arXiv subjects

Arvind Kumar

Publications and source records attributed to Arvind Kumar.

At least 109 records · Page 6Linked to original sources

arXiv2020

$η$ mesons in hot and dense asymmetric nuclear matter

We study the $ηN$ interactions in the hot and dense isospin asymmetric nuclear matter using two different approaches. In the first approach, the in-medium mass and optical potential of $η$-meson have been calculated in the chiral SU(3) model, considering the effect of explicit symmetry breaking term and range terms in the $ηN$ interaction Lagrangian density. In the second scenario, the conjunction of chiral perturbation theory and chiral SU(3) model is employed. In this case, the next-to-leading order $ηN$ interactions are evaluated from the chiral perturbation theory (ChPT), and the in-medium contribution of scalar densities are taken as input from chiral SU(3) model. We observe a larger negative mass-shift in the ChPT+chiral model approach compared to the chiral SU(3) model alone as a function of nuclear density. Moreover, the increase in the asymmetry and temperature cause a decrease in the magnitude of mass-shift. We have also studied the impact of $ηN$ scattering length $a^{ηN}$ on the $η$ meson mass $m^*_η$ and observed that the $m^*_η$ decrease more for increasing the value of scattering length.

nucl-th↗

arXiv2020

Almost complete intersection binomial edge ideals and their Rees algebras

Let $G$ be a simple graph on $n$ vertices and $J_G$ denote the binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the second graded Betti numbers of $J_G$, and we obtain a minimal presentation of it when $G$ is a tree or a unicyclic graph. We classify all graphs whose binomial edge ideals are almost complete intersection, prove that they are generated by a $d$-sequence and that the Rees algebra of their binomial edge ideal is Cohen-Macaulay. We also obtain an explicit description of the defining ideal of the Rees algebra of those binomial edge ideals.

math.AC↗

arXiv2020

Lovász-Saks-Schrijver ideals and parity binomial edge ideals of graphs

Let $G$ be a simple graph on $n$ vertices. Let $L_G \text{ and } \mathcal{I}_G \: $ denote the Lovász-Saks-Schrijver(LSS) ideal and parity binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1,\ldots, x_n, y_1, \ldots, y_n] $ respectively. We classify graphs whose LSS ideals and parity binomial edge ideals are complete intersections. We also classify graphs whose LSS ideals and parity binomial edge ideals are almost complete intersections, and we prove that their Rees algebra is Cohen-Macaulay. We compute the second graded Betti number and obtain a minimal presentation of LSS ideals of trees and odd unicyclic graphs. We also obtain an explicit description of the defining ideal of the symmetric algebra of LSS ideals of trees and odd unicyclic graphs.

math.AC↗

arXiv2020

Regularity of powers of quadratic sequences with applications to binomial ideals

In this article, we obtain an upper bound for the Castelnuovo-Mumford regularity of powers of an ideal generated by a homogeneous quadratic sequence in a polynomial ring in terms of the regularity of its related ideals and degrees of its generators. As a consequence, we compute upper bounds for the regularity of powers of several binomial ideals. We generalize a result of Matsuda and Murai to show that the regularity of $J^s_G$ is bounded below by $2s+\ell(G)-1$ for all $s \geq 1$, where $J_G$ denotes the binomial edge ideal of a graph $G$ and $\ell(G)$ is the length of a longest induced path in $G$. We compute the regularity of powers of binomial edge ideals of cycle graphs, star graphs, and balloon graphs explicitly. Also, we give sharp bounds for the regularity of powers of almost complete intersection binomial edge ideals and parity binomial edge ideals.

math.AC↗

arXiv2020

Properties of analogues of Frobenius powers of ideals

Let $R=\mathbb{K}[X_1, \ldots , X_n ]$ be a polynomial ring over a field $\mathbb{K}$. We introduce an endomorphism $\mathcal{F}^{[m]}: R \rightarrow R $ and denote the image of an ideal $I$ of $R$ via this endomorphism as $I^{[m]}$ and call it to be the $m$ \textit{-th square power} of $I$. In this article, we study some homological invariants of $I^{[m]}$ such as regularity, projective dimension, associated primes and depth for some families of ideals e.g. monomial ideals.

math.AC↗

arXiv2020

Certain Algebraic Invariants of Edge Ideals of Join of Graphs

Let $G$ be a simple graph and $I(G)$ be its edge ideal. In this article, we study the Castelnuovo-Mumford regularity of symbolic powers of edge ideals of join of graphs. As a consequence, we prove Minh's conjecture for wheel graphs, complete multipartite graphs, and a subclass of co-chordal graphs. We obtain a class of graphs whose edge ideals have regularity three. By constructing graphs, we prove that the multiplicity of edge ideals of graphs is independent from the depth, dimension, regularity, and degree of $h$-polynomial. Also, we demonstrate that the depth of edge ideals of graphs is independent from the regularity and degree of $h$-polynomial by constructing graphs.

math.AC↗

arXiv2020

Subadditivity, strand connectivity and multigraded Betti numbers of monomial ideals

Let $R = \mathbb{K}[x_1, \ldots, x_n]$ and $I \subset R$ be a homogeneous ideal. In this article, we first obtain certain sufficient conditions for the subadditivity of $R/I$. As a consequence, we prove that if $I$ is generated by homogeneous complete intersection, then subadditivity holds for $R/I$. We then study a conjecture of Avramov, Conca and Iyengar on subadditivity, when $I$ is a monomial ideal with $R/I$ Koszul. We identify several classes of edge ideals of graphs $G$ such that the subadditivity holds for $R/I(G)$. We then study the strand connectivity of edge ideals and obtain several classes of graphs whose edge ideals are strand connected. Finally, we compute upper bounds for multigraded Betti numbers of several classes of edge ideals.

math.AC↗

arXiv2020

Binomial Edge Ideals of Generalized block graphs

We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo-Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by $m(G)+1$, where $m(G)$ is the number of minimal cut sets of the graph $G$ and obtain an improved upper bound for the regularity in terms of the number of maximal cliques and pendant vertices of $G$.

math.AC↗

arXiv2020

$ϕ$ meson mass and decay width in strange hadronic matter

The in-medium mass and decay width of the $ϕ$ meson in the hot asymmetric strange hadronic matter are calculated using an effective Lagrangian approach for $ϕ$ $K\bar K$ interaction. The in-medium contributions of $K \bar K$ loop to the $ϕ$ meson self-energy are computed by the medium modified kaon and antikaon mass which is evaluated using the chiral SU(3) model. To deal with the ultraviolet divergence, we regularize the loop integral of self-energy with a dipole form factor, and present the results for cut-off mass, $Λ_c$=3 GeV. In chiral model calculations, for strange matter, we find that the mass of kaons and antikaons decreases with the increase in baryonic density whereas the finite temperature causes an increase in the mass. We observed that the in-medium $ϕ$ meson mass decreases slowly with baryonic density whereas the decay width increases rapidly. The results in the present investigation support result in the literature which indicate a small downward shift in mass and a large broadening in the decay width. In the asymmetric strange hadronic matter, the study of the $ϕ$ mesons can be relevant for the compressed strange baryonic matter and experimental observables such as dilepton spectra which can result from the experiments in the future FAIR facility at GSI.

hep-ph↗

arXiv2020

Addressing Ancestry Disparities in Genomic Medicine: A Geographic-aware Algorithm

With declining sequencing costs a promising and affordable tool is emerging in cancer diagnostics: genomics. By using association studies, genomic variants that predispose patients to specific cancers can be identified, while by using tumor genomics cancer types can be characterized for targeted treatment. However, a severe disparity is rapidly emerging in this new area of precision cancer diagnosis and treatment planning, one which separates a few genetically well-characterized populations (predominantly European) from all other global populations. Here we discuss the problem of population-specific genetic associations, which is driving this disparity, and present a novel solution--coordinate-based local ancestry--for helping to address it. We demonstrate our boosting-based method on whole genome data from divergent groups across Africa and in the process observe signals that may stem from the transcontinental Bantu-expansion.

q-bio.GN↗

arXiv2020

Heavy vector and axial-vector $D$ mesons in hot magnetized asymmetric nuclear matter

We observed the impact of finite magnetic field on the in-medium mass and decay constant of isospin averaged vector $D^*(D^{*^+},D^{*^0})$ and axial-vector $D_1(D^+_1, D^0_1)$ mesons. The quark and gluon condensates of the nuclear medium at finite magnetic field, temperature, isospin asymmetry, and density have been obtained by the meson exchange scalar fields within the chiral SU(3) model. The medium attributes modify the scalar and vector density of nuclear medium and this variation reflects in the in-medium mass and decay constant of spin 1 $D$ mesons. We calculate these observables by comparing the Operator Product Expansion (OPE) and the phenomenological side in the QCD Sum Rules. In the results, we observed a positive mass shift for charged vector and axial-vector $D$ mesons with respect to magnetic field. For neutral vector (axial-vector) $D$ mesons we observed negative (positive) mass shift as a function of magnetic field. In the application part, we calculate the in-medium partial decay width of the process $D^*_s$(2715/2860) $\rightarrow$ $D^* K$ by using $^3P_0$ model. The in-medium effects are incorporated through the in-medium masses of $D^*$ and $K$ mesons.

hep-ph↗

arXiv2020

Quark Matter within Polyakov Chiral SU(3) Quark Mean Field Model at Finite Temperature

Thermodynamical properties of asymmetric strange quark matter using the Polyakov Chiral $\text{SU(3)}$ quark mean field (PCQMF) model at finite temperature and chemical potential have been investigated. Within the PCQMF model, the properties of quark matter are calculated through the scalar fields $σ$, $ζ$, $δ$ and $χ$, the vector fields $ω$, $ρ$ and $ϕ$ and the Polyakov loop fields $Φ$ and $\barΦ$. The isospin splitting of constituent quark masses is observed at large isospin asymmetry. The effect of temperature and strangeness fraction on energy per baryon and equation of state is found to be appreciable in quark matter. The effect of the Polyakov loop dynamics on several thermodynamical bulk quantities such as energy density, entropy density, and trace anomaly is presented and compared with recent lattice QCD results.

hep-ph↗

arXiv2019

Depth and Extremal Betti Number of Binomial Edge Ideals

Let $G$ be a simple graph on the vertex set $[n]$ and $J_G$ be the corresponding binomial edge ideal. Let $G=v*H$ be the cone of $v$ on $H$. In this article, we compute all the Betti numbers of $J_G$ in terms of Betti number of $J_H$ and as a consequence, we get the Betti diagram of wheel graph. Also, we study Cohen-Macaulay defect of $S/J_G$ in terms of Cohen-Macaulay defect of $S_H/J_H$ and using this we construct a graph with Cohen-Macaulay defect $q$ for any $q\geq 1$. We obtain the depth of binomial edge ideal of join of graphs. Also, we prove that for any pair $(r,b)$ of positive integers with $1\leq b< r$, there exists a connected graph $G$ such that $reg(S/J_G)=r$ and the number of extremal Betti number of $S/J_G$ is $b$.

math.AC↗

arXiv2019

Drop Impact Printing

Hydrodynamic collapse of a central air-cavity during the recoil phase of droplet impact on a superhydrophobic sieve leads to satellite-free generation of a single droplet through the sieve. Two modes of cavity formation and droplet ejection was observed and explained. The volume of the generated droplet scales with the pore size. Based on this phenomenon, we propose a new drop-on-demand printing technique. Despite significant advancements in inkjet technology, enhancement in mass-loading and particle-size have been limited due to clogging of the printhead nozzle. By replacing the nozzle with a sieve, we demonstrate printing of nanoparticle suspension with 71% mass-loading. Comparatively large particles of 20 micrometer diameter were dispensed in droplets of 80 micrometer diameter. Printing was performed for surface tension as low as 32 mNm-1 and viscosity as high as 33 mPa-s. In comparison to existing techniques, this new way of printing is widely accessible as it is significantly simple and economical.

physics.app-ph↗

arXiv2019

Analysis of pseudoscalar and scalar $D$ mesons and charmonium decay width in hot magnetized asymmetric nuclear matter

In this article, we calculate the mass shift and decay constant of isospin averaged pseudoscalar ($D^+$,$D^0$) and scalar ($D^+_0$,$D^0_0$) mesons by the magnetic field induced quark and gluon condensates at finite density and temperature of asymmetric nuclear matter. We have calculated the in-medium chiral condensates from the chiral SU(3) mean field model and subsequently used these condensates in QCD Sum Rules (QCDSR) to calculate the effective mass and decay constant of $D$ mesons. Consideration of external magnetic field effects in hot and dense nuclear matter lead to appreciable modification in the masses and decay constants of $D$ mesons. Furthermore, we also studied the effective decay width of higher charmonium states ($ψ(3686),ψ(3770),{{χ_c}_0}(3414),{{χ_c}_2}(3556)$) as a by-product by using $^3P_0$ model which can have an important impact on the yield of $J/ψ$ mesons. The results of present work will be helpful to understand the experimental observables of the heavy ion colliders which aim to produce matter at finite density and moderate temperature.

hep-ph↗

arXiv2019

Possibility of $ρ$ Meson Condensation in Neutron Star: Unified Approach of Chiral SU(3) Model and QCD Sum Rules

In the present work the conjunction of chiral SU(3) model with QCD sum rules is employed to explore the possibility of $ρ$ meson condensation in neutron stars. The quark and gluon condensates in terms of which the in-medium masses of $ρ$ mesons can be expressed are calculated using the chiral SU(3) model in the charge neutral matter which is relevant for neutron stars. It is observed that condition of $ρ$ meson condensation is satisfied for the density of about 7$ρ_{0}$, where $ρ_{0}$ is the nuclear saturation density. In the end, a brief qualitative discussion of the magnetic field is also involved to check out for the further possibility of $ρ$ meson condensation.

nucl-th↗

arXiv2019

Charmonia and Bottomonia in asymmetric magnetized hot nuclear matter

We investigate the mass-shift of $P$-wave charmonium (${χ_c}_0$, ${χ_c}_1$) and $S$ and $P$-wave bottomonium ($η_b$, $Υ$, ${χ_b}_0$ and ${χ_b}_1$) states in magnetized hot asymmetric nuclear matter using the unification of QCD sum rules (QCDSR) and chiral $SU(3)$ model. Within QCDSR, we use two approaches, $i.e.$, moment sum rule and Borel sum rule. The magnetic field induced scalar gluon condensate $\left\langle \frac{α_{s}}π G^a_{μν} {G^a}^{μν} \right\rangle$ and the twist-2 gluon operator $\left\langle \frac{α_{s}}π G^a_{μσ} {{G^a}_ν}^σ \right\rangle $ calculated in chiral $SU(3$) model are utilised in QCD sum rules to calculate the in-medium mass-shift of above mesons. The attractive mass-shift of these mesons is observed which is more sensitive to magnetic field in high density regime for charmonium, but less for bottomonium. These results may be helpful to understand the decay of higher quarkonium states to the lower quarkonium states in asymmetric heavy ion collision experiments.

hep-ph↗

arXiv2019

Hilbert Series Of Binomial Edge Ideals

Let $G$ be a finite simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in the polynomial ring $S = K[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the Hilbert series of binomial edge ideal of decomposable graphs in terms of Hilbert series of its indecomposable subgraphs. Also, we compute the Hilbert series of binomial edge ideal of join of two graphs and as a consequence we obtain the Hilbert series of complete $k$-partite graph, fan graph, multi-fan graph and wheel graph.

math.AC↗