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1.
Summary We study a class of generalized gamma functions k (z) which relate to the generalized Euler constants k (basically the Laurent coefficients of(s)) as (z) does to the Euler constant. A new series expansion for k is derived, and the constant term in the asymptotic expansion for log k (z) is studied in detail. These and related constants are numerically computed for 1 k 15.  相似文献   

2.
Suppose an integral function (|A|)q1 defined on the subsets of edges of a hypergraph (X,u,) satisfies the following two conditions: 1) any set W u such that |A|(|A|) for any AW is matroidally independent; 2) if W is an independent set, then there exists a unique partitionW=T1+ T2+...+Tv such that |T i |=(|T i |),i1:v, and for any AW, |A|(|A|) there exists a Ti such that ATi. The form of such a function is found, in terms of parameters of generalized connected components, hypercycles, and hypertrees.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 196–204, 1982.  相似文献   

3.
In this paper, the -subdifferential is introduced for investigating the global behavior of real-valued functions on a normed spaceX. Iff: DX attains its global minimum onD atx *, then 0 f(x *). This necessary condition always holds, even iff is not continuous orx * is at the boundary of its domain. Nevertheless, it is useful because, by choosing a suitable +, many local minima cannot satisfy this necessary condition. For the sufficient conditions, the so-called -convex functions are defined. The class of these functions is rather large. For example, every periodic function on the real line is a -convex function. There are -convex functions which are not continuous everywhere. Every function of bounded variation can be represented as the difference of two -convex functions. For all that, -convex functions still have properties similar to those of convex functions. For instance, each -local minimizer off is at the same time a global one. Iff attains its global minimum onD, then it does so at least at one point of its -boundary.This research was supported by the Alexander von Humboldt Foundation. The author thanks Professors R. Bulirsch, K. H. Hoffmann, and H. G. Bock for inviting him to Munich and Augsburg where this research was done.  相似文献   

4.
All finite fields q (q 2, 3, 4, 5, 7, 9, 13, 25, 121) contain a primitive element for which + 1/ is also primitive. All fields of square order q 2 (q 3, 5) contain an element of order q + 1 for which + 1/ is a primitive element of the subfield q. These are unconditional versions of general asymptotic results.  相似文献   

5.
For a set X, let : exp X exp X satisfy A B whenever A B X. In [4], -open subsets of X, -interior iA and -closure cA of A X have been defined. The purpose of the present paper is to show that, under suitable conditions on , explicit formulas furnish iA and cA.  相似文献   

6.
Elovikov  A. B. 《Mathematical Notes》2003,73(5-6):643-655
A large class of one-generated factorable foliated formations including composition, bicanonical, and other formations is described. V. A. Vedernikov suggested to study foliated formations with directions such that , where and are also some directions, from a unified point of view. We study one-generated factorable foliated formations with directions from the interval [,], where and are the directions of the bicanonical and composition formations, respectively. In particular, all irreducible factorizations of one-generated composition formations are studied.  相似文献   

7.
LetK be an algebraic number field, and for every integer K let () andd(), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (). Asymptotic equalities are proved for the sums () and d 2(), where runs through certain finite sets of integers ofK.  相似文献   

8.
Summary The Cahn-Hilliard model for phase separation in a binary alloy leads to the equations (I) ut=w, (II) w= (u)– u with an associated energy functional F(u)=f [(u)+ +¦u¦2/2] dx. In this paper we discuss the existence theory for initial bounday value problems arising from modifications to the Cahn-Hilliard model due to the addition of the non-differentiable term ¦u¦dx to the energy F(u).  相似文献   

9.
For regular coercive inhomogeneous and eigenvalue problems of the form b(u,) –zk(u,)=(f,), H, with bounded bilinearforms b, k in a Hilbertspace H the approximate solutions, eigenfunctions and eigenvalues calculated by means of the Galerkin method are shown to converge, with the eigenvalues preserving algebraic multiplicity. The above class of regular coercive problems are applicable to integral and differential equations and include for example the K-p.d. and non-K-p.d. operators of PETRYSHYN as special cases.  相似文献   

10.
Summary The aim of the paper is to give upper bounds for the total curvature of smooth curves and surfaces embedded in euclidean space, in terms of other global geometric characters; in particular, for a plane curve , we prove the inequality K() < (2 + f()d()/2), where d() is the geometric degree of and f() is the number of its inflection points. In the case of a surface S, a bound is given in terms of the genus g(S), the number of components of the parabolic points on S and the geometry of its apparent contour.  相似文献   

11.
12.
LetT be a Hamiltonian tournament withn vertices and a Hamiltonian cycle ofT. In this paper we develope a general method to find cycles of lengthk, n+4/2 < k < n, intersecting in a large number of arcs. In particular we can show that if there does not exist a cycle.C k intersecting in at leastk – 3 arcs then for any arce of there exists a cycleC k containinge and intersecting in at leastk – 2(n–3)/n–k+3 – 2 arcs. In a previous paper [3] the case of cycles of lengthk, k n+4/2 was studied.On leave at MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139, USA.  相似文献   

13.
Kabakov has proved that for the finite validity (in Medvedev's sense) of intuitively unprovable propositional formulas it is necessary that an implication occur in the premise or else in the inference of some subformula of the type ( ), and, consequently, that at least two implications be present. Here we prove that every finitely valid, intuitively unprovable formula contains the occurrence of an implication necessarily in the premise of some subformula of the form ( ) and we also present an example of a similar formula containing exactly two implications.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 383–390, September, 1976.  相似文献   

14.
Summary We consider a one dimensional Ising spin system with a ferromagnetic Kac potential J(|r|),J having compact support. We study the system in the limit, »0, below the Lebowitz-Penrose critical temperature, where there are two distinct thermodynamic phases with different magnetizations. We prove that the empirical spin average in blocks of size –1 (for any positive ) converges, as »0, to one of the two thermodynamic magnetizations, uniformly in the intervals of size p , for any given positivep1. We then show that the intervals where the magnetization is approximately constant have lengths of the order of exp(c –1),c>0, and that, when normalized, they converge to independent variables with exponential distribution. We show this by proving large deviation estimates and applying the Ventsel and Friedlin methods to Gibbs random fields. Finally, if the temperature is low enough, we characterize the interface, namely the typical magnetization pattern in the region connecting the two phases.The research has been partially supported by CNR, GNFM, GNSM and by grant SC1CT91-0695 of the Commission of European Communities  相似文献   

15.
The following theorem will be proved: THEOREM. Let (P,) be a linear space with dimension dim(P,) 2, such that each line contains at least three points. Let further Aut(P,) be a two — transitive group of collineations on the point set P, such that every automorphism fixing one flag (p,L), fixes all lines through p. Then (P,) is a desarguesian affine space and contains the whole group of dilatations of (P,). Moreover one can define an addition and a multiplication on the point set, such that (P,+,-) is a nearfield, the line joining the neutral elements is a normal subfield and consists of the affine transformations x a + mx, m 0 and= (K).

Herrn Professor Dr. Helmut Karzel zum 60. Geburtstag  相似文献   

16.
We study questions of the hereditariness of the property of (, )-transitivity (the property of being a plane of translations) of a finite protective plane for its subplanes. In particular it is shown that hereditariness holds for subplanes containing the point .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1101–1102, July–August, 1991.  相似文献   

17.
We present a three-loop calculation for the contribution of the anomalous dimension in the RG function for the full UN-symmetric model using dimensional regularization with d=2+. This model contains an infinite number of independent four-fermion interactions and couplings gn. In the MS scheme, the three-loop contribution in depends on all of the charges. In the symmetric subtraction scheme for =0, only the dependence on the three lower charges g 0,1.2 l remains. The results of a three-loop calculation of for the Thirring model and for the Gross-Neveu model are discussed; they seem to contradict the equivalence of all four-fermion interactions for d=2, N=1. It is shown that this equivalence appears only for the symmetric subtraction scheme. The precise meaning of (2+)-expansions of the critical dimensions is discussed for when the multiplication renormalizability is absent in the Gross-Neveu model.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 3, pp. 359–371, June, 1996.  相似文献   

18.
The order-9 Desarguesian projective plane and the known self-dual non-Desarguesian plane (Carmichael or Hughes plane) each have a 13-collineation displacing all points and all lines. We show that no previously undiscovered 9-plane has this property.  相似文献   

19.
The possible existence of quantum copies of classical soliton solutions that cannot exist if the effective Planck constant of the theory tends to zero is discussed. In the framework of the standard expansion in , such nonclassical solitons have energy of orderO() and thus occupy an intermediate position between purely classical configurations and second-quantized degrees of freedom. Analytic calculations are made for the profile functions, masses, and stability of such configurations in the 4 kink model.Physics Faculty, Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 52–65, January, 1993.  相似文献   

20.
The effects of the three principal possible exact breakdowns which may occur using BiCGStab are discussed. BiCGStab is used to solve large sparse linear systems of equations, such as arise from the discretisation of PDEs. These PDEs often involve a parameter, say . We investigate here how the numerical error grows as breakdown is approached by letting tend to a critical value, say c, at which the breakdown is numerically exact. We found empirically in our examples that loss of numerical accuracy due stabilisation breakdown and Lanczos breakdown was discontinuous with respect to variation of around c. By contrast, the loss of numerical accuracy near a critical value c for pivot breakdown is roughly proportional to |–c|–1.  相似文献   

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