Generalized (f,U s,u t , λ s t )-structures

iauliai Pedagogical Institute, P. Viinskio str. 25, 5419 iauliai, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 33, No. 2, pp. 135–141, April–June, 1993.     

Асимптоический Анализ Распределения Статистики Диксона

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Zur Krümmungskennzeichnung der kinematischen Laguerre-Ketten

In the case of certain geometries () [1] over kinematic algebras [5],[6] the -trace of the system of chains can be characterized by constant curvature. The curvature allows an affine interpretation of non-affine points.     

On Gibbs' phenomenon for Riesz spherical means of multiple Fourier integrals and Fourier series

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Lattice of subgroups

Let D be a subgroup of the group G. The lattice of intermediate subgroups is studied. The subgroup F (D F G) is said to be D-complete, if D^F=u:u F>=F. Let F be the subset of all D-complete intermediate subgroups. The system {F, N_G(F)} is a fan for D in G (RZhMat, 1980, 5A208) if and only if D^x> is a D-complete subgroup for any x G. The set {F_ga} coincides with the collection of subgroups of the form D^A (1 A C G) if and only if for any x G the subgroup D, D^x is D-complete. The last condition holds, for example, for a pronormal subgroup D.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 13–19, 1980.     

Holomorphe Funktionen auf Gebieten über Banach-Räumen zu vorgegebenen Konvergenzradien

Given a function: ₊ on a domain spread over an infinite dimensional complex Banach space E with a Schauder basis such that -log is plurisubharmonic and d (d denotes the boundary distance on ) one can find a holomorphic function f: with _f, where _f is the radius of convergence of f. If, in addition, is locally Lipschitz continuous with constant 1, f can be chosen so that (3M)^–1 _f, where M is the basis constant of E. In the particular case of E= ₁ there are holomorphic functions f on with= _f.     

V-Limit Analysis of Vector-Valued Mappings

For an arbitrary net of mappings defined on subsets of the Hausdorff space (X, ) and acting into a vector topological space (Y, ) semiordered by a solid cone , we introduce the notion of V-limit. We investigate topological and sequential properties of V-limit mappings and establish sufficient conditions for their existence. The results presented can be used as a basis for the procedure of averaging of problems of vector optimization.     

Generalized kolmogorov inequalities for martingales

The classical ebyev inequality leads to an inequality for martingales which is often called the Kolmogorov inequality. It is shown here that many generalized ebyev inequalities for random variables lead in a similar way to martingale inequalities, and that the corresponding martingale inequality is sharp when the ebyev inequality is.On leave from Tel-Aviv University. Presently at the University of California, Berkeley.Research supported by National Science Foundation Grant MPS75-06173     

On simplexes inscribed in the minor arc of a curve

On an arc L of length h, of class Cⁿ, and in Euclidean Eⁿ, the set of n+1 points (the partition of the arc) P={0, ₁ h, , _n–1h, h}, 0<₁<<_n–1<1 determines a simplex S_h(P) inscribed in the arc. For its volume V_h(P) we evaluate lim and prove that its greatest value is obtained for a unique choice of P=P_cr. The exact values for _i from P_cr are found for n=2, 3, 4, 5, 6.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 114–120, 1990.     

Spline polynomials with a prescribed sequence of extrema

In the present note a theorem about strong suitability of the space of algebraic polynomials of degree n in C[a,b] (Theorem A in [1]) is generalized to the space of spline polynomials _{[a, b} ^{]n, k} (n2, 0) in C[a, b]. Namely, it is shown that the following theorem is valid: for arbitrary numbers ₀, ₁, ..., _n+k, satisfying the conditions (_i–_i–1) (_{i+1{ i}< 0(i=1, ..., n +k–1), there is a unique polynomials _n,k (t) _{[a, b} ^]/n,k and pointsa=₀,<₁<...< _n+k– 1< _n+k = b (₁1 <_n, ..., _kk<_n+k–1), such that s_n,k(_i) = _i(i=0, ..., n + k), s_n,k(_i)=0 (i=1, ..., n + k–1).Translated from Matematicheskii Zametki, Vol. 11, No. 3, pp. 251–258, March, 1972.     

Remarks on certain growth conditions in problems of optimal control

In the Tonelli-Nagumo existence theorem for free problems of the calculus of variations, a uniform growth condition (T ₁) was employed to prove the equiabsolute continuity of the trajectories of a minimizing sequence. This same growth condition was shown to be equivalent to a pointwise growth condition (T ₂). Cesari utilized a generalization, condition (), in order to extend the Tonelli-Nagumo existence theorem to optimal control problems.In the present paper, we show that, for problems of optimal control, condition () is equivalent to a uniform growth condition () and that both conditions () and () are stronger than a pointwise growth condition (), a generalization of condition (T ₂). Two situations are given where conditions (), (), and () are equivalent, and the result of Tonelli and Turner concerning the equivalence of conditions (T ₁) and (T ₂) is obtained as a particular case of one of these situations.This research was partially supported by the National Science Foundation, Grant No. GK-234.     

Stability Tests for Two Common Classes of Linear Time‐Delay and Hybrid Systems

The stability of linear timedelay systems with point internal delays is difficult to deal with in practice because of the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. This feature usually causes the system to possess an infinite number of poles. In this paper, stability tests for this class of systems are obtained based either on extensions of classical tests applicable to delayfree systems or on approaches within the framework of twodimensional digital filters. Some of those twodimensional stability tests are also proved to be useful for stability testing of a common class of linear hybrid systems which involve coupled continuous and digital substates after a slightadhoc adaptation of the tests for that situation.     

Extremal problems of Bloch function spaces

Letf be analytic in a hyperbolic region . The Bloch constant _f off is defined by , where (z)|dz| is the Poincaré metric in . Suppose is hyperbolic and where . Then for allf withf() , we have _f 1/(). In this paper we study the extremal functions defined by _f =1/() and the existence of those functions.Supported by the National Natural Science Foundation of China.     

Riesz representation theorem and weak compactness

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On the zetafunction of an arithmetical semigroup

The Zetafunction Z of an additive, multiplicative arithmetical semigroup is a power series with radius of convergence (01), a Dirichlet series with abscissa of convergence (0), respectively.Conditions are given which ensure that >0 and Z()=,< and Z()= hold true, respectively. Jürgen Neukirch zum Gedächtnis Mathematics Subject Classification (2000):11N45, 05A16.     

Fortsetzungssätze und Moduln über Semifields

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Herrn Professor Dr. Frank Terpe zum 60. Geburtstag gewidmet     

Asymptotics of solutions of a cauchy problem

We consider the Cauchy problem (x)ⁿ=at^r + bx + f(t, x, x), x(0)=0. We prove the existence of continuously differentiable solutions and study their asymptotic behavior for t + 0.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 187–193, February, 1991.     

Some inequalities of Hardy-Littlewood type

[3] , >0 n ^– a _n , . , . . , .

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This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant #234.     

On summability of subsequences of partial sums of trigonometric Fourier series

n- (n1) fL ^p ([–, ] ⁿ ),=1 = (L C) . , , f([–, ] ⁿ ).     

On the complexity of diagram testing

In 1987, Neetil and Rödl [4] claimed to have proved that the problem of finding whether a given graphG can be oriented as the diagram of a partial order is NP-complete. A flaw was discovered in their proof by Thostrup [11]. Neetil and Rödl [5] have since corrected the proof, but the new version is rather complex. We give a simpler and more elementary proof, using a completely different approach.