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1.
Given anm-accretive operatorA in a Banach spaceX and an upper semicontinuous multivalued mapF: [0,aX→2 X , we consider the initial value problemu′∈−Au+F(t,u) on [0,a],u(0)=x 0. We concentrate on the case when the semigroup generated by—A is only equicontinuous and obtain existence of integral solutions if, in particular,X* is uniformly convex andF satisfies β(F(t,B))k(t)β(B) for all boundedBX wherekL 1([0,a]) and β denotes the Hausdorff-measure of noncompactness. Moreover, we show that the set of all solutions is a compactR δ-set in this situation. In general, the extra condition onX* is essential as we show by an example in whichX is not uniformly smooth and the set of all solutions is not compact, but it can be omited ifA is single-valued and continuous or—A generates aC o-semigroup of bounded linear operators. In the simpler case when—A generates a compact semigroup, we give a short proof of existence of solutions, again ifX* is uniformly (or strictly) convex. In this situation we also provide a counter-example in ℝ4 in which no integral solution exists. The author gratefully acknowledges financial support by DAAD within the scope of the French-German project PROCOPE.  相似文献   

2.
Let M0 be the Minkowski space, let Λ2(M0) be the space of bivectors in M0, and let G1 ⊂ Λ2(M0) be the manifold of directions of the physical space, consisting of simple bivectors with square −1. A mapping F: U → Λ2(M0), U ⊂ ℝ4, satisfying the Maxwell equations is regarded as the tensor of an electromagnetic field in vacuum. The field is described on the basis of a special decomposition F = eω + h(*ω), where the mapping ω: U → G1 is called the direction of the field, and e: U → (0, +∞) and h: U → ℝ are the electric and magnetic coefficients of the field. The Maxwell equations are reformulated in terms of ω, e, and h. Electromagnetic fields whose set of directions is a point or a one-dimensional subset of G1 are considered. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 118–146.  相似文献   

3.
We show that treating of (non-trivial) pairs of irreducible characters of the group Sn sharing the same set of roots on one of the sets An and Sn \ An is divided into three parts. This, in particular, implies that any pair of such characters χα and χβ (α and β are respective partitions of a number n) possesses the following property: lengths d(α) and d(β) of principal diagonals of Young diagrams for α and β differ by at most 1. Supported by RFBR grant No. 04-01-00463 and by RFBR-NSFC grant No. 05-01-39000. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 3–25, January–February, 2007.  相似文献   

4.
Let C be a closed and convex subset of a real Hilbert space H. Let T be a nonexpansive mapping of C into itself, A be an α-inverse strongly-monotone mapping of C into H and let B be a maximal monotone operator on H, such that the domain of B is included in C. We introduce an iteration scheme of finding a point of F (T)∩(A+B)−10, where F (T) is the set of fixed points of T and (A+B)−10 is the set of zero points of A+B. Then, we prove a strong convergence theorem, which is different from the results of Halpern’s type. Using this result, we get a strong convergence theorem for finding a common fixed point of two nonexpansive mappings in a Hilbert space. Further, we consider the problem for finding a common element of the set of solutions of a mathematical model related to equilibrium problems and the set of fixed points of a nonexpansive mapping.  相似文献   

5.
Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomialsP n α n β n are studied, assuming that
(1)
withA andB satisfyingA>−1,B>−1,A+B<−1. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case, the zeros distribute on the set of critical trajectories Γ of a certain quadratic differential according to the equilibrium measure on Γ in an external field. However, when either α n β n or α n n are geometrically close to ℤ, part of the zeros accumulate along a different trajectory of the same quadratic differential.  相似文献   

6.
This paper presents conditions which are necessary and sufficient for (AB>)+ = B+Aω for all normalized generalized inverses Aω of the complex matrix A. Corresponding conditions are stated which are equivalent to the situation where (AB)+ = BωA+ is satisfied by each weak generalized inverse Bω of B. The results are applied to theorems by Baskett and Katz and by Schwerdtfeger.  相似文献   

7.
8.
Summary For PF2[z] with P(0)=1 and deg(P)≧ 1, let A =A(P) be the unique subset of N (cf. [9]) such that Σn0 p(A,n)zn P(z) mod 2, where p(A,n) is the number of partitions of n with parts in A. To determine the elements of the set A, it is important to consider the sequence σ(A,n) = Σ d|n, dA d, namely, the periodicity of the sequences (σ(A,2kn) mod 2k+1)n1 for all k ≧ 0 which was proved in [3]. In this paper, the values of such sequences will be given in terms of orbits. Moreover, a formula to σ(A,2kn) mod 2k+1 will be established, from which it will be shown that the weight σ(A1,2kzi) mod 2k+1 on the orbit <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>z_i$ is moved on some other orbit zj when A1 is replaced by A2 with A1= A(P1) and A2= A(P2) P1 and P2 being irreducible in F2[z] of the same odd order.  相似文献   

9.
We show that the general solution of the Ornstein-Zernike system of equations for multicomponent solutions has the form hαβ=∑A αβ j exp(-λjr)/r, where λj are the roots of the transcendental equation 1-ρΔ(λj)=0 and the amplitudes Aαβ j can be calculated if the direct correlation functions are given. We investigate the properties of this solution including the behavior of the roots A αβ j and amplitudes Aαβ j in both the low-density limit and the vicinity of the critical point. Several relations on Aαβ j and Cαβ are found. In the vicinity of the critical point, we find the state equation for a liquid, which confirms the Van der Waals similarity hypothesis. The expansion under consideration is asymptotic because we expand functions in series in eigenfunctions of the asymptotic Ornstein-Zernike equation valid at r→∞. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 500–515, June, 2000.  相似文献   

10.
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.  相似文献   

11.
12.
The two-parameter dyadic martingale Hardy spacesH p are introduced and it is proved that the maximal operator of the (C, α, β) means of a two-dimensional Walsh-Fourier series is bounded from Hp to Lp (1/(α+1), 1/(β+1)<p<∞) and is of weak type (H 1 # , L1), where the Hardy space H 1 # is defined by the hybrid maximal function. As a consequence, we obtain that the (C, α, β) means of a function f∈H 1 # converge a.e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on Hp whenever 1/(α+1), 1/(β+1)<p<∞. Thus in case f∈Hp, the (C, α, β) means converge to f in Hp norm. The same results are proved for the conjugate (C, α, β) means, too.  相似文献   

13.
It is proved that ifκ is supercompact, there are at least (2 P κ(β))+normal ultrafilters overP k (β) and ifV=H.O.D. exactly (22• P κ(β)) normal ultrafilters. This is a part of the author’s Ph.D. thesis prepared under the supervision of Professor Azriel Levy for whose help the author is grateful. In 1966–67, Solovay proved Theorem 1 for the caseβ=κ without the condition of extendability. The same result, under a somewhat weaker assumption was proved by Namba in 1967–68. As noted by Solovay, his proof can be adapted to a generalβ (under weaker assumptions; if |P k (β) |=β it is only needed that ℵ is 2β-supercompact). Solovay’s result will be published in [3].  相似文献   

14.
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt Foundation.  相似文献   

15.
Let B be a closed linear transformation of the Banach space X into the Banach space Y and let A be a bounded linear transformation of Y into the Banach space Z. A simple condition is shown to be necessary and sufficient for AB to have closed range. Provided B is relatively regular there is a simple necessary and sufficient condition for AB to be relatively regular. Provided B+ and A+ are pseudoinverses for B and A, respectively, the condition that B+A+ is a pseudoinverse for AB is completely characterized.  相似文献   

16.
Let A be a Banach algebra with unity I and M be a unital Banach A-bimodule. A family of continuous additive mappings D=(δi)iN from A into M is called a higher derivable mapping at X, if δn(AB)=∑i+j=nδi(A)δj(B) for any A,BA with AB=X. In this paper, we show that D is a Jordan higher derivation if D is a higher derivable mapping at an invertible element X. As an application, we also get that every invertible operator in a nontrivial nest algebra is a higher all-derivable point.  相似文献   

17.
The structure of the QFT expansion is studied in the framework of a new “invariant analytic” version of the perturbative QCD. Here, an invariant coupling constant α(Q 2 /Λ 2 ) = β 1 αs(Q 2 )/(4π) becomes a Q 2 -analytic invariant function α an (Q2/Λ 2 ) ≡A(x), which, by construction, is free of ghost singularities because it incorporates some nonperturbative structures. In the framework of the “analyticized” perturbation theory, an expansion for an observable F, instead of powers of the analytic invariant charge A(x), may contain specific functions An(x)=[an(x)] an , the “nth power of a(x) analyticized as a whole.” Functions A n>2(x) for small Q2Λ 2 oscillate, which results in weak loop and scheme dependences. Because of the analyticity requirement, the perturbation series for F(x) becomes an asymptotic expansion à la Erdélyi using a nonpower set {A n (x)}. The probable ambiguities of the invariant analyticization procedure and the possible inconsistency of some of its versions with the renormalization group structure are also discussed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 55–66, April, 1999.  相似文献   

18.
Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any pP, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-empty, finite point sets A 1, ..., A d+1 in ℝ d , if the origin is contained in the convex hull of A i A j for all 1≤i<jd+1, then there is a simplex S containing the origin such that |SA i |=1 for every 1≤id+1. This is a generalization of Bárány’s colored Carathéodory theorem, and in a dual version, it gives a spherical version of Lovász’ colored Helly theorem. Dedicated to Imre Bárány, Gábor Fejes Tóth, László Lovász, and Endre Makai on the occasion of their sixtieth birthdays. Supported by the Norwegian research council project number: 166618, and BK 21 Project, KAIST. Part of the research was conducted while visiting the Courant Institute of Mathematical Sciences. Supported by NSF Grant CCF-05-14079, and by grants from NSA, PSC-CUNY, the Hungarian Research Foundation OTKA, and BSF.  相似文献   

19.
For a set A, let P(A) be the set of all finite subset sums of A. We prove that if a sequence B={b 1<b 2<⋯} of integers satisfies b 1≧11 and b n+1≧3b n +5 (n=1,2,…), then there exists a sequence of positive integers A={a 1<a 2<⋯} for which P(A)=ℕ∖B. On the other hand, if a sequence B={b 1<b 2<⋯} of positive integers satisfies either b 1=10 or b 2=3b 1+4, then there is no sequence A of positive integers for which P(A)=ℕ∖B.  相似文献   

20.
Summary Srivastava [5] proposed a class of rank score tests for testing the hypothesis that β1=⋯β p =0 in the linear regression modely i 1 x 1i 2 x 2i +⋯+β p +x pi i under weaker conditions than Hájek [2]. In this paper, under the same weak conditions, a class of rank score tests is proposed for testing β1=⋯β q =0 in the multivariate linear regression modely i 1 x 1i 2 x 2i +⋯+β p +x pi i ,q≦p, where β i ’s arek-vectors. The limiting distribution of the test statistic is shown to be central χ qk 2 underH and non-central χ qk 2 under a sequence of alternatives tending to the hypothesis at a suitable rate. Research supported by Canada Council and National Research Council of Canada.  相似文献   

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