Steady-state heat conduction in a circular cone

Zusammenfassung Diese Arbeit befasst sich mit der Bestimmung des stationären Temperaturfeldes, das in einem Kreiskegel durch eine unstetige Verteilung der vorgegebenen Oberflächentemperatur hervorgerufen wird. Die Temperatur der Mantelfläche wird oberhalb und unterhalb einer festen Entfernung von der Kegelspitze konstant angenommen. Dieses Problem wird mit Hilfe der Mellin-Transformation streng gelöst. Die so erhaltene Lösung wird in einer später erscheinenden Arbeit auf die Bestimmung der zugehörigen Temperaturspannungen angewendet.

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The results communicated in this paper were obtained in the course of an investigation conducted under Contracts Nonr 562(20) and Nonr 562(25) of Brown University with the Office of Naval Research in Washington, D.C.     

Steady-state thermal stresses in an elastic cone

Zusammenfassung Diese Arbeit befasst sich mit der Bestimmung der stationären Wärmespannungen, die in einem elastischen Kreiskegel durch eine unstetige Verteilung der Oberflächentemperatur hervorgerufen werden. Die Temperatur der Mantelfläche wird oberhalb und unterhalb einer festen Entfernung von der Kegelspitze konstant angenommen. Das zugehörige Wärmeleitungsproblem wurde in einer früheren Veröffentlichung unabhängig gelöst. In der vorliegenden Arbeit wird eine strenge Lösung für die gesuchten Wärmespannungen mit Hilfe der Mellin-Transformation hergeleitet. Das hier benutzte Verfahren ist auch anwendbar auf das gewöhnliche Randwertproblem für einen elastischen Kegel, der durch eine entsprechende unstetige Oberflächenbelastung beansprucht wird.

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The results communicated in this paper were obtained in the course of an investigation conducted under Contracts Nonr 562(20) and Nonr 562(25) of Brown University with the Office of Naval Research in Washington, D. C.     

Stress distribution in the vicinity of a circular hole in an orthotropic spherical shell with finite shear rigidity

The authors consider the problem of stress concentration in the vicinity of a circular hole in an orthotropic spherical shell with finite shear rigidity. The case in which the hole edges are reinforced by a thin elastic ring and some associated special cases are investigated.     

A finite element model of temperature distribution in the human torso

A finite element model is developed for the calculation of steady state temperature distribution throughout the human torso. The torso is considered as a cylinder and the differential equations of the model are expressed in their equivalent variational form. The solution is approximated using a rational finite element basis which fully exploits symmetry.     

An integral representation of subharmonic functions of finite order in a cone

Kharkov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 3, pp. 109–123, May–June, 1989.     

n维球内均匀分布的参数估计

研究了n维球内均匀分布的参数的点估计与区间估计,利用次序统计量得到了球半径的最大似然估计,在此基础上构造了球半径的无偏估计,并且证明了该无偏估计的相合性.利用构造枢轴量的方法得到了球半径的最短置信区间.     

Cylindrical and spherical inflation in compressible finite elasticity

Murphy (1992) examined cylindrical and spherical inflation ofcompressible perfectly elastic materials having three specialforms of the strain-energy function. In this paper a generalprocedure for handling such problems for any strainenergy functionis proposed. This procedure is used to confirm some of the resultsby Murphy as well as to deduce new solutions. One solution obtainedby that author for cylindrical inflation is found to be incorrect.     

On the cone of a finite dimensional compact convex set at a point

Four equivalent conditions for a convex cone in a Euclidean space to be an F_σ-set are given. Our result answers in the negative a recent open problem posed by Tam [5], characterizes the barrier cone of a convex set, and also provides an alternative proof for the known characterizations of the inner aperture of a convex set as given by Brønsted [2] and Larman [3].     

The dual description of a cone integer-valuedly-generated by a finite set of vectors

A discrete analog is obtained in the paper for certain classical results of the theory of linear inequalities.     

Subharmonic functions of finite order in a cone. II (General theory)

This is the second part of an article whose first part was published in the preceding issue of this publication. The numbering of propositions, formulas, and literature citations continues that begun in the first part.     

On the distribution of squares in a finite field

Given the Galois field GF(n) where n is odd we may partition the pairs (g, g+1) where g, g+1 GF(n), g(g+1) 0 into four classes as follows: RR denotes the class of such pairs for which both g and g+1 are squares in GF(n), RN the pairs for which g is a square and g+1 a nonsquare, NR the pairs for which g is a nonsquare and g+1 a square, and NN the pairs for which both g and g+1 are nonsquares. Raber [6] has recently applied geometric arguments to show that each class contains [(n–1)/4]+ elements, where || 1. The exact size of these classes is also known (see, for example, L. E. Dickson's book, Linear Groups, Dover, 1958, p. 48). In this paper we use arguments similar to those used by Raber to obtain the exact size of each class.The author acknowledges financial support by the NRC.     

Charged vector bosons in a magnetic field at a finite temperature

Bose-Einstein condensation does not occur in a charged vector boson gas in the presence of a homogeneous external magnetic field, although a major portion of the bosons are in the ground state. Spontaneous magnetization occurs in a vector boson gas. The total birth probability of vector boson pairs in a vacuum under a strong magnetic field at a finite temperature can be determined. Expressions that can probably characterize the vacuum free energy and magnetic moment are found, and formulas for the density and magnetic moment of the vector boson pairs generated by a magnetic field at a finite temperature are derived. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 114, No. 3, pp. 439–453, March, 1998.     

Random continued fractions and inverse Gaussian distribution on a symmetric cone

In this paper we introduce the inverse Gaussian and Wishart distributions on the cone of real (n, n) symmetric positive definite matricesH _n ⁺ () and more generally on an irreducible symmetric coneC. Then we study the convergence of random continued fractions onH _n ⁺ () andC by means of real Lagrangians forH _n ⁺ () and by new algebraic identities on symmetric cones forC. Finally we get a characterization of the inverse Gaussian distribution onH _n ⁺ () andC.