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R. N. Mohapatra

Publications and source records attributed to R. N. Mohapatra.

At least 19 recordsLinked to original sources
arXiv2026

Jensen-type inequalities on pairs of measure spaces and their applications

We develop applications of a Jensen-type inequality for pairs of positive measure spaces. The framework yields $L^p$ and operator inequalities for positive integral operators, norm and entropy estimates for Fejér means, and probabilistic moment and variance bounds. We also obtain robustness estimates under random and deterministic erasures. These results provide a unified connection between Jensen-type inequalities, harmonic analysis, operator theory, probability, and robust reconstruction.

math.FA↗
arXiv2026

The structure of optimal dual frames for probabilistic erasures under Hilbert--Schmidt norm

Frames provide redundant representations that enable stable signal reconstruction under coefficient losses. In this paper, we study optimal dual frames for probabilistic erasures using the Hilbert--Schmidt norm of the associated error operators. We characterize dual frames that are optimal for $1-$erasures and establish conditions under which the canonical dual is not only optimal but also unique. We further derive lower bounds for the probabilistic reconstruction error for any $m-$ erasure and identify classes of frames for which the canonical dual remains optimal. In addition, we analyze the geometric structure of the set of optimal dual frames, showing that it is a nonempty compact convex set. These results provide new insights into robustness and optimal reconstruction in probabilistic erasure models.

math.FA↗
arXiv2026

Inequalities for Pairs of Measure Spaces and Applications

We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities such as Hölder's and Minkowski's as special cases. The inequality admits sharp characterizations of equality and yields quantitative, variational, and probabilistic refinements under additional convexity assumptions. Several corollaries illustrate power-mean, entropy-type, and erasure-robust inequalities, as well as applications to convolution-type operators and weighted discrete models.

math.FA↗
arXiv2026

When Mathematics Meets Painting: Fibonacci Geometry, Cubism and Visual Abstraction

This paper explores the Fibonacci sequence and the Golden Ratio as organizing principles for visual composition and abstraction in painting. The author shows how recursive proportional systems, long associated with natural growth and aesthetic harmony, inform artistic structure and visual balance. The discussion traces Fibonacci-based geometry from Renaissance art to modern and contemporary practices, with particular attention to Cubism, where fragmentation and multiple viewpoints echo principles of recursion and geometric division. Through selected artistic examples and mathematical insight, the paper demonstrates that Fibonacci geometry functions not merely as a symbolic reference but as a generative framework shaping visual abstraction and artistic expression.

math.HO↗
arXiv2025

Designing optimal dual frames for $\ell^p-$average error optimization

In this paper, we investigates the problem of optimal dual frame selection for signal reconstruction in the presence of erasures. Unlike traditional approaches relying on left inverses, we evaluate performance through the norms of error operators, using the Frobenius norm, spectral radius, and numerical radius as measures. Our central focus is the characterization of dual frames that minimize the $\ell^p-$average under these error operator measurements over all possible erasure patterns. We provide conditions under which the canonical dual frame is uniquely optimal and extend our results to multiple erasures. In the Frobenius norm case, we offer a complete characterization for any number of erasures in uniform tight frames. The paper also examines interconnections between optimality criteria across different norm measures and gives sufficient conditions ensuring uniqueness of the optimal dual.

math.FA↗
arXiv2025

Optimal K dual frames and pairs in the presence of erasures

This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame coefficients. We address two distinct erasure scenarios and examine their impact on the reconstruction process. The optimality criteria are defined in terms of minimizing the spectral radius and the operator norm of the associated error operators. Through this approach, we provide a comprehensive framework for understanding and mitigating the effects of erasures in frame theory, contributing to enhanced robustness in data transmission and recovery.

math.FA↗
arXiv2023

Characterizations of Weighted Generalized Inverses

The main objective of this paper is to introduce unique representations and characterizations for the weighted core inverse of matrices. We also investigate various properties of these inverses and their relationships with other generalized inverses. Proposed representations of the matrix-weighted core inverse will help us to discuss some results associated with the reverse order law for these inverses. Furthermore, this paper introduces an extension of the concepts of generalized bilateral inverse and $\{1,2,3,1^k\}$-inverse and their respective dual for complex rectangular matrices. Furthermore, we establish characterizations of EP-ness and the condition when both $W$-weighted $\{1,2,3\}$ and $W$-weighted $\{1,2,3,1^k\}$ inverses coincide. Then, a W-weighted index-MP, W-weighted MP-index, and W-weighted MP-index-MP matrices for rectangular complex matrices is introduced. In addition, we define the dual inverses for both weighted bilateral inverses and $\{1,2,3,1^k\}$-inverse. Characteristics that lead to self-duality in weighted bilateral inverses are also examined.

math.NA↗
arXiv2023

Generalized Core Inverse in a proper $*$-ring

In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $*$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central weak core invertible elements. We investigated additive properties and a few explicit expressions for these two classes of inverses through other generalized inverses. In addition, numerical examples are provided to validate claims on weak core inverses. Following {\it proper $*$-ring} and their interconnections with Clifford algebra, we also present examples of the group inverse and the weak core inverse of a non-zero non-invertible quaternion $\mathbb{H}_s$.

math.RA↗
arXiv2022

Searches for Baryon Number Violation in Neutrino Experiments: A White Paper

Baryon number conservation is not guaranteed by any fundamental symmetry within the Standard Model, and therefore has been a subject of experimental and theoretical scrutiny for decades. So far, no evidence for baryon number violation has been observed. Large underground detectors have long been used for both neutrino detection and searches for baryon number violating processes. The next generation of large neutrino detectors will seek to improve upon the limits set by past and current experiments and will cover a range of lifetimes predicted by several Grand Unified Theories. In this White Paper, we summarize theoretical motivations and experimental aspects of searches for baryon number violation in neutrino experiments.

hep-ex↗
arXiv2021

Computation of Generalized Inverses of Tensors via $t$-Product

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In this paper, we study different generalized inverses of tensors over a commutative ring and a non-commutative ring. Several numerical examples are provided in support of the theoretical results. We also propose algorithms for computing the inner inverses, the Moore-Penrose inverse, and weighted Moore-Penrose inverse of tensors over a non-commutative ring. The prowess of some of the results is demonstrated by applying these ideas to solve an image deblurring problem.

math.RA↗
arXiv2021

Multipliers for operator-valued Bessel sequences, generalized Hilbert-Schmidt and trace classes

Let $\{λ_n\}_n \in \ell^\infty(\mathbb{N})$. In 1960, R. Schatten \cite{SCHATTEN} studied operators of the form $\sum_{n=1}^{\infty}λ_n (x_n\otimes \bar{y_n})$, where $\{x_n\}_n$, $\{y_n\}_n$ are orthonormal sequences in a Hilbert space. In 2007, P. Balazs \cite{BALAZS3} generalized this by replacing $\{x_n\}_n$ and $\{y_n\}_n$ by Bessel sequences. In this paper, we generalize this by studying the operators of the form $\sum_{n=1}^{\infty}λ_n (A^*_nx_n\otimes \bar{B^*_ny_n})$, where $\{A_n\}_n$ and $\{B_n\}_n$ are operator-valued Bessel sequences and $\{x_n\}_n$, $\{y_n\}_n$ are sequences in the Hilbert space such that $\{\|x_n\|\|y_n\|\}_n \in \ell^\infty(\mathbb{N})$. We next generalize the classes of Hilbert-Schmidt and trace class operators.

math.FA↗
arXiv2020

Neutrino Masses and Mixing in Models with Large Extra Dimensions and Localized Fermions

Using a low-energy effective field theory approach, we study some properties of models with large extra dimensions, in which quarks and leptons have localized wave functions in the extra dimensions. We consider models with two types of gauge groups: (i) the Standard-Model gauge group, and (ii) the left-right symmetric (LRS) gauge group. Our main focus is on the lepton sector of models with $n=2$ extra dimensions, in particular, neutrino masses and mixing. We analyze the requisite conditions that the models must satisfy to be in accord with data and present a solution for lepton wave functions in the extra dimensions that fulfills these conditions. As part of our work, we also present a new solution for quark wave function centers. Issues with flavor-changing neutral current effects are assessed. Finally, we remark on baryogenesis and dark matter in these models.

hep-ph↗
arXiv2020

Weighted Moore-Penrose inverses of arbitrary-order tensors

Within the field of multilinear algebra, inverses and generalized inverses of tensors based on the Einstein product have been investigated over the past few years. In this paper, we explore the singular value decomposition and full-rank decomposition of arbitrary-order tensors using {\it reshape} operation. Applying range and null space of tensors along with the reshape operation; we further study the Moore-Penrose inverse of tensors and their cancellation properties via the Einstein product. Then we discuss weighted Moore-Penrose inverses of arbitrary-order tensors using such product. Following a specific algebraic approach, a few characterizations and representations of these inverses are explored. In addition to this, we obtain a few necessary and sufficient conditions for the reverse-order law to hold for weighted Moore-Penrose inverses of arbitrary-order tensors.

math.NA↗
arXiv2019

The CLIC Potential for New Physics

The Compact Linear Collider (CLIC) is a mature option for the future of high energy physics. It combines the benefits of the clean environment of $e^+e^-$ colliders with operation at high centre-of-mass energies, allowing to probe scales beyond the reach of the Large Hadron Collider (LHC) for many scenarios of new physics. This places the CLIC project at a privileged spot in between the precision and energy frontiers, with capabilities that will significantly extend knowledge on both fronts at the end of the LHC era. In this report we review and revisit the potential of CLIC to search, directly and indirectly, for physics beyond the Standard Model.

hep-ph↗
arXiv2018

CP Violation in the Lepton Sector and Implications for Leptogenesis

We review the current status of the data on neutrino masses and lepton mixing and the prospects for measuring the CP-violating phases in the lepton sector. The possible connection between low energy CP violation encoded in the Dirac and Majorana phases of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix and successful leptogenesis is emphasized in the context of seesaw extensions of the Standard Model with a flavor symmetry Gf (and CP symmetry).

hep-ph↗
arXiv2016

Heavy right-handed neutrino dark matter and PeV neutrinos at IceCube

We discuss a simple non-supersymmetric model based on the electroweak gauge group $SU(2)_L\times SU(2)^\prime\times U(1)_{B-L}$ where the lightest of the right-handed neutrinos, which are part of the leptonic doublet of $SU(2)^\prime$, play the role of a long-lived unstable dark matter with mass in the multi-PeV range. We use a resonant $s$-channel annihilation to obtain the correct thermal relic density and relax the unitarity bound on dark matter mass. In this model, there exists a 3-body dark matter decay mode producing tau leptons and neutrinos, which could be the source for the PeV cascade events observed in the IceCube experiment. The model can be tested with more precise flavor information of the highest-energy neutrino events in future data.

hep-ph↗