arXiv subjects

Ajay Kumar

Publications and source records attributed to Ajay Kumar.

At least 91 records · Page 5Linked to original sources

arXiv2021

Certain Homological Invariants of Bipartite Kneser Graphs

In this paper, we obtain a combinatorial formula for computing the Betti numbers in the linear strand of edge ideals of bipartite Kneser graphs. We deduce lower and upper bounds for regularity of powers of edge ideals of these graphs in terms of associated combinatorial data and show that the lower bound is attained in some cases. Also, we obtain bounds on the projective dimension of edge ideals of these graphs in terms of combinatorial data.

math.AC↗

arXiv2021

X-ray Absorption Spectroscopy Study of La$_{1-y}$Sr$_{y}$Co$_{1-x}$Nb$_x$O$_3$

We use x-ray absorption spectroscopy to investigate the local structure and electronic properties of bulk La$_{1-y}$Sr$_{y}$Co$_{1-x}$Nb$_x$O$_3$ ($y=$ 2$x$ as LSCNO and $y=$ 0 as LCNO) samples. The x-ray absorption near-edge spectra (XANES) of LSCNO at Co K-edge affirm the valence state of Co in 3+. However, in the case of the LCNO, a subtle variation in the valence state of Co ions from 3+ to 2+ is evident with Nb substitution. The detailed analysis of the Fourier transform (FT) of the extended x-ray absorption fine structure (EXAFS) for the LSCNO samples exhibit the two groups of the bond-lengths owing to the Jahn-Teller (JT) distortion in the CoO$_6$ octahedra, which manifest that the Co$^{3+}$ ions exist in the intermediate spin-state (t$^5_{2g}$e$^1_g$) at room temperature. However, we find that the JT distortion is not present in LCNO samples for $x>$0.025 due to an increase in the high-spin Co$^{2+}$/Co$^{3+}$ ions accompanied by the Nb--induced structural transformation. Intriguingly, the La L$_3$-edge spectra for the LSCNO samples exhibit that the La ions exist in the trivalent state and the local disorder around La atoms decreases with Sr and Nb substitution. Interestingly, the simulated FT of the EXAFS spectra at the La L$_3$-edge demonstrates the three groups of La--O bond lengths, which exhibit a monotonous change with Sr and Nb substitution. Moreover, the XANES measured at Sr and Nb K-edges confirm their oxidation state to be in 2+ and 5+, respectively.

cond-mat.mtrl-sci↗

arXiv2021

Regularity, Rees algebra and Betti numbers of certain cover ideals

Let $S={\sf k}[X_1,\dots, X_n]$ be a polynomial ring, where ${\sf k}$ is a field. This article deals with the defining ideal of the Rees algebra of squarefree monomial ideal generated in degree $n-2$. As a consequence, we prove that Betti numbers of powers of the cover ideal of the complement graph of a tree do not depend on the choice of tree. Further, we study the regularity and Betti numbers of powers of cover ideals associated to certain graphs.

math.AC↗

arXiv2021

Herzog, Hibi and Ohsugi conjecture for trees

Let $S=\mathbb{K}[x_1,\dots, x_n]$ be a polynomial ring, where $\mathbb{K}$ is a field, and $G$ be a simple graph on $n$ vertices. Let $J(G)\subset S$ be the vertex cover ideal of $G$. Herzog, Hibi and Ohsugi have conjectured that all powers of vertex cover ideals of chordal graph are componentwise linear. Here we establish the conjecture for the special case of trees. We also show that if $G$ is a unicyclic vertex decomposable graph that does not contain $C_3$ or $C_5$, then symbolic powers of $J(G)$ are componentwise linear.

math.AC↗

arXiv2020

Local operator system structures and their tensor products

We introduce and explore the theory of tensor products in the category of local operator systems. Analogous to minimal operator system OMIN and maximal operator system OMAX, minimal and maximal local operator system structures LOMIN and LOMAX, respectively, are also discussed.

math.OA↗

arXiv2020

Evidence of discrete energy states and cluster-glass behavior in Sr$_{2-x}$La$_x$CoNbO$_6$

We report the detailed analysis of specific heat [C$_{\rm P}$(T)] and ac-susceptibility for magnetically frustrated Sr$_{2-x}$La$_x$CoNbO$_6$ ($x=$ 0--1) double perovskites to understand low temperature complex magnetic interactions and their evolution with $x$. Interestingly, the observed Schottky anomaly in the $x\leqslant$ 0.4 samples shifts gradually towards higher temperature with magnetic field as well as $x$, and the analysis reveal the persistence of the discrete energy states in these samples resulting from the spin-orbit coupling and octahedral distortion. Moreover, the extracted values of Landé g--factor indicate the existence of high-spin state Co$^{3+}$ ions close to non-magnetic low-spin state. The specific heat data show the $λ$-type anomaly for the $x\geqslant$ 0.6 samples due to evolution of the long range antiferromagnetic ordering. Our analysis of low temperature C$_{\rm P}$(T) data for the $x\geqslant$ 0.6 samples demonstrate the 3D isotropic Heisenberg antiferromagnetic (AFM) interactions and the temperature induced second order AFM--paramagnetic phase transition. More interestingly, we demonstrate the presence of the free Co$^{2+}$ like Kramers doublet ground state in the $x =$1 sample. Further, the ac susceptibility and time evolution of the magnetization data reveal the low temperature cluster-glass like behavior in the $x=$ 0--0.4 samples, where spin-spin correlation strength decreases with $x$.

cond-mat.str-el↗

arXiv2020

Estimates for initial coefficients of certain bi-univalent functions

Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent functions. The bounds obtained improve some existing known bounds.

math.CV↗

arXiv2020

Quadratic Sieve Factorization Quantum Algorithm and its Simulation

Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability to solve difficult problems efficiently in contrast to classical computers. Specifically, some well-known public-key cryptosystems depend on the difficulty of factoring large numbers, which takes a very long time. It is expected that the emergence of a quantum computer has the potential to break such cryptosystems by 2020 due to the discovery of powerful quantum algorithms (Shor's factoring, Grover's search algorithm and many more). In this paper, we have designed a quantum variant of the second fastest classical factorization algorithm named "Quadratic Sieve". We have constructed the simulation framework of quantized quadratic sieve algorithm using high-level programming language Mathematica. Further, the simulation results are performed on a classical computer to get a feel of the quantum system and proved that it is more efficient than its classical variants from computational complexity point of view.

quant-ph↗

arXiv2020

Structural, transport, optical and electronic properties of Sr$_2$CoNbO$_6$ thin films

We study the effect of substrate induced strain on the structural, transport, optical and electronic properties of Sr$_2$CoNbO$_6$ double perovskite thin films. The reciprocal space mapping, $ϕ$-scan and high-resolution $θ$-2$θ$ scans of x-ray diffraction patterns suggest the epitaxial nature and high-quality of the films deposited on various single crystal ceramic substrates. A systematic enhancement in the dc electronic conductivity is observed with increase in the compressive strain, while a sharp reduction in case of tensile strain, which are further supported by change in the activation energy and density of states near the Fermi level. The optical band gap extracted from two distinct absorption bands, observed in the visible-near infrared spectroscopy show a non-monotonic behavior in case of compressive strain while significant enhancement with tensile strain. Unlike the bulk Sr$_2$CoNbO$_6$ (Co$^{3+}$ and Nb$^{5+}$), we observe different valence states of Co namely 2+, 3+ and 4+, and tetravalent Nb (4$d^1$) in the x-ray photoemission spectroscopy measurements. Moreover, a reduction in the average oxygen valency with the compressive strain due to enhancement in the covalent character of Co/Nb--O bond is evident. Interestingly, we observe sharp Raman active modes in these thin films, which indicates a significant enhancement in structural ordering as compared to the bulk.

cond-mat.mtrl-sci↗

arXiv2020

Structural and transport properties of La$_{1-x}$Sr$_x$Co$_{1-y}$Nb$_y$O$_3$ thin films

We present the structural and transport properties of La$_{1-x}$Sr$_x$Co$_{1-y}$Nb$_y$O$_3$ ($y=$ 0.1 and $x=$ 0; $y=$ 0.15 and $x=$ 0.3) thin films grown on (001) orientated single crystalline ceramic substrates to investigate the effect of lattice induced compressive and tensile strain. The high resolution x-ray diffraction measurements, including $θ$-2$θ$ scan, $Φ$-scan, and reciprocal space mapping, affirm single phase; four-fold symmetry; good quality of deposited thin films. The atomic force micrographs confirm that these films have small root mean square roughness in the range of $\sim$0.5--7~nm. We observed additional Raman active modes in the films owing to the lowered crystal symmetry as compared to the bulk. More interestingly, the temperature dependent dc-resistivity measurements reveal that films become insulating due to induced lattice strain in comparison to bulk, however for the larger compressive strained films conductivity increase significantly owing to the higher degree of $p-d$ hybridization and reduction in bandwidth near the Fermi level.

cond-mat.mtrl-sci↗

arXiv2020

Unraveling the magnetic interactions and spin state in insulating Sr$_{2-x}$La$_x$CoNbO$_6$

We investigate the structural, magnetic and spin-state transitions, and magnetocaloric properties of Sr$_{2-x}$La$_x$CoNbO$_6$ ($x=$ 0--1) double perovskites. The structural transition from tetragonal to monoclinic phase at $x$ $\geqslant$ 0.6, and an evolution of (101)/(103) superlattice reflections and Raman active modes indicate the enhancement in the B-site ordering with $x$. The magnetic susceptibility data reveal the transition from weak ferromagnetic (FM) to antiferromagnetic (AFM) ordering for $x$ $\geqslant$ 0.6 with T$_{\rm N}$$\approx$9--15~K. Interestingly, the La substitution drives towards more insulating state due to increase in high-spin Co$^{2+}$, whereas a spin-state crossover is observed in Co$^{3+}$ from high-spin to intermediate/low-spin states with $x$. We discuss the correlation between complex magnetic interactions and the presence of various Co spin-states in the system. Moreover, the emergence of metamagnetic nature due to the competition between FM and AFM interactions as well as crossover from conventional to inverse magnetocaloric effect have been demonstrated by detailed analysis of temperature and field dependent change in magnetic entropy.

cond-mat.mtrl-sci↗

arXiv2019

Segmentation-Aware and Adaptive Iris Recognition

Iris recognition has emerged as one of the most accurate and convenient biometric for the human identification and has been increasingly employed in a wide range of e-security applications. The quality of iris images acquired at-a-distance or under less constrained imaging environments is known to degrade the iris matching accuracy. The periocular information is inherently embedded in such iris images and can be exploited to assist in the iris recognition under such non-ideal scenarios. Our analysis of such iris templates also indicates significant degradation and reduction in the region of interest, where the iris recognition can benefit from a similarity distance that can consider importance of different binary bits, instead of the direct use of Hamming distance in the literature. Periocular information can be dynamically reinforced, by incorporating the differences in the effective area of available iris regions, for more accurate iris recognition. This paper presents such a segmentation-assisted adaptive framework for more accurate less-constrained iris recognition. The effectiveness of this framework is evaluated on three publicly available iris databases using within-dataset and cross-dataset performance evaluation and validates the merit of the proposed iris recognition framework.

cs.CV↗

arXiv2019

A Collaborative Approach using Ridge-Valley Minutiae for More Accurate Contactless Fingerprint Identification

Contactless fingerprint identification has emerged as an reliable and user friendly alternative for the personal identification in a range of e-business and law-enforcement applications. It is however quite known from the literature that the contactless fingerprint images deliver remarkably low matching accuracies as compared with those obtained from the contact-based fingerprint sensors. This paper develops a new approach to significantly improve contactless fingerprint matching capabilities available today. We systematically analyze the extent of complimentary ridge-valley information and introduce new approaches to achieve significantly higher matching accuracy over state-of-art fingerprint matchers commonly employed today. We also investigate least explored options for the fingerprint color-space conversions, which can play a key-role for more accurate contactless fingerprint matching. This paper presents experimental results from different publicly available contactless fingerprint databases using NBIS, MCC and COTS matchers. Our consistently outperforming results validate the effectiveness of the proposed approach for more accurate contactless fingerprint identification.

cs.CV↗

arXiv2019

Radii of Starlikeness and Convexity of Bessel Functions

The radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1$, have been determined for normalizations of $q$-Bessel function, Bessel function of first kind of order $ν$, Lommel function of first kind and Legendre polynomial of odd degree.

math.CV↗

arXiv2019

Matrix Product State Based Quantum Classifier

In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated systems. Matrix product state (MPS) is the well-designed class of tensor network states, which plays an important role in processing of quantum information. In this paper, we have shown that matrix product state as one-dimensional array of tensors can be used to classify classical and quantum data. We have performed binary classification of classical machine learning dataset Iris encoded in a quantum state. Further, we have investigated the performance by considering different parameters on the ibmqx4 quantum computer and proved that MPS circuits can be used to attain better accuracy. Further, the learning ability of MPS quantum classifier is tested to classify evapotranspiration ($ET_{o}$) for Patiala meteorological station located in Northern Punjab (India), using three years of historical dataset (Agri). Furthermore, we have used different performance metrics of classification to measure its capability. Finally, the results are plotted and degree of correspondence among values of each sample is shown.

quant-ph↗

arXiv2019

Lemniscate Convexity and Other Properties of Generalized Bessel Functions

Sufficient conditions on associated parameters $p,b$ and $c$ are obtained so that the generalized and \textquotedblleft{normalized}\textquotedblright{} Bessel function $u_p(z)=u_{p,b,c}(z)$ satisfies $|(1+(zu''_p(z)/u'_p(z)))^2-1|<1$ or $|((zu_p(z))'/u_p(z))^2-1|<1$. We also determine the condition on these parameters so that $-(4(p+(b+1)/2)/c)u'_p(z)\prec\sqrt{1+z}$. Relations between the parameters $μ$ and $p$ are obtained such that the normalized Lommel function of first kind $h_{μ,p}(z)$ satisfies the subordination $1+(zh''_{μ,p}(z)/h'_{μ,p}(z))\prec\sqrt{1+z}$. Moreover, the properties of Alexander transform of the function $h_{μ,p}(z) $ are discussed.

math.CV↗

arXiv2019

Quantum finite automata: survey, status and research directions

Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for computations. Quantum automata can be classified thusly: quantum finite automata, quantum sequential machine, quantum pushdown automata, quantum Turing machine and orthomodular lattice-valued automata. These models are useful for determining the expressive power and boundaries of various computational features. In light of the current state of quantum computation theory research, a systematic review of the literature seems timely. This article seeks to provide a comprehensive and systematic analysis of quantum finite automata models, quantum finite automata models with density operators and quantum finite automata models with classical states, interactive proof systems, quantum communication complexity and query complexity as described in the literature. The statistics of quantum finite automata related papers are shown and open problems are identified for more advanced research. The current status of quantum automata theory is distributed into various categories. This research work also highlights the previous research, current status and future directions of quantum automata models.

cs.FL↗

arXiv2019

Continuous abstract wavelet transform on homogeneous space

The support of wavelet transform associated with square integrable irreducible representation of a homogeneous space is shown to have infinite measure. Pointwise homogeneous approximation property for wavelet transform has been investigated. An analogue of Heisenberg type inequality has been also obtained for wavelet transform

math.RT↗