A5113255633- Commutative Algebra and Its Applications
- Algebraic Geometry and Number Theory
- Algebraic structures and combinatorial models
- Polynomial and algebraic computation
- Rings, Modules, and Algebras
- Advanced Topics in Algebra
- Advanced Combinatorial Mathematics
- Advanced Algebra and Geometry
- Molecular spectroscopy and chirality
- Holomorphic and Operator Theory
- Finite Group Theory Research
- Essential Oils and Antimicrobial Activity
- Iterative Methods for Nonlinear Equations
- Fractional Differential Equations Solutions
- Sesquiterpenes and Asteraceae Studies
- Natural product bioactivities and synthesis
- advanced mathematical theories
- Botanical Research and Chemistry
- Synthesis and Properties of Aromatic Compounds
- Ethnobotanical and Medicinal Plants Studies
- Phytochemistry and Biological Activities
- Natural Antidiabetic Agents Studies
- Botany, Ecology, and Taxonomy Studies
- Graph theory and applications
- Plant Diversity and Evolution
Tata Institute of Fundamental Research
1994-2025
University at Buffalo, State University of New York
2025
Hemwati Nandan Bahuguna Garhwal University
2021-2024
University of Mumbai
1991
Analysis Group (United States)
1977
Abstract A density function for an algebraic invariant is a measurable on which measures the ‐scale. This carries lot more information related to without seeking extra data. It has turned out be useful tool, was introduced by third author in Trivedi [Trans. Amer. Math. Soc. 370 (2018), no. 12, 8403–8428], study characteristic invariant, namely Hilbert–Kunz multiplicity of homogeneous ‐primary ideal. Here, we construct functions Noetherian filtration ideals and given saturated powers ideal...
Background: Saussurea is the most diverse genus of Asteraceae family generally found in temperate areas Eurasian countries. This comprises approximately 27 ethnologically important species such as laniceps, S. costus, medusa, obvallata, involucrata, etc. which are traditionally used for treatment various ailments and also have aesthetic religious importance. Methods: study integrated two separate approaches literature review, first we reviewed research work conducted on ethnobotany,...
We give effective bounds on the higher Hilbert coefficients of finitely generated modules over Noetherian local rings (A, m) with respect to m-primary ideals, in terms multiplicity, dimension and lengths cohomology modules. similarly bound Castelnuovo–Mumford regularity associated Rees
For a pair $(R,I)$ , where $R$ is standard graded domain of dimension $d$ over an algebraically closed field characteristic 0, and $I$ ideal finite colength, we prove that the existence $\lim _{p\rightarrow \infty }e_{HK}(R_{p},I_{p})$ equivalent, for any fixed $m\geqslant d-1$ to }\ell (R_{p}/I_{p}^{[p^{m}]})/p^{md}$ . This get as consequence Theorem 1.1: $p\longrightarrow \infty$ convergence Hilbert–Kunz (HK) density function $f(R_{p},I_{p})$ equivalent truncated HK functions...
Flenner's proof in [F] of the Bertini theorem for local rings mixed characteristic is incomplete. In this note, we modify argument to fix gap.
A Mellin transform technique for the asymptotic solution of a nonlinear Volterra integral equation presented earlier by Kumar (1971) has been improved upon in present paper. The application makes it possible to get an arbitrary number terms large values argument. An example worked out detail.
We had shown earlier that for a standard graded ring $R$ and ideal $I$ in characteristic $p>0$, with $\ell(R/I) <\infty$, there exists compactly supported continuous function $f_{R, I}$ whose Riemann integral is the HK multiplicity $e_{HK}(R, I)$. explore further some other invariants, namely shape of graph {\bf m}}$ (where ${\bf m}$ maximal $R$) maximum support (denoted as $\alpha(R,I)$) I}$. In case domain dimension $d\geq 2$, we prove $(R, m})$ regular if only has symmetry m}}(x) = f_{R,...
We give examples of two dimensional normal ${\mathbb Q}$-Gorenstein graded domains, where the set $F$-thresholds maximal ideal is not discrete, thus answering a question by Mustaţa-Takagi-Watanabe. We also prove that, for standard domain $(R, {\bf m})$ over field characteristic $0$, with $I$, if $({\bf m}_p, I_p)$ reduction mod $p$ m}, I)$ then $c^{I_p}({\bf m}_p) \neq c^I_{\infty}({\bf implies $c^{I_p}({\bf m}_p)$ has in denominator.
We give examples of two dimensional normal ${\mathbb Q}$-Gorenstein graded domains, where the set $F$-thresholds maximal ideal is not discrete, thus answering a question by Musta\c{t}\u{a}-Takagi-Watanabe. also prove that, for standard domain $(R, {\bf m})$ over field characteristic $0$, with $I$, if $({\bf m}_p, I_p)$ reduction mod $p$ m}, I)$ then $c^{I_p}({\bf m}_p) \neq c^I_{\infty}({\bf implies m}_p)$ has in denominator.
For a given algebraically closed field $k$ of characteristic $p>0$ we consider the set ${\mathcal C}_k$, graded isomorphism classes {\em standard pairs} $(R, I)$, where $R$ is ring over and $I$ ideal finite colength. Here give homomorphism $\Pi:\Z[{\mathcal C}_k] \longrightarrow H(\C)[X]$, $H(\C)$ denotes entire functions. The related function $\Pi$ keep track two positive invariants, $e_{HK}(R, I)$ $c^I({\bf m})$ ring: (1) composing map with evaluation at $z=0$ gives $\Pi_e:\Z[{\mathcal...