Universality of the Stochastic Airy Operator

We introduce a new method for studying universality of random matrices. Let T-n be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, Tn converges to the stochastic Airy operator. In particular, the top edge of the Dyson beta ensemble and the corresponding eigenvectors are universal. As a byproduct, these ideas lead to conjectured operator limits for the entire family of soft edge distributions. (C) 2015 Wiley Periodicals, Inc.

Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

Trace Formulae in Operator Theory

In this article, we survey several kinds of trace formulas that one encounters in the theory of single and multi-variable operators. We give some sketches of the proofs, often based on the principle of finite-dimensional approximations to the objects at hand in the formulas.

Action of Hopf on the twisted modular Hecke operator

Let Gamma subset of SL2(Z) be a principal congruence subgroup. For each sigma is an element of SL2(Z), we introduce the collection A(sigma)(Gamma) of modular Hecke operators twisted by sigma. Then, A(sigma)(Gamma) is a right A(Gamma)-module, where A(Gamma) is the modular Hecke algebra introduced by Connes and Moscovici. Using the action of a Hopf algebra h(0) on A(sigma)(Gamma), we define reduced Rankin-Cohen brackets on A(sigma)(Gamma). Moreover A(sigma)(Gamma) carries an action of H 1, where H 1 is the Hopf algebra of foliations of codimension 1. Finally, we consider operators between the levels A(sigma)(Gamma), sigma is an element of SL2(Z). We show that the action of these operators can be expressed in terms of a Hopf algebra h(Z).

Selection of Optimal Time-to-go in Generalized Vector Explicit Guidance

A new method of selection of time-to-go (t(go)) for Generalized Vector Explicit Guidance (GENEX) law have been proposed in this paper. t(go) is known to be an important parameter in the control and cost function of GENEX guidance law. In this paper the formulation has been done to find an optimal value of t(go) that minimizes the performance cost. Mechanization of GENEX with this optimal t(go) reduces the lateral acceleration demand and consequently increases the range of the interceptor. This new formulation of computing t(go) comes in closed form and thus it can be implemented onboard. This new formulation is applied in the terminal phase of an surface-to-air interceptor for an angle constrained engagement. Results generated by simulation justify the use of optimal t(go).

On the Capacity and Performance of Generalized Spatial Modulation

Generalized spatial modulation (GSM) uses N antenna elements but fewer radio frequency (RF) chains (R) at the transmitter. In GSM, apart from conveying information bits through R modulation symbols, information bits are also conveyed through the indices of the R active transmit antennas. In this letter, we derive lower and upper bounds on the the capacity of a (N, M, R)-GSM MIMO system, where M is the number of receive antennas. Further, we propose a computationally efficient GSM encoding method and a message passing-based low-complexity detection algorithm suited for large-scale GSM-MIMO systems.

Quantum stochastic calculus associated with quadratic quantum noises

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie dagger-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Ito formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus. (C) 2016 AIP Publishing LLC.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

A Generalized Soft-Sphere for Monte Carlo Simulation

A new collision model, called the generalized soft-sphere (GSS) model, is introduced. It has the same total cross section as the generalized hard-sphere model [Phys. Fluids A 5, 738 (1993)], whereas the deflection angle is calculated by the soft-sphere scattering model [Phys. Fluids A 3, 2459 (1991)]. In virtue of a two-term formula given to fit the numerical solutions of the collision integrals for the Lennard-Jones (6-12) potential and for the Stockmayer potential, the parameters involved in the GSS model are determined explicitly that may fully reproduce the transport coefficients under these potentials. Coefficients of viscosity, self-diffusion and diffusion for both polar and nonpolar molecules given by the GSS model and experiment are in excellent agreement over a wide range of temperature from low to high.

Predictions for Partial-Dislocation-Mediated Processes in Nanocrystalline Ni by Generalized Planar Fault Energy Curves: An Experimental Evaluation

Generalized planar fault energy (GPFE) curves have been used to predict partial-dislocation-mediated processes in nanocrystalline materials, but their validity has not been evaluated experimentally. We report experimental observations of a large quantity of both stacking faults and twins in nc Ni deformed at relatively low stresses in a tensile test. The experimental findings indicate that the GPFE curves can reasonably explain the formation of stacking faults, but they alone were not able to adequately predict the propensity of deformation twinning.

A generalized self-consistent method accounting for fiber section shape

A three-phase confocal elliptical cylinder model is proposed for fiber-reinforced composites, in terms of which a generalized self-consistent method is developed for fiber-reinforced composites accounting for variations in fiber section shapes and randomness in fiber section orientation. The reasonableness of the fiber distribution function in the present model is shown. The dilute, self-consistent, differential and Mori-Tanaka methods are also extended to consider randomness in fiber section orientation in a statistical sense. A full comparison is made between various micromechanics methods and with the Hashin and Shtrikman's bounds. The present method provides convergent and reasonable results for a full range of variations in fiber section shapes (from circular fibers to ribbons), for a complete spectrum of the fiber volume fraction (from 0 to 1, and the latter limit shows the correct asymptotic behavior in the fully packed case) and for extreme types of the inclusion phases (from voids to rigid inclusions). A very different dependence of the five effective moduli on fiber section shapes is theoretically predicted, and it provides a reasonable explanation on the poor correlation between previous theory and experiment in the case of longitudinal shear modulus.

An Extension of 2D Janbu’s Generalized Procedure of Slices for 3D Slope Stability Analysis II—Numerical Method and Applications

This paper provides a numerical approach on achieving the limit equilibrium method for 3D slope stability analysis proposed in the theoretical part of the previous paper. Some programming techniques are presented to ensure the maneuverability of the method. Three examples are introduced to illustrate the use of this method. The results are given in detail such as the local factor of safety and local potential sliding direction for a slope. As the method is an extension of 2D Janbu's generalized procedure of slices (GPS), the results obtained by GPS for the longitudinal sections of a slope are also given for comparison with the 3D results. A practical landslide in Yunyang, the Three Gorges, of China, is also analyzed by the present method. Moreover, the proposed method has the advantages and disadvantages of GPS. The problem frequently encountered in calculation process is still about the convergency, especially in analyzing the stability of a cutting corner. Some advice on discretization is given to ensure convergence when the present method is used. However, the problem about convergency still needs to be further explored based on the rigorous theoretical background.

Discriminative language model adaptation for Mandarin broadcast speech transcription and translation

This paper investigates unsupervised test-time adaptation of language models (LM) using discriminative methods for a Mandarin broadcast speech transcription and translation task. A standard approach to adapt interpolated language models to is to optimize the component weights by minimizing the perplexity on supervision data. This is a widely made approximation for language modeling in automatic speech recognition (ASR) systems. For speech translation tasks, it is unclear whether a strong correlation still exists between perplexity and various forms of error cost functions in recognition and translation stages. The proposed minimum Bayes risk (MBR) based approach provides a flexible framework for unsupervised LM adaptation. It generalizes to a variety of forms of recognition and translation error metrics. LM adaptation is performed at the audio document level using either the character error rate (CER), or translation edit rate (TER) as the cost function. An efficient parameter estimation scheme using the extended Baum-Welch (EBW) algorithm is proposed. Experimental results on a state-of-the-art speech recognition and translation system are presented. The MBR adapted language models gave the best recognition and translation performance and reduced the TER score by up to 0.54% absolute. © 2007 IEEE.

Generalized Maugis-Dugdale Model of an Elastic Cylinder in Non-Slipping Adhesive Contact with a Stretched Substrate

We have recently developed a generalized JKR model for non-slipping adhesive contact between an elastic cylinder and a stretched substrate where both tangential and normal tractions are transmitted across the contact interface. Here we extend this model to a generalized Maugis-Dugdale model by adopting a Dugdale-type adhesive interaction law to eliminate the stress singularity near the edge of the contact zone. The non-slipping Maugis-Dugdale model is expected to have a broader range of validity in comparison with the non-slipping JKR model. The solution shares a number of common features with experimentally observed behaviors of cell reorientation on a cyclically stretched substrate.