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1
Content available remote Convolution of the subclass of Salagean-type harmonic univalent functions with negative coefficients
100%
Dixit K. K. , Porwal S.
Journal of Mathematics and Applications
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2010
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tom Vol. 32
33-37
EN
A recent result of Sibel Yelcin et al. [4] appeared in "Journal of Inequalities in Pure and Applied Mathematics" (2007) concerning the convolution of two harmonic univalent functions in the class [wzór] is improved.
2
Content available remote Sur les fonctions harmoniques conjuguées et les séries de Fourier
88%
Kolmogoroff A.
Fundamenta Mathematicae
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1925
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tom 7
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nr 1
24-29
FR
Théorème: Si f(θ) est une fonction sommable, si de plus f(ρ,θ)=1/(2π) ∫_(-π}^(+π) f(α) (1-ρ^2)/(1+ρ^2-2ρ cos(α-θ))dα, alors, z tendant vers e^(iθ) le long d'un chemin quelconque non tangent à la circonférence, la fonction harmonique g(z) conjuguée à f(z) tend pour presque toutes les valeurs de θ vers une limite déterminée g(θ)= - 1/(2π) ∫_(-π}^(+π) f(θ+α)/tg((α)/2)dα, l'integrale etant comprise comme lim_(ϵ → 0) ∫_(-π)^(+ϵ)∫_(-ϵ)^(+π). Le but de cette note est de démontrer que la fonction |g(θ)|^(1-ϵ) est sommable pour ϵ > 0. Comme une conséquence immédiate, l'auteur démontre un théorème sur la convergence en moyenne de la série de Fourier (on peut déduire de ce théorème que toutes les séries de Fourier-Lebesgue convergent en mesure).
3
Content available Exact solution of the harmonic problem for a rectangular plate in flat deformation by the method of initial functions
75%
Olodo E. T. , Adanhounme V. , Hounkonnou M. N.
International Journal of Applied Mechanics and Engineering
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2017
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tom Vol. 22, no. 2
349--361
EN
A wide range of applications is based nowadays on analytical developments which allow a precise and effective approach and short time of computations compared with the time required for numerical methods; in this way these developments are suitable for calculations in real time. This work proposes an approach for solving a two-dimensional harmonic problem of a rectangular plate under local surface loading using Vlasov’s symbolic method of initial functions and a general solution of the harmonic equation for a rectangle. Substituting the harmonic functions in symbolic form for the corresponding solutions allows us to give the exact solution of the problem in trigonometric form.
4
Content available remote Partial sums of a certain harmonic univalent meromorphic functions
75%
Aouf M. K. , El-Ashwah R. M. , Dziok J. , Stankiewicz J.
Journal of Mathematics and Applications
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2014
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tom Vol. 37
5--12
EN
In the present paper we determine sharp lower bounds of the real part of the ratios of harmonic univalent meromorphic functions to their sequences of partial sums [...].
5
Content available remote On generalization of some classes of Salagean-type multivalent harmonic functions
75%
Atshan W. G. , Kulkarni S. R.
Journal of Mathematics and Applications
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2009
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tom Vol. 31
7-18
EN
In the present paper, we make generalization of the classes in [7] of Salagean-Type multivalent harmonic functions. We introduce sufficient coefficient condition for the class [wzór] and this condition be also necessary if certain restriction is imposed on the coefficients of these harmonic functions. Also we have obtained a representation theorem, inclusion relations and distortion bounds for these functions.
6
Content available remote Subharmonic of not uniformly partially coercive Hamiltonian systems
75%
Timoumi M.
Demonstratio Mathematica
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2008
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tom Vol. 41, nr 1
233-248
EN
In this work, we prove the existence of multiple periodic and subharmonic solutions of the Hamiltonian system [..] when the Hamiltonian H is periodic in a part of the variables and locally coercive in the other part; that is, there exists a decomposition [...] for almost every t in some non empty open subset C of [O, T]. For the resolution, we use an analogy of Egorov's Theorem and a Generalized Saddle Point Theorem.
7
Content available remote Approximation of entire harmonic functions in R3 in Lß - norm
75%
Kumar D. , Kasana H. S.
Fasciculi Mathematici
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2004
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tom Nr 34
55-64
EN
A function which is harmonic in a neighbourhood of the origin in R(3) has there an expansion in spherical harmonics. For HK, he class of all harmonic functions regular in and continuous on DR , the closure of DK, we define approximation error as , is the set of all harmonic polynomials of degree at most n. In this paper we have obtained the necessary and sufficient condition on the rate of decrease of has an analytic continuation as an entire harmonic function with (p, q) - growth.
8
Content available remote A note on the Lie ball
63%
Jarnicki W.
Bulletin of the Polish Academy of Sciences. Mathematics
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2001
|
tom Vol. 49, no 2
177--179
EN
We give an effective formula for the maximal n-circled domain contained in the Lie ball.
9
Content available remote Sharp norm inequalities for martingales and their differential subordinates
63%
Osękowski A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2007
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tom Vol. 55, no 4
373-385
EN
Suppose ƒ = (ƒn), g = (gn) are martingales with respect to the same filtration, satisfying |ƒn-ƒn-i| ≤ |gn -gn-1|, n = 1,2,..., with probability 1. Under some assumptions on ƒo, go and an additional condition that one of the processes is nonnegative, some sharp inequalities between the pth norms of ƒ and g, 0 < p < ∞, are established. As an application, related sharp inequalities for stochastic integrals and harmonic functions are obtained.
10
Content available remote A class of harminic starlike functions with respect to other points defined by Dziok-Srivastava operator
63%
Murugusundaramoorthy G. , Vijaya K. , Auof M. K.
Journal of Mathematics and Applications
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2008
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tom Vol. 30
113-124
EN
Making use of Dziok-Srivastava operator we introduced a new class of complex-valued harmonie functions which are orientation preserving, univalent and starlike with respect to other points. We investigate the coefficient bounds.distortion inequalities, extreme points and inclusion results for the generalized class of functions.
11
Content available Modelowanie udziałów wieloskładnikowej paszy za pomocą funkcji harmonicznej
63%
Królczyk J. , Tukiendorf M.
Inżynieria Rolnicza
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2006
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tom R. 10, nr 3(78)
191-201
PL
W artykule podjęto próbę opisu procesu mieszania czternastoskładnikowej paszy dla gołębi w mieszalniku z pionowym mieszadłem o działaniu okresowym. W wyniku przeprowadzonych pomiarów zaobserwowano charakter zależności zmiany procentowego udziału poszczególnych składników mieszaniny w funkcji czasu mieszania. Charakter tych zmian został opisany za pomocą funkcji drgań tłumionych. Do wymodelowania krzywej drgań tłumionych wykorzystano dwie metody: klasyczną oraz bayesowską.
EN
In the paper a description of the mixing process of a 14-component pigeon pellet in the periodical mixer with vertical agitator has been given. Following the performed measurements, a relation of the components' percentages in time has been observed. To model these changes, a damped vibration function was proposed. To estimate model parameters, a classical and a Bayesian approaches were adopted.
12
Content available Measures of growth and approximation of entire harmonic functions in n-dimensional space in some Banach spaces
51%
Kumar D.
|
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tom Vol. 44
57--70
EN
The relationship between the classical order and type of an entire harmonic function in space Rn, n≥3, and the rate of its best harmonic polynomial approximation for some Banach spaces of functions harmonic in the ball of radius R has been studied.
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