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Jianbin Yang 《Journal of Mathematical Analysis and Applications》2010,371(2):573-584
The regularity of refinable functions is an important issue in all multiresolution analysis and has a strong impact on applications of wavelets to image processing, geometric and numerical solutions of elliptic partial differential equations. The purpose of this paper is to characterize the regularity of refinable functions with exponentially decaying masks and a dilation matrix whose eigenvalues have the same modulus. The main results of this paper are really extensions of some results in Cohen et al. (1999) [5], Jia (1999) [17] and Lorentz and Oswald (2000) [28]. 相似文献
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Shijun Liao Eugen Magyari 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,78(4):777-792
The boundary value problem for the similar stream function f = f(η;λ) of the Cheng–Minkowycz free convection flow over a vertical plate with a power law temperature distribution Tw(x) = T∞ + Axλ in a porous medium is revisited. It is shown that in the λ-range − 1/2 < λ < 0 , the well known exponentially decaying
“first branch” solutions for the velocity and temperature fields are not some isolated solutions as one has believed until
now, but limiting cases of families of algebraically decaying multiple solutions. For these multiple solutions well converging
analytical series expressions are given. This result yields a bridging to the historical quarreling concerning the feasibility
of exponentially and algebraically decaying boundary layers. Owing to a mathematical analogy, our results also hold for the
similar boundary layer flows induced by continuous surfaces stretched in viscous fluids with power-law velocities uw(x)∼ xλ. 相似文献
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Shijun Liao Eugen Magyari 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(5):777-792
The boundary value problem for the similar stream function f = f(η;λ) of the Cheng–Minkowycz free convection flow over a vertical plate with a power law temperature distribution Tw(x) = T∞ + Axλ in a porous medium is revisited. It is shown that in the λ-range − 1/2 < λ < 0 , the well known exponentially decaying
“first branch” solutions for the velocity and temperature fields are not some isolated solutions as one has believed until
now, but limiting cases of families of algebraically decaying multiple solutions. For these multiple solutions well converging
analytical series expressions are given. This result yields a bridging to the historical quarreling concerning the feasibility
of exponentially and algebraically decaying boundary layers. Owing to a mathematical analogy, our results also hold for the
similar boundary layer flows induced by continuous surfaces stretched in viscous fluids with power-law velocities uw(x)∼ xλ.
(Received: June 7, 2005) 相似文献
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Given any infinite tree in the plane satisfying certain topological conditions, we construct an entire function f with only two critical values ±1 and no asymptotic values such that f~(-1)([-1, 1]) is ambiently homeomorphic to the given tree. This can be viewed as a generalization of the result of Grothendieck(see Schneps(1994)) to the case of infinite trees. Moreover, a similar idea leads to a new proof of the result of Nevanlinna(1932) and Elfving(1934). 相似文献
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Hideki Kosaki 《Journal of Functional Analysis》2008,254(1):84-108
For a (point-wisely non-negative) positive definite function a certain criterion for its infinite divisibility (i.e., all its fractional powers are also positive definite) is obtained. This criterion enables us to show infinite divisibility for many positive definite functions appearing naturally in study of operator means. In particular, we determine when the function
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Mathematical Notes - For series of special form, we obtain an expansion in powers of the parameter. The coefficients of the expansion can be written out explicitly in terms of Bernoulli... 相似文献
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In this paper we study the transition densities for a large class of non-symmetric Markov processes whose jumping kernels decay exponentially or subexponentially. We obtain their upper bounds which also decay at the same rate as their jumping kernels. When the lower bounds of jumping kernels satisfy the weak upper scaling condition at zero, we also establish lower bounds for the transition densities, which are sharp. 相似文献
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L. Leindler 《Analysis Mathematica》1977,3(3):207-212
qPУстьs n — ЧАстНАь сУММ А пОРьДкАn РьДА ФУРьЕ сУММИРУЕМОИ ФУНкцИИf, А Ω(f; δ)РАВНОМЕРНыИ МОДУль НЕпРЕРыВНОст И ФУНкцИИf. В НАстОьЩЕИ РАБОтЕ, пР ОДОлжАь ИсслЕДОВАНИ ь ФРОИДА, АВтОРА, лЕИНДлЕРА — НИ кИшИНА, ОскОлкОВА, сАБАДОшА, к ОтОРыЕ жАНИМАлИсь «т ЕОРЕМАМИ ОБРАтНОгО тИпА», Мы ДО кАжыВАЕМ, ЧтО Иж УслОВИь $$\left\| {\mathop \Sigma \limits_{n = 0}^\infty |S_n (x) - f(x)|^p } \right\|_c< \infty , 0< p \leqq 1, \frac{1}{p} = r + \alpha$$ , ВытЕкАУт ОцЕНкИ: БОлЕЕ тОгО, ЕслИ А=1, тОf (r)(x) пРИНАДлЕжИт клАссУ жИгМУНДА. ДОкАжАНО тА кжЕ, ЧтО ОцЕНкИ (*), ВООБЩЕ гОВОРь, НЕ МОг Ут Быть УлУЧшЕНы. О стРУктУРНых сВОИст ВАх ФУНкцИИ, ВытЕкАУЩ Их Иж сИльНОИ АппРОксИМАцИИ сУММА МИ ФУРьЕ л. лЕИНДлЕР. 相似文献
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For an infinite family of modular forms constructed from Klein forms we provide certain explicit formulas for their Fourier coefficients by using the theory of basic hypergeometric series (Theorem 2). By making use of these modular forms we investigate the bases of the vector spaces of modular forms of some levels (Theorem 5) and find its application. 相似文献
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We give a construction of 3-class and 4-class association schemes from s-nonlinear and differentially 2 s -uniform functions, and a construction of p-class association schemes from weakly regular p-ary bent functions, where p is an odd prime. 相似文献
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We establish the existence of viscous profile of an undriven divergent detonation wave. The structure of the wave is a viscous shock followed by a reaction zone containing a sonic point. So the divergent detonation wave profile is a transonic profile. We further establish the existence of classical global solutions of the Cauchy problem. The proof consists of establishing a priori estimates for the solution by a maximum principle and using Hölder estimates for solutions of parabolic equations. Finally, the nonlinear stability of the viscous transonic profile is established. The main reason for the stability is that there is a damping term due to the divergent nature of the problem. 相似文献
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A. Eduardo Gatto Stephen Vá gi 《Proceedings of the American Mathematical Society》1997,125(4):1149-1152
On a space of homogeneous type we consider functions in , , which are potentials of order of functions. We show that these functions belong to the class of smooth functions of Calderón-Scott. This result has applications to tangential convergence.