Steady solution of solitary wave and linear shear current interaction

The steady solution of a solitary wave propagating in the presence of a linear shear background current is investigated by the Green–Naghdi (GN) equations. The steady solution is obtained by use of the Newton–Raphson method. Three aspects are investigated; they are the wave speed, wave profile and velocity field. The converged GN results are compared with results from the literature. It is found that for the opposing-current case of the solitary wave with a small amplitude, the results of the GN equations match results from the literature well, while for the solitary wave with a large amplitude, results from the literature are seen to be not as accurate. In the following-current case, though the amplitude of the solitary wave is small, the GN results are shown to be accurate. The velocity along the water column at the wave crest and the velocity field for different cases are calculated by the GN equations. The results of the GN equations show obvious differences when compared with the results obtained by superposing the no-current results and linear shear current linearly. We find that for the same current strength, the vortex is stronger for the steep solitary-wave case than that for the small solitary-wave case.     

Adaptive refinement procedure for the finite difference method

An adaptive refinement procedure consisting of a localized error estimator and a physically based approach to mesh refinement is developed for the finite difference method. The error estimator is a variation of a successful finite element error estimator. The errors are estimated by computing an error energy norm in terms of discontinuous and continuous stress fields formed from the finite difference results for plane stress problems. The error measure identifies regions of high error which are subsequently refined to improve the result. The local refinement procedure utilizes a recently developed approach for developing finite difference templates to produce a graduated mesh. The adaptive refinement procedure is demonstrated with a problem that contains a well-defined singularity. The results are compared to finite element and uniformly refined finite difference results.     

泛函积分方程的正解与应用

运用锥拉伸与压缩不动点定理,研究一类泛函积分方程的正解．把所得结果应用于研究常微分方程积分边值问题正解的存在性,所得结果推广和本质上改进了马如云等作者最近的一些结果．     

Treatment Evaluation—A Modelling Approach with Application to Acute Myeloid Leukaemia

The work described in the paper was developed during a project carried out jointly by the DHSS OR Unit and a hospital department specializing in the management of acute myeloid leukaemia. One of the aims of this project was to develop a methodology for comparing the results of treatment of patients treated in different clinical trials.The standard OR approach was adopted of using a mathematical model of the results of treatment in a trial as a basis for such comparisons. The paper describes how such a model was built for a particular treatment trial and then used to compare the results of this trial with those obtained in another trial. This comparison indicated important differences between the results of the treatment trials.     

Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming

In this paper it is shown that, in the absence of any regularity condition, sequential Lagrangian optimality conditions as well as a sequential duality results hold for abstract convex programs. The significance of the results is that they yield the standard optimality and duality results for convex programs under a simple closed-cone condition that is much weaker than the well-known constraint qualifications. As an application, a sequential Lagrangian duality, saddle-point conditions, and stability results are derived for convex semidefinite programs.The authors are grateful to the referee and Professor Franco Giannessi for valuable comments and constructive suggestions which have contributed to the final preparation of the paper.     

On the negative value of information in informationally inefficient markets: Calculations for large number of traders

In informationally inefficient markets, classical decision theory assumes the value of information to be positive. Recent developments, however, contradict this paradigm. Schredelseker [Schredelseker, K., 2001. Is the usefulness approach useful? Some reflections on the utility of public information. In: McLeay, S., Riccaboni, A. (Eds.), Contemporary Issues in Accounting Regulation, Kluwer Academic Publishers, Boston, pp. 135–153] proposed a simulation model wherein a single security is traded among non-cooperating and asymetrically informed traders. One of the main results was the fact that badly informed traders could expect higher returns than traders with more information. But Schredelseker was able to give exact results for a small number of traders only. The aim of this paper is to give reliable results for a sufficiently large number of traders for both the expected gain and the probability of gain larger than zero. We are using combinatorial methods in order to get exact results for badly informed traders and simulation techniques for results of traders with higher level of information. The exact results are used (error between exact results and simulation results for the first traders) to determine the number of samples which have to be drawn with the simulation algorithm.     

Classification accuracy and correlation: LDA in failure prediction

The relationship between canonical correlation and classification accuracy in linear discriminant analysis is explored mathematically. The discriminant score is assumed to conform to a uniform distribution on the interval (0, 1]. This distribution is used as a reference distribution to extract a minimum correlation for certain classification accuracy. Four different cases are analyzed. First, a case for equal group size is considered for an overall accuracy of 100%. Second, the results are generalized for unequal group size. Third, existence of discordant observations is allowed. Fourth, the effect of concentration is analyzed for the first case. The results are demonstrated by numerical examples. In addition, a sample of 2092 default and 63,072 non-default Finnish firms are used to empirically illustrate the results in the context of failure prediction. The results show that group size of default firms, number of discordant observations, and bipolar concentration of observations strongly affect both canonical correlation and classification accuracy.     

Support Theorems for the Radon Transform and Cramér-Wold Theorems

This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform lead to Cramér-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists interesting results for the Radon transform that have been developed essentially during the 1980s and 1990s.     

Properties of serial kanban systems

In this paper we show some structural results of a kanban system by using results about the underlying GSMP. The main results from this connection are: dominance of allocations, optimal partition, upper and lower bounds on throughput, consistency of the IPA derivative, convexity of throughput as a function of service time parameters and concavity of throughput with respect to number of kanbans. Although the dominance and the partition results were obtained previously by sample path arguments, the proofs here are less cumbersome and generalize the earlier results. The second-order properties for kanban lines are new. These results form a basis for results in multi-product lines where proofs by sample paths require extensive notation.     

Stability of solutions to a mathematical model for necrotic tumor growth with time delays in proliferation

In this paper, a mathematical model for a solid avascular tumor growth is studied. The model describes tumor growth with a necrotic core and a time delay in proliferation process. The model was proposed by Byrne and Chaplain, and was studied by M. Bodnar and U. Fory? (see [2]). Sufficient conditions which guarantee existence, uniqueness and stability of steady state are given. The results show that the dynamical behavior of the solutions of the model is similar to that of the solutions for the corresponding non-retarded problem under some assumptions. Our results partially improve the corresponding results given by M. Bodnar and U. Fory?. The results make the research for this model more perfect.     

Runtime Analysis of Ant Colony Optimization with Best-So-Far Reinforcement

The paper provides some theoretical results on the analysis of the expected time needed by a class of Ant Colony Optimization algorithms to solve combinatorial optimization problems. A part of the study refers to some general results on the expected runtime of the considered class of algorithms. These results are then specialized to the case of pseudo-Boolean functions. In particular, three well known functions and a combination of two of them are considered: the OneMax, the Needle-in-a-Haystack, the LeadingOnes, and the OneMax-Needle-in-a-Haystack. The results obtained for these functions are also compared to those from the well-investigated (1+1)-Evolutionary Algorithm. The results shed light on a suitable parameter choice for the considered class of algorithms. Furthermore, it turns out that for two of the four studied problems, the expected runtime for the considered class, expressed in terms of the problem size, is of the same order as that for (1+1)-Evolutionary Algorithm. For the other two problems, the results are significantly in favour of the considered class of Ant Colony Optimization algorithms.      

Banach空间中有限个一致李普希兹渐近伪压缩映射的强收敛定理

目的是把对单个渐近T为压缩映射的迭代结果推广到有限个渐近T为压缩映射上.为此,利用数学归纳法的思想,在一定条件下,得出了有限个渐近T为压缩映射强收敛于其公共不动点的结论.此结论推广了以前的结果.     

A Spectral Method for the Electrohydrodynamic Flow in a Circular Cylindrical Conduit

This paper presents a combination of the hybrid spectral collocation technique and the spectral homotopy analysis method(SHAM for short) for solving the nonlinear boundary value problem(BVP for short) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. The accuracy of the present solution is found to be in excellent agreement with the previously published solution. The authors use an averaged residual error to find the optimal convergence-control parameters. Comparisons are made between SHAM generated results, results from literature and Matlab ode45 generated results, and good agreement is observed.     

A generalized f-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities

The purpose of this paper is to present new hybrid Ishikawa iteration process by the generalized f-projection operator for finding a common element of the fixed point set for two countable families of weak relatively nonexpansive mappings and the set of solutions of the system of generalized Ky Fan inequalities in a uniformly convex and uniformly smooth Banach space. Furthermore, we show that our new iterative scheme converges strongly to a common element of the afore mentioned sets. As applications, we apply our results to obtain some new results for finding a solution of a common fixed point of two countable in finite families, a system of generalized Ky Fan inequalities and a common zero-point problem for general B-monotone and maximal monotone operators in Banach spaces. The results presented in this paper improve and extend important recent results.     

Hilbert空间中混合平衡问题与非扩张半群的强收敛定理

在Hilbert空间中引进并研究了一种新的迭代算法,借以寻求混合平衡问题解集与非扩张半群不动点集的一公共元.所得到的结果,推广并改进了最近一些人所发布的新结果.     

Large deviations for stochastic flows and their applications

Large deviations for stochastic flow solutions to SDEs containing a small parameter are studied. The obtained results are applied to establish a C_p,r,-large deviation principle for stochastic flows and for solutions to anticipating SDEs. The recent results of Millet-Nualart-Sans and Yoshida are improved and refined.     

On the Financial Value of Information

Results of Kelly [5] and Breiman [2] relating optimal growth rates for gambling and investing to information distances are generalised to include return distributions for virtually any type of game or asset. These results are achieved by first introducing the notion of the optimal financial derivative instrument for a given gamble or investment and then solving the related optimisation problem. For assets varying continuously over time, a formula for optimal dynamic portfolio adjustment follows for commonly occurring models, assuming no transaction costs. The latter results are applied to assets with normal and lognormal returns. The results for these are demonstrated using simulation.     

Measures and Integrals in Conditional Set Theory

The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In particular, this extends the usual representation results for separable spaces.     

Barndorff-Nielsen and Shephard model: oil hedging with variance swap and option

In this paper the Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for the oil commodity from the Bakken, a new region of oil extraction that is benefiting from fracking technology. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The results indicate that oil can be optimally hedged with the use of a combination of options and variance swaps. Theoretical results related to the variance process are established and implemented for the analysis of the variance swap. In this paper we also determined the optimal amount of the underlying oil commodity that has to be held for minimizing the hedging error. The model and analysis are used to numerically analyze hedging decisions for managing price risk in Bakken oil commodities. From the numerical results, a number of important features of the usefulness of the Barndorff-Nielsen and Shephard model are illustrated.