The Journal of the Indian Mathematical Society https://www.informaticsjournals.com/index.php/jims <div id="i-scholarabout"><img class="media-object" style="width: 222px; float: left; margin: 0px 16px 15px 20px;" src="https://www.informaticsjournals.com/public/journals/9/journalThumbnail_en_US.jpg" /> <p style="margin-left: 261px;"><strong>Editor :</strong> Peeyush Chandra<br /><strong>Online ISSN :</strong> 2455-6475<br /><strong>Print ISSN :</strong> 0019-5839<br /><strong>Frequency :</strong> Quarterly<br /><strong>Publisher/s :</strong> Informatics Publishing Limited, The Indian Mathematical Society</p> <!--div id="jnr_mq" style="color: red; font-size: 18px;">Neither Informatics nor the Indian Mathematical Society has appointed any agent for publishing papers in the Journal of the Indian Mathematical Society. Also, none of us charge any publication/ processing/ page charges or any other fees for publishing a paper</div--> <!--p><a style="color: red; font-size: 20px;" href="/informaticsjournals.com/public/journals/1/ext_list_January_2022.xlsx">Download SCOPUS LIST</a></p--> <p>The Indian Mathematical Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onward, it is published as its current title 'The Journal of Indian Mathematical Society.<br /><br /><span style="color: blue;">The Journal is Indexed in Scopus with <a href="http://scimagojr.com/journalsearch.php?q=21100259506&amp;tip=sid&amp;clean=0" target="_blank" rel="noopener">H Index </a>3. Included in UGC's - CARE List of Journals (Group A) </span></p> </div> <p id="homecontent"><a href="http://jgateplus.com/" target="blank"><img src="https://www.srels.org/public/journals/57/jgate.png" alt="" width="160" height="77" /></a><a href="http://www.i-scholar.in/" target="blank"><img src="https://www.srels.org/public/journals/57/scholar.png" alt="" width="160" height="77" /></a><a href="#" target="_blank" rel="noopener"><img src="https://www.srels.org/public/journals/57/scilit.png" alt="" /></a></p> Informatics Publishing Limited and The Indian Mathematical Society en-US The Journal of the Indian Mathematical Society 0019-5839 Mehler-Fock, Legendre Integral Transforms with Applications https://www.informaticsjournals.com/index.php/jims/article/view/28908 In this paper we study some properties of the Mehler-Fock and Legendre transforms. Certain integrals involving associated Legendre function, Gamma function and modi?ed Bessel’s function are evaluated. Constructive examples are also provided. A. Aghili Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 199 213 10.18311/jims/2022/28908 A Note on f-Biharmonic Curves in Lorentzian Heisenberg and Lorentzian Sol<sub>3</sub> Spaces https://www.informaticsjournals.com/index.php/jims/article/view/28375 Some characterizations are given for f-biharmonic curves in three-dimensional Lorentzian Heisenberg and Lorentzian Sol<sub>3</sub> spaces. Murat Altunbas Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 215 225 10.18311/jims/2022/28375 A Generalization of Class of Humbert - Hermite Polynomials https://www.informaticsjournals.com/index.php/jims/article/view/25345 A generalization of Humbert-Hermite polynomials is de?ned in this paper. Moreover, several generalizations of Hermite-Gegenbauer polynomials, Hermite-Legendre and Hermite-Chebyshev polynomials are established. Saniya Batra Prakriti Rai Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 227 236 10.18311/jims/2022/25345 Fiedler Linearizations for Higher Order State-Space Systems https://www.informaticsjournals.com/index.php/jims/article/view/25773 Consider a higher order state space system and associated system matrix S(?). The aim of this paper is to linearize the higher order system preserving system characteristics. That is, we derive a linearized state space system of the given higher order system preserving system characteristics(e.g., controllability, observability, various zeros and transfer function) for analysis of higher order systems which gives the solution for higher order system. We study recovery of zero directions of higher order state space system from those of the linearizations. That is, the zero directions of the transfer functions associated to higher order state space system are recovered from the eigenvectors of the Fiedler pencils without performing any arithmetic operations. Namita Behera Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 237 261 10.18311/jims/2022/25773 Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces https://www.informaticsjournals.com/index.php/jims/article/view/29627 In this paper, we study biharmonic curves in three-dimensio -nal generalized symmetric spaces, equipped with a left-invariant pseudo- Riemannian metric. We characterize non-geodesic biharmonic curves in three-dimensional generalized symmetric spaces and prove that there ex- ists no non-geodesic biharmonic spacelike helix in three-dimensional gen- eralized symmetric spaces. We also show that a linear map from a Eu- clidean space in three-dimensional generalized symmetric spaces is bihar- monic if and only if it is a harmonic map, and give a complete classification of such maps. Mansour Belarbi Hichem Elhendi Lakehal Belarbi Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 263 277 10.18311/jims/2022/29627 Cyclic and Constacyclic Codes for F<sub>2</sub>[u,v]/<u<sup>2</sup>,v<sup>3</sup> – v,uv,vu> https://www.informaticsjournals.com/index.php/jims/article/view/30791 In this paper, we study cyclic and β-constacyclic codes over the ?nite commutative ring R = F<sub>2</sub>[u,v]/&lt;u<sup>2</sup>,v<sup>3</sup> ? v,uv,vu&gt; with ? = (1+u),(1+u+v+v<sup>2</sup>) and (1+v+v2). We establish a Gray map from R to F<sup>4</sup><sub>2</sub> and prove that the Gray image of a cyclic code is a quasi-cyclic code of index 4. It is also shown that the Gray image of β-constacyclic code overRis either β-equivalent, β-equivalent or β-equivalent to a quasi-cyclic code of length 4n and index 4 over F<sub>2</sub> when ? = (1 + u),(1 + u + v + v<sup>2</sup>) and (1 + v + v<sup>2</sup>), respectively. TH. Rojita Chanu ST. Timothy Kom O. Ratnabala Devi Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 279 291 10.18311/jims/2022/30791 Gowers U<sub>3</sub> Norm of Cubic MMF Bent-Negabent Functions Constructed by using Feistel Functions https://www.informaticsjournals.com/index.php/jims/article/view/29628 We obtain the Gowers U<sub>3</sub> norm of a class of cubic Maiorana-McFarland bent{negabent functions constructed by using Feis- tel functions. Saral Datta Sugata Gangopadhyay Sanjib Kumar Datta Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 293 303 10.18311/jims/2022/29628 Ball Convergence of Modified Homeier-Like's Method in Banach Spaces under Weak Continuity Condition https://www.informaticsjournals.com/index.php/jims/article/view/26313 The aim of this study is to analyze the local convergence of the multi-step Homeier's-like method for solving nonlinear equations in Banach space. Furthermore, we avoid hypotheses on high order derivatives which limit the applicability of the method. Instead, we only use hypotheses on the first derivative. Thus the applicability of the method has been extended by preserving the order of convergence. The convergence of the solution is proved under the weak hypotheses i.e. $\omega$-continuity condition. Some numerical instances where earlier results cannot be applied to solve equations but our results can be applied are provided to validate the theoretical contribution. Neha Gupta J. P. Jaiswal Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 305 316 10.18311/jims/2022/26313 Landau-Kolmogorov and Gagliardo-Nirenberg Inequalities for Differential Operators in Lorentz Spaces https://www.informaticsjournals.com/index.php/jims/article/view/25986 <p>In this paper, we establish some Landau-Kolmogorov inequalities and Gagliardo-Nirenberg inequalities for di?erential operators generated by polynomials. We illustrate the relation between ||P(D)f||<sub>N?</sub> and ||f||N?, ||D<sup>m</sup>(P(D)f)||<sub>N?</sub> as follows</p><p>||P(D)f||<sub>N?</sub> K<sub>1</sub>(E)||f||<sub>N?</sub> + K<sub>2</sub>(E)||D<sup>m</sup>(P(D)f)||<sub>N?</sub></p><p>for all E &gt; 0, where ||.||N? is the norm in Lorentz spaces N?(R). The corresponding inequalities in L<sup>p</sup>(R<sup>n</sup>) is also obtained.</p> Vu Nhat Huy Ngoc Huy Nguyen Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 317 332 10.18311/jims/2022/25986 Convergence Analysis of Havelock-Type Eigenfunction Expansions for Hydroelastic Problems in Water having Infinite Depth https://www.informaticsjournals.com/index.php/jims/article/view/25870 <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>The present paper demonstrates the point-wise convergence of the Havelock-type eigenfunction expansion to the velocity potentials associated with the water waves interaction with flexible plate and membranes in water having infinite depth. To consider the higher-order boundary condition at the mean free surface of the water domain, flexible plate and membranes are assumed to float in the mean water level. In the convergence analysis procedure, firstly, the havelock-type eigenfunction expansion for the unknown velocity potentials associated with the physical problems are obtained. Hereafter, a suitable Green's function is developed for the associated physical problem. Using the developed Green's function and the associated properties, the vertical components of the Havelock-type eigenfunction expansion is expressed in terms of the Dirac delta function. Finally, using appropriate properties of the Dirac delta function, the point-wise convergence of the Havelock-type eigenfunction expansion is demonstrated.</span></p></div></div></div> Santanu Koley Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 333 340 10.18311/jims/2022/25870 Infinite Order of Growth of Solutions of Second Order Linear Differential Equations https://www.informaticsjournals.com/index.php/jims/article/view/26751 We consider the di?erential equation f<sup>''</sup> +A(z)f<sup>'</sup> +B(z)f = 0, where A(z) and B(z) are entire complex functions. We improve various restrictions on coe?cients A(z) and B(z) and prove that all non-trivial solutions are of in?nite order. Naveen Mehra V. P. Pande Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 341 352 10.18311/jims/2022/26751 Congruences for Overpartition Pairs with Restricted Odd Differences https://www.informaticsjournals.com/index.php/jims/article/view/26254 <p>Let b<sup>-(k)</sup> (n) denote the number of overpartition pairs of n where (i) consecutive parts di?er by a multiple of k + 1 unless the larger of the two is overlined, and (ii) the smallest part is overlined unless it is divisible by k+1. We prove many in?nite families of congruences modulo powers of 2 and 3 for b<sup>-(2)</sup> (n) and congruences modulo 4 and 5 for b<sup>-(4)</sup> (n). For example, for all n ? 0 and ?,? ? 0,</p><p> </p><p>b<sup>-(4)</sup>(4·3<sup>4?</sup> ·5<sup>2?</sup>(5n + i) + 3<sup>4?</sup> ·5<sup>2?</sup>)? 0 (mod 5),</p><p>where i = 3,4.</p> M. S. Mahadeva Naika T. Harishkumar Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 353 371 10.18311/jims/2022/26254 Approximation of Fourier Series of Functions in Besov Space by Borel Means https://www.informaticsjournals.com/index.php/jims/article/view/26422 In the present article, a result on degree of approximation of Fourier series of functions in the Besov space by Borel mean is established. B. P. Padhy A. Mishra S. Nanda Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 373 385 10.18311/jims/2022/26422 Eigenvalue Bounds in an Azimuthal Instability Problem of Inviscid Swirling Flows https://www.informaticsjournals.com/index.php/jims/article/view/29629 We consider the eigenvalue problem of azimuthal instability of inviscid swirling ows between coaxial cylinders. It is shown that the complex eigenvalues corresponding to unstable azimuthal normal modes lie inside a semi-ellipse type region whose major axis coincides with the range of the angular velocity of the basic ow while its minor axis depends on the minimum Richardson number, the azimuthal wave number, and the width of the annular region between the coaxial cylinders. S. Prakash M. Subbiah Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 387 405 10.18311/jims/2022/29629 Oscillation Result for Nonlinear Fourth-Order Homogeneous Neutral Delay Dynamic Equations https://www.informaticsjournals.com/index.php/jims/article/view/29630 We introduce an oscillatory result for fourth order homogeneous neutral delay dynamic equations on time scales, which deals with a unification and extension of the differential and difference equations depending upon the time scale defines on a continuous set and a discrete set respectively. N. Sikender S. Rakmaiah Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 407 417 10.18311/jims/2022/29630 Multiple Periodic Solutions for a Class of p-Hamiltonian Systems https://www.informaticsjournals.com/index.php/jims/article/view/24941 In this paper using a variational approach, the existence of three distinct periodic solutions for a class of p-Hamiltonian systems is established. Mohammad Reza Heidari Tavani Abdollah Nazari Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 419 429 10.18311/jims/2022/24941 Conformal Riemannian Morphisms between Riemannian Manifolds https://www.informaticsjournals.com/index.php/jims/article/view/26408 In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of isometric immersions, Riemannian submersions, Riemannian maps and conformal Riemannian maps. R. B. Yadav Srikanth V. Kuppum Copyright (c) 2022 The Journal of the Indian Mathematical Society 2022-08-23 2022-08-23 431 445 10.18311/jims/2022/26408