A reduction theorem for the Alperin weight conjecture

The Alperin Weight Conjecture was stated by J. Alperin in 1986 and constitutes one of the main problems in the representation theory of finite groups. In this paper, we provide a reduction to simple groups and as an application we prove the conjecture in several cases.     

Binary mixing of micelles using Pluronics for a nano-sized drug delivery system

Pluronics with different structural compositions and properties are used for several applications, including drug delivery systems. We developed a binary mixing system with two Pluronics, L121/P123, as a nano-sized drug delivery carrier. The lamellar-forming Pluronic L121 (0.1 wt%) was incorporated with Pluronic P123 to produce nano-sized dispersions (in case of 0.1 and 0.5 wt% P123) with high stability due to Pluronic P123 and high solubilization capacity due to Pluronic L121. The binary systems were spherical and less than 200-nm diameter, with high thermodynamic stability (at least 2 weeks) in aqueous solution. The CMC of the binary system was located in the middle of the CMC of each polymer. In particular, the solubilization capacity of the binary system (0.1/0.1 wt%) was higher than mono-systems of P123. The main advantage of binary systems is overcoming limitations of mono systems to allow tailored mixing of block copolymers with different physicochemical characteristics. These nano-sized systems may have potential as anticancer drug delivery systems with simple preparation method, high stability, and high loading capacity.     

NEAR-INFRARED DYES: Probe Development and Applications in Optical Molecular Imaging

The recent emergence of optical imaging has brought forth a unique challenge for chemists: development of new biocompatible dyes that fluoresce in the near-infrared (NIR) region for optimal use in biomedical applications. This review describes the synthesis of NIR dyes and the design of probes capable of noninvasively imaging molecular events in small animal models.     

Ozonolysis of dipterocarpol and its derivatives

Oxidation of dipterocarpol and its derivatives with ozone gave compounds containing lactone, lactol, alkoxytetrahydrofuran, aldehyde, and methyl ketone fragments in the side chain, as well as 1,2,4-trioxolane fragment in the A ring. The molecular and crystalline structures of dipterocarpol were determined by X-ray analysis.     

The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models

We consider a wide class of gradient damage models which are characterized by two constitutive functions after a normalization of the scalar damage parameter. The evolution problem is formulated following a variational approach based on the principles of irreversibility, stability and energy balance. Applied to a monotonically increasing traction test of a one-dimensional bar, we consider the homogeneous response where both the strain and the damage fields are uniform in space. In the case of a softening behavior, we show that the homogeneous state of the bar at a given time is stable provided that the length of the bar is less than a state dependent critical value and unstable otherwise. However, we also show that bifurcations can appear even if the homogeneous state is stable. All these results are obtained in a closed form. Finally, we propose a practical method to identify the two constitutive functions. This method is based on the measure of the homogeneous response in a situation where this response is stable without possibility of bifurcation, and on a procedure which gives the opportunity to detect its loss of stability. All the theoretical analyses are illustrated by examples.     

Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region

Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily coincide with the mechanism of shear thickening under step shear flow. In this study, we have systematically investigated the nonlinear rheology of non-colloidal (>1???m) hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region in order to better understand the strain stiffening behavior. The suspensions near liquid-and-crystal coexistence region are known to locally form the closed packing structure. The critical strain amplitude which is the onset of strain stiffening was different for the storage and loss modulus. But they converged to each other as the suspension forms a more crystalline structure. The critical strain amplitude was independent of medium viscosity, imposed angular frequency, and particle size, but was strongly dependent upon particle volume fraction. The onset of strain stiffening was explained in terms of shear-induced collision due to particle motion in the closed packing structure. Nonlinear stress wave-forms, which reflect the micro-structural change, were observed with the onset of strain stiffening. During the strain stiffening, enhanced elastic stress before and after flow reversal was observed which originates from changes in the suspension microstructure. Nonlinearity of the shear stress in terms of Fourier intensity was extremely increased up to 0.55. Beyond the strain stiffening, the suspension responded liquid-like and the nonlinearity decreased but the elastic shear stress was still indicating the microstructure rearrangement within a cycle.     

Mechanics and mechanism of cut resistance of protective materials

A sliding sharp edge penetrating material is one of the most dangerous cases of cutting because it requires the smallest applied load. A better understanding of the cutting mechanism is a fundamental step to develop new and more performing protective materials. This study aims at analyzing cutting mechanics and mechanism in the presence of friction. The International Standard ISO 13997 cut test method consists in measuring the distance that a straight blade slides horizontally to cut through a material under a constant applied normal force and was used to investigate cutting phenomena.In practice, cut resistance of a material is contributed by the intrinsic strength of material and the frictional distribution. Two types of friction distributions are involved in cutting: a macroscopic friction induced by the gripping of the material and by the applied normal load on the two sides of the blade; and the other the sliding friction associated with cut through of the material that occurs along the face of the blade tip. For most materials, frictional forces due to lateral gripping could be several times greater than the friction due to the applied normal force. Thus, the cutting energy required for breaking molecular chains is much smaller than the energy dissipated for friction. The elastic modulus, the structure of the material as well as the sliding velocity have significant influence on the friction. Therefore all these properties can affect the cutting resistance results.     

Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact

In the present paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate, yet highly accurate secular equation of fourth-order in terms of the dimensionless thickness of the layer is derived. From the secular equation obtained, an approximate formula of third-order for the velocity of Rayleigh waves is established. The approximate secular equation and the formula for the velocity obtained in this paper are potentially useful in many practical applications.     

A ghost-cell immersed boundary method for large-eddy simulations of compressible turbulent flows

A methodology to perform a ghost-cell-based immersed boundary method (GCIBM) is presented for simulating compressible turbulent flows around complex geometries. In this method, the boundary condition on the immersed boundary is enforced through the use of ‘ghost cells’ that are located inside the solid body. The computations of variables on these ghost cells are achieved using linear interpolation schemes. The validity and applicability of the proposed method is verified using a three-dimensional (3D) flow over a circular cylinder, and a large-eddy simulation of fully developed 3D turbulent flow in a channel with a wavy surface. The results agree well with the previous numerical and experimental results, given that the grid resolution is reasonably fine. To demonstrate the capability of the method for higher Mach numbers, supersonic turbulent flow over a circular cylinder is presented. While more work still needs to be done to demonstrate higher robustness and accuracy, the present work provides interesting insights using the GCIBM for the compressible flows.     

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

In this paper, two splitting extragradient-like algorithms for solving strongly pseudomonotone equilibrium problems given by a sum of two bifunctions are proposed. The convergence of the proposed methods is analyzed and the R-linear rate of convergence under suitable assumptions on bifunctions is established. Moreover, a noisy data case, when a part of the bifunction is contaminated by errors, is studied. Finally, some numerical experiments are given to demonstrate the efficiency of our algorithms.