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951.
Recently, folk questions on the smoothability of Cauchy hypersurfaces and time functions of a globally hyperbolic spacetime M, have been solved. Here we give further results, applicable to several problems:
Even more, accurate versions of this last result are obtained if the Cauchy hypersurface S were non-spacelike (including non-smooth, or achronal but non-acausal). 相似文献
(1) | Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, but a continuous extension (in fact, valid for any compact achronal subset K) is still possible. |
(2) | Given any spacelike Cauchy hypersurface S, a Cauchy temporal function (i.e., a smooth function with past-directed timelike gradient everywhere, and Cauchy hypersurfaces as levels) with is constructed – thus, the spacetime splits orthogonally as in a canonical way. |
952.
A.A. Zabolotskii 《Physica D: Nonlinear Phenomena》2008,237(4):540-550
We develop the inverse scattering transform for the recently found integrable system of reduced Maxwell-Bloch equations with two components of polarization and with an anisotropic dipole momentum. The model describes few-cycle pulses of optical or other field propagations. We find that the existence of a nontrivial group of symmetry of the corresponding Lax pair leads to a particular form of the inverse scattering transform equations. We show that solutions can be expressed in terms of the solution of a matrix Riemann-Hilbert problem formulated for the complex plane with a nontrivial group of automorphisms. 相似文献
953.
Cauchy problem for the generalized Davey-Stewartson systems in Besov spaces and some counterexamples
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In this paper, the Cauchy problem of the generalized ellipse-ellipse type Davey-Stewartson systems is discussed. When the dimension of space is greater than or equal to two, we get a unique global solution in Besov spaces by contraction mapping argument. Moreover, by using the F-expansion method, the exact periodic wave solutions for the generalized ellipse-ellipse type Davey-Stewartson systems are discussed, some counter examples are given. 相似文献
954.
Pingrun Li 《Journal of Applied Analysis & Computation》2019,9(3):1071-1082
In this paper, we study a class of singular integral-different equations of convolution type with Cauchy kernel. By means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation, we transform the equations into the Riemann-Hilbert problems with discontinuous coefficients and obtain the general solutions and conditions of solvability in class $\{0\}$. Thus, the result in this paper generalizes the classical theory of integral equations and boundary value problems. 相似文献
955.
956.
Masayuki Fujimoto 《Linear and Multilinear Algebra》2018,66(8):1564-1577
In this paper, by virtue of the matrix geometric mean and the polar decomposition, we present new Wielandt type inequalities for matrices of any size. To this end, based on results due to J.I. Fujii, we reform a matrix Cauchy–Schwarz inequality, which differs from ones due to Marshall and Olkin. As an application, we show a new block matrix version of Wielandt type inequalities under the block rank additivity condition. 相似文献
957.
958.
对改进的L’Hospital法则提供了一个证明,所用的知识主要是函数极限的定义和柯西中值定理,而后又提供四个例子,作为改进的L’Hospital法则的应用. 相似文献
959.
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called Dirac operator, which factorizes the Laplacian; monogenic functions may thus also be seen as a generalization of holomorphic functions in the complex plane. Hermitian Clifford analysis offers yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitian (or h-) monogenic functions, of two Hermitian Dirac operators which are invariant under the action of the unitary group. In Brackx et al. (2009) [8] a Clifford-Cauchy integral representation formula for h-monogenic functions has been established in the case of domains with smooth boundary, however the approach followed cannot be extended to the case where the boundary of the considered domain is fractal. At present, we investigate an alternative approach which will enable us to define in this case a Hermitian Cauchy integral over a fractal closed surface, leading to several types of integral representation formulae, including the Cauchy and Borel-Pompeiu representations. 相似文献
960.
We show that if −A generates a bounded α-times resolvent family for some α∈(0,2], then −Aβ generates an analytic γ-times resolvent family for and γ∈(0,2). And a generalized subordination principle is derived. In particular, if −A generates a bounded α-times resolvent family for some α∈(1,2], then −A1/α generates an analytic C0-semigroup. Such relations are applied to study the solutions of Cauchy problems of fractional order and first order. 相似文献