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1.
The Generalized Riemann Problem (GRP) for a nonlinear hyperbolic system of m balance laws (or alternatively “quasi-conservative” laws) in one space dimension is now well-known and can be formulated
as follows: Given initial-data which are analytic on two sides of a discontinuity, determine the time evolution of the solution
at the discontinuity. In particular, the GRP numerical scheme (second-order high resolution) is based on an analytical evaluation
of the first time derivative. It turns out that this derivative depends only on the first-order spatial derivatives, hence
the initial data can be taken as piecewise linear. The analytical solution is readily obtained for a single equation (m = 1) and, more generally, if the system is endowed with a complete (coordinate) set of Riemann invariants. In this case it
can be “diagonalized” and reduced to the scalar case. However, most systems with m > 2 do not admit such a set of Riemann invariants. This paper introduces a generalization of this concept: weakly coupled
systems (WCS). Such systems have only “partial set” of Riemann invariants, but these sets are weakly coupled in a way which
enables a “diagonalized” treatment of the GRP. An important example of a WCS is the Euler system of compressible, nonisentropic
fluid flow (m = 3). The solution of the GRP discussed here is based on a careful analysis of rarefaction waves. A “propagation of singularities”
argument is applied to appropriate Riemann invariants across the rarefaction fan. It serves to “rotate” initial spatial slopes
into “time derivative”. In particular, the case of a “sonic point” is incorporated easily into the general treatment. A GRP
scheme based on this solution is derived, and several numerical examples are presented. Special attention is given to the
“acoustic approximation” of the analytical solution. It can be viewed as a proper linearization (different from the approach
of Roe) of the nonlinear system. The resulting numerical scheme is the simplest (second-order, high-resolution) generalization
of the Godunov scheme. 相似文献
2.
Aequationes mathematicae - We prove that every K–subadditive set–valued map weakly K–upper bounded on a “large” set (e.g. not null–finite, not... 相似文献
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4.
Ron Aharoni 《Combinatorica》1984,4(1):1-6
Steffens [3] introduced a substructure (called below a “compressed set”) which prevents a graph from having a perfect matching,
and proved that a countable graph possesses a perfect matching if and only if it does not contain such a substructure. In
this paper we study some properties of compressed sets.
Dedicated to Paul Erdős on his seventieth birthday 相似文献
5.
We prove that for every polynomial-like holomorphic mapP, ifaεK (filled-in Julia set) and the componentK
aofK containinga is either a point ora is accessible along a continuous curve from the complement ofK andK
ais eventually periodic, thena is accessible along an external ray. Ifa is a repelling or parabolic periodic point, then the set of arguments of the external rays converging toa is a nonempty closed “rotation set”, finite (ifK
ais not a one point) or Cantor minimal containing a pair of arguments of external rays of a critical point in ℂ. In the Appendix
we discuss constructions via cutting and glueing, fromP to its external map with a “hedgehog”, and backward.
Partially supported by the Edmund Landau Center for Research in Mathematical Analysis, sponsored by the Minerva Foundation
(Germany).
Supported by the Polish KBN Grants 210469101 “Iteracje i Fraktale” and 210909101 “Uklady Dynamiczne”. 相似文献
6.
Stephen J. Wright 《Mathematical Programming》1987,37(2):232-252
Methods for minimization of composite functions with a nondifferentiable polyhedral convex part are considered. This class
includes problems involving minimax functions and norms. Local convergence results are given for “active set” methods, in
which an equality-constrained quadratic programming subproblem is solved at each iteration. The active set consists of components
of the polyhedral convex function which are active or near-active at the current iteration. The effects of solving the subproblem
inexactly at each iteration are discussed; rate-of-convergence results which depend on the degree of inexactness are given. 相似文献
7.
Sylvia Chiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,151(1):940-959
We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact
vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that
the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the
contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction”
solution.
We prove that this solution satisfies a family of convex entropies (in the Lax’s sense). Next, we construct an infinitely
large family of weak solutions to the “interaction”. Suppose further that any of these solutions satisfy a convex entropy,
it is necessary and suffcient that these solutions reduce to only the “no-effect-from-interaction” solution. In [1], Bouchut
constructed another entropy satisfying solution. As with other previous papers, it is obvious that it will not be sufficient
that a “correct” solution satisfies a convex entropy, in a non-strictly hyperbolic conservation laws system. 相似文献
8.
Sylvia Chiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):940-959
We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact
vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that
the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the
contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction”
solution.
We prove that this solution satisfies a family of convex entropies (in the Lax’s sense). Next, we construct an infinitely
large family of weak solutions to the “interaction”. Suppose further that any of these solutions satisfy a convex entropy,
it is necessary and suffcient that these solutions reduce to only the “no-effect-from-interaction” solution. In [1], Bouchut
constructed another entropy satisfying solution. As with other previous papers, it is obvious that it will not be sufficient
that a “correct” solution satisfies a convex entropy, in a non-strictly hyperbolic conservation laws system.
Research done in the University of Michigan-Ann Arbor, submission from Temasek Laboratories, National University of Singapore. 相似文献
9.
Sandra Saliani 《Constructive Approximation》2011,33(1):15-39
Wavelet packets provide an algorithm with many applications in signal processing together with a large class of orthonormal
bases of L
2(ℝ), each one corresponding to a different splitting of L
2(ℝ) into a direct sum of its closed subspaces. The definition of wavelet packets is due to the work of Coifman, Meyer, and
Wickerhauser, as a generalization of the Walsh system. A question has been posed since then: one asks if a (general) wavelet
packet system can be an orthonormal basis for L
2(ℝ) whenever a certain set linked to the system, called the “exceptional set” has zero Lebesgue measure. This answer to this
question affects the quality of wavelet packet approximation. In this paper we show that the answer to this question is negative
by providing an explicit example. In the proof we make use of the “local trace function” by Dutkay and the generalized shift-invariant
system machinery developed by Ron and Shen. 相似文献
10.
Shmuel Rosset 《Israel Journal of Mathematics》1981,39(3):255-258
We prove that the Brauer class of a crossed product is a sum of symbols iff its “local” components are. Analogously we show
that a solution of the “Goldie rank conjecture” would follow from the “local” statements; an extension of a result of Cliff-Sehgal
is an easy corollary. 相似文献
11.
Dušan Teodorović Vijay Varadarajan Jovan Popović Mohan Raj Chinnaswamy Sharath Ramaraj 《Annals of Operations Research》2006,143(1):123-131
In this paper, an “intelligent” isolated intersection control system was developed. The developed “intelligent” system makes
“real time” decisions as to whether to extend (and how much) current green time. The model developed is based on the combination
of the dynamic programming and neural networks. Many tests show that the outcome (the extension of the green time) of the
proposed neural network is nearly equal to the best solution. Practically negligible CPU times were achieved, and were thus
absolutely acceptable for the “real time” application of the developed algorithm. 相似文献
12.
In this paper, the Lax-Wendroff and “cabaret” schemes for the Buckley-Leverett equation are studied. It is shown that these schemes represent unstable solutions. The choice of an unstable solution depends on the Courant number only. A finite-element version of the “cabaret” scheme is given. 相似文献
13.
Michel Schreiber 《Israel Journal of Mathematics》1977,28(4):287-312
The “convex derived set” of a symmetric probability lawF on the real line is defined as the set of limits of laws ∗
j−1/k
n
F(t
j
n
η), inf 1≤j≤k
n t
j
n
→∞ ifn→∞ and the stable laws it contains are exhibited. A new criterion of stochastic compacity of the set of the powers of a probability
law is established. Finally, an isomorphism theorem between somel
p andL
0 spaces is given.
Laboratoire associé au C.N.R.S. no 224 “Processus stochastiques et applications”. 相似文献
Laboratoire associé au C.N.R.S. no 224 “Processus stochastiques et applications”. 相似文献
14.
D. -F. Li 《Fuzzy Optimization and Decision Making》2007,6(3):237-254
The aim of this paper is to develop a new fuzzy closeness (FC) methodology for multi-attribute decision making (MADM) in fuzzy
environments, which is an important research field in decision science and operations research. The TOPSIS method based on
an aggregating function representing “closeness to the ideal solution” is one of the well-known MADM methods. However, while
the highest ranked alternative by the TOPSIS method is the best in terms of its ranking index, this does not mean that it
is always the closest to the ideal solution. Furthermore, the TOPSIS method presumes crisp data while fuzziness is inherent
in decision data and decision making processes, so that fuzzy ratings using linguistic variables are better suited for assessing
decision alternatives. In this paper, a new FC method for MADM under fuzzy environments is developed by introducing a multi-attribute
ranking index based on the particular measure of closeness to the ideal solution, which is developed from the fuzzy weighted
Minkowski distance used as an aggregating function in a compromise programming method. The FC method of compromise ranking
determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum individual regret for
the “opponent”. A real example of a personnel selection problem is examined to demonstrate the implementation process of the
method proposed in this paper. 相似文献
15.
J. L. Lions 《Israel Journal of Mathematics》1972,13(1-2):155-172
A Bingham flow is described by a so-called variational inequality of evolution type which contains the Navier Stokes equations
as a particular case. These variational inequalities were introduced and studied by Duvaut and the author. We recall here
a number of known results for these “Bingham inequalities” and initiate the study of the behaviour of the solution when the
“viscosity” tends to zero. 相似文献
16.
For multidimensional equations of flow of thin capillary films with nonlinear diffusion and convection, we prove the existence
of a strong nonnegative generalized solution of the Cauchy problem with initial function in the form of a nonnegative Radon
measure with compact support. We determine the exact upper estimate (global in time) for the rate of propagation of the support
of this solution. The cases where the degeneracy of the equation corresponds to the conditions of “strong” and “weak” slip
are analyzed separately. In particular, in the case of “ weak” slip, we establish the exact estimate of decrease in the L
2-norm of the gradient of solution. It is well known that this estimate is not true for the initial functions with noncompact
supports.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 250–271, February, 2006. 相似文献
17.
We construct an asymptotics of the solution the Laplace equation in a “long” rectangle with the directional derivative given
on its “long sides” and Dirichlet data on its “short sides.” By using the asymptotics, we calculate one of the integral characteristics,
namely, the magnetoresistance. We obtain new formulas for the low-magnetic field magnetoresistance.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 520–532, April, 1999. 相似文献
18.
Shiran Rachmilevitch 《International Journal of Game Theory》2011,40(1):63-85
We provide new characterizations of the egalitarian bargaining solution on the class of strictly comprehensive n-person bargaining problems. The main axioms used in all of our results are Nash’s IIA and disagreement point monotonicity—an
axiom which requires a player’s payoff to strictly increase in his disagreement payoff. For n = 2 these axioms, together with other standard requirements, uniquely characterize the egalitarian solution. For n > 2 we provide two extensions of our 2-person result, each of which is obtained by imposing an additional axiom on the solution.
Dropping the axiom of anonymity, strengthening disagreement point monotonicity by requiring player i’s payoff to be a strictly decreasing function of the disagreement payoff of every other player j ≠ i, and adding a “weak convexity” axiom regarding changes of the disagreement point, we obtain a characterization of the class
of weighted egalitarian solutions. This “weak convexity” axiom requires that a movement of the disagreement point in the direction
of the solution point should not change the solution point. We also discuss the so-called “transfer paradox” and relate it
to this axiom. 相似文献
19.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
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