Exact linearization of one-dimensional jump-diffusion stochastic differential equations

Necessary and sufficient conditions for the linearization of the one-dimensional Itô jump-diffusion stochastic differential equations (JDSDE) are given. Stochastic integrating factor has been introduced to solve the linear JDSDEs. Exact solutions to some linearizable JDSDEs have been provided.     

Synthesis,characterization, fluorescence and redox features of new <Emphasis Type="Italic">vic</Emphasis>-dioxime ligand bearing pyrene and its metal complexes

A new vic-dioxime ligand, N,N′-bis(aminopyreneglyoxime) (LH₂), and its copper(II), nickel(II) and cobalt(II) metal complexes were synthesized and characterized by elemental analyses, IR, UVVIS and ¹H and ¹³C NMR spectra (for the ligand). Mononuclear complexes were synthesized by a reaction of ligand (LH₂) and salts of Co(II), Ni(II), and Cu(II) in ethanol. The complexes have the metal-ligand ratio of 1: 2 and metals are coordinated by N,N′ atoms of vicinal dioximes. The ligand acts in a polydentate fashion bending through nitrogen atoms in the presence of a base, as do most vic-dioximes. Detection of a H-bonding in the Co(II), Ni(II), and Cu(II) complexes by IR revealed the square-planar MN₄ coordination of mononuclear complexes. Fluorescent properties of the ligand and its complexes arise from pyrene units conjugated with a vic-dioxime moiety. Fluorescence emission spectra of the ligand showed a drastic decrease in its fluorescence intensity upon metal binding. The electrochemical properties of the complexes were studied by the cyclic voltammetry technique. The nickel complex displayed an irreversible oxidation process while the copper complex exhibited a quasi-reversible oxidation and reduction processes based on the copper Cu(II)/Cu(III) and Cu(II)/Cu(I) couples, respectively.     

Dissolution kinetics of fluorapatite in the hydrochloric acid solution

A thermochemical study of hydrochloric acid attack of synthetic fluorapatite was performed by a DRC. The calculated thermogenesis curves show one peak. The plot of the heat quantity as a function of the dissolved mass undergoes only one straight segment, and the thermogenesis curves present a single peak, suggesting the occurrence of a one-step dissolution process. The dissolution kinetics was examined according to the heterogeneous reaction models and showed that the dissolution is controlled by the product layer diffusion process with a reaction rate expressed by the following semiempirical equation; \(\left[ {1 + 2(1 - X) - 3(1 - X)^{{\frac{2}{3}}} } \right] = 3195 \times 10^{ - 2} C^{0.145} \left( {\frac{S}{L}} \right)^{ - 0.628} e^{{ - \frac{2600}{\text T}}} t\). The activation energy was determined as 21.6 ± 1.5 kJ mol^?1     

Pentagalloyl Glucose (PGG) Partially Prevents Arterial Mechanical Changes Due to Elastin Degradation

Experimental Mechanics - Elastic fibers are composed primarily of the protein elastin and they provide reversible elasticity to the large arteries. Degradation of elastic fibers is a common...     

Induced and Coinduced Representations of Hopf Group Coalgebras

The induction theory for a Hopf group coalgebra is outlined. Given a Hopf group coalgebra H, the notions of a quotient Hopf group coalgebra and group coisotropic quantum subgroup of H are introduced. The properties of (co)induced representations are studied and the geometric interpretation and simplicity theory of such representations are given.      

Weighted Hardy and Rellich type inequalities on Riemannian manifolds

In this paper we present new results on two‐weight Hardy, Hardy–Poincaré and Rellich type inequalities with remainder terms on a complete noncompact Riemannian Manifold M. The method we use is flexible enough to obtain more weighted Hardy type inequalities. Our results improve and include many previously known results as special cases.     

Stabilized mixed triangular finite elements at large deformations using area bubble functions

In this paper stabilized mixed triangular finite elements are presented in order to avoid volume locking and to damp stress oscillations. Geometrically non-linear elastic problems are addressed. The mixed method of incompatible modes and the mixed method of enhanced strains are considered as special cases. As a key idea, volume and area bubble functions are used for the method of incompatible modes and the enhanced strain method [1], thus giving both the interpretation of a mixed finite element method with stabilization terms. Concerning non-linear problems these are non-linearly dependent on the current deformation state, however, linearly dependent stabilization terms are used [1]. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step is completely avoided. The variational formulation for the standard two-field method, the method of incompatible modes and the enhanced strain method in finite deformation problems is derived for a hyper elastic Neo-Hookean material. In the representative example Cook's membrane problem illustrates the good performance of the presented approaches compared to existing finite element formulations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs

In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first-order system and solved using existing Runge–Kutta method. The results clearly shown the advantage and the efficiency of the new method.