arXiv subjects
Publications and source records attributed to A. K. Das.
The paper aims to find the solution of oligopoly market equilibrium problem through system of nonlinear equations. We propose modified newton method to obtain the solution of system of nonlinear equations. We show that our proposed method has higher order of convergence. Keywords: System of nonlinear equations, modified newton method, oligopolistic market equilibrium problem.
The paper aims to show the equivalency between nonlinear complementarity problem and the system of nonlinear equations. We propose a homotopy method with vector parameter $λ$ in finding the solution of nonlinear complementarity problem through a system of nonlinear equations. We propose a smooth and bounded homotopy path to obtain solution of the system of nonlinear equations under some conditions. An oligopolistic market equilibrium problem is considered to show the effectiveness of the proposed homotopy continuation method. Keywords: Nonlinear complementarity problem, system of nonlinear equations, homotopy function with vector parameter, bounded smooth curve, oligopolistic market equilibrium.
In this article we establish error bound for linear complementarity problem with $P$-matrix using plus function. We introduce a fundamental quantity associated with a $P$-matrix and show how this quantity is useful in deriving error bounds for the linear complementarity problem of the $P$-type. We also obtain (upper and lower) bounds for the quantity introduced. Keywords: Linear complementarity problem, plus function, error bound, relative error bound.
In this article, we consider nonlinear complementarity problem. We introduce a new homotopy function for finding the solution of nonlinear complementarity problem through the trajectory . We show that the homotopy path approaching the solution is smooth and bounded . Numerical example of an oligopoly equilibrium problem is illustrated to show the effectiveness of the proposed algorithm. Keywords: Nonlinear complementarity problem, homotopy continuation method, Oligopoly equilibrium problem.
In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the involved functions are special polynomials defined by a tensor. Semipositive and strictly semipositive tensors play an important role in the study of the tensor complementarity problem. The article considers some important properties of semipositive tensor. We establish invariance property of semipositive tensor. We prove necessary and sufficient conditions for a tensor to be semipositive tensor. A relation between even order row diagonal semipositive tensor and its majorization matrix is proposed. Keywords: Tensor complementarity problem, semipositive tensor, semimonotone matrix, null vector, majorization matrix.
The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a tensor. We propose a new homotopy function with smooth and bounded homotopy path to obtain solution of the tensor complementarity problem under some conditions. A homotopy continuation method is developed based on the proposed homotopy function. Several numerical examples are provided to show the effectiveness of the proposed homotopy continuation method.
In multilinear algebra, some special classes of matrices are extended to higher order structured tensors. The local $w$-uniqueness solution to the linear complementarity problem can be identified by the column competent matrix. Motivated by this $w$-uniqueness property, we introduce column competent tensor in the context of tensor complementarity problem. We consider some important properties. In the theory of linear complementarity problem, column competent matrices are introduced to study local $w$-uniqueness property of LCP solution. We present the inheritance property and invariance property of column competent tensors. We study the tensor complementarity problem using column competent tensors and several results are established. Some examples are illustrated to support the results. Keywords: Tensor complementarity problem, column competent tensor, nondegenerate tensor, $ω$-solution. AMS subject classifications: 90C33, 90C30, 15A69, 46G25.
In this paper, we introduce a homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of two-person zero-sum discounted stochastic ARAT game. We show that the algorithm has the higher order of convergence. For the proposed algorithm, the homotopy path approaching the solution is smooth and bounded. Two numerical examples are illustrated to show the effectiveness of the proposed algorithm.
In this article we introduce column adequate tensor in the context of tensor complementarity problem and consider some important properties. The tensor complementarity problem is a class of nonlinear complematarity problems with the involved function being defined by a tensor. We establish the inheritance property and invariant property of column adequate tensors. We show that TCP$(q,\mathcal{A})$ has $ω$-unique solution under some assumptions.
First-principles calculations, within the framework of density functional theory, have been performed on the well-studied 2H and the less explored 1T$^{\prime}$ phase of single-layer MoS$_{2}$. We have addressed the strain-induced tunability of the electronic and phononic properties of both phases, and compared their stability against the applied strain. By considering a large number of strain profiles for both tensile and compressive stress, we have found that the electronic properties of both 2H and 1T$^{\prime}$ phases are sensitive to the direction of the applied strain and can be tuned in a controlled way. For the 2H phase, in most cases, a direct to indirect band gap transition at lower strain and a semiconductor to metal transition at higher strain is observed. The applied strain destroys the semimetallic nature of the 1T$^{\prime}$ phase via the overlapping of the bulk states with the topologically protected edge states. Significant strain-induced changes in the phononic properties, in the frequency of the phonon branches, as well as in the nature of the dispersion curves, are observed. A systematic change in the frequency of the optical phonon modes at the zone centre is seen for both phases. With increasing strain, the out-of-plane acoustic mode (ZA) turns imaginary, indicating a possibility of phase transition or instability of the crystal structure. The 2H phase appears to withstand a larger amount of strain and therefore possesses better stability compared to the 1T$^{\prime}$ phase since the imaginary branch starts to appear at much lower values of strain in the latter case. We highlight the significance of strain engineering in tuning the electronic and phononic properties and the safe limit of the strain application in different polymorphs of single-layer MoS$_{2}$.
In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem. The proposed approach extends the processability of the larger class of linear complementarity problem and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded with positive tangent direction of the homotopy path. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm and the superiority of the algorithm among other existing iterative methods.
In this article we introduce $K$-type block matrices which include two new classes of block matrices namely block triangular $K$-matrices and hidden block triangular $K$-matrices. We show that the solution of linear complementarity problem with $K$-type block matrices can be obtained by solving a linear programming problem. We show that block triangular $K$-matrices satisfy least element property. We prove that hidden block triangular $K$-matrices are $Q_0$ and processable by Lemke's algorithm. The purpose of this article is to study properties of $K$-type block matrices in the context of the solution of linear complementarity problem.
Spherical nanoparticles (NPs) of size 14 nm, made of intermetallic Fe2CoAl (FCA) Heusler alloy, are synthesized via the co-precipitation and thermal deoxidization method. X-ray diffraction (XRD) and selected area electron diffraction (SAED) patterns confirm that the present nanoalloy is crystallized in A2-disordered cubic Heusler structure. Magnetic field (H) and temperature (T) dependent magnetization (M) results reveal that the NPs are soft ferromagnetic (FM) with high saturation magnetization (Ms) and Curie temperature (Tc). Fe2CoAl nanoalloy does not follow the Slater Pauling (SP) rule, possibly because of the disorder present in the system. We also investigate its magnetic phase transition (MPT) and magnetocaloric (MC) properties. The peak value of the magnetic entropy change vs T curve at a magnetic field change of 20 kOe corresponds to about 2.65 J/kg-K, and the observed value of refrigeration capacity (RCP) is as large as 44 J/kg, suggesting a large heat conversion in magnetic refrigeration cycle. The Arrott plot and the nature of the universal curve accomplish that the FM to paramagnetic (PM) phase transition in Fe2CoAl nanoalloy is of second-order. The present study suggests that the Fe2CoAl nanoscale system is proficient, useful and a good candidate for the spintronics application and opens up a window for further research on full-Heusler based magnetic refrigerants.
We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local $w$-uniqueness of the solutions to the linear complementarity problem can be identified by the column competent matrices. We establish some new results on $w$-uniqueness properties in connection with column competent matrices. These results are significant in the context of matrix theory as well as algorithms in operations research. We prove some results in connection with locally $w$-uniqueness property of column competent matrices. Finally we establish a connection between column competent matrices and column adequate matrices with the help of degree theory.
A giant magnetocaloric effect across the ferromagnetic (FM) to paramagnetic (PM) phase transition was observed in chemically synthesized Co2FeAl Heusler alloy nanoparticles with a mean diameter of 16 nm. In our previous report, we have observed a significant enhancement in its saturation magnetization (Ms) and Curie temperature (Tc) as compared with the bulk counterpart. Motivated from those results, here, we aim to explore its magnetocaloric properties near the Tc. The magnetic entropy change shows a positive anomaly at 1252 K. Magnetic entropy change increases linearly with the magnetic field, and a large value of ~15 J/Kg-K is detected under a moderate field of 14 kOe. It leads to a net relative cooling power of 89 J/Kg for the magnetic field change of 14 kOe. To confirm the nature of magnetic phase transition, a detailed study of its magnetization is performed. The Arrott plot and nature of the universal curve conclude that FM to PM phase transition in the present system is of second-order.
Here, we report the synthesis and physical properties of Co2FeGe (CFG) Heusler alloy (HA) nanoparticles (NPs). The NPs of size 23 nm are prepared using the co-precipitation method. X-ray and selected area electron diffraction patterns have confirmed the cubic Heusler phase of the NPs with the A2-disorder. These NPs are soft ferromagnetic, and exhibit a high saturation magnetization (Ms) along with a very high Curie temperature (Tc) of 1060 K. The observed Tc value matches closely with the theoretically calculated one following a model provided by Wurmehl et al. [1]. The high Ms and Tc make the present system a potential candidate for magnetically activated nano-devices working at high temperatures. The near-integral value 5.9 mehoB/f.u. of Ms at low temperatures indicates that the half-metallic ferromagnetism is preserved even in the particles even on the 20 nm length scale. Additionally, we have facilitated the existing HA-NP preparation method, which can be used in synthesizing other HA-NPs. The first-principles density functional theory computations complement the experimental results.
Density functional theory calculations within the generalized gradient approximation are employed to study the ground state of Co2FeAl. Various magnetic configurations are considered to find out its most stable phase. The ferromagnetic ground state of the Co2FeAl is energetically observed with an optimized lattice constant of 5.70 Å. Thereafter, the system was subjected under uniform and non-uniform strains to see their effects on spin polarization (P) and half-metallicity. The effect of spin orbit coupling is considered in the present study. Half-metallicity (and 100 % P) is only retained under uniform strains started from 0 to +4%, and dropped rapidly from 90% to 16% for the negative strains started from -1% to -6%. We find that the present system is much sensitive under tetragonal distortions as half-metallicity (and 100% P) is preserved only for the cubic case. The main reason for the loss of half-metallicity is due to the shift of the bands with respect to the Fermi level. We also discuss the influence of these results on spintronics devices.
The physical properties of Fe2CoAl (FCA) Heusler alloy are systematically investigated using the first-principles calculations within generalized gradient approximation (GGA) and GGA+U. The influence of atomic ordering with respect to the Wyckoff sites on the phase stability, magnetism and half metallicity in both the conventional L21 and XA phases of FCA is focused in this study. Various possible hypothetical structures viz., L21, XA-I, and XA-II are prepared by altering atomic occupancies at their Wyckoff sites. At first, we have determined the stable phase of FCA considering various non-magnetic (or paramagnetic), ferromagnetic (FM) and antiferromagnetic (AFM) configurations. Out of these, the ferromagnetic (FM) XA-I structure is found to be energetically most stable. The total magnetic moments per cell are not in agreement with the Slater-Pauling (SP) rule in any phases; therefore, the half-metallicity is not observed in any configurations. However, FM ordered XA-I type FCA shows 78% spin polarization at EF. Interestingly, the results of XA-I type FCA are closely matched with the experimental results.