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    Approximation of entire function solutions of the Helmholtz equation having slow growth

    Kumar, Devendra
    Journal of Applied Analysis, 2012, Vol.18(2), pp.179-196 [Peer Reviewed Journal]
    Walter de Gruyter GmbH
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    Title: Approximation of entire function solutions of the Helmholtz equation having slow growth
    Author: Kumar, Devendra
    Publisher: Walter de Gruyter GmbH
    Subject: Generalized Order ; Entire Function ; Helmholtz Equation ; Chebyshev Approximation Error
    Description: In this paper, we study the Chebyshev polynomial approximation of entire solutions of Helmholtz equations in in Banach spaces ( space, Hardy space and Bergman space). Some bounds on generalized order of entire solutions of Helmholtz equations of slow growth have been obtained in terms of the coefficients and approximation errors using function theoretic methods.
    Is part of: Journal of Applied Analysis, 2012, Vol.18(2), pp.179-196
    Identifier: 1425-6908 (ISSN); 1869-6082 (E-ISSN); 10.1515/jaa-2012-0012 (DOI)

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    Generalized growth and best approximation of entire functions in L p -norm in several complex variables

    Kumar, Devendra
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2011, Vol.57(2), pp.353-372 [Peer Reviewed Journal]
    Springer Science & Business Media B.V.
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    Title: Generalized growth and best approximation of entire functions in L p -norm in several complex variables
    Author: Kumar, Devendra
    Subject: Generalized order and type ; Extremal polynomials ; Approximation and interpolation errors ; Pluricomplex Green function and slow growth
    Description: The paper deals with the characterization of generalized order and generalized type of entire functions in several complex variables in terms of the coefficients of the development with respect to the sequence of extremal polynomials and the best L p -approximation and interpolation errors, 0 
    Is part of: ANNALI DELL'UNIVERSITA' DI FERRARA, 2011, Vol.57(2), pp.353-372
    Identifier: 0430-3202 (ISSN); 1827-1510 (E-ISSN); 10.1007/s11565-011-0130-8 (DOI)

    • Several versions

    Convergence and Characterization of Wavelets Associated with Dilation Matrix in Variable Spaces

    Kumar, Devendra
    Journal of Mathematics, 2013, Vol.2013, 7 pages [Peer Reviewed Journal]

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    Generalized growth and approximation of entire function solution of Helmholtz equation in Banach spaces

    Kumar, Devendra
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2016, Vol.62(1), pp.83-97 [Peer Reviewed Journal]
    Springer Science & Business Media B.V.
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    Title: Generalized growth and approximation of entire function solution of Helmholtz equation in Banach spaces
    Author: Kumar, Devendra
    Subject: Generalized order and type ; Helmholtz equation ; Polynomial approximation ; Smirnov space
    Description: In this paper, we study the generalized growth and polynomial approximation of entire function solution of Helmholtz equation in $$R^2$$ R 2 in Smirnov spaces [ $$\varepsilon _p (S)$$ ε p ( S ) and $$\varepsilon ^{^\prime }_p(S), 1\le p\le \infty $$ ε p ′ ( S ) , 1 ≤ p ≤ ∞ ] where S is finitely simply connected domain in the complex plane with the boundary that belongs to the Al’per class (Izv AN SSSR Ser Matem 19(3):423–444, 1955). Some bounds on generalized order and generalized type of entire solution of Helmholtz equation have been obtained in terms of the coefficients and approximation errors using function theoretic methods. Our results extend and improve the results of Kumar (J Appl Anal 18:179–196, 2012).
    Is part of: ANNALI DELL'UNIVERSITA' DI FERRARA, 2016, Vol.62(1), pp.83-97
    Identifier: 0430-3202 (ISSN); 1827-1510 (E-ISSN); 10.1007/s11565-015-0233-8 (DOI)

    • Several versions

    On the Rational Approximation of Analytic Functions Having Generalized Types of Rate of Growth

    Kumar, Devendra
    International Journal of Mathematics and Mathematical Sciences, 2012, Vol.2012, 10 pages [Peer Reviewed Journal]

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    Growth and approximation of solutions to a class of certain linear partial differential equations in ℝ N

    Kumar, Devendra
    Mathematica Slovaca, 2014, Vol.64(1), pp.139-154 [Peer Reviewed Journal]
    Springer Science & Business Media B.V.
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    Title: Growth and approximation of solutions to a class of certain linear partial differential equations in ℝ N
    Author: Kumar, Devendra
    Subject: axisymmetric harmonic polynomials ; axi-convex region ; order and type ; Lagrange polynomial ; approximation and interpolation errors ; Bergman operator and hypersphere
    Description: In this paper we consider the equation ∇ 2 φ + A ( r 2 ) X · ∇φ + C ( r 2 ) φ = 0 for X ∈ ℝ N whose coefficients are entire functions of the variable r = | X |. Corresponding to a specified axially symmetric solution φ and set C n of ( n + 1) circles, an axially symmetric solution Λ n * ( x , η ; C n ) and Λ n ( x , η ; C n ) are found that interpolates to φ ( x , η ) on the C n and converges uniformly to φ ( x , η ) on certain axially symmetric domains. The main results are the characterization of growth parameters order and type in terms of axially symmetric harmonic polynomial approximation errors and Lagrange polynomial interpolation errors using the method developed in [MARDEN, M.: Axisymmetric harmonic interpolation polynomials in ℝ N , Trans. Amer. Math. Soc. 196 (1974), 385–402] and [MARDEN, M.: Value distribution of harmonic polynomials in several real variables , Trans. Amer. math. Soc. 159 (1971), 137–154].
    Is part of: Mathematica Slovaca, 2014, Vol.64(1), pp.139-154
    Identifier: 0139-9918 (ISSN); 1337-2211 (E-ISSN); 10.2478/s12175-013-0192-4 (DOI)

    • Several versions

    Spin-glass like dynamics of ferromagnetic clusters in La\(_{0.75}\)Ba\(_{0.25}\)CoO\(_3\)

    Kumar, Devendra
    arXiv.org, Jan 8, 2016 [Peer Reviewed Journal]

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    Faculty Use of Internet Services at a University of Agriculture and Technology

    Kumar, Devendra
    Library Philosophy and Practice, Feb 2010, pp.1-8 [Peer Reviewed Journal]
    © ProQuest LLC All rights reserved, ProQuest Library Science, Library & Information Science Abstracts, Publicly Available Content Database, Research Library China, ProQuest Research Library, ProQuest Central, Research Library (Alumni edition), Library and Information Science Abstracts (LISA), Library & Information Science Collection, ProQuest Central (new), ProQuest Central K-12, ProQuest Central Korea, Research Library Prep, Social Science Premium Collection, ProQuest Central Essentials, ProQuest Central China, ProQuest One Academic
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    Title: Faculty Use of Internet Services at a University of Agriculture and Technology
    Author: Kumar, Devendra
    Is part of: Library Philosophy and Practice, Feb 2010, pp.1-8
    Identifier: 15220222 (E-ISSN)

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    IMAGES IN CLINICAL MEDICINE. Eggshell Calcifications of the Bladder

    Nepal, Pankaj, Kumar, Devendra
    The New England journal of medicine, 25 February 2016, Vol.374(8), pp.e9 [Peer Reviewed Journal]
    MEDLINE/PubMed (U.S. National Library of Medicine)
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    Title: IMAGES IN CLINICAL MEDICINE. Eggshell Calcifications of the Bladder
    Author: Nepal, Pankaj; Kumar, Devendra
    Subject: Calcinosis -- Diagnostic Imaging ; Dysuria -- Etiology ; Schistosomiasis Haematobia -- Diagnostic Imaging ; Urinary Bladder Diseases -- Diagnostic Imaging
    Description: A 43-year-old man presented with dysuria and intermittent hematuria. Similar episodes had occurred several times in the preceding 6 months, with episodes of rectal bleeding. CT revealed hydroureteronephrosis of the right ureter and kidney, with mural calcifications. A 43-year-old man presented with a 1-month history of dysuria and intermittent hematuria. Similar episodes had occurred several times in the 6 months preceding presentation, along with episodes of rectal bleeding. The physical examination was unremarkable. Laboratory investigations revealed an elevated albumin:creatinine ratio (96 mg of albumin per millimole of creatinine), with dysmorphic red cells in the urine. Two urine cultures were sterile. A serum schistosoma antibody titer was 1:256. Renal ultrasonography revealed mild hydroureteronephrosis. Computed tomography of the abdomen and pelvis without the administration of contrast material revealed hydroureteronephrosis of the right ureter and kidney,...
    Is part of: The New England journal of medicine, 25 February 2016, Vol.374(8), pp.e9
    Identifier: 1533-4406 (E-ISSN); 26933870 Version (PMID); 10.1056/NEJMicm1504759 (DOI)

    • Several versions

    Measures of Growth of Entire Solutions of Generalized Axially Symmetric Helmholtz Equation

    Kumar, Devendra, Singh, Rajbir
    Journal of Complex Analysis, 2013, Vol.2013, 6 pages [Peer Reviewed Journal]