Convergence rates of cascade algorithms

We consider solutions of a refinement equation of the form

where is a finitely supported sequence called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the cascade algorithm associated with , i.e., the convergence of the sequence in the -norm.

Our main result gives estimates for the convergence rate of the cascade algorithm. Let be the normalized solution of the above refinement equation with the dilation matrix being isotropic. Suppose lies in the Lipschitz space , where 0$"> and . Under appropriate conditions on , the following estimate will be established:

where and is a constant. In particular, we confirm a conjecture of A. Ron on convergence of cascade algorithms.

     

Continuous-Time Controlled Markov Chains with Discounted Rewards

This paper studies denumerable state continuous-time controlled Markov chains with the discounted reward criterion and a Borel action space. The reward and transition rates are unbounded, and the reward rates are allowed to take positive or negative values. First, we present new conditions for a nonhomogeneous Q(t)-process to be regular. Then, using these conditions, we give a new set of mild hypotheses that ensure the existence of -optimal (0) stationary policies. We also present a martingale characterization of an optimal stationary policy. Our results are illustrated with controlled birth and death processes.     

Continuous-flow optical pumping NMR in a closed circuit system

In a typical continuous-flow optical pumping setup, the chemical shift of xenon in the adsorbed phase depends on the gas flow rate due to warming of the sample surface by the gas stream. Calibration of the system using the (207)Pb resonance of solid lead nitrate is necessary to determine the actual sample temperature. Optimum pulse repetition rates are strongly affected by gas flow and spin-lattice relaxation rates. The interplay of flow and pulse repetition rate alters signal intensity ratios and may lead to the complete suppression of signals.     

Transmutation of 129I, 237Np, 238Pu, 239Pu, and 241Am using neutrons produced in target-blanket system ‘Energy plus Transmutation’ by relativistic protons

Target-blanket facility ‘Energy + Transmutation’ was irradiated by proton beam extracted from the Nuclotron Accelerator in Laboratory of High Energies of Joint Institute for Nuclear Research in Dubna, Russia. Neutrons generated by the spallation reactions of 0.7, 1.0, 1.5 and 2 GeV protons and lead target interact with subcritical uranium blanket. In the neutron field outside the blanket, radioactive iodine, neptunium, plutonium and americium samples were irradiated and transmutation reaction yields (residual nuclei production yields) have been determined using γ-spectroscopy. Neutron field's energy distribution has also been studied using a set of threshold detectors. Results of transmutation studies of ¹²⁹I, ²³⁷Np, ²³⁸Pu, ²³⁹Pu and ²⁴¹Am are presented.      

The matrix rate of return

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous analysis of evolution of baskets parameterized by complex variables in both continuous and discrete time models.     

基于等额本息按揭贷款的脉冲增加还款模型

利用一阶线性差分方程建立了每隔半年增加还款一次的按揭贷款数学模型,并通过实例说明了其在经济生活中的具体应用.     

Initial guess by improved population-based intelligent algorithms for large inter-frame deformation measurement using digital image correlation

Digital image correlation (DIC) has received a widespread research and application in experimental mechanics. In DIC, the performance of subpixel registration algorithm (e.g., Newton-Raphson method, quasi-Newton method) relies heavily on the initial guess of deformation. In the case of small inter-frame deformation, the initial guess could be found by simple search scheme, the coarse-fine search for instance. While for large inter-frame deformation, it is difficult for simple search scheme to robustly estimate displacement parameters and deformation parameters simultaneously with low computational cost. In this paper, we proposed three improving strategies, i.e. Q-stage evolutionary strategy (T), parameter control strategy (C) and space expanding strategy (E), and then combined them into three population-based intelligent algorithms (PIAs), i.e. genetic algorithm (GA), differential evolution (DE) and particle swarm optimization (PSO), and finally derived eighteen different algorithms to calculate the initial guess for qN. The eighteen algorithms were compared in three sets of experiments including large rigid body translation, finite uniaxial strain and large rigid body rotation, and the results showed the effectiveness of proposed improving strategies. Among all compared algorithms, DE-TCE is the best which is robust, convenient and efficient for large inter-frame deformation measurement.     

The expectation hypothesis of interest rates and network theory: The case of Brazil

This paper investigates the topological properties of the Brazilian term structure of interest rates network. We build the minimum spanning tree (MST), which is based on the concept of ultrametricity, using the correlation matrix for interest rates of different maturities. We show that the short-term interest rate is the most important within the interest rates network, which is in line with the Expectation Hypothesis of interest rates. Furthermore, we find that the Brazilian interest rates network forms clusters by maturity.     

索赔次数为复合Poisson-Geometric过程的常利率风险模型的罚金函数

讨论了常利率下索赔次数为复合Poisson-Geometric过程的风险模型的罚金函数,得到了罚金函数的期望所满足的积分方程,并由所得到的积分方程推出了破产概率所满足的积分方程,初始盈余为0时,得到了罚金函数的期望及破产概率的精确解.     

On the asymptotic behaviour for an electromagnetic system with a dissipative boundary condition

In this work we study some properties of solutions for the systemdescribing a three-dimensional non-homogeneous non-conductingdielectric with a general boundary condition with memory. Wefirst show the existence of the inverse of this boundary condition,which allows us to introduce a boundary free energy, similarto the one considered by Fabrizio & Morro (1996, Arch. Rat.Mech. Anal., 136, 359–381). Then, we prove existence anduniqueness theorems for weak and strong solutions of the evolutiveproblem in a finite time interval. Moreover, following Rivera& Olivera (1997, Boll. U.M.I., 11-A, 115–127), weexamine some dissipative properties of the boundary conditionand of its inverse and we give a useful energy estimate. Finally,when there is no memory in the boundary condition the exponentialdecay of the solution is proved.