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51.
Gapeev Pavel V. Kort Peter M. Lavrutich Maria N. Thijssen Jacco J. J. 《Methodology and Computing in Applied Probability》2022,24(2):789-813
Methodology and Computing in Applied Probability - We present closed-form solutions to some double optimal stopping problems with payoffs representing linear functions of the running maxima and... 相似文献
52.
Pavel M. Bleher Denis V. Kosygin Yakov G. Sinai 《Communications in Mathematical Physics》1995,170(2):375-403
We consider the Weyl asymptotic formula
相似文献
53.
We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S1. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H1(S1), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then limtT* w(t,·) exists in C1(S1) but vanishes at some point. We show further that if T* > (1 + √3)/16π2 √3 then T* = ∞ and limt∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc. 相似文献
54.
Pavel Novotný 《Geometriae Dedicata》1994,50(1):53-55
This paper deals with the following kind of approximation of a convex bodyQ in Euclidean space E
n
by simplices: which is the smallest positive numberh
S(Q) such thatS
1 Q S
2 for a simplexS
1 and its homothetic copyS
2 of ratioh
S(Q). It is shown that ifS
0 is a simplex of maximal volume contained inQ, then a homothetic copy ofS
0 of ratio 13/3 containsQ. 相似文献
55.
Pavel Pyrih 《Potential Analysis》1994,3(3):273-281
We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.LetI denote the set of complex functionsf: for which there exists a quasi-analytic classC{M
n} containingf. Let denote the set of complex functionsf: for which there exist a fine domainU containing the real line and a function
finely holomorphic onU satisfyingf(x)=
(x) for allx . The power of unique continuation is incomparable in these two cases (I\ is non-empty, \I is non-empty).Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University. 相似文献
56.
We investigate the statistics of the numberN(R, S) of lattice pointsnZ
2, in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c
1
T,c
2,T],c
2>c
1>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area. 相似文献
57.
Pavel Valtr 《Combinatorica》1996,16(4):567-573
We show thatn random points chosen independently and uniformly from a triangle are in convex position with probability $$\frac{{2^n (3n - 3)!}}{{((n - 1)!)^3 (2n)!}}$$ . 相似文献
58.
Pavel Valtr 《Combinatorica》1996,16(2):269-294
LetP be a set ofn points in the plane. We say thatP isdense if the ratio between the maximum and the minimum distance inP is of order
. A setC of line segments in the plane is calleda crossing family if the relative interiors of any two line segments ofC intersect. Vertices of line segments of a crossing familyC are calledvertices of C. It is known that for any setP ofn points in general position in the plane there is a crossing family of size
with vertices inP. In this paper we show that ifP is dense then there is a crossing family of almost linear size with vertices inP.The above result is related to well-known results of Beck and of Szemerédi and Trotter. Beck proved that any setP ofn points in the plane, not most of them on a line, determines at least (n
2) different line. Szemerédi and Trotter proved that ifP is a set ofn points and is a set ofm lines then there are at mostO(m
2/3
n
2/3
+m+n) incidences between points ofP and lines of . We study whether or not the bounds shown by Beck and by Szemerédi and Trotter hold for any dense setP even if the notion of incidence is extended so that a point is considered to be incident to a linel if it lies in a small neighborhood ofl. In the first case we get very close to the conjectured bound (n
2). In the second case we obtain a bound of order
.The work on this paper was supported by Czech Republic grant GAR 201/94/2167, by Charles University grants No. 351 and 361, by Deutsche Forschungsgemeinschaft, grant We 1265/2-1, and by DIMACS. 相似文献
59.
Pavel Jano Hana Chromá Vlastimil Kubá 《Fresenius' Journal of Analytical Chemistry》1996,355(2):135-140
Separations of metal cations on a column packed with the strongly acidic cation exchanger Separon SGX CX were investigated in the presence of -hydroxyisobutyric acid (HIBA) in the mobile phase. A retention model based on the general theory of side equilibria was elaborated and relations describing dependences of capacity factors of analytes on the compositon of the mobile phase were derived. Effects of HIBA concentration and pH of the mobile phase on the analyte retention were studied in detail. Stability constants of divalent metal cations (Cd2+, Co2+, Mn2+, Ni2+ and Zn2+) with HIBA were calculated from the experimental dependences of the reciprocal values of capacity factors on the ligand concentration. 相似文献
60.
Based on thermodynamic analysis of interfacial segregation, the segregation enthalpy H
o of a solute I in a given matrix was found to depend linearly on two mutually independent terms reflecting the type of interface and the solid solubility limit X
infI
sup*
at temperature T and can be written as In this equation, the structural dependence of interfacial segregation is contained in H
*() which corresponds to the extrapolated segregation enthalpy of a solute with unlimited solubility in the matrix. The product [Tln(X
infI
sup*
)] is essentially constant with temperature, and can therefore be obtained from data for maximum solid solubility, [Tln(X
infI
sup*
)]max. The parameter v>0 represents the relationship between the activity a
infI
sup*
of a solute at the bulk solid solubility limit in a given matrix and X
infI
sup*
, a
infI
sup*
=(X
infI
sup*
)
v
, and is characteristic for the matrix. Using recent experimental data for silicon, phosphorus, and carbon segregation at well-characterized grain boundaries in oriented bicrystals of -iron, the averaged value
was determined. Values of H
*() range from -8 kJ/mol (general grain boundaries) up to +8 kJ/mol (special grain boundaries). These values are discussed and used for a more precise and generalized construction of grain boundary segregation diagrams of -iron. 相似文献
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