Dyck paths with a first return decomposition constrained by height

We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height $k$ with a flat (resp. with no flats) at the maximal height.     

Strong （Weak） Exact Controllability and Strong （Weak） Exact Observability for Quasilinear Hyperbolic Systems

Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws.     

Stochastic Dynamics for Passage Times and Diffusion Approximations for Finite Capacity Storage Models with Different Kinds of Barriers

In this article, we discuss a number of storage models of finite capacity with random inputs, random outputs, and linear release policy. They form a class of one-dimensional master equations with separable kernels. For this class of problems, the integral equations for first overflow or first emptiness can be transformed exactly into ordinary differential equations. Analysis is done with separable kernel. For all the stochastic models, two barriers are considered: one at X = 0 and the other at X = k, and the barriers are treated as absorbing or reflecting. The imbedding method is used to derive a third order differential equation. We consider first passage times for overflow without or with emptiness of the dam. We also study the passage times for first emptiness with and without overflows. The expected amount of overflows in a given time is also calculated. Finally, by suitable statistical features, all these models are converted into diffusion process with drift. Closed form solutions are obtained for all the problems in terms of Laplace transform functions. For the diffusion process with drift first passage time density is arrived at by treating X = 0 and X = k as absorbing barriers. One of the barriers as reflecting is also studied.     

Two hyperfinite constructions of the brownian bridge

Infinitesimal Analysis is used to give two constructions of the brownian bridge process. In the first construction a hyperfinite tied down random walk is used and a brownian bridge is obtained via the standard part map. As a consequence it is shown that the brownian bridge is the weak limit of a sequence of normalized tied down random walks. The second construction is based on a hyperfinite uniform empirical process. This construction gives an almost trivial proof of Donsker's Invariance Principle for the uniform empirical process     

Electronic and lattice vibrational properties of cubic BaHfO3 from first principles calculations

Through first principles calculations, we investigated the electronic structure and lattice vibrational properties of BaHfO₃. The optimized lattice constant of BaHfO₃ is in agreement with experimental and theoretical results. Our results show that cubic BaHfO₃ is an insulator with an indirect band gap of 3.5 eV. Besides, the calculation using the screened exchange local density approximation (sX-LDA) has been performed with the predicted minimum gap of 5.3 eV. The phonon dispersion curves of BaHfO₃ were also calculated. All positive phonon frequencies in the Brillouin zone were found, indicating the stability of BaHfO₃ structure.     

Magnetic properties in zinc-blende CdS induced by Cd vacancies

The magnetic property induced by neutral Cd and S vacancies in CdS bulk and thin film are investigated, using first principles simulation. For bulk CdS, the magnetism originates from Cd, instead of S, vacancies. The ferromagnetism with a Curie temperature above room temperature can be expected. For CdS thin film, both Cd and S vacancies does not yield any magnetism at the (111) surface, while local magnetic moments at the outermost S plane of the (001) surface is ascribed to the surface effect. The ferromagnetism at S-terminated (001) surface can account for the experimental observation.     

On the Uniform Poincaré Inequality

We give a proof of the Poincaré inequality in W ^{1, p} (Ω) with a constant that is independent of Ω ? , where  is a set of uniformly bounded and uniformly Lipschitz domains in ? ⁿ . As a byproduct, we obtain the following: The first non vanishing eigenvalues λ₂(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the domains Ω vary and remain uniformly bounded and uniformly Lipschitz regular.     

The Convexity Estimates for the Solutions of Two Elliptic Equations

In this paper, for the solutions of two elliptic equations we find the auxiliary curvature functions which attain respective minimum on the boundary. These results are the generalization of the classical ones in Makar-Limanov [17 Makar-Limanov , L.G. ( 1971 ). Solution of Dirichlet's problem for the equation Δu = ?1 on a convex region . Math. Notes Acad. Sci. USSR 9 : 52 – 53 .[Crossref] , [Google Scholar]] for the torsion equation and Acker et al. [1 Acker , A. , Payne , L.E. , Philippin , G. ( 1981 ). On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem . Z. Angew. Math. Phys. 32 : 683 – 694 .[Crossref], [Web of Science ®] , [Google Scholar]] for the first eigenfunction of the Laplacian in convex domains of dimension 2. Then we get the new proof of the specific convexity of the solutions of the above two elliptic equations. As a consequence, for the elliptic equation vΔv = ? (1 + |?v|²) in a smooth, bounded and strictly convex domain Ω in ? ⁿ with homogeneous Dirichlet boundary value condition, we also get a sharply lower bound estimate of the Gaussian curvature for the solution surface by the curvature of the boundary of the domain.     

Simultaneous Determination of Naproxen and Diflunisal using Synchronous Luminescence Spectrometry

Binary mixtures of naproxen and diflunisal can be resolved by using zero-crossing first derivative emission spectrofluorimetry, first derivative constant wavelength synchronous luminescence spectrometry and first derivative constant energy synchronous luminescence spectrometry. These methods do not require any previous separation steps. The lowest quantitation limits for both drugs were obtained with first derivative constant wavelength synchronous luminescence spectrometry (0.002 and 0.015 μg ml⁻¹ for naproxen and diflunisal, respectively). The measurements were performed in 40% methanolic aqueous medium at pH 8.0 provided by adding 0.02 M phosphate buffer solution. The proposed methods were successfully applied to the simultaneous determination of naproxen and diflunisal in pharmaceuticals and human serum samples with high precision and accuracy. Linearity, accuracy, precision, limits of detection, limits of quantitation, and other aspects of analytical validation are included in the text.