Random walk on a discrete Heisenberg group

We use the estimate of paths in Z ² enclosing a null algebraic area to compute correction terms on the random walk on certain discrete Heisenberg groups. We obtain that the probability to return at the origin of the simple random walk on this group is $\frac{1}{4n^{2}}+O(\frac{1}{n^{3}})$ .     

Symmetrical and Unsymmetrical Bishophonate Esters Chemistry: Synthesis,Selective Hydrolysis,Isomerization

Abstract

Over thc past few years, bisphosphonatcs have bcen receiving increased auention as a new class of pharmacologically active compound. As a continuation of our research program (1,2,3) in connection with the synthesis of bisphosphonate esw I. we present here some results about thc synthesis of symmetrical and unsymmcuical bisphosphonate esms. These compounds were selectively hydrolizcd to give the following mono, di, d and tcua acids II.     

A Simple and Efficient Procedure for the Synthesis of an Alendronate-Oligonucleotide Conjugate Via a Carbamate Linker

Abstract

Alendronate. an munobisphosphonate used clinically for thc treatment of osteoporosis and others bones deseases is a synthetic analog of pyrophosphate in which the labiie phosphoanhydride bond (HO)₂P(O)-O-P(O)(OH)₂ is replaced by a stable hydroxymethylene group (HO), P(O)-C(OH)R-P(O)(OH). The most important action of this bisphosphonate is the inhibition of the bone resorption. The mechanism of action is not completely elucided. One hypothesis is hat thc bisphosphonate act by suppressing osteoclast activity.[1] are used for the enzyme inhibition or for the antisens strategy parriculary in oncology The pharmacological interest of these two moieties encouraged us to bind a bisphosphonate at the 5′ OH of an oligonucleotide via a carbarnate bond. In the first time he synthesis conditions have been studied on model alcohol.     

A meshless method for numerical simulation of depth‐averaged turbulence flows using a k‐ϵ model

A three‐dimensional numerical model is developed to analyze free surface flows and water impact problems. The flow of an incompressible viscous fluid is solved using the unsteady Navier–Stokes equations. Pseudo‐time derivatives are introduced into the equations to improve computational efficiency. The interface between the two phases is tracked using a volume‐of‐fluid interface tracking algorithm developed in a generalized curvilinear coordinate system. The accuracy of the volume‐of‐fluid method is first evaluated by the multiple numerical benchmark tests, including two‐dimensional and three‐dimensional deformation cases on curvilinear grids. The performance and capability of the numerical model for water impact problems are demonstrated by simulations of water entries of the free‐falling hemisphere and cone, based on comparisons of water impact loadings, velocities, and penetrations of the body with experimental data. For further validation, computations of the dam‐break flows are presented, based on an analysis of the wave front propagation, water level, and the dynamic pressure impact of the waves on the downstream walls, on a specific container, and on a tall structure. Extensive comparisons between the obtained solutions, the experimental data, and the results of other numerical simulations in the literature are presented and show a good agreement. Copyright © 2015 John Wiley & Sons, Ltd.     

n-gr-coherent rings and Gorenstein graded modules

Let R be a graded ring and n ? 1 be an integer. We introduce and study the notions of Gorenstein n-FP-gr-injective and Gorenstein n-gr-flat modules by using the notion of special finitely presented graded modules. On n-gr-coherent rings, we investigate the relationships between Gorenstein n-FP-gr-injective and Gorenstein n-gr-flat modules. Among other results, we prove that any graded module in R-gr (or gr-R) admits a Gorenstein n-FP-gr-injective (or Gorenstein n-gr-flat) cover and preenvelope, respectively.