arXiv subjects

Om Prakash

Publications and source records attributed to Om Prakash.

66 records · Page 4Linked to original sources

arXiv2018

Skew cyclic and skew $(α_1 + uα_2 + vα_3 + uvα_4)$-constacyclic codes over $F_q + uF_q + vF_q + uvF_q$

In this note, we study skew cyclic and skew constacyclic codes over the ring $\mathcal{R}=F_{q}+uF_{q}+vF_{q}+uvF_{q}$ where $q=p^{m},$ $p$ is an odd prime, $u^{2}=u,~v^{2}=v,~uv=vu$. We show that Gray images of a skew cyclic and skew $α$-constacyclic code of length $n$ are skew quasi-cyclic code of length $4n$ over $F_{q}$ of index 4. Also, it is shown that skew $α$-constacyclic codes are either equivalent to $α$-constacyclic codes or $α$-quasi-twisted codes over $\mathcal{R}$. Further, structural properties, specially, generating polynomials and idempotent generators for skew cyclic and skew constacyclic codes are determined by decomposition method.

cs.IT↗

arXiv2017

Skew constacyclic codes over Fq+uFq+vFq

In this paper skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv = vu = 0 are studied. We show that Gray image of a skew alpha-constacyclic cyclic code of length n over R is a skew alpha-quasi-cyclic code of length $3n$ over F_{q} of index 3. It is also shown that skew alpha-constacyclic codes are either equivalent to alpha-constacyclic codes or alpha-quasi-twisted codes over R. Further, the structural properties of skew constacyclic over R are obtained by decomposition method.

cs.IT↗

arXiv2017

Divisor graph of complement of Gamma(R)

Let overline{Γ(R)} be the complement of zero divisor graph of a finite commutative ring R. In this article, we have provided the answer of the question (ii) raised by Osba and Alkam in their paper and prove that overline{Γ(R)} is a divisor graph if R is a local ring. It is shown that when R is a product of two local rings, then overline{Γ(R)} is a divisor graph if one of them is an integral domain. Also, we prove that if cardinality of Ass(R) = 2, then overline{Γ(R)} is a divisor graph.

math.CO↗

arXiv2017

Extension of Almost Armendariz Rings

A ring $R$ is said to be an almost Armendariz ring if whenever product of two polynomials in $R[x]$ is zero, then product of their coefficients are in $N_{*}(R)$. In this article, for an endomorphism $α$ on $R$, we define an $α$-almost Armendariz ring of $R$ considering the polynomials in skew polynomial ring $R[x; α]$ instead of $R[x]$. It is the generalisation of an almost Armendariz ring [9] and an $α$-Armendariz ring [4]. Moreover, for an endomorphism $α$ of $R$, we define an $α$-skew almost Armendariz ring, and prove that a reversible ring $R$ with certain condition on endomorphism $α$, its polynomial ring $R[x]$ is an $\overlineα$-skew almost Armendariz ring.

math.RA↗

arXiv2017

On Almost Armendariz Rings

In this paper, we introduce the notion of almost Armendariz ring which is the generalization of Armendariz ring and discuss some of its properties. We prove that a ring R is almost Armendariz if and only if n X n upper triangular matrix ring T_{n}(R) is almost Armendariz ring. Similarly, If R is almost Armendariz if and only if R[x] is almost Armendariz. It is observed that every almost Armendariz ring is weak Armendariz but converse need not be true. But, if R is semicommutative ring, then weak Armendariz ring is almost Armendariz ring. Moreover, the class of minimal noncommutative almost Armendariz rings is completely determined, up to isomorphism (minimal means having smallest cardinality).

math.RA↗

arXiv2017

Very cost effective bipartition in Gamma(Z_n)

Let Z_n be the finite commutative ring of residue classes modulo n and Gamma(Z_n) be its zero-divisor graph. The nilradical graph and non-nilradical graph of Z_n are denoted by N(Z_n) and Omega(Z_n) respectively. In 2012, Haynes et al. [5] introduced the concept of very cost effective graph. For a graph G = (V,E) and a set of vertices S subset of V, a vertex v in S is said to be very cost effective if it is adjacent to more vertices in V§than in S. A bipartition Pi = {S, V§} is called very cost effective if both S and V§are very cost effective sets [5,6]. In this paper, we investigate the very cost effective bipartition of Gamma(Z_n), where n = p_1 p_2 ... p_m, here all p_i's are distinct primes. In addition, we discuss the cases in which N(Z_n) and Omega(Z_n) graphs have very cost effective bipartition for different n. Finally, we derive some results for very cost effective bipartition of the Line graph and Total graph of Gamma(Z_n), denoted by L(Gamma(Z_n)) and T(Gamma(Z_n)) respectively.

math.CO↗

arXiv2016

Experimental evidence for bulk superconductivity in pure Bismuth single crystal at ambient pressure

Bulk rhombohedral Bismuth (Bi) at ambient pressure is a semimetal and it remains in the normal state down to 10~mK. The superconductivity (SC) in bulk Bi is thought to be very unlikely due to extremely low carrier density. The question of SC in Bi has remained unsolved both theoretically and experimentally. Here, we report first ever observation of bulk SC in highly pure Bi single crystals (99.9999\%) below 0.53~mK under ambient pressure with an estimated critical magnetic field of 5.2~$μ$T at 0~K. The conventional Bardeen-Cooper-Schrieffer (BCS) theory cannot explain the observed SC in Bi, since the adiabatic approximation of the BCS theory, $ω_D/E_F<< 1$, does not hold true for Bi. Bi has a multi-valley type electronic band structure and SC in Bi could be brought about by the inter-valley electron-phonon coupling. Such a scenario calls for new theoretical ideas to understand SC in such low carrier systems with unusual band structure in the non-adiabatic limit, $ω_D/E_F \gtrsim 1$. The observation of SC in Bi makes it the lowest carrier density superconductor surpassing the record held by doped SrTiO$_3$ for nearly 50 years.

cond-mat.supr-con↗

arXiv2016

Ferromagnetic ordering of minority Ce$^{3+}$ spins in a quasi-skutterudite Ce${_3}$Os${_4}$Ge$_{13}$ single crystal

We report site disorder driven ferromagnetic ordering of nearly 8$\%$ Ce atoms in single crystalline Ce${_3}$Os${_4}$Ge$_{13}$ below 0.5~K. Ce${_3}$Os${_4}$Ge$_{13}$ crystallizes in a cubic structure with space group $\it{Pm\bar{3}n}$. The structural analysis shows the presence of site-disorder in the system, where 2(a) Ge site is partially occupied by the Ce atoms. Due to the small Ce $4f$-ligand hybridization, these Ce atoms are in the Ce$^{3+}$ (magnetic) state while rest of the Ce atoms in the unit cell are in Ce$^{4-δ}$ (non-magnetic) state. The heat capacity shows a peak below 0.5~K corresponding to the ferromagnetic ordering of the Ce$^{3+}$ moments. The ferromagnetic ordering below 0.5~K is also seen in the ac-susceptibility data. At low temperatures (1.8~K$\leq T\leq 6$~K), the magnetization shows $log(T)$ dependence, whereas the resistivity shows power law ($T^n$) temperature dependence indicating the non-Fermi liquid behavior of the quasiparticles.

cond-mat.str-el↗

arXiv2015

{Multiband Superconductivity in Lu$_3$Os$_4$Ge$_{13}$

Intermetallic R$_3$T$_4$X$_{13}$ series consists of cage like structure and have been in focus due to their unconventional electronic ground states. In this work, we report the normal and superconducting state properties of a high quality single crystal of Lu$_3$Os$_4$Ge$_{13}$. Lu$_3$Os$_4$Ge$_{13}$ belongs to the above mentioned series and crystallizes in a cubic crystal structure with the space group $\it{Pm\bar{3}n}$. Using electrical transport, magnetization and heat capacity measurements, we show that Lu$_3$Os$_4$Ge$_{13}$ is a type-II multi-band superconductor ($T{_c} =3.1$~K) with unusual superconducting properties. The analysis of the low temperature heat capacity data suggests that Lu$_3$Os$_4$Ge$_{13}$ is a moderately coupled multi-band BCS superconductor with two gaps ($2Δ/ {k{_B}T{_c}} = 3.68 \pm {0.04} ~\& ~0.34 \pm {0.02}$) in the superconducting state. The dc-magnetization ($M-H$) shows a large reversible region in the superconducting state similar to the vortex liquid phase observed in high-$T{_c}$ superconductors. The value of the Ginzburg number $G_{i}$ suggests that the thermal fluctuations, though small as compared to those in high-$T{_c}$ cuprates, may play an important role in the unpinning of the vortices in this compound. The electronic band structure calculations show that three bands cross the Fermi level and constitute a complex Fermi surface in Lu$_3$Os$_4$Ge$_{13}$

cond-mat.supr-con↗

arXiv2014

Superconductivity in Y$_3$Ru$_4$Ge$_{13}$ and Lu$_3$Os$_4$Ge$_{13}$: A comparative study

A variety of unconventional superconductors have low carrier density as a common factor. However, the underlying mechanism of superconductivity in such low carrier density systems is not well understood. Besides, small carrier density is an unfavourable component for conventional superconductivity as described by the Bardeen-Cooper-Schrieffer (BCS) theory. Therefore, studying low carrier density systems can lead to a better understanding in such systems. In this paper, we report superconductivity property studies in low carrier density systems, Y$_3$Ru$_4$Ge$_{13}$ and Lu$_3$Os$_4$Ge$_{13}$, using various experimental techniques. Single crystals of Y$_3$Ru$_4$Ge$_{13}$ and Lu$_3$Os$_4$Ge$_{13}$ have been grown using the Czochralski crystal pulling method in a tetra-arc furnace. The x-ray diffraction experiment reveals that both compounds crystallize in cubic structure {(space group $\it{Pm3n}$, no. 223)}. The transport, magnetization and heat capacity measurements show that Y$_3$Ru$_4$Ge$_{13}$ single crystal undergoes a superconducting transition at 2.85~K, whereas, Lu$_3$Os$_4$Ge$_{13}$ becomes superconductor at 3.1~K.

cond-mat.supr-con↗

arXiv2013

Superconductivity in a low carrier density system: A single crystal study of cubic Y$_3$Ru$_4$Ge$_{13}$

We have successfully grown the single crystal of a low carrier density system Y$_3$Ru$_4$Ge$_{13}$ which crystallizes in the cubic crystal structure with the space group Pm3n. Y$_3$Ru$_4$Ge$_{13}$ exhibits super conductivity below 2.85 K as determined from the electrical resistivity, magnetic susceptibility and heat capacity measurements. The bulk measurements indicate multiband superconductivity in this low carrier system. Hall effect measurements show that the Hall coefficient R$_H$ is positive and it decreases rapidly with temperature which is highly unusual. The simple estimation of the carrier concentration gives a value (\sim 10$^{20}$/cm$^3$) which is 2-3 orders of magnitude lower than that of a conventional metal like Cu which seems to suggest that Y$_3$Ru$_4$Ge$_{13}$ is a semimetal that display multiband superconductivity.

cond-mat.supr-con↗

arXiv2012

Disk Scheduling: Selection of Algorithm

The objective of this paper is to take some aspects of disk scheduling and scheduling algorithms. The disk scheduling is discussed with a sneak peak in general and selection of algorithm in particular.

cs.OS↗