代数体函数及其微分多项式

本文证明了v值代表体函数w的微分多项式p(w)是-λ(1<λ相似文献   

On Finite Model Property for Admissible Rules

Our investigation is concerned with the finite model property (fmp) with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown (Theorem 4.3) that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics (which is equipotent to all these λ extend a certain subframe logic defined over S4 by omission of four special frames) have fmp w.r.t. admissibility.     

C0-半群关于参数的可微性及其应用

考虑了C0-半群关于参数的可 微性,而参数含在半群的无穷小生成元中. 证明了：无穷小生成元关于参数的广义连续 性及强可微性蕴含着该C0-半群关于参数的可微性. 这些结果被应用于证明线性延 滞微分方程的解关于延滞量的可微性质.     

Characterizations of Translation Generalized Quadrangles

If x is a regular point of the generalizedquadrangle of order (s,t), s 1 t, then x defines a dual net . If contains a line L of regularpoints and if for at least one point x on Lthe automorphism group of the dual net satisfies certain transitivityproperties, then is a translation generalized quadrangle. Thisresult has many applications. We give one example. Ifs=t 1, then is a dual affine plane. Let be a generalizedquadrangle of orders,s odd and s 1, which contains a lineL of regular points. If for at least one pointx on L the plane is Desarguesian, then is isomorphic to the classical generalizedquadrangleW(s).     

Co—半群关于参数的可微性及其应用

考虑了Co-半群关于参数的可微性,而参数含在半群在无穷小生成元中,证明了：无穷小生成元关于参数的广义连续性及强可微性蕴含着Co-半群关于参数的可微性。这些结果被应用于证明线性延滞微分方程的解关于延滞量的可微性质。     

The Hölder property of singular invariant measures of circle homeomorphisms with single corners

Any circle homeomorphism with a corner has an invariant measure that is singular w.r.t. the Lebesgue measure. It is proved that the singularity of the invariant measure has the Hölder property.     

Allgemeine Zerlegungstheorie

The notion -disjoint decomposition is introduced as a common generalization of the elementary geometric decomposition of polyhedras and the disjoint decomposition of sets: Let Rø be a set, G a subgroup of the symmetric group S_R and 2^R with ø and ¦¦>1; then A, B 2^R are called -disjoint if ø. is the only set of contained in A B, and then A B A B is called the disjoint union. If fullfills the axioms (0, I, II, III) of §2, then can be provided in a natural way with certain binary relations. With respect to the decomposition equivalence can be turned in a partially ordered commutative semigroup with identity (cf. Satz §5).

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Dedicated to Prof.R.Artzy on the occasion of his 80. birthday     

Invariant subspaces and unicellularity of operators of generalized integration in spaces of analytic functionals

Invariant subspaces are described and the unicellularity is proved of one class of operators of generalized integration in spaces of analytic functionals. As one of the realizations it is established that every nontrivial subspace, invariant relative to the integrationF(t)dt, in the space of functions analytic in an arbitrary convex domain (a), is determined by a positive integer m and consists of all functions equal to zero at pointa together with all derivatives up to order m–1.Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 221–230, August, 1997.     

变换图的直径及Brualdi猜想

设Ｒ＝（ｒ１，ｒ２…ｒｍ）及 Ｓ＝（Ｓ１，Ｓ２，…，Ｓｎ）为两个正整数向量，满足Σｍｉ＝１ｒｉ＝Σｎｊ＝１ｓｊ＝ Ｋ．记Ｇ（Ｒ，Ｓ）为（０，１）－矩阵类 Ｕ（Ｒ，Ｓ）的变换图．Ｂｒｕａｌｄｉ在文山中给出了 Ｇ（Ｒ，Ｓ）的直径厂（Ｇ（Ｒ，Ｓ））的一个上界：ｍｎ／２－１，并猜想Ｄ（Ｇ（Ｒ，Ｓ））≤ｍｎ／４．本文通过对有向图围长的研究得到了Ｄ（Ｇ（Ｒ，Ｓ））的一个新的上界：１／２ｍｎ－１／６ｔ（ｔ－１）（４ｔ＋１），其中Ｔ＝　　．     

Functional limit theorems for cumulative processes and stopping times

Summary Consider a cumulative regenerative process with increments between regeneration points being i.i.d. r.v.'s. Let the d.f. of those increments belong to the domain of attraction of a stable distribution with exponent less than two. A functional limit theorem in the Skorohod M ₁-topology is proved for this process. The M ₁-topology is more useful than the J ₁-topology in this case, because it allows the cumulative process to be continuous.The second part of the paper concerns a stopping time process, (t)--inf(s>0:w(s)>tg(s)), where w(t) is a process with positive drift for which a functional limit theorem holds and g(t)=t ^p L(t) with 0p<1 and L(t) varying slowly at infinity. Weak convergence for the process (t) is proved under certain conditions in the J ₁- and M ₁-topologies.     

Angle theorems for the Lagrangian mean curvature flow

We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. . Received: 11 April 2001 / Published online: 29 April 2002     

Topological transitivity of cylindrical cascades

The existence is proved of a topologically transitive (t.t.) homeomorphism U of the space W = × Z of the formU (, z)=(T,, z+f ()) ( , z Z), where is a complete separable metric space, T is a t.t. homeomorphism of onto itself, Z is a separable banach space, andf is a continuous map: z. For the special case W = S¹×R, T=+ ( is incommensurable with 2) the existence is proved of t.t. homeomorphisms (1) of two types: 1) with zero measure of the set of transitive points, 2) with zero measure of the set of intransitive points. An example is presented of a continuous functionf: S¹R for which the corresponding homeomorphism (1) is t.t. for all incommensurable with 2.Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 441–452, September, 1973.The author thanks D. V. Anosov for advice and interest in the work.     

Residual Finiteness for Admissible Inference Rules

We look into methods which make it possible to determine whether or not the modal logics under examination are residually finite w.r.t. admissible inference rules. A general condition is specified which states that modal logics over K4 are not residually finite w.r.t. admissibility. It is shown that all modal logics over K4 of width strictly more than 2 which have the co-covering property fail to be residually finite w.r.t. admissible inference rules; in particular, such are K4, GL, K4.1, K4.2, S4.1, S4.2, and GL.2. It is proved that all logics over S4 of width at most 2, which are not sublogics of three special table logics, possess the property of being residually finite w.r.t. admissibility. A number of open questions are set up.     

Contractions Satisfying the Absolute Value Property

Let B(H) denote the algebra of operators on a complex Hilbert space H, and let U denote the class of operators which satisfy the absolute value condition . It is proved that if is a contraction, then either A has a nontrivial invariant subspace or A is a proper contraction and the nonnegative operator is strongly stable. A Putnam-Fuglede type commutativity theorem is proved for contractions A in , and it is shown that if normal subspaces of . It is proved that if are reducing, then every compact operator in the intersection of the weak closure of the range of the derivation with the commutant of A* is quasinilpotent.     

傅立叶超函数和扩充傅立叶超函数与爱米特热方程

证明了傅立叶超函数和扩充傅立叶超函数可用爱米特热方程的解来表示,且用以表示的解有很良好的性质.     

Attracting properties for one dimensional flows of a general barotropic viscous fluid. Periodic flows

Summary We consider the motion of a barotropic compressible fluid in a one dimensional bounded region with impermeable boundary, see equation (1.1). Here, u(t, q) denotes the velocity and v(t, q) the specific volume. The quantity log v(t, q) measures the displacement of v(t, q) with respect to the equilibrium v 1. For the sake of brevity we denote here different norms by the simbol . We show that there is a positive constant r₀=r₀(), a small ball B₁ (r) (with radius R₁ (r), ), and a large ball B(r) (with radius R(r), ) such that the following holds, for each r [0, r₀ [(i) If f(t) < r for all t 0, and if (u(0), log v(0))R(r) (i.e. (u(0), log v(0)) B(r)) then, for sufficiently large values of t, (u(t), log v(t))R₁ (r); (ii) The solutions starting at time t=0 from the large ball B(r) have all the same asymptotic behaviour (see (1.11)); (iii) If f is T-periodic then there is a (unique) T-periodic solution (u(t), log v(t)) inside the small ball B₁ (r). This periodic solution atracts all solutions which intersect the large ball B(r). Periodic solutions had been previously studied only for very specific pressure laws, namely p(v)-log v and p(v)-v^–1.     

The problem of boundary correspondence

It is proved that those points of the boundary of the disk, to which a homeomorphism of the class BLP, cannot be extended according to Carathéodory (from the disk), form a set of zero (p-)-capacity. Estimates for the distortion of distances under these mappings are given.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 103–108, July, 1977.     

Asymptotic properties of local densities of measures generated by semimartingales

For families of probability measures (P , )) generated by semimartingales, we consider the local density)(y, )= _t (y, )) _t0 of a, measureP _y with respect to the measureP whose logarithm is the difference of a local martingale and a positive predictable increasing locally bounded process. Conditions are obtained under which the relations and hold, wherey _t depends in some way ont, while _t ast . Applications of these relations are exhibited and an example is given when the hypotheses of the theorems proved can be verified.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 48–55, 1986.     

Construction of librational invariant tori in the spin-orbit problem

We investigate the stability of the synchronous spin-orbit resonance. In particular we construct invariant librational tori trapping periodic orbits in finite regions of phase space. We first introduce a mathematical model describing a simplification of the physical situation. The corresponding Hamiltonian function has the formH(,x,t)=(²/2) + V(x,t), whereV is a trigonometric polynomial inx, t and is the perturbing parameter representing the equatorial oblateness of the satellite.We perform some symplectic changes of variables in order to reduce the initial Hamiltonian to a form which suitably describes librational tori. We then apply Birkhoff normalization procedure in order to reduce the size of the perturbation. Finally the application of KAM theory allows to prove the existence of librational tori around the synchronous periodic orbit. Two concrete applications are considered: the Moon-Earth and the Rhea-Saturn systems. In the first case one gets the existence of trapping orbits for values of the perturbing oblateness parameter far from the real physical value by a factor 5. In the Rhea-Saturn case we construct the trapping tori for values of the parameters consistent with the astronomical measurements.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.