Discrete models in time and space of Fishers equation, ∂u ∂t = ∂ 2 u ∂x 2 + f(u) , in reaction diffusion are numerous in mathematical biology ( Weinberger, SIAM J. Math. Anal. 13 , 353 (1982) and the references therei...
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Discrete models in time and space of Fishers equation, ∂u ∂t = ∂ 2 u ∂x 2 + f(u) , in reaction diffusion are numerous in mathematical biology ( Weinberger, SIAM J. Math. Anal. 13 , 353 (1982) and the references therein). For f ( u ) = u (1− u ) and no dissipation, May ( Nature 261 , 459 (1976) ), using the Euler discretization of the time derivative, found stable solutions (period 2 in time) provided the time step satisfies 2 < k ⩽ √6, the linearized stability for period 1 solutions being 0 < k ⩽ 2. When the dissipation term in discretised form is added to May's ordinary difference scheme, it is shown by 4. , 6. , and Sleeman ( Proc. Roy. Soc. London Ser. A 425 , 17 (1989) ) that the stable period 2 in time solutions persist. Here it is shown (Sleeman, op. cit. ), that when the dissipation term in continuous form is added to May's difference equation, solutions period 2 in time for each value of x satisfy a Hamiltonian system in space. The latter, being non integrable, is solved numerically by Symplectic difference schemes constructed to maintain the values of the Hamiltonain energy up to large values of the space variable ( 1. , 2. ). The shape of the solution, in calculations involving 200,000 space steps, is shown to depend crucially on the type and location of the fixed points of the Hamiltonian system in phase space at the position of the initial data at x =0 relative to these fixed points.
In a previous work, quasidiscrete quantum Markov processes were considered. In order to describe certain continuum situations, the concept of a regular quantum Markov process is now developed. First, the general theor...
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In a previous work, quasidiscrete quantum Markov processes were considered. In order to describe certain continuum situations, the concept of a regular quantum Markov process is now developed. First, the general theory of such processes will be presented. Then, methods for constructing these processes will be considered. To accomplish this, the classical construction of measures on trajectory spaces to complex measures is generalized. A class of processes that have an associated family of transition amplitude operators is constructed. The paper concludes with various examples that illustrate the theory.
For a large class of linear mixed type partial differential equations, theorems on local and semi-global solvability are stated and rely on a prior result of the author about the non-trapping of null-bicharacteristics...
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For a large class of linear mixed type partial differential equations, theorems on local and semi-global solvability are stated and rely on a prior result of the author about the non-trapping of null-bicharacteristics over compact sets and the theory of Hormander. A global solvability result module smooth error is demonstrated for a slightly reduced class which includes the equations found most commonly in the literature. The key point is the proof of an additional global convexity property for the bicharacteristic flow which results from the construction of a type of convex hull. All of the results are independent of lower order terms as they depend only on the Hamiltonian system associated to the principal symbol. This independence allows for the interpretation of the results in the context of general relativity and semi-Riemannian geometry. (C) 1997 Academic Press.
In the last few decades,gravastars have been proposed as an alternative to black *** stability of a gravastar has been examined in many modified theories of gravity along with Einstein's *** f(Q,T)gravity,a succes...
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In the last few decades,gravastars have been proposed as an alternative to black *** stability of a gravastar has been examined in many modified theories of gravity along with Einstein's *** f(Q,T)gravity,a successfully modified theory of gravity for describing the current accelerated expansion of the universe,has been used in this study to examine gravastar in different *** to Mazur and Mottola[***.101,9545(2004);Gravitational condensate stars:An alternative to black holes,I12-011,(2002)],a gravastar has three regions with three different equations of *** this study,we examined the interior of a gravastar by consid-ering p=-ρ EoS to describe the dark sector for the interior *** next region is a thin shell of ultrarelativistic stiff fluid,in which we investigated several physical properties,including proper length,energy,entropy,and surface energy ***,we examined the surface redshift and speed of sound to check the potential stability of our proposed thin-shell gravastar ***,we used the entropy maximization technique to verify the stability of the gravastar model.A gravastar's outer region is a complete vacuum described by exterior Schwarzschild ***,we presented a stable gravastar model,which is singularity-free and devoid of any incom-pleteness in classical black hole theory.
Investigates the dual relationship between systems and their users in the context of information systems. Summarizes the result as system-user duality, which contains two facets: multiple-user views on a single logica...
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Investigates the dual relationship between systems and their users in the context of information systems. Summarizes the result as system-user duality, which contains two facets: multiple-user views on a single logical system, and a single physical system adapted to multiple-user models. Not only gives a better understanding on the role of users in systems, but also suggests an important principle of designing systems adapted to user models.
We present a new concept for online multiobjective optimization and its application to the optimization of the operating point assignment for a doubly-fed linear motor. This problem leads to a time-dependent multiobje...
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A new family of binary cyclic (n,(n + 1)/2) and (n,(n - 1)/2) codes are introduced, which include quadratic residue (QR) codes when n is prime. These codes are defined in terms of their idempotent generators, and they...
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A new family of binary cyclic (n,(n + 1)/2) and (n,(n - 1)/2) codes are introduced, which include quadratic residue (QR) codes when n is prime. These codes are defined in terms of their idempotent generators, and they exist for all odd n = p_{1}^{a_{1}} p_{2}^{a_{2}} \cdots p_{r}^{a_{r}} where each p_{i} is a prime \equiv \pm 1 \pmod{8} . Dual codes are identified. The minimum odd weight of a duadic (n,(n + 1)/2) code satisfies a square root bound. When equality holds in the sharper form of this bound, vectors of minimum weight hold a projective plane. The unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent (73,37,9) duadic codes. All duadic codes of length less than 127 are identified, and the minimum weights of their extensions are given. One of the duadic codes of length 113 has greater minimum weight than the QR code of that length.
For graphs G and H we write G ind under right arrow H if every 2-edge colouring of G yields an induced monochromatic copy of H. The induced Ramsey number for H is defined as r(ind)(H) = min{\V/(G)\: G ind under right ...
For graphs G and H we write G ind under right arrow H if every 2-edge colouring of G yields an induced monochromatic copy of H. The induced Ramsey number for H is defined as r(ind)(H) = min{\V/(G)\: G ind under right arrow H}. We show that for every d greater than or equal to 1 there exists an absolute constant C-d such that r(ind)(H-n,H- d) less than or equal to n(cd) for every graph H-n,H- d with n vertices and the maximum degree at most d. This confirms a conjecture suggested by W.T. Trotter. (C) 1996 Academic Press, Inc.
We define a class of codes that corresponds to a class of matroids called paving matroids. This class of codes includes maximum-distance-separable (MDS) codes, and some other interesting codes such as the (12, 6) tern...
We define a class of codes that corresponds to a class of matroids called paving matroids. This class of codes includes maximum-distance-separable (MDS) codes, and some other interesting codes such as the (12, 6) ternary Golay code. Some basic properties of these codes are established using techniques from matroid theory. Our results raise a natural existence question to which we obtain partial answers using known results about the non-existence of Steiner systems of the type S(t - 1, t, 2t).
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