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AN ITERATIVE METHOD FOR ORTHOGONAL PROJECTIONS OF GENERALIZED INVERSES
Srivastava, Shwetabh,Gupta, D.K. The Korean Society for Computational and Applied M 2014 Journal of applied mathematics & informatics Vol.32 No.1
This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.
Electronic structure, magnetic and structural properties of Ni doped ZnO nanoparticles
Kumar, S.,Vats, P.,Gautam, S.,Gupta, V.P.,Verma, K.D.,Chae, K.H.,Hashim, Mohd.,Choi, H.K. Pergamon Press 2014 Materials research bulletin Vol.59 No.-
We report structural, magnetic and electronic structural properties of Ni doped ZnO nanoparticles prepared by auto-combustion method. The prepared nanoparticles were characterized by using X-ray diffraction (XRD), high resolution transmission electron microscopy (HR-TEM), near edge X-ray absorption fine structure (NEXAFS) spectroscopy, and dc magnetization measurements. The XRD and HR-TEM results indicate that Ni doped ZnO nanoparticles have single phase nature with wurtzite lattice and exclude the presence of secondary phase. NEXAFS measurements performed at Ni L<SUB>3,2</SUB>-edges indicates that Ni ions are in +2 valence state and exclude the presence of Ni metal clusters. O K-edge NEXAFS spectra indicate an increase in oxygen vacancies with Ni-doping, while Zn L<SUB>3,2</SUB>-edge show the absence of Zn-vacancies. The magnetization measurements performed at room temperature shows that pure and Ni doped ZnO exhibits ferromagnetic behavior.
An iterative method for orthogonal projections of generalized inverses
Shwetabh Srivastava,D.K. Gupta 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.1
This paper describes an iterative method for orthogonal projections AA⍭ and A⍭A of an arbitrary matrix A, where A⍭ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If Zk k = 0, 1, 2, ... represents the k-th iterate obtained by our method then the sequence of the traces {trace(Zk)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace(I - Zk)} is a monotonically decreasing sequence converging to the nullity of A*.
Gupta, R.K.,Tam, K.C.,Ong, S.H.,Jenkins, R.D. The Korean Society of Rheology 2000 Korea-Australia rheology journal Vol.12 No.2
The interactions between methylated $\beta$-cyclodextrin (CD) and hydrophobically modified alkali-soluble associative polymers (HASE) were examined by a rheological technique. The effect of "capping" of hydrophobes by methylated $\beta$-cyclodextrin on the viscosity and modulus was evaluated. Model HASE polymers with $C_1$to $C_{20}$ alkyl hydrophobic groups ethoxylated with~10 moles of ethylene-oxide (EO 10) and at concentrations up to 3 wt% were examined. With the addition of methylated $\beta$-CD, the steady shear viscosity profiles shift from a Newtonian profile to one that display a shear-thinning characteristic. Significant "capping" of the hydrophobes occurs for HASE polymers with $C_{l2}$, $C_{16}$ and $C_{20}$ hydrophobes as reflected by the large reduction in the viscosity. However, the steady shear viscosity remains constant when the concentration of $\beta$-CD exceeds 1 wt%, suggesting that $\beta$-CD is not able to fully encapsulate the hydrophobes of the HASE polymer. The temperature variation plots indicate that the activation energy of the HASE-EO10-$C_{20}$ system and $\beta$-CD is dependent on the magnitude of the applied shear stress. These results further reinforce the hypothesis that $\beta$-CD is not able to completely remove all the hydrophobic associations.phobic associations.
ASYMPTPTIC DISTRIBUTION OF LIKELINOOD RATIO STATISTIC FOR TESTING MULTISAMPLE SPHERICITY
Gupta, A.K.,Nagar, D.K.,Jain, Kalpana The Korean Statistical Society 1992 Journal of the Korean Statistical Society Vol.21 No.1
In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing multisample sphericity have been derived in the null and nonnull cases when the alternatives are close to the null hypothesis. These expansions are obtained in the form of series of data distributions.
Nonnull Disribution of the Determinant of B-staistic in the Complex Case
Gupta, A.K.,Nagar, D.K. The Korean Statistical Society 1986 Journal of the Korean Statistical Society Vol.15 No.1
In this paper distribution of the determinant of B-statistic in the complex case has been derived in terms of incomplete gamma functions. Asymptotic expansion of the distribution has also been derived.
High-Field Solenoid Development for Axion Dark Matter Search at CAPP/IBS
Gupta, R.,Anerella, M.,Ghosh, A.,Sampson, W.,Schmalzle, J.,Konikowska, D.,Semertzidis, Y. K.,Shin, Y. Institute of Electrical and Electronics Engineers 2016 IEEE transactions on applied superconductivity Vol.26 No.4
<P>Construction and test results of a 100-mm-bore solenoid made with the high-temperature superconductor (HTS) producing a peak field of over 10 T are presented. This is the first step toward building a very high field solenoid (35-40 T) one of the key components of the proposed state-of-the-art facility for dark matter search at the Center for Axion and Precision Physics Research, Institute for Basic Science in Korea. The coils made with HTS are expected to provide a field of similar to 25 T, and the coils made with low-temperature superconductors are expected to provide a field of 10-15 T. REBCO HTS tapes were provided by SuNAM along with the measurements at 20 K in 3.5- to 4-T applied field. The Brookhaven National Laboratory measured several samples at 4 K in the applied field of 4-8 T. This paper will present a series of test results of the conductor, six pancake coils, and the fully assembled solenoid.</P>
Gupta, D.K. 한국전산응용수학회 2001 The Korean journal of computational & applied math Vol.8 No.1
A heuristic method TABU-CSP using Tabu Search (TS) is described for solving Constraint Satisfaction Problems (CSPs). The method is started with a complete but inconsistent solution of a binary CSP and obtained in prespecified number of iterations either a consistent solution or a near optimal solution with an acceptable number of conflicts. The repair in the solution at each iterative step is done by using two heuristics alternatively. The first heuristic is a min-conflicts heuristic that chooses a variable with the maximum number of conflicts and reassigns it the value which leads to the minimum number of conflicts. If the acceptable solution is not reached after the search continued for a certain number of iterations, the min-conflict heuristic is changed and the variable selected least number of times is chosen for repair. If an acceptable solution is not reached, the method switches back to the min-conflict heuristic and proceeds further. This allowed the method to explore a different region of search space space for the solution as well as to prevent cycling. The demonstration of the method is shown on a toy problem [9]which has no solution. The method is then tested on various randomly generated CSPs with different starting solutions. The performance of the proposed method in terms of the average number of consistency is checked and the average number of conflicts is conflicts is compared with that of the Branch and Bound(BB) method used to obtain the same solution. In almost all cases, the proposed method moves faster to the acceptable solution than BB. AMS Mathematical Subject Classification : 68T20, 68R10
Distribution of Votaw's $\lambda_1$(mvc) Criterion
Nagar, D.K.,Gupta, A.K. The Korean Statistical Society 1994 Journal of the Korean Statistical Society Vol.23 No.2
In this paper, distribution of Votaw's $\lambda_1$(mvc) criterion has been obtained using inverse Mellin transform, residue theorem and properties of special functions.