Stopping checks in a system with two degrees-of-freedom and friction-affected constraints governed by both generalized co-ordinates

Summary A multi-body system with two degrees-of-freedom and several friction-affected constraints is considered. It is supposed that the original system and all systems, which must be considered as result of sticking co-ordinates, are kinetostatical determinate structures. The case is analysed, when several friction-affected constraints are governed by both generalized co-ordinates. The accelerations of the system, when relative velocities in several or all friction-affected constraints vanish, are determined with a trial- and -error method based on Lagrange's equations of the second kind and conditions of dynamic equilibrium. Computations for particular systems revealed numerical particularities, which are helpful in reducing the necessary number of trials.

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Zusammenfassung Ein Mehrkörpersystem mit zwei Freiheitsgraden und mehreren reibungsbehafteten Bindungen wird betrachtet und angenommen, daß dieses System und alle Systeme, die zu berücksichtigen sind, wenn in einigen Bindungen Haften auftritt, kineto-statisch bestimmt sind. Es wird der Fall untersucht, wenn die Lageparameter einiger reibungsbehafteter Bindungen von beiden verallgemeinerten Koordinaten abhängen. Mit einem trial- and -error Verfahren werden die Beschleunigungen des Systems bestimmt, wenn die Relativgeschwindigkeiten in einigen oder allen reibungsbehafteten Bindungen gleich Null sind. Dazu werden die Lagrangeschen Gleichungen zweiter Art und die dynamischen Gleichgewichtsbedingungen verwendet. Berechnungsbeispiele offenbarten numerische Besonderheiten, die zur Verringerung der Anzahl der notwendingen Tests beitragen.

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Dedicated to Professor Dr. G. Schmidt, Berlin, on the occasion of his 65th birthday.     

О Сходимости метода подобластей

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Maximal inequalities,convexity inequality,and their duality. II

, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , .     

Convergence of simultaneous Padé approximants to two dilogarithms

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Fractional integration and differentiation of variable order

I ^(x) D ^(x) . , L _p ^(x) , , (I ^(x) )^–1, (I ^(x) )^–1, , I ^(x) (L _p ).

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Partly supported by the Fulbright grant during author's Visiting Professorship at the University of New Haven, Mathematics Department, West Haven, Connecticut 06516, USA, and by the Russian Foundation for Basic Research (Project 94-01-00577-a).     

On the Riemann derivatives ofC sP-integrable functions

[4] , .     

Discrete Newton methods and iterated defect corrections

Summary In this paper we present a general theory for discrete Newton methods, iterated defect corrections via neighbouring problems and deferred corrections based on asymptotic expansions of the discretization error.Dedicated to Professor Dr. J. Weisinger on the occasion of his sixty-fifth birthday     

Quasianapole Interaction of Charged Fermions

We obtain the analytic expression for the total cross section of the reaction e ^– e ⁺l ^– l ⁺ (l=,) taking possible quasianapole interaction effects into account. We find numerical restrictions on the interaction parameter value from data for the reaction e ^– e ^+–+ in the energy domain below the Z ⁰ peak.     

On measures that agree on balls

The fundamental result: if and v are two finite Borel measures, defined in the spaceL ^p[0, 1] (1p<) or in C(K) (K is a metric compactum without isolated points), then from the equalities (B)=v(B) for all balls B of radius 1 there follows that =v. In addition, in the spaces C(K) and _p (1p<) from the inequalities (B) v(B) there follows that v.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 122–128, 1989.     

Relaxation of a Quadratic Functional Defined by a Nonnegative Unbounded Matrix

We study the lower semicontinuous envelope in L^p(), F, of a functional F of the form F(u)=A uudx where A=A(x) is not strictly elliptic and not bounded. We prove that F; may also be written as F;(u)= Buudx with B=AP A for a matrix P which is the matrix of an orthogonal projection. In the one-dimensional case, we characterize the domain of F and we explicit the matrix P.     

Exact estimates for partially monotone approximation

f(x) — , - [–1,1], (f, ) — , as— f, . . (- ) (x _i,x _{i+ 1}) (i=0, 1, ...,s–1; =–1,x _s,=1), f(x) . , n=0,1,... _n() , [– 1,1] signf(x) sign _n(x) 0, ¦f(x)– _n(x)¦ C(s) (f, 1/n+1, C(s) s. , - , « » .     

Local invariants of differential equations

We consider an analytic system X=(X) in the neighborhood of the fixed point X=0. Depending on the characteristic numbers of the matrix (/x)₀, we define the integer d 0 as the dimension of the normal form or as the multiplicity of the resonance. We show that a system with d=1, subject to certain additional assumptions, has a finite number of invariants relative to reversible formal changes of variablesx = (Y). All these invariants are the coefficients of some normal form. We touch upon questions concerning invariants of relatively smooth and continuous substitutions.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 499–507, October, 1973.     

Lower central series and derived series of net subgroups of the general linear group

Over a commutative ring R with invertible element 2 and with radical , nets (i.e., tables =(_ij) of ideals _ij such that _{irrj ij}) such that _ii are considered. Such nets are called pseudoradical. The groups of the lower central series and the derived series are explicitly constructed for the corresponding net subgroups G () (of the general linear group GL (n,R)) in terms of .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 180–186, 1982.     

Structures of topological type

In this paper we continue the study of structures of various types initiated by the author in the earlier paper Structures of extensions (Ref. Zh. Mat., 1974, 4A361). The present paper is devoted to the so-called structure of topological type. By a structure of topological type on the set X is meant a topological structure, defined on some set obtained from X, and possibly additional sets, by a totally ordered sequence of operations of unions of sets, products of sets, and passage to the set of subsets. We study certain structures of topological type: bitopological (Sec. 2) and settopological (Sec. 3). A bitopological structure on the set X is any topological structure on the set X×X, and a bitopological space is a pair (X,). This concept is a natural extension of the concept of a bitopological space as a set X on which there are given two topological structures ₁ and ₂-these structures define a structure =₁×₂ on the set X×X. A settopological structure on the set X is any topological structure on the set={A¦A. There are given representations of piecewise-linear structures (Sec. 4) and smooth structures (Sec. 5) as settopological structures.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 83, pp. 5–62, 1979.     

Equivalent Characterization of Entire Functions of Exponential Type

In this paper, we show that a necessary and sufficient condition for the fulfillment of the relation s _m ^(k) (f) – f^(k) _p 0 as m , 1 < p < , k 0,1,2,..., is that f B _,p , where B _,p = B L _p (R), and B denotes the subset of all entire functions of exponential type which are bounded on R, B _,p is usually called Paley-Wiener class, and s _m (f) is the unique cardinal spline of degree m – 1 interpolating f at the integers. Moreover, we obtain three equivalent forms for the characterization of the class B _,p .     

Subsets with Restricted Movement

Let G be a finite permutation group on a set with no fixed points in and let m and k be integers with 0 < m < k. For a finite subset of the movement of is defined as move() = max_gG| ^g \ |. Suppose further that G is not a 2-group and that p is the least odd prime dividing |G| and move() m for all k-element subsets of . Then either || k + m or k (7m – 5) / 2, || (9m – 3)/2. Moreover when || > k + m, then move() m for every subset of .     

A Generalization of the Hausdorff-Young Theorem

Considering mixed-norm sequence spaces lp,q, p, q 1, C. N. Kellogg proved the following theorem: if 1 < p 2 then lp,2 and lp,2 , where 1/p + 1/p = 1. This result extends the Hausdorff-Young Theorem.We introduce here multiple mixed-norm sequence spaces , examine their properties and characterize the multipliers of spaces of the form lp,[s;n],q, with the index s repeated n times. By an interpolation-type argument we prove that (l,[2;n],2, lp,[1;n],1) for 1 < p 2. Using these results we obtain a further generalization of the Hausdorff-Young Theorem: if 1 < p 2 then lp,[2;n] and lp,[2;n] for each n = 0, 1, 2, ¨. The spaces lp,[2;n] decrease and lp,[2;n] increase properly with n for 1 < p < 2 and 1/p + 1/p = 1. We also extend a theorem of J. H. Hedlund on multiplers of Hardy spaces and deduce other results.     

Sharpening of Stečkin's theorem to strong approximation with exponentp

— , B _n , B p1., , p=1 , - . , , , p.     

Factorization of a selfadjoint nonanalytic operator function II. Single spectral zone

We consider a selfadjoint and smooth enough operator-valued functionL() on the segment [a, b]. LetL(a)0,L(b)0, and there exist two positive numbers and such that the inequality |(L()f, f)|< ([a, b] f=1) implies the inequality (L'()f, f)>. Then the functionL() admits a factorizationL()=M()(I-Z) whereM() is a continuous and invertible on [a, b] operator-valued function, and operatorZ is similar to a selfadjoint one. This result was obtained in the first part of the present paper [10] under a stronge conditionL()0 ( [a,b]). For analytic functionL() the result of this paper was obtained in [13].     

The trace to subsets ofR n of Besov spaces in the general case

R ⁿ. , , , F R ⁿ, F , R ⁿ R ⁿ . ^p,q (Rⁿ), >0, 1, q, — ( ) Rⁿ. , ^p,q (Rⁿ) ^F Rⁿ. , q B ^p,q (F), = – (n–)/, >0, — « », ad — F, . , . : , F=R ^d,F— « » F— R ⁿ, « », F. .

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This work has been supported in part by the Swedish Natural Science Research Council.