The Journal of the Indian Mathematical Society

On Level 3 Ramanujan-Sato Type Series for 1/π

K. R. Vasuki, T. Anusha, H. T. Shwetha — Mon, 01 Jan 2024 00:00:00 +0530

Srinivasa Ramanujan developed seventeen fast convergent series for 1/π. Motivated by Ramanujan’s series for 1/π many mathematicians have developed many theories for deriving new series for 1/π. In this article we obtain new series for 1/π using Eisenstein series of level three.

On the q-Hypergeometric Matrix Function _rφ_s(A, B; C_i; D_j; q; z) and Its q-Fractional Calculus

Ravi Dwivedi, Reshma Sanjhira — Mon, 01 Jan 2024 00:00:00 +0530

In this paper, we introduce a q-hypergeometric matrix function _rφ_s(A, B; C_i; D_j; q; z) and investigate their regions of convergence. We determine some q-matrix contiguous function relations, a q-integral representation and q-difference formulas satisfied by _rφ_s(A, B; C_i; D_j; q; z) Certain properties of this matrix function have also been studied from q-fractional calculus point of view. Finally, we emphasize on the special cases of _rφ_s(A, B; C_i; D_j; q; z).

Kolmogorov’s Axioms for Bihyperbolic Valued Probabilities

Soumen Mondal, Chinmay Ghosh , Sanjib Kumar Datta — Mon, 01 Jan 2024 00:00:00 +0530

In this paper we introduce probabilistic measure which takes values in bihyperbolic numbers and generalize Kolmogorov’s system of axioms. We study the zero divisors of the set of bihyperbolic numbers and keeping it in mind, we define conditional bihyperbolic probability and prove bihyperbolic analogues of the multiplication theorem, of the law of total probability and Bayes’ theorem.

Almost Balancing-Like Sequences

A. K. Panda, C. Rout — Mon, 01 Jan 2024 00:00:00 +0530

Balancing-like sequences are generalizations of the balancing sequence obtained by altering a coefficient in the recurrence relation for the balancing sequence. Almost balancing numbers are solutions of a Diophantine equation resulting from slight alteration of the defining equation of the balancing numbers. Almost balancing-like sequences are variants of the balancing-like sequences and serve as generalizations of the almost balancing sequences.

Value Distribution and Uniqueness of General Differential-Difference Polynomials

Rajib Mandal, Raju Biswas — Mon, 01 Jan 2024 00:00:00 +0530

We mainly study the possible value distribution and uniqueness results of the general differential-difference polynomials of transcendental entire functions with finite order when they share a small function under weighted sharing and weakly weighted sharing hypotheses. These are significant generalization of earlier results. As a very special case, we obtain the results of Majumder et al. (A note on the uniqueness of certain types of differential-difference polynomials, Ukrainian Mathematical Journal, 73(5), 791-810(2021)). We fortify some examples to claim that the used conditions are best possible in the paper.

Euclidean Algorithm in Imaginary Abelian Sextic Number Fields

M. Subramani , Usha K. Sangale — Mon, 01 Jan 2024 00:00:00 +0530

We prove that all imaginary abelian sextic number fields ofunit rank less than 3 and having class number 1 are Euclidean

Convex-Cyclicity and K-Transitivity Of Semigroups of Operators on Finite and Infinite Dimensional Spaces

Abhay Kumar — Mon, 01 Jan 2024 00:00:00 +0530

We study convex-cyclicity, various weak notions of convexcyclicity, and their relation to somewhere density. Further, we give another proof that does not use the structure theorem of the result that there does not exist a k-transitive semigroup T of matrices for k ≥ 2 given by Adlene Ayadi.

Homological Quantum Codes Associated With A Class of Surface Maps

Marbarisha M. Kharkongor, Debashis Bhowmik, Dipendu Maity — Mon, 01 Jan 2024 00:00:00 +0530

The study of error-correcting quantum codes associated with combinatorial objects is an active area of research. These codes play an important role in several results in computational theory. There are classes of such codes whose encoding rates are close to 0 and 1. In this article, we introduce a few new classes of codes associated with a class of combinatorial structures of surfaces. The encoding rates of these classes of codes are between p and q where 0 < p, q < 1.

Some Congruence Properties of Stirling Numbers of the Second Kind

A. Lalchhuangliana, S. S. Singh, Jitender Singh — Mon, 01 Jan 2024 00:00:00 +0530

This paper establishes certain formulas for p-adic valuation of Stirling numbers of the second kind S(pⁿ, k) where p is a prime and some related classes. The parity of k also affects the p-adic valuation of S(n, k) if k is divisible by p. In fact, vp(S(p², kp)) ≥ 5 if k is even. The congruence properties of S(pⁿ, k) (mod p²) depend on the sum of the p-adic digits of k when k is not a multiple of p.

On Mac Lane’s Conditions and Disjointness Properties for Posets

R. S. Shewale, Vilas Kharat — Mon, 01 Jan 2024 00:00:00 +0530

In This Paper, We Generalized the Mac Lane’s Conditions And Disjointness Properties of Lattices for Posets and Relations Amongst Them Are Studied.

On the Turan Type Inequalities and k-Analogue of Some Special Functions

Jeet B. Gajera, Ranjan Kumar Jana — Mon, 01 Jan 2024 00:00:00 +0530

In this paper we deduced Tur´an-type inequalities for n^thderivative of k-gamma function, k-gauss hypergeometric functions, k-confluent hypergeometric functions, and k-Appell series F_1,k by using different generalizations of Cauchy-Bunyakovsky-Schwarz inequalities with parameter k > 0. Some special cases are also derived.

On Regular Genus and G-Degree of PL 4-Manifolds With Boundary

Biplab Basak, Manisha Binjola — Mon, 01 Jan 2024 00:00:00 +0530

In this article, we introduce two novel PL-invariants: weighted regular genus and weighted G-degree for manifolds with boundaries. We establish that for any PL 4-manifoldM with non-spherical boundary components, the regular genus G(M) of M is at least the weighted regular genus Ḡ(M). Additionally, another inequality asserts that the weighted G-degree ^-˜D_G(M) of M is always greater than or equal to the G-degree D_G(M) of M.

Furthermore, we derive lower bounds for the weighted regular genus ˜Ḡ (M) and weighted G-degree ˜D_G(M) for a PL 4-manifold with nonspherical boundary components. This contributes to an enhancement of the existing lower bounds for the regular genus G(M) of the manifold. Subsequently, we define two classes of gems for a PL 4-manifold M with boundary: one comprised of semi-simple gems and the other consisting of weak semi-simple gems. We prove that the lower bounds for the weighted G-degree and weighted regular genus are achieved within these two classes, respectively.

Total Variation Diminishing (TVD) Method For Elastohydrodynamic Lubrication (EHL) Problem On Parallel Computers

Peeyush Singh, Pravir K. Dutt — Mon, 01 Jan 2024 00:00:00 +0530

In this article, we offer a novel parallel approach for the solution of elastohydrodynamic lubrication line and point contact problems using a class of total variation diminishing (TVD) schemes on parallel computers. A direct parallel approach is presented by introducing a novel solver named as projected alternate quadrant interlocking factorization (PAQIF) by solving discrete variational inequality. For one-dimensional EHL case, we use weighted change in Newton-Raphson approximation to compute the Jacobian matrix in the form of a banded matrix by dividing two subregions on the whole computation domain. Such subregion matrices are then assembled by measuring the ratio of diffusive coefficient and discrete grid length on the domain of the interest. The banded matrix is then processed to parallel computers for solving discrete linearized complementarity system using PAQIF algorithm. The idea is easily extended in two-dimensional EHL case by taking appropriate splitting in x and y alternating directions respectively. Numerical experiments are performed and analyzed to validate the performance of computed solution on serial and parallel computers.

Backward Error of Approximate Eigenelements Of a Regular Rational Matrix

Namita Behera — Mon, 01 Jan 2024 00:00:00 +0530

We consider a minimal realization of a rational matrix. We perturb all the coefficients of matrix polynomial and some coefficients from the realization part present in the realization form of rational matrix. We derive explicit computable formulae for backward error of approximate eigenvalues and eigenpairs of regular rational matrix. We also determine minimal perturbations for all the coefficients of matrix polynomial and some coefficients from the realization part for which approximate eigenvalues are exact eigenvalues of the perturbed rational matrix.

Φ − X - Elements in Multiplicative Lattices

Sachin Sarode — Mon, 01 Jan 2024 00:00:00 +0530

In this paper, author presents a generalization of an X-element in a multiplicative lattice L. For a particular M-closed subset X, author defines the concept of ϕ − r-element, ϕ − n-element, and ϕ − J-element. These elements generalize the notion of ϕ − r-ideals, ϕ − n-ideals, and ϕ − J-ideals of a commutative ring with unity to multiplicative lattices. An ideal I of a commutative ring R with unity is a ϕ − n-ideal (ϕ − Jideal) of R if and only if I is a ϕ − n-element (ϕ − J-element) of Id(R), the ideal lattice of R is proved.

Uniqueness Concerning Derivatives of A Meromorphic Function and Its Difference Polynomial

Renukadevi S. Dyavanal, Deepa N. Angadi — Mon, 01 Jan 2024 00:00:00 +0530

This paper presents an investigation of the uniqueness problem of derivatives of a meromorphic function and its difference polynomial in view of a partially sharing. As a consequence of the main result, we improve the recent result of W. J. Chen and Z. G. Huang with the weaker hypotheses and also supplement several results in particular cases.

The Boundedness of Fractional Hardy-Littlewood Maximal Operator On Variable ℓ^p(·)(Z) Spaces Using Calderon-Zygmund Decomposition

A. Sri Sakti Swarup, A. Michael Alphonse — Mon, 01 Jan 2024 00:00:00 +0530

In this paper, we prove strong type and weak type inequalities of the Hardy-Littlewood maximal operator(M) and fractional Hardy- Littlewood maximal operator(M_α) on variable sequence spaces ℓ^p(·)(Z). This is achieved using Calderon-Zygmund decomposition for sequences, properties of modular functional and Log Holder continuity.

The Sharp Bounds of the Hankel Determinants For the Class of Convex Functions With Respect to Symmetric Points

Biswajit Rath, K. Sanjay Kumar, D. Vamshee Krishna, G. K. Surya Viswanadh — Mon, 01 Jan 2024 00:00:00 +0530

In this paper, we estimate sharp bounds for certain Hankel determinants, H_2,3(f), H_3,1(f) and Zalcman functional |a₃² − a₅| for the class of convex function with respect to symmetric points, hence proving the recent conjecture made by Virendra et al., that affirms the sharp bound for the third Hankel determinant in the classes of convex functions with respect to symmetric points is 4/135.

Modeling the Role of Seasonal Variability On The Dynamics of Mosquito-Borne Diseases

Omprakash Singh Sisodiya, O. P. Misra, Joydip Dhar — Mon, 01 Jan 2024 00:00:00 +0530

In this article, we have proposed an non-autonomous mathematical model to describe the dynamics of mosquito-borne diseases taking into account seasonal variation. In the proposed model, the disease transmission rate and the growth rate of aquatic mosquito populations are considered seasonally. The non-autonomous model is shown to have a disease-free, globally asymptotically stable cyclic state whenever the time-dependent reproduction number R_C(t) is less than unity. From the model analysis, we find that a unique positive endemic periodic solution of a non-autonomous system exists only when R_C(t) > 1. The persistence and severity of an epidemic can be described by a time-dependent periodic reproduction number R_C(t). Furthermore, it is shown that if R_C(t) <1, the disease will not spread and may eventually disappear. We also propose an optimal control problem applied to control the disease with two other parameters namely insecticide and spraying. It has been shown that a control strategy consisting of insecticides and combined spraying can have a synergistic effect in reducing the incidence of mosquito-borne diseases. Finally, numerical simulations are performed to illustrate the results of our analysis.