FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON－STRICTLY HYPERBOLIC SYSTEM

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.     

双曲分布及其在VaR模型分析中的应用

传统的计算V aR的R iskM etrics方法不能对市场风险分布的“厚尾”现象给出较为满意的刻画和计算方法.本文引入双曲分布及其算法并将双曲分布应用到V aR模型的计算之中,事实上通过对股票市场的实证研究表明,股票市场数据呈厚尾现象,用双曲分布对数据的拟合要比R iskM etrics方法假定的正态分布更符合金融市场数据的实际情况,故本文的结论与方法对金融风险管理和其他金融建模是有价值的.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

This paper is a continuation of the authors'previous paper[1].In this paper the authorsprove,assuming additional conditions on the initial data,some results about the existence anduniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolicsystem a_t+(au)_x_2au/x=0,u_t+1/2(a~2+u~2)_x=0,x>0,t≥0.     

ON HYPERBOLIC TIME DISCOUNTING IN EXHAUSTIBLE RESOURCE MODELS: AN APPLICATION TO WORLD OIL RESOURCES

ABSTRACT. Recent research on discounting in long term economic models involves hyperbolic discounting, in which the marginal discount rate shrinks as time passes. To investigate hyperbolic discounting and exhaustible resource allocation, this work develops a discrete‐time world oil model and model solution procedure, then uses the model to examine the consequences of adopting conventional (constant annual) discounting when hyperbolic discounting is appropriate, of adopting one hyperbolic discount rate path when a different hyperbolic path is appropriate, and of adopting hyperbolic discounting when conventional discounting is appropriate. Five conventional and two hyperbolic discount rate paths are considered. One hyperbolic path is that used by Nordhaus and Boyer [2000]; the other is that recommended by Weitzman [2001]. The generality of the findings is also assessed.     

Interference of probabilities and number field structure of quantum models

We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p‐adic representations.     

Low‐gain adaptive stabilization of semilinear second‐order hyperbolic systems

In this paper low‐gain adaptive stabilization of undamped semilinear second‐order hyperbolic systems is considered in the case where the input and output operators are collocated. The linearized systems have an infinite number of poles and zeros on the imaginary axis. The adaptive stabilizer is constructed by a low‐gain adaptive velocity feedback. The closed‐loop system is governed by a non‐linear evolution equation. First, the well‐posedness of the closed‐loop system is shown. Next, an energy‐like function and a multiplier function are introduced and the exponential stability of the closed‐loop system is analysed. Some examples are given to illustrate the theory. Copyright © 2004 John Wiley & Sons, Ltd.     

The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Monotonicity criteria for difference schemes designed for hyperbolic equations

Previously formulated monotonicity criteria for explicit two-level difference schemes designed for hyperbolic equations (S.K. Godunov’s, A. Harten’s (TVD schemes), characteristic criteria) are extended to multileveled, including implicit, stencils. The characteristic monotonicity criterion is used to develop a universal algorithm for constructing high-order accurate nonlinear monotone schemes (for an arbitrary form of the desired solution) based on their analysis in the space of grid functions. Several new fourth-to-third-order accurate monotone difference schemes on a compact three-level stencil and nonexpanding (three-point) stencils are proposed for an extended system, which ensures their monotonicity for both the desired function and its derivatives. The difference schemes are tested using the characteristic monotonicity criterion and are extended to systems of hyperbolic equations.     

在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.