaces with respect to a bounded linear operator. Atomic subspaces generalize fusion frames and this generalization leads to the notion of K-fusion frames. Characterizations of K-fusion frames are discussed. Various properties of K-fusion frames, for example, direct sum, intersection, are studied.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Jayanta Borah, Swaroop Nandan Bora

In this article, we establish sufficient conditions for existence and uniqueness of integral solution for some non-densely defined non-instantaneous impulsive evolution equations on a Banach space involving Caputo fractional derivative. The results are obtained by means of characteristic functions based on probability density. Finally, the main results are illustrated through examples.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
S. Pirzada, Hilal A. Ganie, A. Alhevaz, M. Baghipur

Let G be a connected graph with n vertices, m edges and having distance signless Laplacian eigenvalues ρ1≥ ρ2 ≥ … ≥ ρn≥ 0. For any real number α ≠ 0, let $${m_\alpha }\left( G \right) = \sum\nolimits_{i = 1}^n {\rho _i^\alpha }$$ be the sum of αth powers of the distance signless Laplacian eigenvalues of the graph G. In this paper, we obtain various bounds for the graph invariant mα(G), which connects

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06

This paper describes the construction of a natural Hermitian holomorphic line bundle on the stratified moduli space of complex representations of a finite quiver, which are semistable with respect to a fixed rational weight and have a fixed type. It is shown that the curvature of this Hermitian line bundle on each stratum of the moduli space is essentially the Kahler form of that stratum.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Lin Chen, Jianhua Zhang

In this paper, we characterize the *-Jordan semi-triple derivable mappings (i.e. a mapping Φ from * algebra $$\mathcal{A}$$ into $$\mathcal{A}$$ satisfying Φ(AB*A) = Φ(A)B*A + AΦ(B)*A + AB* Φ(A) for every A, B $$\mathcal{A}$$) in the finite dimensional case and infinite dimensional case.

更新日期：2020-10-07
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06
Qinxiu Sun, Xiao Yu, Hongliang Li

Weight criteria for the boundedness and compactness of generalized Hardy-type operators $$Tf(x) = {u_1}(x)\int_{\left\{ {\phi (y) \le \psi (x)} \right\}} {f(y){u_2}(y){v_0}(y)d\mu (y),\;\;\;\;\;x \in X},$$((0.1)) in Orlicz-Lorentz spaces defined on measure spaces is investigated where the functions ϕ, ψ, u1, u2, v0 are positive measurable functions. Some sufficient conditions of boundedness of $$T:\;\Lambda 更新日期：2020-10-07 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-10-06 Mozhgan Mohammadpour, Rajab Ali Kamyabi-Gol, Ghosheh Abed Hodtani A Grassmannian fusion frame is an optimal configuration of subspaces of a given vector space, that are useful in some applications related to representing data in signal processing. Grassmannian fusion frames are robust against noise and erasures when the signal is reconstructed. In this paper, we present an approach to construct optimal Grassmannian fusion frames based on a given Grassmannian frame 更新日期：2020-10-07 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Mohsen Ghasemi; Rezvan Varmazyar Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 5p2 is given. 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Sukjith Singh; Eulalia Martínez; P. Maroju; Ramandeep Behl We present a local convergence study of a fifth order iterative method to approximate a locally unique root of nonlinear equations. The analysis is discussed under the assumption that first order Fréchet derivative satisfies the Lipschitz continuity condition. Moreover, we consider the derivative free method that obtained through approximating the derivative with divided difference along with the local 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Liang Li; Pengtong Li In this paper, we study the dilation of g-frame generators and the dual g-frame generators for an abstract wavelet system. By the semi-orthogonality of a special unitary system, we prove the dual g-frame generators can be dilated to a pair of dual g-Riesz basis generators for some larger Hilbert space. We first show the existence of the dual g-frame generators with the same structure of a g-frame generator 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Samina; Kamal Shah; Rahmat Ali Khan In the current manuscript, we investigate existence of solutions to a coupled system of fractional hybrid differential equations (FHDEs). With the help of mixed type Lipschitz and Caratheodory conditions, some conditions for the existence of solutions to the considered problem are established. Considering the tools of nonlinear analysis and hybrid fixed points theory, we establish our results. Further 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Shane Chern; Dazhao Tang; Ernest X. W. Xia Let Tℓ(n) denote the number of ℓ-regular partition triples of n. In this paper, we consider the arithmetic properties of T7(n). An infinite family of congruences modulo powers of 7 and several congruences modulo 7 are established. For instance, we prove that for all n ≥ 0 and α ≥ 1,{T_7}\left( {{7^{2\alpha }}n + \frac{{3 \times {7^{2\alpha }} - 3}}{4}} \right) \equiv 0\;(\bmod {7^\alpha }) 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 N. Amiri; M. Zivari-Rezapour In this paper, we investigate two optimization problems related to a quasilinear elliptic equation with p-Laplacian, logistic-type growth rate function such that the admissible set is a class of rearrangements of a fixed function. Under some suitable assumptions, we prove existence and representation of the maximizers and existence, uniqueness and representation of the minimizer. Also, when the domain 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Mohammad Shahriari; Behzad Nemati Saray; Jalil Manafian In this manuscript, we study second–order differential operators with a constant delay and transmission boundary conditions. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. Also, we construct the potential function by using the Fourier series and delay point of the Sturm–Liouville differential operator. 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Abdullah Mir In this paper we establish a family of comparison inequalities between rational functions with prescribed poles for the sup-norms on the unit circle in the complex plane. Certain estimates for the modulus of the derivative of rational functions as well as some inequalities of Turán’s type are also obtained. The obtained results produce many inequalities for polynomials and polar derivatives as special 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Homayoon Arabyani The concept of the Schur multiplier of a Lie algebra was introduced by Batten et al. (1996). This concept was extended to that of a c-nilpotent multiplier of a Lie algebra, and then further extended to a theory of a c-nilpotent multiplier of a pair of Lie algebras, by the author and others. In this paper we present some new inequalities for the dimension of the c-nilpotent multiplier of a pair of Lie 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Emrah Kılıç; Helmut Prodinger Some Gaussian q-binomial sum identities from  are further generalized, introducing two additional parameters. We prove the claimed results by q-calculus. Finally we present applications to the generalized Fibonomial sums as corollaries. 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Shahnaz Jafari; Maryam Shams In this paper, we define the concepts of ϕ-contraction in probabilistic generalized Menger space. We prove that ϕ-contraction mappings in probabilistic generalized Menger space have a unique fixed point. Also we prove some fixed point theorems related this concept. Some examples are given to support the obtained results. 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Ziyad A. Alhussain; Essam A. Ahmed In this article we consider statistical inferences about the unknown parameters of the exponentiated Nadarajah-Haghighi (ENH) distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures, maximum likelihood (ML) and least square estimators of the unknown parameters are derived. The Bayes estimators are obtained based on both the symmetric (squared 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Eduardo Ruíz Duarte; Jaap Top We prove the Hasse-Weil inequality for genus 2 curves given by an equation of the form y2 = f(x) with f a polynomial of degree 5, using arguments that mimic the elementary proof of the genus 1 case obtained by Yu. I. Manin in 1956. 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Hong-Ying Li; Yang Pu; Jia-Feng Liao In this paper, we are interested in considering the following singular elliptic problem with concaveconvex nonlinearities\left\{ {\begin{array}{*{20}{l}} { - \Delta u - \frac{\mu }{{|x{|^2}}}u = f(x)|u{|^{p - 2}}u + g(x)|u{|^{q - 2}}u,}&{in\;\;\Omega \backslash \{ 0\} ,} \\ {u = 0,}&{on\;\;2\Omega ,} \end{array}} \right.where Ω ⊂ ℝN(N ≥ 3) is a smooth bounded domain with 0 ∈ Ω, \(0 < \mu < \bar\mu 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Hamid Baghani An open problem proposed by Rhoades is the following. Is there a contractive condition which guarantees the existence of a fixed point, but does not require the mapping to be continuous at the point? In this paper, we generalize a celebrated result of Eshaghi et al., [On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18 (2017), 569–578], which allows us to find a new solution to 更新日期：2020-06-23 • Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23 Baghdadi Aloui; Wathek Chammam Let Tc := D(x - c)((x - c)D + 2II) be a second-order linear differential operator, where c is an arbitrary complex number, \(D: = \frac{d}{{dx}}$$ and II represents the identity on the linear space of polynomials with complex coefficients. The aim of this paper is to describe all of the Tc-classical orthogonal polynomials. Two canonical situations appear: the Laguerre $$\{L_n^{(2)}\}_{n\geq0}$$ and

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
Oussama Bouanani; Saâdia Rahmani; Ali Laksaci; Mustapha Rachdi

Based on the local polynomial smoother idea, we construct a local linear estimator of the conditional mode for dependent functional covariables. Precisely, observations are assumed to be a sequence of stationary α-mixing random variables. Then, we establish the asymptotic normality of the constructed estimator.

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
R. Alagammai; V. Vijayalakshmi

In this paper, we determine the exact values of the game chromatic number of some interconnection network graph families such as shuffle exchange network, cube-connected cycles and wrapped around butterflies

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23

In this paper, we deal with the Schrödinger’s problems, in the first part we study the theoretical side, we show the existence of at least three weak solutions, our main tools are based on variational inequalities, more precisely, using the three critical points theorem due to Ricceri, existence and multiplicity results are established. In the second part, we are interested in the application side

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
Snehajit Misra

Let π : X = ℙC(E) → C be a ruled surface over an algebraically closed field k of characteristic 0, with a fixed polarization L on X. In this paper, we show that pullback of a (semi)stable Higgs bundle on C under π is a L-(semi)stable Higgs bundle. Conversely, if (V, θ) is a L-(semi)stable Higgs bundle on X with c1(V) = π* (d) for some divisor d of degree d on C and c2(V) = 0, then there exists a (semi)stable

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
T. Tamizh Chelvam; S. Anukumar Kathirvel; M. Balamurugan

Let R be a finite commutative ring with nonzero identity and U(R) be the set of all units of R. The graph Γ is the simple undirected graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u in U(R) such that x + uy is a unit in R. Also, $$\overline{\Gamma}$$ denotes the complement of Γ. In this paper, we find the domination number γ of

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
Sanjay Kumar; Poonam Rani

In this paper we prove some normality criteria for a family of meromorphic functions, which involves the zeros of certain differential polynomials generated by the members of the family.

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
Haining Jiang

Target Set Selection (TSS) was initially proposed to study the problem of the spread of information, ideas or influence through a social network and had formulated many problems arising in various practical applications. We consider a particular type of graphs, namely n-dimensional m-sided pancake graph mPn, which is one class of Cayley graphs and is widely used in the symmetric interconnection networks

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
Jamal Kazemiasl; Farhad Khaksar Haghani; Shahram Heidarian

In this paper, we obtain some relations between Noetherian and Artinian BL-algebras. Further, we derive some theorems and lemmas for composition series, Artinian BL-argebera, as well as the relations between Noetherian, Artinian and short exact sequences. We further study the Noetherian and Artinian over homomorphism BL-algebras and obtain some new results concerning to the essential deductive systems

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
Arshi Meraj; Dwijendra N. Pandey

The aim of this article is to study approximate controllability of a class of non-autonomous Sobolev type integro-differential equations having non-instantaneous impulses with nonlocal initial condition. The results will be proved with the help of evolution system and Krasnoselskii fixed point theorem. An example is presented to show how our abstract results can be applied.

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-06-23
JinMyong Kim; HyonJin Kim; HakMyong Mun

In this paper we present a method to generate new fractal interpolation curves. We ensure that attractors of nonlinear iterated function systems (IFSs) constructed by Geraghty contractions are graphs of some continuous functions which interpolate the given data. In particular, we give an explicit illustrative example to demonstrate the effectiveness of obtained results. Concerning IFSs, our methods

更新日期：2020-06-23
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
V. Uma

Let X be a toric hyperKähler manifold. The purpose of this note is to describe the topological K-ring K*(X) of X. We give a presentation for the topological K-ring in terms of generators and relations similar to the known description of the cohomology ring of these manifolds.

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
S. M. Tabatabaie; M. Pourgholamhossein; M. Amini; M. K. Hokmabad

We give a set of axioms for the notion of locally compact hypergroupoids, as an extension of both groupoids and hypergroups, and study their basic properties. We show that, adding a natural condition on the continuity of support, one of the axioms assumed by Renault on the left Haar system automatically follows. We show that an irreducible representation of a compact hypergroupoid is fiberwise finite

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Vikram Singh; Dwijendra N. Pandey

In this paper, an abstract multi-term time-fractional differential system is considered and the existence, uniqueness and exact controllability results are investigated. In this theory, we use the notion of bounded integral contractor introduced by Altman to come up with a new set of sufficient conditions for the exact controllability by constructing a sequencing technique. Moreover, in this technique

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Tushar Bag; Abdullah Dertli; Yasemin Cengellenmis; Ashish K. Upadhyay

In this paper, we study the quantum codes over $${F_{{p^m}}}$$, which are obtained from (λ1 + λ2)-constacyclic codes over the semi local ring $${F_{{p^m}}} + v{F_{{p^m}}}$$, where v2 = 1, p is odd prime. We decompose a (λ1 + λ2)-constacyclic code over $${F_{{p^m}}} + v{F_{{p^m}}}$$ into two constacyclic codes over $${F_{{p^m}}}$$ such as (λ1 + λ2)-constacyclic and (λ1–λ2)-constacyclic. We give the

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Thierry E. Huillet

Scientists reinvent stochastic mechanisms leading to the emergence of a distribution discovered by H.A. Simon, in the context of the study of word frequencies occurring in a textbook. Simon distributions are heavy-tailed as a result of a reinforcement mechanism that produced them, related to the modern notion of preferential attachment. The Simon distribution is a particular case of a distribution

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Fuad Ali Ahmed Almahdi; Abdellah Mamouni; Mohammed Tamekkante

In this paper, we generalize the Posner’s theorem on derivations in rings as follows: Let R be an arbitrary ring, P be a prime ideal of R, and d be a derivation of R. If [[x, d(x)], y] ∈ P for all x, y ∈ R, then d(R) ⊆ P or R/P is commutative. In particular, if R is semiprime and d is a centralizing derivation of R, we prove that either R is commutative or there exists a minimal prime ideal P of R

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Absos Ali Shaikh; Pinaki Ranjan Ghosh

The main motive of the paper is to look on rectifying and osculating curves on a smooth surface. In this paper we find the normal and geodesic curvature for a rectifying curve on a smooth surface and we also prove that geodesic curvature is invariant under the isometry of surfaces such that rectifying curves remain. We find a sufficient condition for which an osculating curve on a smooth surface remains

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Gajendra Singh

For a non-zero algebraic integer α, let ℚ(α) denote the simple extension of the field of rational numbers ℚ. ℤ[α] is the smallest subring of ℚ(α) containing both ℤ and α. In this article, we present an account for testing irreducibility of a given polynomial with coefficients in ℤ[α] over the field ℚ(α).

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Richard F. Patterson; Rabia Savas; Ekrem Savas

In 1964 Borwein presented functional characterization of the normed linear spaces wp and Wp. These two spaces are clearly linked to Cesàro summability [C, 1] in particular it should be noted that a sequence x in wp if and only if x is Cesàro summable. The goal of this paper includes extension of these notions to double function space thus producing multidimensional analog of Borwein’s results.

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Sriraman Sridharan; Patrick Vilamajó

We define two families of graphs and prove the strong and the weak path partition conjectures for subfamilies of these graphs.

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13

Difference sets are subsets of a group satisfying certain combinatorial property with respect to the group operation. They can be characterized using an equality in the group ring of the corresponding group. In this paper, we exploit the special structure of the group ring of an Abelian group to establish a one-to one correspondence of the class of difference sets with specific parameters in that group

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Kenta Watanabe

Let X be a K3 surface and let H be a very ample line bundle on X of sectional genus g ≤ 9. In this paper, we characterize the destabilizing sheaf of the Lazarsfeld-Mukai bundle EC,Z of rank 2 associated with a smooth curve C ∈ |H| and a base point free divisor Z on C with h0(OC(Z)) = 2, in the case where it is not H-slope stable.

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Anjiao Wang

In this paper, we consider a two-firm default contagion model with counterparty risk and jumpdiffusion interest rate risk. Under this model, we study the pricing of total return swap(TRS). We assume that the interest rate follows the Vasicek jump-diffusion model, and obtain the Libor market interest rate. The case that default is related to the interest rate is considered. Using the method of change

更新日期：2020-03-13
• Indian J. Pure Appl. Math. (IF 0.516) Pub Date : 2020-03-13
Yingchun Deng; Xuan Huang; Ya Huang; Xuyan Xiang; Jieming Zhou

In this paper, we adopt a Poisson approach to find Laplace transforms of joint occupation times over n disjoint intervals for pre-exit diffusion processes. Then we generalize previous result for the 2-dimensional case and the 3-dimensional case.

更新日期：2020-03-13
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