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991.
A. Cordón-Franco A. Fernández-Margarit F.F. Lara-Martín 《Archive for Mathematical Logic》2004,43(3):371-398
In this paper we continue the study of the theories I n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that I n+1 (T) is n+2 –axiomatizable. In particular, I n+1 (I n+1 ) gives an axiomatization of Th n+2 (I n+1 ) and is not finitely axiomatizable. This fact relates the fragment I n+1 (I n+1 ) to induction rule for n+1 –formulas. Our arguments, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for n+2 and n+1 formulas (see [2]).Research partially supported by grant PB96–1345 (Spanish Goverment)Mathematics Subject Classification (2000): 03F30, 03H15 相似文献
992.
993.
Pavol?QuittnerEmail author 《NoDEA : Nonlinear Differential Equations and Applications》2004,11(2):237-258
Consider the Dirichlet problem for the parabolic equation
in
, where
$\Omega$ is a bounded domain in
and f has superlinear subcritical growth in u.
If f is independent of t and satisfies some
additional conditions then using a dynamical method we find multiple (three, six or infinitely many) nontrivial
stationary solutions. If f has the form
where m is periodic, positive and m,g satisfy some technical
conditions then we prove the existence of a positive periodic solution and
we provide a locally uniform bound for all global solutions. 相似文献
994.
We say that a subset of Cn is hypoconvex if its complement is the union of complex hyperplanes. We say it is strictly hypoconvex if it is smoothly bounded
hypoconvex and at every point of the boundary the real Hessian of its defining function is positive definite on the complex
tangent space at that point. Let Bn be the open unit ball in Cn.Suppose K is a C∞ compact manifold in ∂B1 × Cn, n > 1, diffeomorphic to ∂B1 × ∂Bn, each of whose fibers Kz over ∂B1 bounds a strictly hypoconvex connected open set. Let K be the polynomialhull of K. Then we show that K∖K is the union of
graphs of analytic vector valued functions on B1. This result shows that an unnatural assumption regarding the deformability of K in an earlier version of this result is
unnecessary. Next, we study an H∞ optimization problem. If pis a C∞ real-valued function on ∂B1× Cn, we show that the infimum γρ = infƒ∈H
∞ (B1)n ‖ρ(z, ƒ (z))‖∞ is attained by a unique bounded ƒ provided that the set (z, w) ∈ ∂B1 × C n|ρ(z, w) ≤ γρ has bounded connected strictly hypoconvex fibers over the circle. 相似文献
995.
For any subset A of the unit sphere of a Banach space X and for [0,2) the notion of -flatness is introduced as a measure of non-flatness of A. For any positive , construction of locally finite tilings of the unit sphere by -flat sets is carried out under suitable -renormings of X in a quite general context; moreover, a characterization of spaces having separable dual is provided in terms of the existence of such tilings. Finally, relationships between the possibility of getting such tilings of the unit sphere in the given norm and smoothness properties of the norm are discussed. 相似文献
996.
Luigi?C.?BerselliEmail author Renato?ManfrinEmail author 《Journal of Evolution Equations》2004,4(2):193-211
In this paper we study some criteria for the full (space-time) regularity of weak
solutions to the Navier-Stokes equations. In particular, we generalize some
classical and very recent criteria involving the velocity, or its
derivatives. More specifically, we show with elementary tools that if a weak
solution, or its vorticity, is small in appropriate Marcinkiewicz spaces, then it
is regular. 相似文献
997.
The quasilinear degenerate evolution equation of parabolic type
0< t T considered in a Banach space X is written, putting Mv = u, in the from
0< t T, where A(u)=L(u)M–1 are multivalued linear operators in X for u K, K being a bounded ball ||u||Z<R in another Banach space Z continuously embedded in X. Existence and uniqueness of the local solution for the related Cauchy problem are given. The results are applied to quasilinear elliptic-parabolic equations and systems. 相似文献
998.
Haiyan Chen Jizhi Dai Yongzhi Liu 《International Journal of Infrared and Millimeter Waves》2004,25(12):1791-1798
IR integrated photonic amplifiers at 1.55m operation will have good foreground in optical phasedarray radars for splitters and signal processing. The saturation gain characteristics of IR integrated photonic waveguide amplifiers (taken Er3+Yb3+ co-doped phosphate glass waveguide amplifiers as an example) are studied theoretically. For the homemade laser glass materials the calculated saturation intensities are 2.22kw /cm2 for signal and 10.15kw/cm2 for pump. The effects of absorption saturation of signal and pump lights on the gain of amplifiers are discussed. 相似文献
999.
Neural Network Models for Finline Discontinuities 总被引:1,自引:0,他引:1
The radial basis network is used as the finline discontinuities electromagnetic artifical neural network(EMANN) models. EM software analysis is employed to characterize finline discontinuities. EMANN models are then trained using physical parameters and frequency as inputs and equivalent electric circuit element parameters of finline discontinuities as outputs. Once trained , the EMANN models can simulate equivalent electric circuit element parameters of finline step, notch and strip very fast and efficiently. 相似文献
1000.
We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date. 相似文献