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Tryfan G. Rogers Allen C. Pipkin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1963,14(4):334-343
Zusammenfassung Die Beschränkungen, welche die Symmetrie des Materials den Nachgiebigkeitsmatrizen anisotroper viskoelastischer Stoffe auferlegt, werden ohne Bezug auf thermodynamisch bedingte Symmetrien abgeleitet. Experimente zur Überprüfung der thermodynamischen Theorien lassen sich auf die Unterschiede gründen, die zwischen den mit oder ohne Annahmen über Matrix-Symmetrie erhaltenen Formen bestehen. Transversale Isotropie und kubische Symmetrie werden im Detail behandelt.
This paper was prepared under Contract No. 562(10) with the Office of Naval Research. 相似文献
This paper was prepared under Contract No. 562(10) with the Office of Naval Research. 相似文献
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Nimrod Megiddo 《Mathematical Programming》1977,12(1):60-66
This paper generalizes the answers that were given by R.W. Cottle to questions that were originally raised by G. Maier.Essentially, we give necessary and sufficient conditions for some notions of monotonicity of solutions for the parametric linear complementarity problem. Our proofs are direct ones and not algorithmic, as Cottle's proofs are, and also cover a broader class of matrices. 相似文献
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In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures. This allows many multistep methods of practical interest to be included in the theory. In a related manner, we also consider contractivity and stability in arbitrary norms.
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For a set A of positive integers and any positive integer n, let R1(A,n), R2(A,n) and R3(A,n) denote the number of solutions of a+a′=n with the additional restriction a,a′∈A; a,a′∈A,a<a′ and a,a′∈A,a≤a′ respectively. In this paper, we specially focus on the monotonicity of R3(A,n). Moreover, we show that there does not exist any set A⊂N such that R2(A,n) or R3(A,n) is eventually strictly increasing. 相似文献
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In this paper we study radial symmetry and monotonicity of positive solutions of an integral equation arising from some higher-order semilinear elliptic equations in the whole space Rn. Instead of the usual method of moving planes, we use a new Hardy-Littlewood-Sobolev (HLS) type inequality for the Bessel potentials to establish the radial symmetry and monotonicity results. 相似文献
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Mitsuru Uchiyama 《Integral Equations and Operator Theory》2000,37(1):95-105
LetA, B be bounded selfadjoint operators on a Hilbert space. We will give a formula to get the maximum subspace
such that
is invariant forA andB, and
. We will use this to show strong monotonicity or strong convexity of operator functions. We will see that when 0≤A≤B, andB−A is of finite rank,A
t
≤B
t
for somet>1 if and only if the null space ofB−A is invariant forA. 相似文献
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LetS denote the class of regular and univalent functions in |z|<1 with the normalizationf(0)=0,f′(0)=1. Denoted f=inf f∈s {|α||f(z)≠ α, |z|<1} and letS(d)={f¦f∈S,d f=d, 1/4≦d≦1}. The analytic functionf(z) is univalent in |z|<1 if and only if $$log\frac{{f(z) - f(\zeta )}}{{z - \zeta }} = \sum\limits_{m,n = 0}^\infty {d_{mn} z^m \zeta ^n } $$ converges in the bicylinder |z|<1, |ξ|<1. LetC mn =√mnd mn andC nn (d)= Max fεS(d){Re(C nn )}. The paper deals with the monotonicity ofc nn(d) and related functionals. 相似文献
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Feng Qi Senlin Guo Bai-Ni Guo 《Journal of Computational and Applied Mathematics》2010,233(9):2149-331
In the present paper, we establish necessary and sufficient conditions for the functions xα|ψ(i)(x+β)| and α|ψ(i)(x+β)|−x|ψ(i+1)(x+β)| respectively to be monotonic and completely monotonic on (0,∞), where i∈N, α>0 and β≥0 are scalars, and ψ(i)(x) are polygamma functions. 相似文献
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We are concerned with the shock structure in viscoelasticity of rate type. The existence of a shock profile, which in the vanishing relaxation limit becomes an elastic shock, is demonstrated by an explicit construction of the solution of viscoelastic equations provided that the equilibrium stress–strain relation is governed by a parabolic law. For a more general stress–strain law which does not differ substantially from a parabolic one, the solution is obtained from a perturbation expansion. 相似文献
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欧拉Gamma函数是一种非常重要的函数,在数学的许多分支以及物理、工程等学科中都有着十分重要的作用.而完全单调性以及对数完全单调性是Gamma函数的重要性质.主要证明了一些包含Gamma函数和Psi函数在内的特殊函数的完全单调性和对数完全单调性,并由此推出了一些重要的不等式. 相似文献
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Some monotonicity results are given for the remainder terms in the asymptotic expansion for x → ∞ of the function Jv(x)Jv+n(x) + Yv(x Yv+n(x), v ε R, n ε Z. 相似文献
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Vittorino Pata 《Milan Journal of Mathematics》2009,77(1):333-360
In this survey paper, we discuss the decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ${\partial_{tt}}u(t) - \Delta u(t) + {\int_0^\infty} \mu(s) \Delta u(t - s) {\rm{d}}s = 0$ describing the dynamics of linearly viscoelastic bodies. 相似文献
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Gabriele Guerriero 《Rendiconti del Circolo Matematico di Palermo》1982,31(3):351-364
Adoperando il metodo della funzione peso, si dimostrano teoremi di unicità e dipendenza continua per le soluzioni della teoria dinamica della viscoelasticità lineare anisotropa nei domini esterni. 相似文献
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Chao-Ping Chen 《Journal of Mathematical Analysis and Applications》2007,336(2):812-822
We present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions. This extends some known results due to S.-L. Qiu and M. Vuorinen. 相似文献