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61.
In this paper we prove a new Representation Formula for slice regular functions, which shows that the value of a slice regular function f at a point q=x+yI can be recovered by the values of f at the points q+yJ and q+yK for any choice of imaginary units I,J,K. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a much larger class of domains, called axially symmetric domains. We show, in particular, that axially symmetric domains play, for slice regular functions, the role played by domains of holomorphy for holomorphic functions. 相似文献
62.
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models.Where well posedness was known only locally in time,it is here extended to all of R+.The result... 相似文献
63.
Rinaldo M. Colombo Helge Holden 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(5):131
In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial data in the subsonic regime, with small total variation about a stationary solution. The proof relies on the front-tracking method and is based on [1]. 相似文献
64.
Y. Aharonov F. Colombo I. Sabadini D. C. Struppa J. Tollaksen 《Journal of Fourier Analysis and Applications》2016,22(4):751-767
In a series of papers (J Phys A 44:365304, 2011; Complex Anal Oper Theory 7:1299–1310, 2013; J Math Pures Appl 99:165–173, 2013; J Math Pures Appl 103:522–534, 2015), we have investigated some mathematical properties of superoscillating sequences in one variable, and their persistence in time. In this paper we study the notion of superoscillation in several variables and we show how to construct examples of sequences that exhibit this property. 相似文献
65.
Fabrizio Colombo Samuele Mongodi Marco Peloso Stefano Pinton 《Mathematical Methods in the Applied Sciences》2019,42(5):1662-1686
Let e?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory. 相似文献
66.
67.
We consider the problem of sending a message from a sender to a receiver through an unreliable network by specifying in a protocol what each vertex is supposed to do if it receives the message from one of its neighbors. A protocol for routing a message in such a graph is finite if it never floods with an infinite number of copies of the message. The expected reliability of a given protocol is the probability that a message sent from reaches when the edges of the network fail independently with probability .We discuss, for given networks, the properties of finite protocols with maximum expected reliability in the case when is close to 0 or 1, and we describe networks for which no one protocol is optimal for all values of . In general, finding an optimal protocol for a given network and fixed probability is challenging and many open problems remain. 相似文献
68.
Rinaldo M. Colombo Francesca Marcellini 《Journal of Mathematical Analysis and Applications》2010,361(2):440-456
Consider the p-system describing the subsonic flow of a fluid in a pipe with section a=a(x). We prove that the resulting Cauchy problem generates a Lipschitz semigroup, provided the total variation of the initial datum and the oscillation of a are small. An explicit estimate on the bound of the total variation of a is provided, showing that at lower fluid speeds, higher total variations of a are acceptable. An example shows that the bound on TV(a) is mandatory, for otherwise the total variation of the solution may grow arbitrarily. 相似文献
69.
Fabrizio Colombo Graziano Gentili Irene Sabadini 《Annals of Global Analysis and Geometry》2010,37(4):361-378
In this article, we show how to construct a regular, non-commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results. 相似文献
70.
This paper proposes a problem decomposition approach to solve hard Frequency Assignment Problem instances with standard meta-heuristics. The proposed technique aims to divide the initial problem into a number of easier subproblems, solve them and then recompose the partial solutions into one of the original problem. We consider the COST-259 MI-FAP instances and other Cardiff University test problems in order to simulate larger and more realistic networks. For both benchmarks the standard implementations of meta-heuristics do not generally produce a satisfactory performance within reasonable times of execution. However, the decomposed assignment approach can improve their results, both in terms of solution quality and runtime. 相似文献