Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme

We describe a method that serves to simultaneously determine the topological configuration of the intersection curve of two parametric surfaces and generate compatible decompositions of their parameter domains, that are amenable to the application of existing perturbation schemes ensuring exact topological consistency of the trimmed surface representations. To illustrate this method, we begin with the simpler problem of topology resolution for a planar algebraic curve F(x,y)=0 in a given domain, and then extend concepts developed in this context to address the intersection of two tensor-product parametric surfaces p(s,t) and q(u,v) defined on (s,t)∈[0,1]² and (u,v)∈[0,1]². The algorithms assume the ability to compute, to any specified precision, the real solutions of systems of polynomial equations in at most four variables within rectangular domains, and proofs for the correctness of the algorithms under this assumption are given. Mathematics subject classification (2000)  65D17     

Synthesis of composite of ZnO spheres with polyaniline and their microwave absorption properties

Three-dimensional (3D) ZnO microspheres with the composite of polyaniline (PANI) have been successfully synthesized by one-pot solvothermal and in-suit polymerization method. The obtained microspheres were uniform having the diameter of 4 μm–7 μm. These microspheres, inside cushion of PANI polymer, exhibit excellent microwave absorption properties. Composite of ZnO microspheres with PANI increased the complex permeability and enhanced the dielectric loss. Thus, the microwave absorption properties of the composite have been intensified. Despite the fact that the composite of ZnO with PANI herein dissipate the microwaves by dielectric loss, their performance is admirable compared to most of PANI-based composites reported. The morphological, structural and spectral properties have been investigated using scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD) and the Fourier transform infrared (FT-IR). It is found that the maximum reflection loss value of [email protected] reaches ?41 dB at 14 GHz with a thickness of 3.5 mm that is superior to the previously reported composite of PANI with other materials.     

Explicit formulas for repeated games with absorbing states

Explicit formulas are given for the asymptotic value lim_{λ → 0} v(λ) and the asymptotic minmax lim w(λ) of finite λ-discounted absorbing games together with new simple proofs for the existence of the limits as λ goes to zero. Similar characterizations for stationary Nash equilibrium payoffs are obtained. The results may be extended to absorbing games with compact metric action sets and jointly-continuous payoff functions.     

Exploring the potential of tetraazaacene derivatives as photovoltaic materials with enhanced photovoltaic parameters

A series of D-π-A type molecules have been designed for their potential use in organic photovoltaic devices. Photovoltaic and optoelectronic properties of newly designed molecules have been explored by comparing with a reference molecule R comprising of the central core (2,3,8,9-tetrakis(thiophen-2-ylethynyl)-5,7,10,12-tetrakis((trimethylsilyl)ethynyl)pyrazino[2,3-b]phenazine) and π-bridge (thiophene). The end groups are (2-(2-ethylidene-3-oxo-2,3-dihydro-1H-inden-1 ylidene)malononitrile), (2-ethylidenemalonitrile), (methyl 2-cyanoacrylate) and (3-methyl-5-methylene-2-thioxothiazolidin-4-one) in the newly designed molecules. Among the investigated molecules M1 and M2 exhibit a broad absorption range of 627 and 626 nm with respect to the reference. All the designed molecules exhibited a lower bandgap as compared to R which indicates a better transfer of electron density from highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO). The reorganization energy values show that all designed molecules have efficient charge transport capability. This study proves that end-capped acceptor modification is an effective strategy for designing optimistic molecule for high performance future organic solar cells fabrication.     

Solution of elementary equations in the Minkowski geometric algebra of complex sets

The solution of elementary equations in the Minkowski geometric algebra of complex sets is addressed. For given circular disks and with radii a and b, a solution of the linear equation in an unknown set exists if and only if ab. When it exists, the solution is generically the region bounded by the inner loop of a Cartesian oval (which may specialize to a limaçon of Pascal, an ellipse, a line segment, or a single point in certain degenerate cases). Furthermore, when a<b<1, the solution of the nonlinear monomial equation is shown to be the region that is bounded by a single loop of a generalized form of the ovals of Cassini. The latter result is obtained by considering the nth Minkowski root of the region bounded by the inner loop of a Cartesian oval. Preliminary consideration is also given to the problems of solving univariate polynomial equations and multivariate linear equations with complex disk coefficients.     

Dicarbonyldi‐μ‐chloro‐cis,cis‐η4‐1,5‐cyclo­octa­dienedirhodium(I)

The title compound, dicarbonyl‐1κ²C‐di‐μ‐chloro‐1:2κ⁴Cl‐[cis,cis‐2(η⁴)‐1,5‐cyclo­octa­diene]­di­rhodium(I), [Rh₂Cl₂(C₈H₁₂)(CO)₂], consists of a di­chloro‐bridged dimer of rhodium, with a non‐bonded Rh?Rh distance of 3.284 (2) Å. One Rh atom is coordinated to two carbonyl ligands, while the other Rh atom is coordinated to the cyclo­octa­diene moiety.     

Efficient Mittag-Leffler Collocation Method for Solving Linear and Nonlinear Fractional Differential Equations

In this paper, a new approximation method for fractional differential equations based on Mittag-Leffler function is developed. Finite Mittag-Leffler function and its fractional-order derivatives are investigated. An efficient technique for solving linear and nonlinear fractional order differential equations is developed. The proposed method combines Mittag-Leffler collocation method and optimization technique. Error estimation of the approximation is stated and proved. We present numerical results and comparisons of previous treatments to demonstrate the efficiency and applicability of the proposed method. Making use of small number of unknowns, the resulting solution converges to the exact one in the linear case and it has a very small error in the nonlinear case.     

Rerouting chlorambucil to mitochondria combats drug deactivation and resistance in cancer cells

The difficulty of accessing the mitochondrial matrix has limited the targeting of therapeutics to this organelle. Here, we report, to our knowledge, the first successful delivery of an active DNA alkylating agent--chlorambucil--to mitochondria, and describe unexpected features that result from rerouting this drug within the cell. Mitochondrial targeting of this agent dramatically potentiates its activity, and promotes apoptotic cell death in a variety of cancer cell lines and patient samples. This retention of activity is observed even in cells with resistance to chlorambucil or disabled apoptotic triggering.