arXiv subjects
Publications and source records attributed to Deepak Kumar.
Let $R$ be any ring containing a non-tivial idempotent element $e$. Let $\Im: R\rightarrow R$ be a mapping such that $\Im(ab)=\Im(b)a+b\Im(a)$ for all $a,b\in R$. In this note, our aim is to show that under some suitable restrictions imposed on $R,$ $\Im$ is additive.
We study the existence, multiplicity and regularity results of non-negative solutions of following doubly nonlocal problem: $$ (P_\la) \left\{ \begin{array}{lr}\ds \quad (-Δ)^{s_1}u+\ba (-Δ)^{s_2}_{p}u = \la a(x)|u|^{q-2}u+ \left(\int_{\Om}\frac{|u(y)|^r}{|x-y|^μ}~dy\right)|u|^{r-2} u \quad \text{in}\; \Om, \quad \quad\quad \quad u =0\quad \text{in} \quad \mb R^n\setminus \Om, \end{array} \right. $$ where $\Om\subset\mb R^n$ is a bounded domain with $C^2$ boundary $\pa\Om$, $0 2 s_1$, $1< q 0$ and $a\in L^{\frac{d}{d-q}}(\Om)$, for some $q<d<2^{*}_{s_1}:=\frac{2n}{n-2s_1}$, is a sign changing function. We prove that each nonnegative weak solution of $(P_\la)$ is bounded. Furthermore, we obtain some existence and multiplicity results using Nehari manifold method.
We report a comprehensive investigation of La0.2Pr0.4Ca0.4MnO3 to clarify the micrometre scale phase separation phenomenon in the mixed valent manganite (La,Pr,Ca)MnO3. The compound shows multiple magnetic transitions, in which the charge-ordered state is converted into a ferromagnetic state in steps with the application of a magnetic field. The ac susceptibility measurements show that the glassy transition at low temperatures does not depend on the frequency, thus indicating the absence of any spin glass behaviour. Magnetization as well as heat capacity measurements indicate that this low temperature transition is magnetic field dependent. The field dependent resistivity at 2K shows a sharp drop indicating that the sample behaviour changes from a high resistive state to a low resistive state, corroborating the conversion of charge-ordered insulating (COI) phase to a ferromagnetic metallic (FMM) phase. Our results point towards the existence of phase separation, rigidity of the low temperature glassy-like phase as well as the conversion of COI phase to FMM phase by the application of magnetic fields.
We estimate here chiral susceptibility at finite temperature within the framework of the Nambu-Jona-Lasinio model (NJL) using the Wigner function approach. We also estimate it in the presence of chiral chemical potential ($μ_5$) as well as a non vanishing magnetic field ($B$). We use medium separation regularization scheme (MSS) to calculate the chiral condensate and corresponding susceptibility. It is observed that for a fixed value of chiral chemical potential ($μ_5$), transition temperature increases with the magnetic field. While for the fixed value of the magnetic field, transition temperature decreases with chiral chemical potential. For a strong magnetic field, we observe non degeneracy in susceptibility for up and down type quarks.
Transition-metal oxides with an ABO$_3$ perovskite structure exhibit strongly entangled structural and electronic degrees of freedom and thus, one expects to unveil exotic phases and properties by acting on the lattice through various external stimuli. Using the Jahn-Teller active praseodymium vanadate Pr$^{3+}$V$^{3+}$O$_3$ compound as a model system, we show that PrVO$_3$ Néel temperature T$_N$ can be raised by 40 K with respect to the bulk when grown as thin films. Using advanced experimental techniques, this enhancement is unambiguously ascribed to a tetragonality resulting from the epitaxial compressive strain experienced by the films. First-principles simulations not only confirm experimental results, but they also reveal that the strain promotes an unprecedented orbital-ordering of the V$^{3+}$ d electrons, strongly favouring antiferromagnetic interactions. These results show that an accurate control of structural aspects is the key for unveiling unexpected phases in oxides.
This article deals with the study of the following nonlinear doubly nonlocal equation: \begin{equation*} (-Δ)^{s_1}_{p}u+\ba(-Δ)^{s_2}_{q}u = \la a(x)|u|^{δ-2}u+ b(x)|u|^{r-2} u,\; \text{ in }\; \Om, \; u=0 \text{ on } \mathbb{R}^n\setminus \Om, \end{equation*} where $\Om$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary, $1< \de \le q\leq p p s_1$ and $\la, \ba>0$ are parameters. Here $a\in L^{\frac{r}{r-\de}}(\Om)$ and $b\in L^{\infty}(\Om)$ are sign changing functions. We prove the $L^\infty$ estimates, weak Harnack inequality and Interior Hölder regularity of the weak solutions of the above problem in the subcritical case $(r<p_{s_1}^*).$ Also, by analyzing the fibering maps and minimizing the energy functional over suitable subsets of the Nehari manifold, we prove existence and multiplicity of weak solutions to above convex-concave problem. In case of $\de=q$, we show the existence of solution.
Private information retrieval (PIR) allows a user to retrieve a desired message from a set of databases without revealing the identity of the desired message. The replicated databases scenario was considered by Sun and Jafar, 2016, where $N$ databases can store the same $K$ messages completely. A PIR scheme was developed to achieve the optimal download cost given by $\left(1+ \frac{1}{N}+ \frac{1}{N^{2}}+ \cdots + \frac{1}{N^{K-1}}\right)$. In this work, we consider the problem of PIR from storage constrained databases. Each database has a storage capacity of $μKL$ bits, where $L$ is the size of each message in bits, and $μ\in [1/N, 1]$ is the normalized storage. On one extreme, $μ=1$ is the replicated databases case. On the other hand, when $μ= 1/N$, then in order to retrieve a message privately, the user has to download all the messages from the databases achieving a download cost of $1/K$. We aim to characterize the optimal download cost versus storage trade-off for any storage capacity in the range $μ\in [1/N, 1]$. For any $(N,K)$, we show that the optimal trade-off between storage, $μ$, and the download cost, $D(μ)$, is given by the lower convex hull of the $N$ pairs $\left(μ= \frac{t}{N},D(μ) = \left(1+ \frac{1}{t}+ \frac{1}{t^{2}}+ \cdots + \frac{1}{t^{K-1}}\right)\right)$ for $t=1,2,\ldots, N$. To prove this result, we first present the storage constrained PIR scheme for any $(N,K)$. We next obtain a general lower bound on the download cost for PIR, which is valid for the following storage scenarios: replicated or storage constrained, coded or uncoded, and fixed or optimized. We then specialize this bound using the uncoded storage assumption to obtain lower bounds matching the achievable download cost of the storage constrained PIR scheme for any value of the available storage.
The magnetic properties in manganite have been found to be highly sensitive to the doping and structural manipulations. Here, we report the effect of B-site bismuth doping on the magnetic and transport properties in La0.5Ca0.5Mn1-xBixO3 (LCMBO) thin films (for x = 0, 0.02 and 0.05) for high-efficiency spintronics devices. For thin film of LCMBO (with x = 0.02), a significant increase in the magnetization and ferromagnetic ordering temperature (TC) are observed. Also, about 98% magnetoresistance (MR) and unusually large (~ 42%) anisotropic magnetoresistance (AMR) is observed at 50 K in the same LCMBO (for x = 0.02) thin film. This observed improvement in TC, MR and AMR in LCMBO (with x = 0.02) thin film may be attributed to the modulation of the trapped electrons through JT-distortions due to the replacement of Mn+3 ions by larger Bi+3 ions. With further increase in bismuth doping (for x = 0.05) at the B-site, a significant decrease in magnetization and TC have been observed.
The $ε$-subdifferential of convex univariate piecewise linear-quadratic functions can be computed in linear worst-case time complexity as the level-set of a convex function. Using dichotomic search, we show how the computation can be performed in logarithmic worst-case time. Furthermore, a new algorithm to compute the entire graph of the $ε$-subdifferential in linear time is presented. Both algorithms are not limited to convex PLQ functions but are also applicable to any convex piecewise-defined function with little restrictions.
Private information retrieval (PIR) allows a user to retrieve a desired message out of $K$ possible messages from $N$ databases without revealing the identity of the desired message. Majority of existing works on PIR assume the presence of replicated databases, each storing all the $K$ messages. In this work, we consider the problem of PIR from storage constrained databases. Each database has a storage capacity of $μKL$ bits, where $K$ is the number of messages, $L$ is the size of each message in bits, and $μ\in [1/N, 1]$ is the normalized storage. In the storage constrained PIR problem, there are two key design questions: a) how to store content across each database under storage constraints; and b) construction of schemes that allow efficient PIR through storage constrained databases. The main contribution of this work is a general achievable scheme for PIR from storage constrained databases for any value of storage. In particular, for any $(N,K)$, with normalized storage $μ= t/N$, where the parameter $t$ can take integer values $t \in \{1, 2, \ldots, N\}$, we show that our proposed PIR scheme achieves a download cost of $\left(1+ \frac{1}{t}+ \frac{1}{t^{2}}+ \cdots + \frac{1}{t^{K-1}}\right)$. The extreme case when $μ=1$ (i.e., $t=N$) corresponds to the setting of replicated databases with full storage. For this extremal setting, our scheme recovers the information-theoretically optimal download cost characterized by Sun and Jafar as $\left(1+ \frac{1}{N}+ \cdots + \frac{1}{N^{K-1}}\right)$. For the other extreme, when $μ= 1/N$ (i.e., $t=1$), the proposed scheme achieves a download cost of $K$. The interesting aspect of the result is that for intermediate values of storage, i.e., $1/N < μ<1$, the proposed scheme can strictly outperform memory-sharing between extreme values of storage.
It is understood from the recent experimental studies that prompt/resonant breakup, and transfer followed by breakup in the weakly bound $^{6,7}$Li-induced reactions play a significant role in the complete-incomplete fusion (CF-ICF), suppression/enhancement in the fusion cross section around the Coulomb barrier. Investigation of ICF over CF was done by measuring cross sections of the populated residues in the $^{7}$Li-induced reaction on $^{\text{nat}}$Nb target within 3--6.5 MeV/nucleon energy region. Measured excitation functions of different channels were compared with different equilibrium (EQ) and preequilibrium (PEQ) models. The enhancement in cross sections in the proton ($\sim$ 20--30 MeV) and $α$-emitting channels, which may be ascribed to ICF, was observed in the measured energy range when compared to the Hauser-Feshbach and exciton model calculations using EMPIRE, which satisfactorily reproduces the neutron channels, compared to the Weisskopf-Ewing model and Hybrid Monte Carlo calculations. The increment of the incomplete fusion fraction was observed with rising projectile energy.
In this paper, we establish some common fixed point results for two pairs of weakly compatible mappings in the setting of $C$-complex valued metric space. Also, as application of the proved result, we obtain the existence and uniqueness of a common solution of the system of the Urysohn integral equations: \begin{eqnarray*} x(t)=ψ_i(t)+\int_{a}^{b}K_i(t,s,x(s))ds \end{eqnarray*} where $i=1, 2, 3, 4, a,b\in \mathbb{R}$ with $a\leq b, t\in [a,b], x, ψ_i\in C([a,b],\mathbb{R}^n)$ and $K_i:[a,b]\times [a,b]\times \mathbb{R}^n\rightarrow \mathbb{R}^n$ is a mapping for each $i=1, 2, 3, 4$.
Several investigations on the complete-incomplete fusion (CF-ICF) dynamics of $α$-cluster well-bound nuclei has been contemplated above the Coulomb barrier ($\sim$ 4-7 MeV/nucleon) in recent years. It is therefore expected to observe significant ICF over CF in the reactions induced by a weakly bound $α$-cluster nucleus at slightly above the barrier. In order to investigate CF-ICF in the loosely bound system, $^{\text{7}}$Li beam was bombarded on the $^{\text{nat}}$Mo foils, separated by the aluminium (Al) catcher foils alternatively, within $\sim$ 3-6.5 MeV/nucleon. Evaporation residues produced in each foil were identified by the $γ$-ray spectrometry. Measured cross section data of the residues were compared with the theoretical model calculations based on the equilibrium (EQ) and preequilibrium (PEQ) reaction mechanisms. The experimental cross section of $^{\text{101m,100,99m,97}}$Rh, $^{\text{97,95}}$Ru, $^{\text{99m,96,95,94,93m+g}}$Tc and $^{\text{93m}}$Mo residues measured at various projectile energies were satisfactorily reproduced by the simplified coupled channel approach in comparison to single barrier penetration model calculation. Significant cross section enhancement in the $α$-emitting channels was observed compared to EQ and PEQ model calculations throughout observed energy region. The ICF process over CF was analyzed by comparing with EMPIRE. The increment of the incomplete fusion fraction was observed with increasing projectile energies. Theoretical model calculations reveal that compound reaction mechanism is the major contributor to the production of residues. Theoretical evaluations substantiate the contribution of ICF over the CF in $α$-emitting channels.
The heavy-ion induced reactions on intermediate mass targets are complex in nature, even at the low energies. To understand those nuclear reaction phenomena in detail, more experimental studies are required in a wide range of energy. Heavy-ion reactions were investigated by measuring production cross sections of the residues produced in the $^{11}$B-induced reactions on $^{89}$Y and $^{93}$Nb at low energies, near and above the barrier, and to check the effectiveness of the different nuclear models to explain them. Further, aim is also to optimize the production parameters of neutron deficient medically relevant $^{97}$Ru and $^{101m}$Rh radioisotopes produced in those reactions, respectively. The $^{11}$B-beam was allowed to impinge on $^{89}$Y and $^{93}$Nb foils supported by an aluminum catcher foil, arranged in a stack, in 27.5-58.7 and 30.6-62.3 MeV energy range, respectively. The $γ$-spectrometry was carried out after EOB to measure the activity of the radionuclides produced in each foil and cross sections were calculated. Measured cross-sectional data were analyzed in terms of compound and precompound model calculations. The measured cross sections of the residues showed good agreement with the model calculations based on the Hauser-Feshbach formulation and exciton model. A substantial preequilibrium contribution was noticed in the 3$n$ reaction channel in both the reactions. Theoretical estimations confirmed that major production yields are mostly contributed by the compound reaction process. Preequilibrium emissions contributed at the high energy tail of the 3$n$ channel for both the reactions. Moreover, an indirect signature of a direct reaction influence was also observed in the $^{90m}$Y production.
Background: Interaction of weakly bound heavy-ions with an intermediate or heavy target is not yet understood completely due to the scarcity of experimental data. In order to develop a clear understanding of breakup fusion or preequilibrium emission even at low energy range, 3--10 MeV/nucleon, more experimental investigations are necessary. Purpose: Study of reaction mechanisms involved in the weakly bound heavy-ion induced reaction, $^7$Li + $^{93}$Nb, at low energies by measuring the production cross sections of the residual radionuclides. Method: Natural niobium ($^{93}$Nb) foil, backed by aluminium (Al) catcher, arranged in a stack was bombarded by $^{7}$Li ions of 20-45 MeV energy. Activity of the residues produced in each $^{93}$Nb target was measured by off-line $γ$-ray spectrometry after the end of bombardment (EOB) and cross sections were calculated. Experimental cross sections were compared with those computed using compound and precompound models. Results: In general, measured excitation functions of all residues produced in $^{7}$Li + $^{93}$Nb reaction showed good agreement with the model calculations based on Hauser-Feshbach formalism and exciton model for compound and precompound processes, respectively. Significant preequilibrium emission of neutrons was observed at the relatively high energy tail of the excitation function of $^{97}$Ru. Conclusions: Preequilibrium process played an important role for the enhancement of cross-section in $xn$ reaction channel over the compound reaction mechanism at higher energies for $^{7}$Li + $^{93}$Nb reaction. Additionally, indirect evidence of incomplete or breakup fusion was also perceived.
A model for a controlled single-photon beam-splitter is proposed and analysed. It consists of two crossed optical-cavities with overlapping waists, dynamically coupled to a single flying atom. The system is shown to route a single photon with near-unity efficiency in an effective "weak-coupling" regime. Furthermore, two such nodes, forming a segment of a quantum network, are shown to perform several controlled quantum operations. All one-qubit operations involve a transfer of a photon from one cavity to another in a single node, while two-qubit operations involve transfer from one node to a next one, coupled via an optical fiber. Novel timing protocols for classical optical fields are found to simplify possible experimental realizations along with achievable effective parameter regime. Though our analysis here is restricted to a cavity-QED scenario, basic features of the model can be extended to various other physical systems including gated quantum dots, circuit-QED or opto-mechanical elements.
An FPGA-based digital-receiver has been developed for a low-frequency imaging radio interferometer, the Murchison Widefield Array (MWA). The MWA, located at the Murchison Radio-astronomy Observatory (MRO) in Western Australia, consists of 128 dual-polarized aperture-array elements (tiles) operating between 80 and 300\,MHz, with a total processed bandwidth of 30.72 MHz for each polarization. Radio-frequency signals from the tiles are amplified and band limited using analog signal conditioning units; sampled and channelized by digital-receivers. The signals from eight tiles are processed by a single digital-receiver, thus requiring 16 digital-receivers for the MWA. The main function of the digital-receivers is to digitize the broad-band signals from each tile, channelize them to form the sky-band, and transport it through optical fibers to a centrally located correlator for further processing. The digital-receiver firmware also implements functions to measure the signal power, perform power equalization across the band, detect interference-like events, and invoke diagnostic modes. The digital-receiver is controlled by high-level programs running on a single-board-computer. This paper presents the digital-receiver design, implementation, current status, and plans for future enhancements.
Particle swarm optimization is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The approach of particle swarms is an example for interior point methods in optimization as an iterative technique. This approach is novel and deals with classification problems without the use of a traditional classifier. Our method determines the optimal hyperplane or classification boundary for a data set. In a binary classification problem, we constrain each class as a cluster, which is enclosed by an ellipsoid. The estimation of the optimal hyperplane between the two clusters is posed as a quadratically constrained quadratic problem. The optimization problem is solved in distributed format using modified particle swarms. Our method has the advantage of using the direction towards optimal solution rather than searching the entire feasible region. Our results on the Iris, Pima, Wine, and Thyroid datasets show that the proposed method works better than a neural network and the performance is close to that of SVM.