The Wigner distribution function for the time-dependent quadratic Hamiltonian system in the coherent Schrödinger cat state is investigated. The type of state we consider is a superposition of two coherent states, which are by an angle of π out of phase with each other. The exact Wigner distribution function of the system is evaluated under a particular choice of phase, δ_{c, q}. Our development is employed for two special cases, namely, the Caldirola–Kanai oscillator and the frequency stable damped harmonic oscillator. On the basis of the diverse values of the Wigner distribution function that were plotted, we analyze the nonclassical behavior of the systems.

A new method based on the Clenshaw-Curtis quadrature for the numerical solution of the integro-differential Schrodinger equation is investigated. The method shows that it converges quickly and the truncation errors decrease faster than any power of the inverse number of the Chebyshev support points. Discretization technique is presented in detail. Accompanying C^+^+ code for the Fredholm type method is available upon request.

Diffraction by a flat airfoil in uniform flow in analytically examined, g on the acquisition of an accurate series solution for both low-and high-frequency incident waves. formulation of integral equations is based on the use of the Wiener-Hopf technique in the complex domain. As the kernels of the Integral equations are multivalued functions having a branch cut in the complex domain, the unknown in the integral operator is assumed to be a constant. Therefore, the solution is a zeroth-order approximate solution adequate for a high-frequency problem. In this stury, the unknown is expanded by a Taylor series of an arbitrary order in the analytic region, and the solution is obtained in series form involving a special function called a generalized gamma function Gamma(m) (u,z). As the generalized gamma functions occuring in finite diffraction theroy have the specific argument u as "nonnegative Integer +1/2," the authors used their previously determined exact and closed-form formulas of this special function to obtain the complete series solution. The present series solution exhibits faster convergence at a high frequency compared to a low frequency, whereas the Mathieu series solution in the elliptic coordinates converges faster at a low frequency relative to a higher frequency. Through exact and asymptotic evaluations of inverse Fourier transforms, the scattered and total acoustic fields are visualized in a physical domain and each term of the solution is physically interpreted as 1) semi-infinite leading-edge scattering, 2) trailing-edge correction, and 3) interaction between leading and trailing edges, respectively.

Exact formulas of generalized gamma functions, Γ _m (u, z), occurring in finite diffraction theory are derived in closed form for arbitrary m, u=n+1/2 (m and n are non-negative integers), and for both real and complex arguments z. For m=1 and real argument z, the formula consists of polynomials and the complementary error function. And, for m=1 and purely imaginary argument z occurring in the Wiener–Hopf integral equation for a finite diffraction problem, the formula is expressed by polynomials and the Fresnel integral which is a well-known function in mathematical theory of diffraction. The formulas for an arbitrary positive integer m are also obtained simply by differentiating Γ _m (u, z) with respect to z. These exact formulas are graphically shown and compared with Kobayashi's asymptotic formulas for various m and n values.

Abdalla et al. proposed a gateway-oriented password-based authenticated key exchange (GPAKE) protocol among a client, a gateway, and an authentication server, where a password is only shared between the client and the authentication server. The goal of their scheme is to securely establish a session key between the client and the gateway by the help of the authentication server without revealing any information on the password to the gateway. Recently, Byun et al. showed that Abdalla et al.'s GPAKE is insecure against undetectable on-line password guessing attacks. They also proposed a modified version to overcome the attacks. In this letter, we point out that Byun et al.'s modified GPAKE protocol is still insecure against the same attacks. We then make a suggestion for improvement.

Fingerprinting is a technique for generating a representation-independent functional signature for a game playing agent. Fingerprints can be used to compare agents across representations in an automatic fashion. The theory of fingerprints is developed for software agents that play the iterated prisoner's dilemma. Examples of the technique for computing fingerprints are given. This paper summarizes past results and introduces the following new results. Fingerprints of prisoner's dilemma strategies that are represented as finite-state machines must be rational functions. An example of a strategy that does not have a finite-state representation and which does not have a rational fingerprint function is given: the majority strategy. It is shown that the AllD- and AllC-based fingerprints can be derived from the tit-for-tat fingerprint by a simple substitution. Fingerprints for four new probe strategies are introduced, generalizing previous work in which tit-for-tat is the sole probe strategy. A trial comparison is made of evolved prisoner's dilemma strategies across three representations: finite-state machines, feedforward neural nets, and lookup tables. Fingerprinting demonstrates that all three representations sample the strategy space in a radically different manner, even though the neural net's and lookup table's parameters are alternate encodings of the same strategy space. This space of strategies is also a subset of those encoded by the finite-state representation. Shortcomings of the fingerprint technique are outlined, with illustrative examples, and possible paths to overcome these shortcomings are given.

Recently developed gene set analysis methods evaluate differential expression patterns of gene groups instead of those of individual genes. This approach especially targets gene groups whose constituents show subtle but coordinated expression changes, which might not be detected by the usual individual gene analysis. The approach has been quite successful in deriving new information from expression data, and a number of methods and tools have been developed intensively in recent years. We review those methods and currently available tools, classify them according to the statistical methods employed, and discuss their pros and cons. We also discuss several interesting extensions to the methods.

In the present work, we study the stationary Korteweg–de Vries (KdV) equation with a forcing for a flow of an inviscid and incompressible fluid. The stationary fKdV equation is defined in an infinite domain and it is reduced to a bounded domain by introducing absorbing boundary conditions. A new numerical method is proposed to solve this boundary value problem. New multiple numerical solitary wave solutions of the stationary KdV equation are discussed for various forcings. Numerical examples are provided to confirm and illustrate the accuracy and effectiveness of the method.