Global divergence of spatial coalescents

We study several fundamental properties of a class of stochastic processes called spatial Λ-coalescents. In these models, a number of particles perform independent random walks on some underlying graph G. In addition, particles on the same vertex merge randomly according to a given coalescing mechanism. A remarkable property of mean-field coalescent processes is that they may come down from infinity, meaning that, starting with an infinite number of particles, only a finite number remains after any positive amount of time, almost surely. We show here however that, in the spatial setting, on any infinite and bounded-degree graph, the total number of particles will always remain infinite at all times, almost surely. Moreover, if ${G\,=\,\mathbb{Z}^d}$ , and the coalescing mechanism is Kingman’s coalescent, then starting with N particles at the origin, the total number of particles remaining is of order (log* N) ^d at any fixed positive time (where log* is the inverse tower function). At sufficiently large times the total number of particles is of order (log* N) ^d-2, when d?>?2. We provide parallel results in the recurrent case d?=?2. The spatial Beta-coalescents behave similarly, where log log N is replacing log* N.     

Syntheses and characterization of lisinopril-coated gold nanoparticles as highly stable targeted CT contrast agents in cardiovascular diseases

Lisinopril was used as the targeting moiety to prepare gold nanoparticle-based functional CT contrast agents. Pure lisinopril, thioctic acid-lisinopril conjugate, and reduced thioctic acid-lisinopril conjugate were used to obtain GNP-Lis, GNP-TA-Lis, and GNP-RTA-Lis, respectively, via ligand exchange reaction on citrate-coated gold nanoparticles (GNPs). These lisinopril-decorated GNPs were fully characterized, and their chemical stabilities in biological relevant media and in high salt concentration were compared. Their relative stabilities toward lyophilization and against cyanide-induced decomposition were also investigated. Because of their higher stability, GNP-TA-Lis were used to assess the targeting of angiotensin converting enzyme (ACE) using X-ray computed tomography (CT). The images obtained displayed high contrast in the region of the lungs and heart, clearly indicating the targeting of ACE, whose overexpression is associated with development of cardiac and pulmonary fibrosis. Thus, the new nanoprobes prepared here will serve as very useful tools for the monitoring of cardiovascular pathophysiologies using CT imaging.     

A novel anticancer diterpenoid from Jatropha gossypifolia

Jatropha gossypifolia root bark is used in ethnomedicine for bacterial infections and cancer of the lungs. Phytochemical investigation resulted in the isolation and characterization of a potent anticancer and novel lathyrane diterpenoid compound, abiodone, with an unusual methylene group. The structure of this novel compound was established by 1D, and 2D NMR spectroscopic experiments a nd confirmed by X-ray analysis.     

On representations distinguished by unitary groups

Let E/F be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on $\operatorname {GL}_{n}( \mathbf {A}_{E})$ over a unitary group of a Hermitian form with respect to E/F. We provide factorization for these periods into locally defined functionals, express these factors in terms of suitably defined local periods and characterize global distinction. We also study in detail the analogous local question and analyze the space of invariant linear forms under a unitary group.     

Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads

Optimum design of dynamic vibration absorbers (DVAs) installed on linear damped systems that are subjected to random loads is studied and closed-form design formulas are provided. Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass. Exact optimum design parameters for the velocity case, which to the best knowledge of the author do not exist in the literature, are derived for the first time. Exact solutions are found to be directly applicable for practical use with no simplification needed. For displacement and acceleration cases, a solution for the optimum absorber frequency ratio is obtained as a function of optimum absorber damping ratio. Numerical simulations indicate that optimum absorber damping ratio is not significantly related to the structural damping, especially when the displacement variance is minimized. Therefore, optimum damping ratio derived for undamped systems is proposed for damped systems for the displacement case. When acceleration variance is minimized, however, the optimum damping ratio derived for undamped systems is found not as accurate for damped systems. Therefore, a more accurate approximate expression is derived. Numerical comparisons with published approximate expressions at the same level of complexity indicated that proposed design formula yield more accurate estimates. Another important finding of the paper is that for specific applications where all of the response parameters are desired to be minimized simultaneously, DVAs designed per velocity criteria provide the best overall performance with the least complexity in the design equations.     

The stiffness of self-similar fractals

A method to derive the stiffness of self-similar elastic fractals is presented based on structural mechanics principles and a physically motivated similarity criterion, which is assumed as a postulate. Using this method, the stiffnesses of both the Von Koch curve and the Sierpiński gasket in the small-deformation regime are derived. For these fractal structures, it is shown that the stiffness matrix is completely determined by a single elastic constant. The procedure to tile a planar domain with Sierpiński gaskets is explored and shown to require the consideration of hexagonal-shaped combinations of gaskets joined continuously along their edges. This continuity leads to a phenomenon of geometrically induced inextensibility along the common edges. After deriving the stiffness matrix for the basic hexagon, the analog of the Boussinesq–Flamant problem for a tiled half-plane is solved numerically to demonstrate the potential of the method in modeling of solid mechanics applications.     

Conformable variational iteration method,conformable fractional reduced differential transform method and conformable homotopy analysis method for non-linear fractional partial differential equations

In this paper, we introduce conformable variational iteration method (C-VIM), conformable fractional reduced differential transform method (CFRDTM) and conformable homotopy analysis method (C-HAM). Between these methods, the C-VIM is introduced for the first time for fractional partial differential equations (FPDEs). These methods are new versions of well-known VIM, RDTM and HAM. In addition, above-mentioned techniques are based on new defined conformable fractional derivative to solve linear and non-linear conformable FPDEs. Firstly, we present some basic definitions and general algorithm for proposal methods to solve linear and non-linear FPDEs. Secondly, to understand better, the presented new methods are supported by some examples. Finally, the obtained results are illustrated by the aid of graphics and the tables. The applications show that these new techniques C-VIM, CFRDTM and C-HAM are extremely reliable and highly accurate and it provides a significant improvement in solving linear and non-linear FPDEs.     

Analysis of individual platelet-derived microparticles,comparing flow cytometry and capillary electrophoresis with laser-induced fluorescence detection

Platelet-derived microparticles (PMPs) formed by vesiculation during platelet activation seem to play a role in blood coagulation and in pathological disease states. Flow cytometry is currently the gold standard to characterize platelets and PMPs. Using this technique we distinguished between platelets and PMPs based on size and the presence of phosphatidyl serine (PS); PMPs were arbitrarily defined to be smaller than one micrometer and capable of forming a stable complex with fluorescently-labeled Annexin V, a protein that forms a calcium-dependent complex with PS. Further confirmation of PMP and platelet identity was done by use of fluorescently-labeled antibodies against CD41a, a glycoprotein found on the surface of both platelets and PMPs. In this report we also introduce the use of capillary electrophoresis with post-column laser-induced fluorescence detection (CE-LIF) for the analysis of fluorescently labeled platelets and PMPs. While both flow cytometry and CE-LIF can measure individual fluorescent events, only CE-LIF allowed us to calculate individual electrophoretic mobilities of activated platelets and PMPs that were then represented as distributions. A comparison between distributions suggests that PMPs have less negative mobilities. The fact that activated platelet preparations include PMPs partially obscure the interpretation of the data. While PMP and platelet number ml(-1) determined by flow cytometry is lower than the same parameter determined by CE-LIF, signal-to-noise ratio was 20 fold better for flow cytometry than for CE-LIF. This is the first time that a direct comparison between these two techniques is reported.