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61.
M. Frigon 《Journal of Fixed Point Theory and Applications》2007,1(2):189-194
We present results on the global existence of analytic solutions to the Cauchy problem in starshaped or convex complex domains.
No growth conditions are imposed. Our results rely on a notion of solution-tube that we introduce.
à la mémoire de Jean Leray 相似文献
62.
63.
Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4 相似文献
64.
Marilyn Breen 《Journal of Geometry》1989,36(1-2):8-16
LetS be a compact, simply connected set inR
2. If every boundary point ofS is clearly visible viaS from at least one of the three pointsa, b, c, thenS is a union of three starshaped sets whose kernels containa, b, c, respectively. The result fails when the number three is replaced by four.As a partial converse, ifS is a union of three starshaped sets whose kernels containa, b, c, respectively, then the set of points in the boundary ofS clearly visible from at least one ofa, b, orc is dense in the boundary ofS.Supported in part by NSF grant DMS-8705336. 相似文献
65.
Summary We consider a class of infinite delay equations of neutral type which includes Volterrra type integral und integrodifferential equations. Using abstract approximation results (cf. Trotter-Kato-type) for strongly continuous semigroups we develop an approximation scheme which is based on approximation of the system state by Laguerre (and Legendre) polynomials. Numerical examples demonstrate the feasibility of the scheme and show infinite order convergence for smooth data.Supported in part by the Air Force Office of Scientific Research under Contracts AFORS-84-0398 and AFORS-85-0303 and the National Aeronautics and Space Administration under NASA Grant NAG-1-517 and by NSF under Grant UINT-8521208Supported in part by the Air Force Office of Scientific Research under Contract AFORS-84-0398 and in part by the Fonds zur Förderung der wissenschaftlichen Forschung, Austria, under project No. S3206 相似文献
66.
Valery Agoshkov Paola Gervasio Alfio Quarteroni 《Mediterranean Journal of Mathematics》2006,3(2):147-176
New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second
order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence
results are proved for the coupled problem, and the convergence of iterative processes is analyzed.
The work was supported by the Russian Foundation for Basic Research (04-01-00615) and it was partly carried out while the
first author was visiting the IACS at EPFL. 相似文献
67.
We introduce symmetric Boundary Value Methods for the solution of second order initial and boundary value problems (in particular
Hamiltonian problems). We study the conditioning of the methods and link it to the boundary loci of the roots of the associated
characteristic polynomial. Some numerical tests are provided to assess their reliability.
Dedicated to the memory of Professor Aldo Cossu 相似文献
68.
Martin Loebl 《Advances in Mathematics》2007,211(2):546-565
We define a q-chromatic function and q-dichromate on graphs and compare it with existing graph functions. Then we study in more detail the class of general chordal graphs. This is partly motivated by the graph isomorphism problem. Finally we relate the q-chromatic function to the colored Jones function of knots. This leads to a curious expression of the colored Jones function of a knot diagram K as a chromatic operator applied to a power series whose coefficients are linear combinations of long chord diagrams. Chromatic operators are directly related to weight systems by the work of Chmutov, Duzhin, Lando and Noble, Welsh. 相似文献
69.
We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes. 相似文献
70.
Piotr Borodulin-Nadzieja 《Topology and its Applications》2007,154(18):3107-3124
We investigate properties of minimally generated Boolean algebras. It is shown that all measures defined on such algebras are separable but not necessarily weakly uniformly regular. On the other hand, there exist Boolean algebras small in terms of measures which are not minimally generated. We prove that under CH a measure on a retractive Boolean algebra can be nonseparable. Some relevant examples are indicated. Also, we give two examples of spaces satisfying some kind of Efimov property. 相似文献