An asymptotic analysis of transonic wind-tunnel interference based on the full potential theory

Summary The transonic flow over an airfoil in a wind tunnel with perforated walls has been analyzed asymptotically based on the full potential equation. By matching the flow regions about the airfoil and near the wall, the analysis yields explicitly the effects of wall constraints and transonic nonlinearity on the flow in the tunnel. The analysis indicates that in general the wall interference is uncorrectable. However, it is also shown that if a limit wall control is applied, the interference becomes correctable and the resulting corrections are given implicitly.

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Résumé L'écoulement transsonique autour d'un profil aérodynamique dans une soufflerie à parois perforées a été analysé asymptotiquement à partir de l'équation complète du potentiel. En comparant les écoulements autour du profil et près des parois, on obtient explicitement les effets des contraintes imposées par les parois et de la non-linéarité transsonique sur l'écoulement en soufflerie. L'analyse a révélé en général que les contraintes liées aux parois ne peuvent être corrigées. Par contre, elle démontre aussi que si l'on peut déterminer une paroi limite, les contraintes qui y sont associées peuvent alors être corrigées, et les corrections qui en résultent sont données implicitement.

     

On the representation theory for full decomposable forms

Let $\text{k}\text{Q}$ be any finite normal extension and fix an order D of k invariant under the galois group $\text{G(}\text{k}\text{Q}\text{)}$. The ring class field K corresponding to D is normal over Q. We solve the problem of determining which full decomposable forms associated to the invertible ideals of D integrally represent a given positive integer m. First we establish a one-to-one correspondence between the improperly equivalent classes of such forms and the conjugacy classes of $\text{G(}\text{K}\text{Q}\text{)}$ which are contained in $\text{G(}\text{K}\text{k}\text{)}$. The solution is then seen to rest upon determining the Artin class in $\text{G(}\text{K}\text{Q}\text{)}$ of the unramified primes dividing m. This is accomplished by evaluating certain induced characters of $\text{G(}\text{K}\text{Q}\text{)}$ congruentially in terms of an associated integer linear recurrence sequence.     

Variational problems of potential theory

A series of variational problems are formulated and investigated on classes of charges, associated with space condensers. Solvability statements are established and the properties of the investigated extremal quantities are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 347–354, March, 1991.     

Variational problems of potential theory

A series of variational problems are formulated and investigated on classes of charges, associated with space condensers. Solvability statements are established and the properties of the investigated extremal quantities are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 347–354, March, 1991.     

Construction of full H-matrices with the given eigenvalues based on the Givens matrices

The inverse eigenvalue problem is about how to construct a desired matrix whose spectrum is the given number set. In this paper, in view of the Givens matrices, we prove that there exist three classes of full H-matrices which include strictly diagonally dominant full matrix, $\alpha$-strictly diagonally dominant full matrix and $\alpha$-double strictly diagonally dominant full matrix, and their spectrum are all the given number set. In addition, we design some numerical algorithms to explain how to construct the above-mentioned full H-matrices.     

An algebraic theory for statistical information based on the theory of hints

Statistical problems were at the origin of the mathematical theory of evidence, or Dempster–Shafer theory. It was also one of the major concerns of Philippe Smets, starting with his PhD dissertation. This subject is reconsidered here, starting with functional models, describing how data is generated in statistical experiments. Inference is based on these models, using probabilistic assumption-based reasoning. It results in posterior belief functions on the unknown parameters. Formally, the information used in the process of inference can be represented by hints. Basic operations on hints are combination, corresponding to Dempster’s rule, and focussing. This leads to an algebra of hints. Applied to functional models, this introduces an algebraic flavor into statistical inference. It emphasizes the view that in statistical inference different pieces of information have to be combined and then focussed onto the question of interest. This theory covers Bayesian and Fisher type inference as two extreme cases of a more general theory of inference.     

Stress potential in the nonlinear theory of viscoelasticity

By introducing a functional derivative and the line integral of a functional the author supplies an energy proof of the nonlinear theory of viscoelasticity. The stress potential for small strains, analogous to the potential proposed by Coleman for large strains [7], is considered for comparison.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 633–642, July–August, 1970.     

Initial-value problems in potential theory

Potential theory characteristically leads to partial differential equations under boundary conditions. It is shown that these boundary-value problems can be converted directly into equivalent initial-value problems. These initial-value problems are shown to lead to a number of standard and nonstandard numerical procedures.This research was supported by the National Institutes of Health under Grants Nos. GM-16197-01 and GM-16437-01 and by the Atomic Energy Commission under Contract No. AT(11-1)-113, Project No. 19.     

Isoperimetric inequalities in potential theory

Given a non-empty bounded domainG in ⁿ ,n2, letr ₀(G) denote the radius of the ballG ₀ having center 0 and the same volume asG. The exterior deficiencyd _e (G) is defined byd _e (G)=r _e (G)/r ₀(G)–1 wherer _e (G) denotes the circumradius ofG. Similarlyd _i (G)=1–r _i (G)/r ₀(G) wherer _i (G) is the inradius ofG. Various isoperimetric inequalities for the capacity and the first eigenvalue ofG are shown. The main results are of the form CapG(1+cf(d _e (G)))CapG ₀ and ₁(G)(1+cf(d _i (G)))₁(G ₀),f(t)=t ³ ifn=2,f(t)=t ³/(ln 1/t) ifn=3,f(t)=t ^(n+3)/2 ifn4 (for convex G and small deficiencies ifn3).     

Removability of singularities in potential theory

IfQ is a compact metric space, a system of its closed subsets andg: R a prescribed nonnegative function, the conditions ong, and a closedF Q are specified guaranteeing the existence of a nontrivial Borel measure with support inF such that (L)g(L), L.For some kernels in potential theory these conditions permit to characterize geometrically those sets which contain support of a nontrivial measure whose potential belongs to a given class of functions. Several applications concerning removability of singularities of partial differential equations are presented.