Amitabha Tripathi
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View article: The Long-Term Impact of Corporate Social Responsibility on Financial Performance: Evidence from Emerging Markets
The Long-Term Impact of Corporate Social Responsibility on Financial Performance: Evidence from Emerging Markets Open
Corporate Social Responsibility (CSR) has gained significant traction in emerging markets, where businesses are increasingly integrating social and environmental considerations into their corporate strategies. This study examines the longt…
View article: On the Frobenius Problem for Some Generalized Fibonacci Subsequences -- I
On the Frobenius Problem for Some Generalized Fibonacci Subsequences -- I Open
For a set $A$ of positive integers with $\gcd(A)=1$, let $\langle A \rangle$ denote the set of all finite linear combinations of elements of $A$ over the non-negative integers. The it is well known that only finitely many positive integers…
View article: Measures of closeness to cordiality for graphs
Measures of closeness to cordiality for graphs Open
A graph $G$ is cordial if there exists a function $f$ from the vertices of $G$ to $\{0,1\}$ such that the number of vertices labelled $0$ and the number of vertices labelled $1$ differ by at most $1$, and if we assign to each edge $xy$ the…
View article: On the two-colour Rado number for $\sum_{i=1}^m a_ix_i=c$
On the two-colour Rado number for $\sum_{i=1}^m a_ix_i=c$ Open
Let $a_1,\ldots,a_m$ be nonzero integers, $c \in \mathbb Z$ and $r \ge 2$. The Rado number for the equation \[ \sum_{i=1}^m a_ix_i = c \] in $r$ colours is the least positive integer $N$ such that any $r$-colouring of the integers in the i…
View article: On Disjunctive Rado Numbers for Some Sets of Equations
On Disjunctive Rado Numbers for Some Sets of Equations Open
Given a set of linear equations $S$ with positive integral parameters $a_1,\ldots,a_k$, $k \ge 2$, the disjunctive Rado number for the set $S$ is the least positive integer $R=R_d(S)$, if it exists, such that every $2$-coloring $\chi$ of t…
View article: Extensions of Midy's Theorem for Periodic Decimals
Extensions of Midy's Theorem for Periodic Decimals Open
See the abstract in the attached pdf.
View article: On proportionally modular numerical semigroups that are generated by arithmetic progressions
On proportionally modular numerical semigroups that are generated by arithmetic progressions Open
A numerical semigroup is a submonoid of ${\mathbb Z}_{\ge 0}$ whose complement in ${\mathbb Z}_{\ge 0}$ is finite. For any set of positive integers $a,b,c$, the numerical semigroup $S(a,b,c)$ formed by the set of solutions of the inequalit…
View article: On a generalization of the Monkey and Coconuts Problem
On a generalization of the Monkey and Coconuts Problem Open
The original version of the Monkey and Coconuts Problem describes a hypothetical situation where five sailors and a monkey are trapped on an island and plan on equally sharing coconuts. The number of coconuts turns out to be one more than …
View article: On the least size of a graph with a given degree set -- II
On the least size of a graph with a given degree set -- II Open
The degree set of a finite simple graph $G$ is the set of distinct degrees of vertices of $G$. A theorem of Kapoor, Polimeni & Wall asserts that the least order of a graph with a given degree set $\mathscr D$ is $1+\max \mathscr D$. Tripat…
View article: On the Nested Local Postage Stamp Problem
On the Nested Local Postage Stamp Problem Open
See the abstract in the attached pdf.
View article: Elastic Scattering of Electrons from Methane Molecule
Elastic Scattering of Electrons from Methane Molecule Open
Here we present our theoretical results for the differential scattering cross section and spin polarization parameters for elastic scattering of electrons from methane molecule at 100.00 eV using relativistic Dirac equation. The calculated…
View article: Relativistic Calculations of Positron Scattering from Xenon (Xe) Atom
Relativistic Calculations of Positron Scattering from Xenon (Xe) Atom Open
We present relativistic calculations of the differential, integrated elastic, momentum transfer, total cross sections and spin polarization parameters for positrons scattered from xenon atom using a simple optical model potential to repres…
View article: A note on the Frobenius and the Sylvester numbers
A note on the Frobenius and the Sylvester numbers Open
Positive integers that cannot be represented by a linear form with relatively prime coefficients and over nonnegative integers are finite in number.We describe a connection between the largest number in this set and the cardinality of this…
View article: Some results on a class of mixed van der Waerden numbers
Some results on a class of mixed van der Waerden numbers Open
The mixed van der Waerden number ${w}(k_1, \\ldots ,k_r;r)$ is the least positive integer $n$ such that every $r$-coloring of $[1,n]$ admits a monochromatic arithmetic progression of length $k_i$, for at least one $i$. We denote by ${w}_2(…
View article: On Changes in the Frobenius and Sylvester Numbers
On Changes in the Frobenius and Sylvester Numbers Open
See the abstract in the attached pdf.