Searcharxiv⌕ Search

arXiv subjects

Om Prakash

Publications and source records attributed to Om Prakash.

At least 55 records · Page 3Linked to original sources
arXiv2022

Fragile electronic superconductivity in Bi Single crystal

It was presumed that semimetal Bismuth (Bi) would not show superconductivity (SC) even at ultra-low temperatures ($<$10 mK) due to its very low carrier density ($\approx 3\times10^{17}$cm$^{-3}$). Recently, we have established bulk superconductivity in ultra-pure (99.9999\%) Bi single crystal at $\mathrm{T_C = 0.53}$ mK with an extrapolated upper critical field $\mathrm{H_C(0) = 5.2μ}$T measured along the [$0001$] (trigonal) -crystallographic direction. At very low concentrations of the charge carriers, we are dealing with fragile Cooper pairs with an estimated large coherence length $\mathrm{ξ_{GL}(0)\approx 96 μ}$m. We also stated that one needs to go beyond the conventional electron-phonon coupling (BCS-like) mechanism to understand the SC state in Bi. Bi is a compensated semi-metal with electrons and holes as charge carriers. In order to find the charge carriers responsible for the SC, we report the temperature dependence of the anisotropic critical field along the [$01\bar 10$] (bisectrix)-crystallographic direction and compared it with the earlier data from measurements along the trigonal. Our theoretical analysis of the anisotropy of critical fields suggests that the light electrons in the three pockets of Bi bands are responsible for the SC and indicates that Bi is an extremely weak type-II (close to type-I) superconductor. Finally, we review the current theories proposed to explain the SC in Bi.

cond-mat.supr-con↗
arXiv2022

New Results on Generalization of Jordan centralizers over matrix rings

This paper presents a study on Jordan maps over matrix rings with some functional equations related to additive maps on these rings. We first show that every Jordan left (right) centralizer over a matrix ring is a left (right) centralizer. Moreover, every two-sided centralizer over the matrix ring is of a particular form. Further, we prove that any additive map satisfying functional equations over matrix rings becomes a two-sided centralizer. Finally, we conclude our work with some results on the Jordan left $\star$- centralizer over matrix rings and establish some results on functional equations that arise for the $\star$-centralizer.

math.RA↗
arXiv2021

Statistical properties of the aftershocks of stock market crashes revisited: Analysis based on the 1987 crash, financial-crisis-2008 and COVID-19 pandemic

During any unique crisis, panic sell-off leads to a massive stock market crash that may continue for more than a day, termed as mainshock. The effect of a mainshock in the form of aftershocks can be felt throughout the recovery phase of stock price. As the market remains in stress during recovery, any small perturbation leads to a relatively smaller aftershock. The duration of the recovery phase has been estimated using structural break analysis. We have carried out statistical analyses of the 1987 stock market crash, 2008 financial crisis and 2020 COVID-19 pandemic considering the actual crash-times of the mainshock and aftershocks. Earlier, such analyses were done considering an absolute one-day return, which cannot capture a crash properly. The results show that the mainshock and aftershock in the stock market follow the Gutenberg-Richter (GR) power law. Further, we obtained a higher $β$ value for the COVID-19 crash compared to the financial-crisis-2008 from the GR law. This implies that the recovery of stock price during COVID-19 may be faster than the financial-crisis-2008. The result is consistent with the present recovery of the market from the COVID-19 pandemic. The analysis shows that the high magnitude aftershocks are rare, and low magnitude aftershocks are frequent during the recovery phase. The analysis also shows that the distribution $P(τ_i)$ follows the generalized Pareto distribution, i.e., $\displaystyle~P(τ_i)\propto\frac{1}{\{1+λ(q-1)τ_i\}^{\frac{1}{(q-1)}}}$, where $λ$ and $q$ are constants and $τ_i$ is the inter-occurrence time. This analysis may help investors to restructure their portfolios during a market crash.

q-fin.ST↗
arXiv2021

Cyclic codes over a non-chain ring $R_{e,q}$ and their application to LCD codes

Let $\mathbb{F}_q$ be a finite field of order $q$, a prime power integer such that $q=et+1$ where $t\geq 1,e\geq 2$ are integers. In this paper, we study cyclic codes of length $n$ over a non-chain ring $R_{e,q}=\mathbb{F}_q[u]/\langle u^e-1\rangle$. We define a Gray map $φ$ and obtain many { maximum-distance-separable} (MDS) and optimal $\mathbb{F}_q$-linear codes from the Gray images of cyclic codes. Under certain conditions we determine { linear complementary dual} (LCD) codes of length $n$ when $\gcd(n,q)\neq 1$ and $\gcd(n,q)= 1$, respectively. It is proved that { a} cyclic code $\mathcal{C}$ of length $n$ is an LCD code if and only if its Gray image $φ(\mathcal{C})$ is an LCD code of length $4n$ over $\mathbb{F}_q$. Among others, we present the conditions for existence of free and non-free LCD codes. Moreover, we obtain many optimal LCD codes as the Gray images of non-free LCD codes over $R_{e,q}$.

cs.IT↗
arXiv2021

Parameterised Counting in Logspace

In this paper, we introduce a new framework for parameterised counting in logspace, inspired by the parameterised space bounded models developed by Elberfeld, Stockhusen and Tantau (IPEC 2013, Algorithmica 2015). They defined the operators paraW and paraBeta for parameterised space complexity classes by allowing bounded nondeterminism with multiple-read and read-once access, respectively. Using these operators, they characterised the parameterised complexity of natural problems on graphs. In the spirit of the operators paraW and paraBeta by Stockhusen and Tantau, we introduce variants based on tail-nondeterminism, paraW[1] and paraBeta-Tail. Then, we consider counting versions of all four operators applied to logspace and obtain several natural complete problems for the resulting classes: counting of paths in digraphs, counting first-order models for formulas, and counting graph homomorphisms. Furthermore, we show that the complexity of a parameterised variant of the determinant function for (0,1)-matrices is #paraBeta-Tail-L-hard and can be written as the difference of two functions in #paraBetaTail-L. For example, we show that the closure of #paraBetaTail-L under parameterised logspace parsimonious reductions coincides with #paraBeta-L, that is, modulo parameterised reductions, tail-nondeterminism with read-once access is the same as read-once nondeterminism. We show that all introduced classes are closed under addition and multiplication, and those without tail-nondeterminism are closed under parameterised logspace parsimonious reductions. Finally, we underline the significance of this topic by providing a promising outlook showing several open problems and options for further directions of research.

cs.LO↗
arXiv2020

Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shape recovery

The emergence of the COVID-19 pandemic, a new and novel risk factor, leads to the stock price crash due to the investors' rapid and synchronous sell-off. However, within a short period, the quality sectors start recovering from the bottom. A stock price model has been developed during such crises based on the net-fund-flow ($Ψ_t$) due to institutional investors, and financial antifragility ($ϕ$) of a company. We assume that during the crash, the stock price fall is independent of the $ϕ$. We study the effects of shock lengths and $ϕ$ on the stock price during the crises period using the $Ψ_t$ obtained from synthetic and real fund flow data. We observed that the possibility of recovery of stock with $ϕ>0$, termed as quality stock, decreases with an increase in shock-length beyond a specific period. A quality stock with higher $ϕ$ shows V-shape recovery and outperform others. The shock length and recovery period of quality stock are almost equal that is seen in the Indian market. Financially stressed stocks, i.e., the stocks with $ϕ<0$, show L-shape recovery during the pandemic. The stock data and model analysis shows that the investors, in uncertainty like COVID-19, invest in quality stocks to restructure their portfolio to reduce the risk. The study may help the investors to make the right investment decision during a crisis.

q-fin.ST↗
arXiv2020

New non-binary quantum codes from skew constacyclic codes over the ring $\mathbb{F}_{p^m}+v\mathbb{F}_{p^m}+v^2 \mathbb{F}_{p^m}$

In this article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring $\mathcal{R}= \mathbb{F}_{p^m}[v]/\langle v^3 =v \rangle$ where $p$ is an odd prime and $m \geq 1$. In order to obtain such quantum codes, first we study the structural properties of skew constacyclic codes and their Euclidean duals over the ring $\mathcal{R}$. Then a necessary and sufficient condition for skew constacyclic codes over $\mathcal{R}$ to contain their Euclidean duals is established. Finally, with the help of CSS construction and using Gray map, many new non-binary quantum codes are obtained over $\mathbb{F}_{p^m}$.

cs.IT↗
arXiv2019

Reversible cyclic codes over $\mathbb{F}_q + u \mathbb{F}_q$

Let $q$ be a power of a prime $p$. In this paper, we study reversible cyclic codes of arbitrary length over the ring $ R = \mathbb{F}_q + u \mathbb{F}_q$, where $u^2=0 mod q$. First, we find a unique set of generators for cyclic codes over $R$, followed by a classification of reversible cyclic codes with respect to their generators. Also, under certain conditions, it is shown that dual of reversible cyclic code is reversible over $\mathbb{Z}_2+u\mathbb{Z}_2$. Further, to show the importance of these results, some examples of reversible cyclic codes are provided.

cs.IT↗
arXiv2018

Adjacency Matrix and Energy of the Line Graph of $Γ(\mathbb{Z}_n)$

Let $Γ(\mathbb{Z}_n)$ be the zero divisor graph of the commutative ring $\mathbb{Z}_n$ and $L(Γ(\mathbb{Z}_n))$ be the line graph of $Γ(\mathbb{Z}_n)$. In this paper, we discuss about the neighborhood of a vertex, the neighborhood number and the adjacency matrix of $L(Γ(\mathbb{Z}_n))$. We also study Wiener index and energy of $L(Γ(\mathbb{Z}_n))$, where $n=pq$, $p^2$ respectively for $p$ and $q$ are primes. Moreover, we give MATLAB coding of our calculations.

math.CO↗
arXiv2018

Pancyclic zero divisor graph over the ring $\mathbb{Z}_n[i]$

Let $Γ(\mathbb{Z}_n[i])$ be the zero divisor graph over the ring $\mathbb{Z}_n[i]$. In this article, we study pancyclic properties of $Γ(\mathbb{Z}_n[i])$ and $\overline{Γ(\mathbb{Z}_n[i])}$ for different $n$. Also, we prove some results in which $L(Γ(\mathbb{Z}_n[i]))$ and $\overline{L(Γ(\mathbb{Z}_n[i]))}$ to be pancyclic for different values of $n$.

math.CO↗
arXiv2018

A note on lower nil M-Armendariz rings

In this article, we prove some results for lower nil M-Armendariz ring. Let M be a strictly totally ordered monoid and I be a semicommutative ideal of R. If R/I is a lower nil M-Armendariz ring, then R is lower nil M-Armendariz. Similarly, for above M, if I is 2-primal with N_{*}(R) subset of I and R/I is M-Armendariz, then R is a lower nil M-Armendariz ring. Further, we observe that if M is a monoid and N a u.p.-monoid where R is a 2-primal M-Armendariz ring, then R[N] is a lower nil M-Armendariz ring.

math.RA↗
arXiv2018

Remarks on Jordan derivations over matrix algebras

Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we extend the result for Jordan derivation on full matrix algebra M_n(C).

math.RA↗
arXiv2018

Jordan {g, h}-derivations on algebra of matrices

In this article, we show that every Jordan {g, h}-derivation over T_n(C) is a {g, h}-derivation under an assumption, where C is a commutative ring with unity 1 not equal to 0. We give an example of a Jordan {g, h}-derivation over T_n(C) which is not a {g, h}-derivation. Also, we study Jordan {g, h}-derivation over M_n(C).

math.RA↗
arXiv2018

Jordan left {g, h}-derivations over some algebras

In this article, left {g, h}-derivation and Jordan left {g, h}-derivation on algebras are introduced. It is shown that there is no Jordan left {g, h}-derivation over $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$, for g not equal to h. Examples are given which show that every Jordan left $\{g, h\}$-derivation over $\mathcal{T}_n(C)$, $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$ are not left $\{g, h\}$-derivations. Moreover, we characterize left $\{g, h\}$-derivation and Jordan left $\{g, h\}$-derivation over $\mathcal{T}_n(C)$, $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$ respectively. Also, we prove the result of Jordan left $\{g, h\}$-derivation to be a left $\{g, h\}$-derivation over tensor products of algebras as well as for algebra of polynomials.

math.RA↗
arXiv2018

Skew cyclic codes over F_{p}+uF_{p}+\dots +u^{k-1}F_{p}

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;θ]-submodules of R_{k}[x;θ]/\langle x^{n}-1\rangle and construct their generators and minimal generating sets. Also, an algorithm has been provided to encode and decode these skew cyclic codes.

cs.IT↗
arXiv2018

Armendariz ring with weakly semicommutativity

In this article, we introduce the weak ideal-Armendariz ring which combines Armendariz ring and weakly semicommutative properties of rings. In fact, it is a generalisation of an ideal-Armendariz ring. We investigate some properties of weak ideal Armendariz rings and prove that R is a weak ideal-Armendariz ring if and only if R[x] is weak ideal-Armendariz ring. Also, we generalise weak ideal-Armendariz as strongly nil-IFP and a number of properties are discussed which distinguishes it from other existing structures. We prove that if I is a semicommutative ideal of a ring R and R/I is a strongly nil-IFP, then R is strongly nil-IFP. Moreover, if R is 2-primal, then R[x]/ is a strongly nil-IFP.

math.RA↗