Parametric oscillations of solutions to the telegraph equation with moderately small diffusion

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 79–86, November–December, 1992.     

Boundary properties of conformal and quasiconformal mappings of polygons

Novosibirsk. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 31–38, November–December, 1992.     

On estimating parameters of a multitype Galton-Watson process by ϕ-branching processes

Kazan'. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 4, pp. 175–185, July–August, 1992.     

On existence of admissible and weakly admissible limits for functions of several complex variables

Kishinev. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 4, pp. 212–214, July–August, 1992.     

On the extension principle in internal set theory

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 66–78, November–December, 1992.     

Verification of boundedness for the powers of symplectic matrices with the help of averaging

Novosibirsk. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 3–13, November–December, 1992.     

On the paper “Asymptotic behavior of meromorphic functions of completely regular growth and of their logarithmic derivatives”

Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 4, pp. 219–219, July–August, 1992.     

On interrelation between the problem of unique determination of a domain in R N and a problem of recovery of a locally euclidean metric

Novosibirsk. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 4, pp. 206–211, July–August, 1992.     

An approach to the boundary value problems for equations of composite type

Novosibirsk. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 47–53, November–December, 1992.     

On a method of studying multipoint boundary value problems

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 87–93, November–December, 1992.     

On monotone dominated sublinear functionals on the space of measurable functions

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 94–105, November–December, 1992.     

Norm behavior and zero distribution for orthogonal polynomials with nonsymmetric weights

The asymptotic behavior of thenth root of the leading coefficient of orthogonal polynomials on (–,) and the distribution of their zeros is studied for nonsymmetric weights that behave like exp(–2B|x|) whenx>0 and exp(–2Ax ) whenx<0,>AB. These results generalize previous investigations of Rakhmanov and Mhaskar and Saff who handle the symmetric caseA=B.Communicated by Paul Nevai.     

Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents

We are concerned with the semilinear polyharmonic model problem (–)K v = v +v|v| ^s–1 inB,D v|B = 0 for ¦|<-K – 1. HereK ,B is the unit ball in ⁿ,n >2K, is the critical Sobolev exponent. Let ₁ denote the first Dirichlet eigenvalue of (-)^K inB. The existence of a positive radial solutionv is shown for

On the convergence of multivariable Lagrange interpolants

LetA _dj be a triangular array in a compact setXC ⁿ . Forf analytic in a neighborhood ofX, letL _d (f) denote the Lagrange interpolant tof at staged of the array. In the caseX is locally regular, we construct a continuous function satisfying the complex Monge-Ampère equation onC ⁿ –X, such that iff is analytic onR forR>1 then, for someB>0, we have L _d (f)–f _x B exp(–d logR. In particular, since1 onX, iff is analytic on1, then lim _d L _d (f)–f _x =0.Communicated by Edward B. Saff.     

Partial order complementation graphs

Two partial ordersP andQ on a setX arecomplementary (written asPQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integern we form a graph Pos _n consisting of all nonempty partial orders on {1, ,n} with edges denoting complementation. We investigate here properties of the graphs Pos _n . In particular, we show:

Comparative cooperative game theory

Given two side-payment gamesv andw, both defined for the same finite player-setN, the following three welfare criteria are characterized in terms of the datav andw: (A) For everyy C(w) there existsx C(v) such thatyx; (A) For everyxC(v) there existsyC(w) such thatyx; and (B) There existyC(w) andxC(v) such thatyx. (HereC(v) denotes the core ofv.) Given two non-side-payment gamesv andw, sufficient conditions for the criteria (A) and (B) are established, by observing that an ordinal convex game has a large core.In memory of my teacher in Japan, Professor Ryuichi Watanabe, 1928–1986.     

The GHS inequality and the Riemann hypothesis

LetV(t) be the even function on (–, ) which is related to the Riemann xi-function by (x/2)=4 _– exp(ixt–V(t))dt. In a proof of certain moment inequalities which are necessary for the validity of the Riemann Hypothesis, it was previously shown thatV'(t)/t is increasing on (0, ). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely thatV' is convex on [0, ). The possible relevance of the convexity ofV' to the Riemann Hypothesis is discussed.Communicated by Richard Varga.     

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

On the Pólya conjecture concerning the maximum and minimum of the modulus of an entire function of finite order given by a lacunary power series

, (fz) , ,