arXiv subjects

Ram Kumar

Publications and source records attributed to Ram Kumar.

22 records · Page 2Linked to original sources

arXiv2019

Hypergeometric functions and algebraic curves $y^e=x^d+ax+b$

Let $q$ be a prime power and $\mathbb{F}_q$ be a finite field with $q$ elements. Let $e$ and $d$ be positive integers. In this paper, for $d\geq2$ and $q\equiv1(\mathrm{mod}~ed(d-1))$, we calculate the number of points on an algebraic curve $E_{e,d}:y^e=x^d+ax+b$ over a finite field $\mathbb{F}_q$ in terms of $_dF_{d-1}$ Gaussian hypergeometric series with multiplicative characters of orders $d$ and $e(d-1)$, and in terms of $_{d-1}F_{d-2}$ Gaussian hypergeometric series with multiplicative characters of orders $ed(d-1)$ and $e(d-1)$. This helps us to express the trace of Frobenius endomorphism of an algebraic curve $E_{e,d}$ over a finite field $\mathbb{F}_q$ in terms of the above hypergeometric series. As applications, we obtain some transformations and special values of $_2F_{1}$ Gaussian hypergeometric series.

math.NT↗

arXiv2019

Existence of a critical canting angle of magnetic moments to induce multiferroicity in the Haldane spin-chain system, Tb2BaNiO5

We report an unusual canted magnetism due to 3d and 4f electrons, occupying two different crystallographic sites, with its consequence to electric dipole order. This is based on neutron powder diffraction measurements on Tb2BaNiO5 (orthorhombic, Immm centrosymmetric space group), exhibiting Neel order below (TN) 63 K, to understand multiferroic behavior below 25 K. The magnetic structure is made up of Ni and Tb magnetic moments, which are found to be mutually canted in the entire temperature range below TN, though collinearity is seen within each sublattice, as known in the past. First-principles density functional theory calculations (GCA plus SO and GCA plus U plus SO approximations) support such a canted ground state. The intriguing finding, being reported here, is that there is a sudden increase in this Tb-Ni relative cantingle angle at the temperature (that is, at 25 K) at which spontaneous electric polarization sets in, with bond distance and bong angle anomalies. This finding emphasizes the need for a new spin-driven polarization mechanism, that is, a critical canting angle coupled with exchangestriction, to induce multiferroicity in magnetic insulators with canted spins.

cond-mat.str-el↗

arXiv2016

Directed graphs and its Boundary Vertices

Suppose that $D=(V,E)$ is a strongly connected digraph. Let $u,v\in V(D)$. The maximum distance $md (u,v)$ is defined as $md(u,v)$=max\{$\overrightarrow{d}(u,v), \overrightarrow{d}(v,u)$\} where $\overrightarrow{d}(u,v)$ denote the length of a shortest directed $u-v$ path in $D$. This is a metric. The boundary, contour, eccentric and peripheral sets of a strong digraph $D$ are defined with respect to this metric. The main aim of this paper is to identify the above said metrically defined sets of a large strong digraph $D$ in terms of its prime factor decomposition with respect to cartesian product.

cs.DM↗

arXiv2016

Correlation of exchange bias with magneto-structural effects across the compensation temperature of Co(Cr$_{1-x}$Fe$_{x}$)$_2$O$_4$ (x = 0.05 and 0.075)

A small amount of Fe (5% and 7.5%) substitution in the Cr-site of the multiferroic compound CoCr2O4 leads to a magnetization reversal. In these compounds, we report a sign change in the exchange bias across the compensation temperature, accompanied by a non-monotonic change in the local moments across the compensation temperature. Such non-monotonic change in the magnetic moments is triggered by a similar change in the lattice structure. We relate here the sign change of exchange bias with that of the crystalline energy of the lattice and the Zeeman energy term arising from the anti-site disorder.

cond-mat.str-el↗