### 0 QUANTITATIVE UNIFORM IN TIME CHAOS PROPAGATION FOR BOLTZMANN COLLISION PROCESSES

, 2010

"... ar ..."

### (Department of Applied Science, Yamaguchi University)

"... We define q-logarithm function as follows; lnq x = x1−q − 1 1 − q, (x ≥ 0, q ≥ 0, q = 1). Then we have the following properties; (1) limq→1 lnq x = log x. (in uniformly) (2) lnq xy = lnq x + lnq y + (1 − q) lnq x lnq y. (3) lnq x: concave in x for q ≥ 0. Definition 1 (Tsallis entropy) For density o ..."

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We define q-logarithm function as follows; lnq x = x1−q − 1 1 − q, (x ≥ 0, q ≥ 0, q = 1). Then we have the following properties; (1) limq→1 lnq x = log x. (in uniformly) (2) lnq xy = lnq x + lnq y + (1 − q) lnq x lnq y. (

*3*) lnq x: concave in x for q ≥ 0. Definition 1 (Tsallis entropy) For density### unknown title

"... This paper investigates the interpolation formulae and the sampling theorem for bandpass signals in the linear canonical transform LCT domain. Firstly, one of the important relationships between the bandpass signals in the Fourier domain and the bandpass signals in the LCT domain is derived. Second ..."

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. Secondly, two interpolation formulae from uniformly sampled points at half of the sampling rate associated with the bandpass signals and their generalized

*Hilbert*transform or the derivatives in the LCT domain are obtained. Thirdly, the interpolation formulae from nonuniform samples are investigated### COSMOLOGICAL MODELS OF MODIFIED GRAVITY

, 2013

"... The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple brane ..."

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The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple branes float in a five-dimensional anti-de Sitter bulk, while the second investigates a class of dark energy models from an effective field theory perspective. Investigations of models including extra dimensions have led to modifications of gravity involving a number of interesting features. In particular, the Randall-Sundrum model is well-known for achieving an amelioration of the hierarchy problem. However, the basic model relies on Minkowski branes and is subject to solar system constraints in the absence of a radion stabilization mechanism. We present a method by which a four-dimensional low-energy description can be obtained for braneworld scenarios, allowing for a number of generalizations to the original models. This method is applied to orbifolded and uncompactified N-brane models, deriving an effective four-dimensional action. The parameter space of this theory is constrained using observational evidence, and it is found that the generalizations do not weaken solar system constraints on the original model. Furthermore, we find that general

### ON CARATH EO D O RY TYPE SELECTORS

, 1981

"... Abstract. In this paper we consider a set-valued function of two variables, measurable in the first and continuous in the second variable. Using metric projections we construct for this function a family of selectors which are Caratheodory maps. The existence of Caratheodory selectors was studied by ..."

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by Castaing [2], [

*3*], Cellina [4], Fryszkowski [9] and the first author [11]. 1. Notation and definitions. Let (T, ST) be a measurable space, X a topological space and Y a*Hilbert*space. By 0>C(Y) we denote the family of all non-empty closed convex subsets of Y. We shall consider 9 C ( Y### UCRL-JRNL-226292 Phase retrieval and saddle-point optimization

, 2006

"... Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid inputoutput algorithm has demonstrated remarkable success in performing gigaelement nonlinear optimization, escaping local minima and producing images at r ..."

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in optimization techniques (see e.g. 1 for a review), primarily the introduction of a controlfeedback method proposed by Fienup (Hybrid Input Output-HIO 2,

*3*). The important theoretical insight that these iterations may be viewed as projections in*Hilbert*space 4,5 has allowed theoreticians to analyze and improve### ABSTRACT Title of dissertation: Weakly Compressible Navier-Stokes Approximation of Gas Dynamics

"... This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coeffi-cients (viscosity and thermal conductivity) are small and ..."

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This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coeffi-cients (viscosity and thermal conductivity) are small and (2) the gas is near an abso-lute equilibrium — a spatially uniform, stationary state. When we consider regimes in which both the transport scales and Re vanish, we derive the weakly compressible Stokes approximation — a linear system. When we consider regimes in which the transport scales vanish while Re maintains order unity, we derive the weakly com-pressible Navier-Stokes approximation—a quadratic system. Each of these weakly compressible approximations govern both the acoustic and the incompressible modes of the gas. In the fluid dynamical setting, our derivations begin with the fully compress-ible Navier-Stokes system. We show that the structure of the weakly compressible Navier-Stokes system ensures that it has global weak solutions, thereby extending the Leray theory for the incompressible Navier-Stokes system. Indeed, we show that