Department of Mathematics

Let Af (n) be the Fourier coefficients of a normalized Hecke eigenform f of weight k for the full modular group SL(2, Z). For j ? 2, let Asym f (n) be the coefficients of the Dirichlet series of the jth symmetric power L-function associated with f. Let o(n) and $(n) be the sum of the divisors function and the Euler totient function, respectively. For given real numbers b and c, we prove asymptotic results for the higher power moments of (n) (n) (n) and for the second power moments of symi f (n) o (n) & (n) over sequences of positive integers given by two distinct polynomials.

A theoretical analysis of viscous fingering instability for a reactive system ??+??????? with an infinitely fast reaction in a porous medium for a rectilinear flow is presented. By contrast to the traditional quasi-steady-state analysis (QSSA), a non-modal analysis (NMA) based on the fundamental matrix formulation is employed to study the reactive displacement, considering reactants and products with mismatched viscosities. This study investigates the transient growth of perturbations by analysing the singular values and singular vectors to address the optimal energy amplification. We illustrate that an increase in the viscosity contrast, |??????????|, resulting from a chemical reaction for a given endpoint viscosity contrast ????, leads to a more unstable system. However, there exist some reactions when ????>?????, the onset delays than the equivalent non-reactive case, ????=?????. It suggests that the stability of the flow is primarily influenced when instability develops downstream within the flow. Furthermore, ???? is found to significantly affect the spatio-temporal evolution of perturbations and the underlying physical mechanism. It is demonstrated that the QSSA is inadequate to address the transient growth, and NMA is the most suitable approach to studying the underlying physical mechanism of instability. Furthermore, NMA results align more consistently with non-linear simulations compared with QSSA.

This study examines the impact of sinusoidal time-dependent injection velocities on miscible thermo-viscous fingering instabilities observed in enhanced oil recovery. Linear stability analysis (LSA) and nonlinear simulations (NLS) are used to investigate fingering dynamics, considering parameters such as thermal mobility ratio (R?), solutal mobility ratio (Rc), Lewis number (Le), and thermal-lag coefficient (?). The LSA employs a quasi-steady state approximation in a transformed self-similar coordinate system, while NLS uses a finite element solver. Two injection scenarios are explored: injection-extraction (?=2) and extraction-injection (?=?2), with fixed periodicity (T=100). Results show that for unstable solutal and thermal fronts (Rc>0,R?>0), increasing Le with fixed ??1 leads to more prominent mixing and interfacial length for ?=2 compared to constant injection and ?=?2. While for unstable solutal fronts (Rc>0) and stable thermal fronts (R?<0), increasing Le results in more prominent mixing and interfacial length for ?=?2, except during early diffusion. Thus, when porous media are swept using cold fluid, increasing the Lewis number intensifies the level of flow instability for ?=?2; whereas when hot fluid is used, the instability enhances for ?=2. Furthermore, it is observed that the high thermal diffusion (Le?1) and enhanced thermal redistribution between solid and fluid phases (??1) effectively mitigate destabilizing effects associated with positive R?, reducing overall instability. Overall, in extraction-injection scenarios, the phenomenon of tip-splitting and coalescence is attenuated, and the channeling regime is observed

Let S(p) represent the collection of meromorphic univalent functions f in the unit disc D which possess a simple pole at z=p(0<p<1) and meet the normalization f(0)=f?(0)-1=0. In this article, we determine bounds for Hermitian Toeplitz determinants whose entries are the Taylor coefficients of functions in S(p). Furthermore, we derive bounds for Hermitian Toeplitz determinants for two specific subclasses of S(p). © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2025

The present investigation delves into the intricate dynamics of diabetic population, accounting for genetic, hereditary, social, environmental, and lifestyle determinants in the progression from prediabetes to diabetes. The model encompasses comorbidities, articulated through a suite of six nonlinear differential equations. Employing numerical methodologies alongside comprehensive stability and sensitivity analyses, it unveils nuanced insights into both biological and social interactions. Theoretical discoveries are vividly illustrated, and the model’s credibility is attested through empirical validation. Conclusions drawn from the findings underscore pivotal parameters, endowing invaluable perspectives on the dynamical system in concert with stability elucidations. © 2025 L&H Scientific Publishing, LLC. All rights reserved

The offset linear canonical transform (OLCT) is an important tool in signal processing and optics. Recently, the quaternion offset linear canonical transform (QOLCT) has been introduced which is the quaternion extension of the OLCT and the generalized form of quaternion Fourier transform(QFT). In this article, the Plancherel’s theorem of the scalar inner product for the two-sided QOLCT is introduced. Also, the quaternion inner product theorems for the right sided and left sided QOLCT have been discussed. Further, as an application of the Plancherel’s theorem, the real Paley-Wiener theorem and Donoho-Stark uncertainty principle have been explored as well as the solution of particular type of quaternion differential equations are discussed using QOLCT. Additionally, the advantages of QOLCT over QLCT and QFT is illustrated graphically using example and the use of Plancherel’s theorem in filter analysis is demonstrated

We study the smoothness of the moduli space of finite quiver vector bundles over the smooth complex projective curves

Assume F is a finite field of order and q is an odd prime for which , where and . In this article, we obtain the order of the symmetric and the unitary subgroup of the semisimple group algebra Further, for the extension G of by an abelian group A of order with , we prove that if or and , then G does not have a normal complement in V(FG)

This paper addresses how the ocean currents can influence the class II Bragg resonance of surface waves with non-zero surface tension interacting with bottom topography comprising of two different wavenumbers under the assumption of a small-amplitude wave theory. A multi-scale analysis technique is applied up to the third-order to obtain the analytical expressions for reflection and transmission coefficients by solving the coupled evolution equations involving the amplitudes of both reflected and transmitted waves. In the absence of current and surface tension, the findings are validated with the existing literature results. The Bragg peak decreases with increasing U and reaches closely to zero for U lying between 2.75 and 2.81cm/s and further peak started to increase with increasing U. Phase shifting in the Bragg peak is observed in a non-monotonic manner with an increase in U as there is upshift when U changes from 0 to 2.75cm/s, with sudden downshift at U=2.77 cm/s and followed again by upshift for U=2.81 cm/s. There is asymmetrical behavior in the amplitude of left and right subharmonic peaks that are observed for U lying between 2.75 and 2.81cm/s and also, in the same range of U, the resonance bandwidth B is too short. These different qualitative behavior in the Bragg resonance is contingent upon the role played by the both positive and negative group velocities. The role of surface tension parameter T is also not trivial as the Bragg peak increases when T increases up to U=2.81 cm/s but beyond this range, the effect of T is opposite which means the Bragg peak decreases when T increases. In addition to this, this study predicted that the choice of number of ripples M to achieve full reflection is dependent upon the value of U, and it is possible to accurately capture the effect of reflected energy for large values of M. Moreover, the subcritical detuning is observed in proximity to the Bragg resonance. This study has potential to build an understanding about the role of currents on higher-order Bragg resonance on the coastal bathymetries and extremely important for coastal rehabilitation.

We introduce the localization operator associated with the linear canonical continuous Dunkl wavelet transform. We analyze the boundedness of the operator for various classes of symbols and wavelet functions. We also establish the compactness of the localization operator on spaces, where . Additionally, we explore the properties of the localization operator in Schatten-von Neumann classes and demonstrate that, with appropriate choices of symbols and wavelet functions, the localization operator can be identified as both a trace class operator and a Hilbert–Schmidt operator.

We consider inference upon unknown parameters of the family of inverted exponentiated distributions when it is known that data are doubly censored. Maximum likelihood and Bayes estimates under different loss functions are derived for estimating the parameters. We use Metropolis-Hastings algorithm to draw Markov chain Monte Carlo samples, which are used to compute the Bayes estimates and construct the Bayesian credible intervals. Further, we present point and interval predictions of the censored data using the Bayesian approach. The performance of proposed methods of estimation and prediction are investigated using simulation studies, and two illustrative examples are discussed in support of the suggested methods. Finally, we propose the optimal plans under double censoring scheme.

Klann and Ramlau [16] hypothesized fractional Tikhonov regularization as an interpolation between generalized inverse and Tikhonov regularization. In fact, fractional schemes can be viewed as a generalization of the Tikhonov scheme. One of the motives of this work is the major pitfall of the a priori parameter choice rule, which primarily relies on source conditions that are often unknown. It necessitates the need for advocating a data-driven approach (a posteriori choice strategy). We briefly overview fractional scheme in learning theory and propose a modified Engl type [9] discrepancy principle, thus integrating supervised learning into the field of inverse problems. In due course of the investigation, we effectively explored the relation between learning from examples and the inverse problems. We demonstrate the regularization properties and establish the convergence rate of this scheme. Finally, the theoretical results are corroborated using two well known examples in learning theory.

Impulsive point sources are one of the external forces which can create a wave motion in the body. This article investigates the propagation characteristics of Love waves in a visco-porous piezoelectric (VPPE) material layered over a functionally graded piezoelectric (FGPE) substrate, with a point source applied at the interface. Green’s function approach and the Fourier transform are used to derive an analytical solution, of which the real part yields the frequency curve and the imaginary part yields the attenuation curve. Some particular cases are derived and compared with the existing studies for validation. Numerical illustrations are provided, showing the variation of phase velocity and attenuation with respect to different parameters, using lithium niobate as the substrate and PZT-5A as the visco-porous piezoelectric material. The findings of the study will be useful in the development and enhancement of surface acoustic wave devices.

The authors exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. They also prove the 3-divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields. At the end, they provide some numerical examples supporting our results

We prove that an involution on certain examples of surfaces of general type with , acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when the quotient is an Enriques surface and show that the Bloch conjecture holds for such surfaces

The quaternion Fourier Transform (QFT) finds extensive applications across various domains, such as signal processing and optics. This paper strengthens two important uncertainty principles for QFT. First, we proposed two different sharper versions of generalized Heisenberg's uncertainty principle associated with quaternion Fourier trans-form in LP(R2, H) space for p? [1, 2]. Also a new version of Donoho Stark's uncertainty principle associated with QFT is discussed. Furthermore, in some particular case this new Donoho-Stark's uncertainty principle is the sharper version than the existing one in quaternion sense.

We define the notion of Tate–Shafarevich group and Selmer group of the Chow group of zero cycles of degree zero of an abelian variety defined over a global function field and prove that the Selmer group is finite

Hyperlipidemia is recognized as a significant health concern in the human body. In this study, a novel mathematical framework is developed to investigate targeted therapeutic strategies for reducing hyperlipidemia through a fifth-compartment mathematical model. The model consists of five compartments: the liver, blood, gallbladder, intestine, and tissue. To address hyperlipidemia, direct drug administration into the bloodstream is incorporated. Potential treatments for lowering cholesterol levels in the blood and tissue are explored, contributing to advancements in medical research. Sensitivity analysis is performed to determine the impact of various parameters on equilibrium stability. Stability tests evaluate the model’s long-term stability, ensuring greater accuracy in predictive modeling. The variation in cholesterol levels and drug concentration over time is analyzed using MATLAB software, with graphical results demonstrating a gradual decline in cholesterol levels following drug administration. Both analytical and numerical assessments confirm the model’s effectiveness in characterizing cholesterol transport and optimizing therapeutic strategies for hyperlipidemia management.

We study the Bochner modular relation (Lambert series) for the kth power of the product of two Riemann zeta-functions with difference ?, an integer with the Vorono? function weight Vk. In the case of V1(x)=e?x, the results reduce to Bochner modular relations, which include the Ramanujan formula, Wigert–Bellman approximate functional equation, and the Ewald expansion. The results abridge analytic number theory and the theory of modular forms in terms of the sum-of-divisor function. We pursue the problem of (approximate) automorphy of the associated Lambert series. The ?=0 case is the divisor function, while the ?=1 case would lead to a proof of automorphy of the Dedekind eta-function à la Ramanujan.

We study the class which includes functions f that are meromorphic in the unit disk and have a simple pole at for some with the normalization. We establish a sufficient condition for functions in this class to be univalent. Making use of this condition, we introduce a subfamily consisting of univalent functions satisfying a certain differential inequality in . Next, we obtain a representation formula for such functions. Additionally, we establish necessary and sufficient conditions on the coefficients for functions of the form belong to this class. Furthermore, we determine sharp upper bounds for all. Finally, we establish a sharp estimate for the Fekete-Szego functional associated with the newly introduced subclass