Remark on the method of intermediate assertions, Soviet Math. Dokl. 24 (1), 91-93.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... 1 # # dx. Hence 1 1 # # G(#) 1 # # dx = # # G(#)# # dx . 6 Then we minimise the amended potential # # ) 4) Babenko s transformation The normal derivative operator G(#) depending in a subtle way on #, we perform Babenko s transform [3, 2, 26, 13] on the amended potential, so that G(#) is replaced (loosly speaking) by the normal derivative operator N relative to the domain R ( 1, 0) with Dirichlet s condition at the bottom. Babenko s transform is defined by Nw ds, w(t) #(x) where t is a new spatial variable (it does not ....

, Some remarks on the theory of surface waves of finite amplitude, Soviet Math. Doklady 35 (1987), 599--603.

....BA2 7AY, UK jft maths.bath.ac.uk December 2001 Abstract By applying the mountain pass lemma to an energy functional, we establish the existence of two dimensional water waves on the surface of an in nitely deep ocean in a constant gravity eld. The formulation used, which is due to K. I. Babenko [3, 4] (and later to others, independently) has as its independent variable an amplitude function which gives the surface elevation, its nonlinear term is purely quadratic but it is nonlocal because it involves the Hilbert transform. Moreover the energy functional from which it is derived is rather ....

....diculties with the idea and introduced a di erent variational approach which led to the existence of solitary waves on the surface of a uid layer of nite depth. In the absence of surface tension, it is known that solitary waves do not exist if the depth is in nite [10] More recently Babenko [3, 4] introduced a new variational formulation of the periodic water wave problem, but used non variational methods to study it. See also [14] Plotnikov [15] discovered the analogous formulation for solitary waves. See [19] for references to other independent discoveries of Babenko s formulation. ....

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, Some remarks on the theory of surface waves of nite amplitude, Soviet Math. Doklady 35 (1987), 599-603.

....University of Bath, Claverton Down, Bath, BA2 7AY, UK. i Introduction Using local finite dimensional reduction followed by a constrained minimisa tion argument, Stuart [15] following Krasnosel skii [12] gave a bifurcation theory for variational problems which was applied in [6] to Babenko s [2] quasi linear equation for Stokes waves. But how to deal with such problems directly, using variational methods in infinite dimensions, remained unclear. In [8] we took a step in this direction by adapting some ideas of Turner [17] and the mountain pass lemma in infinite dimensions to obtain an ....

__, Some remarks on the theory of surface waves of finite amplitude, Soviet Math. Doklady 35 (1987), 599-603.

....case # 0, in the elliptic case # 0, and in the mixed case. The general hyperbolic problem has been studied in [Mo] in [Gr] the stable and unstable manifolds of the tori are also determined. The elliptic and mixed cases have been considered in great detail in several papers starting with [Me]; the reader will find, besides original results, a complete description of the subsequent results and the relevant references in the recent paper [R] with some very recent further results, on a subject that keeps being under intense study, in [XY] and [BKS] Our case can be reduced to the (1.10) ....

V.K. Mel'nikov: On some cases of conservation of conditionally periodic motions under a small change of the Hamiltonian function, Soviet Math. Dokl. 6 (

....on the primary solution. As one example we mention problems in perfect plasticity. Here, discontinuities may occur in the displacement eld u due to slip lines in the micro structure, whereas the stresses , determined by linear combinations of derivatives of u, have a smoother behaviour (see [7] [6]) From a practical point of view, the stresses are required with high accuracy. Therefore mixed methods treating the stresses directly are often more adequate for solving problems in continuum mechanics. In this note, we consider the following model situation: The displacement of a thin linear ....

G.A.Seregin: On the regularity of weak solutions of variational problems in plasticity theory, Soviet Math. Dokl. Vol. 42, 683-688 (1991).

....in mathematics and in circuit theory, control theory, and system theory. Not surprisingly, this rich subject can be approached in many ways and in different settings. We cannot give a full account of the many prior contributions to this literature. The works of Krein and Nudelman [126] Nudelman [149, 150], Foias and Frazho [76] Ball, Gohberg, and Rodman [20] Rosenblum and Rovnyak [169] Landau [127, 128] Helton [100] Kovalishna and Potapov [125] and Dym [71] may be consulted for this. 6.1.1. Analytic Interpolation Problems. In this section, we briefly describe a recursive solution to ....

, On a generalization of classical interpolation problems, Dokl. Akad. Nauk SSR, 256 (1981), pp. 790--793. Soviet Math. Dokl., vol. 23, pp. 125--128, 1981.

....Moreover, we find an intrinsic expression for the Helmholtz morphism using a technique introduced by Kol ar that we have adapted to our context. Introduction The theory of variational bicomplexes was established at the end of the seventies by several authors [AnDu80] OlSh78] Tak79] Tul77] [Vin77]. In these works there is the idea that one can give a geometric formulation of the calculus of variations without using integrals. But, except of [AnDu80] in these works the variational bicomplex is built over the space of infinite jets of a fibred manifold. This procedure is suggested by the ....

A. M. Vinogradov: On the algebro--geometric foundations of Lagrangian field theory, Soviet Math. Dokl., 18 (1977), 1200--1204.

....family of periodic orbits disappear in saddle node bifurcations [11, 10] If on the other hand the eigenvalues of the fixed point satisfied jae=j 1, only a finite number of periodic orbits are present. Homoclinic connections to non hyperbolic fixed points were also considered by Sil nikov [28], but their unfolding received attention only recently [18, 23, 5, 7] In those articles the bifurcations considered where saddle node, pitchfork and transcritical, requiring a codimension 2 geometric model. In all of the cases considered, a homoclinic bifurcation tangent to the local bifurcation ....

, On the generation of a periodic motion from a trajectory which leaves and re-enters a saddle-saddle state of equilibrium, Soviet Math. Dokl., 7 (1966), pp. 155--1158.

....fiber. Therefore the greatest common divisor of any pair among the monomials l m; l 2 ; m 2 is different from 1. This contradicts to gcd( l 2 ; m 2 ) 1. Hence b does not have a basic fiber. The minimal free resolution of k over a Golod ring is constructed by Golod in [G2]. Thus, we get Corollary 2.2. Let R be a generic toric ring. The minimal free resolution of k over R is the Golod resolution. 3. Koszulness A well studied property, which is defined via the minimal free resolution of k over R, is Koszulness. Koszul toric rings were studied in [H R W, P R S] ....

E. Golod: On the homology of some local rings, Soviet Math. Dokl. 3 (1962), 745--749.

....integral operator for 0 t 1 and using then the group property. 6 A counterexample to asymptotic completeness In this Section, we will give a counterexample to asymptotic completeness which is inspired by a construction of Yajima [Ya] Another class of counterexamples has been given by Yafaev [Y]. We start with the observation that the unitary evolution U 1 (t) generated by the time dependent hamiltonian H 1 (t) 1 2 D 2 Cx 2 t 2 can be constructed explicitely. Indeed if we put T t u(x) t Gamman=4 u( x t 1 2 ) U 0 u(x) e Gammaix 2 =4 u(x) it is an easy ....

D.Yafaev: On the violation of unitarity in time-dependent scattering, Soviet Math. Dokl. 19(6) (1978) p 1517-1521.

.... stacking constructions of ergodic theory are organized in a way that makes them conveniently accessible to combinatorial analysis, and which has certain universality properties (such as containing a uniquely ergodic version of every ergodic, measure preserving transformation on a Lebesgue space [55]) Transversal flows had been investigated by Sinai [49] Kubo [29] and Kowada [26, 27] and also by S. Ito [24] who proved ergodicity of the adic transformation on an SFT for its measure of maximal entropy, a particular case of our Theorem 3.3. Adic transformations for actions of amenable ....

, A theorem on the Markov periodic approximation in ergodic theory, J. Soviet Math. 28 (1985), 667--673.

....that PA is a set partitioning polytope. Even if A is not in general position, by introducing extra variables for the interior (d Gamma1) simplices of A, PA can be realized as a set partitioning polytope. This has important implications for enumeration and optimization purposes. For example, Trubin [15] shows that if P is a set partitioning polytope and Q its linear relaxation then P is quasi integral, i.e. every edge of P is also an edge of Q. Balas and Padberg [3] and Matsui and Tamura [10] have given a characterization of adjacency between vertices of P . This leads to an algorithm for ....

V.A. Trubin On a method of solution of integer linear programming problems of a special kind, Soviet Math. Doklady, 10 (1969), 1544-1546.

....3.2 is proved. Remarks. 1. In the proof of Lemma 3.3, we have employed some ideas first used in [PR1] to prove that if T = then G(K) G(K) G(K) 2. In the case where V ae V K f , one can give another proof of Proposition 3. 2 using Sury s generalization [Su] of Margulis theorem [M2] describing normal subgroups of G(K) as before, we may assume that V oe T : Consider an abstract group theoretic section ffi : G(K) E and a continuous section : Omega E of , over G(K) and some open subgroup Omega of G(V ) respectively. Then, as is easily seen, ffi and coincide on N = ....

....G(K) in the topology induced from G(V ) and the continuity of ffi follows. However, our argument is more direct and allows us to include also archimedean places. Besides, as we will show in x8, once we have an independent proof of Proposition 3. 2, the result of [Su] can be derived directly from [M2]. To prove the triviality of the metaplectic kernel, it suffices to establish the following: Theorem 3.4 Suppose S contains a noncomplex place v 0 such that D Omega K K v0 M 2 (K v0 ) and let q be a prime. Assume that q = 2 if v 0 is real. Then M(S;G) does not contain elements of order q: ....

G. A. Margulis: On the multiplicative group of a quaternion algebra over a global field. Soviet Math. Dokl., 21 (1980), 780-784

....6, 15] In contrast to [8] we no longer appeal to the mountain pass principle nor to Morse theory, and therefore the present proof is simpler. Much more is known about steady water waves using global continuation methods [5, 6, 7] numerical investigations [9, 13] and computer assisted proofs [3, 4]. But the need for a global or semi global variational theory of these and similarly degenerate variational problems, including Morse indices of solutions etc. remains our focus. 2 Abstract setting Consider a real Hilbert space Xo with inner product ( 0 and norm II II0, and suppose that A ....

__, On a demonstrative experiment in the theory of surface waves of finite amplitude, Soviet Math. Dokl. 38 (1989), 626-630.

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Remark on the method of intermediate assertions, Soviet Math. Dokl. 24 (1), 91-93.

No context found.

, On the generation of a periodic motion from a trajectory which leaves and re-enters a saddle-saddle state of equilibrium, Soviet Math. Dokl., 7 (1966), pp. 155--1158.

No context found.

, A theorem on the Markov periodic approximation in ergodic theory, J. Soviet Math. 28 (1985), 667-673.

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B. A. Trakhtenbrot, On autoreducibility. Soviet Math. Doklady, 11:814-817, 1970. 13

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On a problem of Yu.V.Linnik. DAN SSSR 211 (1973), no.1, 31--34. (Russian); Engl. transl. Soviet Math. Dokl. 14 (1973), 950--953. MR 48 #7337

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On the possible values of the lower order of an entire function with a finite deficient value. DAN SSSR 159 (1964), no.5, 968--970. (Russian); Engl. transl.: Soviet Math. Dokl. 5 (1964), 1631--1633. MR 30 #247

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On the growth of an entire function along a ray. DAN SSSR 152 (1963), no.5, 1049--1050. (Russian); Engl. transl.: Soviet Math. Dokl. 4 (1963). 1491--1493. MR 27 # 4933

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B. Trakhtenbrot. On autoreducibility. Soviet Math. dokl., 11:814--817, 1970.

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