On the concentration of stresses due to a small elliptic inclusion on the neutral axis of a deep beam under constant bending moment

Zusammenfassung Es wird die Spannungsverteilung untersucht, die sich in einem breiten Balken mit konstanter Höhe unter einem konstanten Biegemoment ausbildet, wenn er eine kleine elliptische Einschliessung mit Zentrum auf der Neutralachse enthält. Insbesondere werden die Fälle eines sehr starren Einschlusses sowie eines elliptischen Loches im Detail diskutiert.

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Nomenclature x, y Cartesian coordinates - , elliptic coordinates - u, v (u ,u )=components of displacements - , unit elongations in -and -directions - shearing strain - , normal stress components in elliptical coordinates - shearing stress in elliptic coordinates - _x , _y normal stress in Cartesian coordinates - _xy shearing stress in Cartesian coordinates - E Young's modulus for the beam - v Poisson's ratio for the beam - 1/h ₁, 1/h ₂ stretch ratios - e _x + _y dilatation - 2 rotation - M bending moment     

On Piecewise-Constant Approximation of Continuous Functions of n Variables in Integral Metrics

We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (₁, ..., _n ) = ₁(₁) + ... + _n ( _n ), where _i ( _i ) are ordinary moduli of continuity that depend on one variable. In the case where _i ( _i ) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L ₂ for (₁, ..., _n ) = ₁(₁) + ... + _n ( _n ); (ii) in the integral metric L _p (p 1) for (₁, ..., _n ) = c ₁₁ + ... + c _{n n} ; (iii) in the integral metric L _{(2, ..., 2, 2r)} (r = 2, 3, ...) for (₁, ..., _n ) = ₁(₁) + ... + _{n – 1}( _{n – 1}) + c _{n n} .     

The Parametric Buffer Phenomenon for a Singularly Perturbed Telegraph Equation with a Pendulum Nonlinearity

We consider the boundary-value problem u _tt + u _t + (1 + cos2)sin u =² u _xx, u _x|_x=0=u_x|_x==0, where 0<1, =(1+)t, ,> 0, and the sign of is arbitrary. It is proved that for an appropriate choice of the external parameters and and for sufficiently small the number of exponentially stable solutions 2-periodic in can be made equal to an arbitrary predefined number.     

Approximating derivations on ideals ofC *-algebras

For each^*-derivation of a separableC ^*-algebraA and each >0 there is an essential idealI ofA and a self-adjoint multiplierx ofI such that (–ad(ix))|I< and x.     

On the topology of foliations with a first integral

The main objective of this article is to study the topology of the fibers of a generic rational function of the type in the projective space of dimension two. We will prove that the action of the monodromy group on a single Lefschetz vanishing cycle generates the first homology group of a generic fiber of . In particular, we will prove that for any two Lefschetz vanishing cycles ₀ and ₁ in a regular compact fiber of , there exists a mondromyh such thath( ₀)=± ₁.Partially supported by CNPq-Brazil.     

On the construction and calculation of optimal nonlifting critical airfoils

Numerical calculations are carried out in the hodograph plane to construct optimal critical airfoil shapes and the flow about them. These optimal airfoil shapes give the highest free-stream Mach numberM for a given thickness ratio and tail angle _t (nonlifting) for which the flow is nowhere supersonic. A relationship betweenM and for various _t is given. Analytical and numerical solutions to the same problem are found on the basis of transonic small-disturbance theory. These results provide a limiting case asM 1, 0 and agree well with the calculations of the full problem. Using a numerical method to calculate the flow about general (subsonic) airfoils, a comparison is made between the critical free-stream Mach numbers for some standard airfoil shapes and the optimal free stream Mach number of the corresponding and _t . A significant increase in the critical free-stream Mach number is found for the optimal airfoils.     

Generalization of Gδ*-Diagonals and ωΔ-Spaces

In this paper we introduce the concepts of a quasi-G*-diagonal and quasi--space as generalizations of the concepts of G*-diagonal and -space respectively. It is shown that a quasi-Moore space may be characterized in terms of these concepts. As a consequence we obtain the following metrization theorems: every paracompact -space with quasi-G-diagonal is metrizable and every collectionwise normal quasi--space is metrizable.     

Martingale Hardy spaces,BMO and VMO spaces with nonlinearly ordered stochastic basis

VMO. , ⁺, «» VMO . « » .     

Some remarks on the existence of densities for sums with weights

One considers the weighted sums , where X_k, are independent random variables, having no densities, and _k() are nonnegative functions, defined on the interval (0, 1). One investigates the conditions under which S(()) has a density; one proves a local limit theorem; one studies the form of the distribution in the case when ()=^k and the variables X_k take only a finite number of values.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 83–94, 1986.     

Problem of correctness of the best approximation in the space of continuous functions

Let W^rH _w be the subclass of those functions of C^r[a, b], for which (f ^(r),)(), where () is a given modulus of continuity, and P_n be the space of algebraic polynomials of degree at most n and _n(f) be the polynomial of best approximation for f(x) on [a, b]. Estimates for and moduli of continuity of the operators of best approximation on W^rH _w are established. For example, if ()=, then Translated from Matematicheskie Zametki, Vol. 23, No. 3, pp. 351–360, March, 1978.The author thanks S. B. Stechkin for the formulation of the problem and assistance with the article.     

Net subgroups of Chevalley groups. II. Gauss decomposition

This paper is a continuation of RZhMat 1980, 5A439, where there was introduced the subgroup () of the Chevalley group G(,R) of type over a commutative ring R that corresponds to a net , i.e., to a set =(),, of ideals of R such that ₊ whenever ,,+ . It is proved that if the ring R is semilocal, then () coincides with the group ₀ considered earlier in RZhMat 1976, 10A151; 1977, 10A301; 1978, 6A476. For this purpose there is constructed a decomposition of () into a product of unipotent subgroups and a torus. Analogous results are obtained for sub-radical nets over an arbitrary commutative ring.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 62–76, 1982.In conclusion, the authors would like to thank Z. I. Borevich for his interest in this paper.     

Generalization of the Hardy-Littlewood theorem on functions with derivatives in the space H1

Suppose f is a function that is analytic in the disk D = {z:¦z1¦ < 1} and belongs to the Hardy space H₁. Then, by the Hardy-Littlewood theorem, the following conditions are equivalent: (a) f H₁; (b) f coincides with some function of bounded variation almost everywhere on D; (c) almost everywhere on D, the function f coincides with some absolutely continuous function; (d) for an integral modulus of continuity (f, ) for the function f, we have (f, ) = O(). This article presents a generalization of this theorem to higher derivatives in the space H_p. The notions of generalized absolute continuity, generalized variation, and higher-order moduli of smoothness are used for this purpose.Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 87–93, July, 1992.     

Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in derL p -Theorie

Zusammenfassung Die Hörmander-Klassen _1, ⁰ (0<1) von Pseudodifferentialoperatoren sind -Algebren. Insbesondere ist die Inverse eines inL(L ^p ( ⁿ )) invertierbaren Pseudodifferentialoperators der Klasse _1, ⁰ selbst wieder ein Pseudodifferential-operator derselben Klasse.Der Beweis beruht auf den von R. Beals, R. R. Coifman, Y. Meyer und H. O. Cordes entwickelten Methoden zur Charakterisierung von Algebren von Pseudodifferentialoperatoren.     

Windschiefe Kongruenzflächen konstanten Dralls

In this paper we study the curves of a surface ( _T -lines) which are base curves of ruled surfaces for which the parameter of distribution O has a constant value. Moreover we assume that the ruled surfaces belong to a given congruenceT of surface tangents of . Relations are established between the _T -lines and other curves of (asymptotic lines, lines of curvature, k _T -lines). The _T -lines are used to characterize the pseudospheres and the helicoids. The _T -lines of the surfaces of revolution are determined if the congruenceT consists of the tangents of the circles of latitude.

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Herrn WERNER BURAU zum 70.Geburtstag     

Orthonormal systems satisfying an inequality of S. M. Nikol'skii

N- (p, q) (1 pN-, L _p - L _q -. , , , L L _q - , , .     

Graphs of Constant Mean Curvature in Hyperbolic Space

We study the problem of finding constant mean curvature graphsover a domain of a totally geodesic hyperplane andan equidistant hypersurface Q of hyperbolic space. We findthe existence of graphs of constant mean curvature H overmean convex domains Q and with boundary for –H < H |h|, where H > 0 is the mean curvature of the boundary . Here h is the mean curvature respectively of the geodesic hyperplane (h= 0) and of the equidistant hypersurface (0 < |h|< 1). The lower bound on H is optimal.     

Bounds for bounded motion around a perturbed fixed point

We consider a dissipative map of the plane with a bounded perturbation term. This perturbation represents e.g. an extra time dependent term, a coupling to another system or noise. The unperturbed map has a spiral attracting fixed point. We derive an analytical/numerical method to determine the effect of the additional term on the phase portrait of the original map, as a function of the bound on the perturbation. This method yields a value _c such that for< _c the orbits about the attractor are certainly bounded. In that case we obtain a largest region in which all orbits remain bounded and a smallest region in which these bounded orbits are captured after some time (the analogue of basin and attractor respectively).The analysis is based on the Lyapunov function which exists for the unperturbed map.     

Quasiclassical asymptotic behavior of the scattering cross section for asymptotically homogeneous potentials

One considers the total scattering cross section on the potential gV(x), x^m, m3, for large values of the coupling constant g and of the wave number k. One assumes that V(x)(x/|1x|)|x|^–, 2>m+1, as ¦x¦. It is shown that for gk^–1 , g^3–ak^2(a–2) the scattering cross section is equal asymptotically to _a(gk^–1), x=(m–1)(–1)^–1. Here the coefficient _a is determined only by the function and the number . Under the additional conditions >0, V>0, the indicated asymptotic behavior holds in the large domain gk^–1 , gk^a–z c(gk^–1), >0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 105–136, 1986.     

Amalgams of Weyl algebras and theA (V, δ, Γ) conjecture

Summary We prove a long standing conjecture ([5, Conjecture 5.6]) concerning the algebrasA (V, , ). Namely, two such algebrasA (V, , ),A (W, , ) are isomorphic if and only if there is an isomorphism between the triples (V, , ), (W, , ) from which they are constructed. As a consequence, to each primitive ideal in the enveloping algebra of a solvable Lie algebra there is associated a unique (V, , ).