Modified Kirchhoffs theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoffs boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis. (C) 2011 Elsevier Ltd. All rights reserved.

Growth inhibitory, apoptotic and anti-inflammatory activities displayed by a novel modified triterpenoid, cyano enone of methyl boswellates

Triterpenoids are pentacyclic secondary metabolites present in many terrestrial plants. Natural triterpenoids have been reported to exhibit anti-inflammatory and anti-carcinogenic activities. Here, we show that modifications of ring A of boswellic acid (2 cyano, 3 enone) resulted in a highly active growth inhibitory, anti-inflammatory, pro-differentiative and anti-tumour triterpenoid compound called cyano enone of methyl boswellates (CEMB). This compound showed cytotoxic activity on a number of cancer cell lines with IC50 ranging from 0.2 to 0.6 mu M. CEMB inhibits DNA synthesis and induces apoptosis in A549 cell line at 0.25 mu M and 1 mu M concentrations, respectively. CEMB induces adipogenic differentiation in 3T3-L1 cells at a concentration of 0.1 mu M. Finally, administration of CEMB intra-tumourally significantly inhibited the growth of C6 glioma tumour xenograft in immuno-compromised mice. Collectively, these results suggest that CEMB is a very potent anti-tumour compound.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Growth mechanism of phases, Kirkendall voids, marker plane position, and indication of the relative mobilities of the species in the interdiffusion zone

Often, wrong conclusions about the mobilities of species are drawn from the position of the Kirkendall marker plane or voids in the interdiffusion zone. To clarify, I have discussed the growth mechanism of the phases and the position of the marker plane depending on the relative mobilities of the species. The formation of different kinds of voids in the interdiffusion zone is discussed. Further, the microstructure that could be found because of the Kirkendall effect is also explained.

Inhibition of hepatitis C virus replication by herbal extract: Phyllanthus amarus as potent natural source

Hepatitis C virus infection is a major health problem worldwide. Developing effective antiviral therapy for HCV is the need of the hour. The viral enzymes NS3 protease and NS5B RNA dependent RNA polymerase are essential enzymes for polyprotein processing and viral RNA replication and thus can be potential targets for screening anti-HCV compounds. A large number of phytochemicals are present in plants, which are found to be promising antiviral agents. In this study, we have screened inhibitory effect of different plant extracts against the NS3 and NS5B enzymes of hepatitis C virus. Methanolic extracts were prepared from various plant materials and their inhibitory effects on the viral enzymes were determined by in vitro enzyme assays. Effect on viral RNA replication was investigated by using TaqMan Real time RT-PCR. Interestingly, Phyllanthus amarus root (PAR) extract showed significant inhibition of HCV-NS3 protease enzyme; whereas P. amarus leaf (PAL) extract showed considerable inhibition of NS5B in the in vitro assays. Further, the PAR and PAL extracts significantly inhibited replication of HCV monocistronic replicon RNA and HCV H77S viral RNA in HCV cell culture system. However, both PAR and PAL extracts did not show cytotoxicity in Huh7 cells in the MTT assay. Furthermore, addition of PAR together with IFN-alpha showed additive effect in the inhibition of HCV RNA replication. Results suggest the possible molecular basis of the inhibitory activity of PA extract against HCV which would help in optimization and subsequent development of specific antiviral agent using P. amarus as potent natural source. (C) 2011 Elsevier B.V. All rights reserved.

Boundary conditions at a rigid wall for rough granular gases

We derive boundary conditions at a rigid wall for a granular material comprising rough, inelastic particles. Our analysis is confined to the rapid flow, or granular gas, regime in which grains interact by impulsive collisions. We use the Chapman-Enskog expansion in the kinetic theory of dense gases, extended for inelastic and rough particles, to determine the relevant fluxes to the wall. As in previous studies, we assume that the particles are spheres, and that the wall is corrugated by hemispheres rigidly attached to it. Collisions between the particles and the wall hemispheres are characterized by coefficients of restitution and roughness. We derive boundary conditions for the two limiting cases of nearly smooth and nearly perfectly rough spheres, as a hydrodynamic description of granular gases comprising rough spheres is appropriate only in these limits. The results are illustrated by applying the equations of motion and boundary conditions to the problem of plane Couette flow.

Video coding mode decision as a classification problem

In this paper, we show that it is possible to reduce the complexity of Intra MB coding in H.264/AVC based on a novel chance constrained classifier. Using the pairs of simple mean-variances values, our technique is able to reduce the complexity of Intra MB coding process with a negligible loss in PSNR. We present an alternate approach to address the classification problem which is equivalent to machine learning. Implementation results show that the proposed method reduces encoding time to about 20% of the reference implementation with average loss of 0.05 dB in PSNR.

The restriction mapping problem revisited

In computational molecular biology, the aim of restriction mapping is to locate the restriction sites of a given enzyme on a DNA molecule. Double digest and partial digest are two well-studied techniques for restriction mapping. While double digest is NP-complete, there is no known polynomial-time algorithm for partial digest. Another disadvantage of the above techniques is that there can be multiple solutions for reconstruction. In this paper, we study a simple technique called labeled partial digest for restriction mapping. We give a fast polynomial time (O(n(2) log n) worst-case) algorithm for finding all the n sites of a DNA molecule using this technique. An important advantage of the algorithm is the unique reconstruction of the DNA molecule from the digest. The technique is also robust in handling errors in fragment lengths which arises in the laboratory. We give a robust O(n(4)) worst-case algorithm that can provably tolerate an absolute error of O(Delta/n) (where Delta is the minimum inter-site distance), while giving a unique reconstruction. We test our theoretical results by simulating the performance of the algorithm on a real DNA molecule. Motivated by the similarity to the labeled partial digest problem, we address a related problem of interest-the de novo peptide sequencing problem (ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000, pp. 389-398), which arises in the reconstruction of the peptide sequence of a protein molecule. We give a simple and efficient algorithm for the problem without using dynamic programming. The algorithm runs in time O(k log k), where k is the number of ions and is an improvement over the algorithm in Chen et al. (C) 2002 Elsevier Science (USA). All rights reserved.

A stereospecific approach to cis-anti-cis triquinanes

A methodology for the synthesis of compounds containing the cis-anti-cis fused triquinane system has been developed starting from tricyclo[5.2. 1.0(2.6)]deca-4,8-dien-3-(exo)ol 6 involving Ireland ester Claisen rearrangement and intramolecular diazo ketone cyclopropanation reactions as key steps.

A waveguide problem involving a thick iris in the theory of electromagnetism

The problem of electromagnetic wave propagation in a rectangular waveguide containing a thick iris is considered for its complete solution by reducing it to two suitable integral equations, one of which is of the first kind and the other is of the second kind. These integral equations are solved approximately, by using truncated Fourier series for the unknown functions. The reflection coefficient is computed numerically from the two integral equation approaches, and almost the same numerical results are obtained. This is also depicted graphically against the wave number and compared with thin iris results, which are computed by using complementary formulations coupled with Galerkin approximations. While the reflection coefficient for a thin iris steadily increases with the wave number, for a thick iris it fluctuates and zero reflection occurs. The number of zeros of the reflection coefficient for a thick iris increases with the thickness. Thus a thick iris becomes completely transparent for some discrete wave numbers. This phenomenon may be significant in the modelling of rectangular waveguides.

On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions

Closed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

A Convex Optimization Framework for Almost Budget Balanced Allocation of a Divisible Good

We address the problem of allocating a single divisible good to a number of agents. The agents have concave valuation functions parameterized by a scalar type. The agents report only the type. The goal is to find allocatively efficient, strategy proof, nearly budget balanced mechanisms within the Groves class. Near budget balance is attained by returning as much of the received payments as rebates to agents. Two performance criteria are of interest: the maximum ratio of budget surplus to efficient surplus, and the expected budget surplus, within the class of linear rebate functions. The goal is to minimize them. Assuming that the valuation functions are known, we show that both problems reduce to convex optimization problems, where the convex constraint sets are characterized by a continuum of half-plane constraints parameterized by the vector of reported types. We then propose a randomized relaxation of these problems by sampling constraints. The relaxed problem is a linear programming problem (LP). We then identify the number of samples needed for ``near-feasibility'' of the relaxed constraint set. Under some conditions on the valuation function, we show that value of the approximate LP is close to the optimal value. Simulation results show significant improvements of our proposed method over the Vickrey-Clarke-Groves (VCG) mechanism without rebates. In the special case of indivisible goods, the mechanisms in this paper fall back to those proposed by Moulin, by Guo and Conitzer, and by Gujar and Narahari, without any need for randomization. Extension of the proposed mechanisms to situations when the valuation functions are not known to the central planner are also discussed. Note to Practitioners-Our results will be useful in all resource allocation problems that involve gathering of information privately held by strategic users, where the utilities are any concave function of the allocations, and where the resource planner is not interested in maximizing revenue, but in efficient sharing of the resource. Such situations arise quite often in fair sharing of internet resources, fair sharing of funds across departments within the same parent organization, auctioning of public goods, etc. We study methods to achieve near budget balance by first collecting payments according to the celebrated VCG mechanism, and then returning as much of the collected money as rebates. Our focus on linear rebate functions allows for easy implementation. The resulting convex optimization problem is solved via relaxation to a randomized linear programming problem, for which several efficient solvers exist. This relaxation is enabled by constraint sampling. Keeping practitioners in mind, we identify the number of samples that assures a desired level of ``near-feasibility'' with the desired confidence level. Our methodology will occasionally require subsidy from outside the system. We however demonstrate via simulation that, if the mechanism is repeated several times over independent instances, then past surplus can support the subsidy requirements. We also extend our results to situations where the strategic users' utility functions are not known to the allocating entity, a common situation in the context of internet users and other problems.