A commutativity theorem

LetR be an associative ring with identity which satisfies the identities(xy) ^k =(yx) ^k and(xy) ^l =(yx) ^l , wherek andl are relatively prime positive integers, depending onx andy. ThenR is commutative. Moreover, examples are given which show thatR need not be commutative if either of the above identities is dropped. This theorem is also true for groups. Presented by N. S. Mendelsohn.     

Stress in aerogel during depressurization of autoclave: II. Silica gels

Although supercritical drying avoids the capillary stresses that tend to warp and crack xerogels, there are other sources of stress that interfere with the preparation of monolithic aerogels. In this paper, we present experimental results showing that there is a limit to the rate at which the pressure can be released from the autoclave without causing cracking, and that the maximum rate decreases as the gel size increases. Using an analysis developed in a companion paper, the stresses generated during depressurization are compared to the modulus of rupture of our aerogels. The calculations require knowledge of the pressure-dependence of the density of the vapor (ethanol, in our experiments), as well as the permeability and modulus of the gel network. Measurements of those properties were performed on a series of silica gels made under basic and neutral conditions. We find that the calculated stresses are large enough to account for the cracking of our gels at high rates of depressurization; moreover, the predicted dependence of stress on gel diameter is in agreement with experiment.     

Nanosensors having dipicolinic acid imprinted nanoshell for Bacillus cereus spores detection

Molecular imprinted polymers (MIPs) as a recognition element for sensors are increasingly of interest and MIP nanoclusters have started to appear in the literature. In this study, we have proposed a novel thiol ligand-capping method with polymerizable methacryloylamido-cysteine (MAC) attached to gold–silver nanoclusters, reminiscent of a self-assembled monolayer and have reconstructed surface shell by synthetic host polymers based on molecular imprinting method for recognition. In this method, methacryloylamidoantipyrine–terbium ((MAAP)₂–Tb(III)) has been used as a new metal-chelating monomer via metal coordination–chelation interactions and dipicolinic acid (DPA) which is main participant of Bacillus cereus spores used as a model. Nanoshell sensors with templates give a cavity that is selective for DPA. The DPA can simultaneously chelate to Tb(III) metal ion and fit into the shape-selective cavity. Thus, the interaction between Tb(III) ion and free coordination spheres has an effect on the binding ability of the gold–silver nanoclusters nanosensor. The binding affinity of the DPA imprinted nanoclusters has been investigated by using the Langmuir and Scatchard methods, and the respective affinity constants (K _affinity) determined were found to be 1.43 × 10⁴ and 9.1 × 10⁶ mol L^?1.     

Converses of the Jensen inequality derived from the Green functions with applications in information theory

Jensen integral inequality has got much importance regarding their applications in different fields of mathematics. In this paper, two converses of Jensen integral inequality for convex function are obtained. The results are applied to establish converses of Hölder and Hermite-Hadamard inequalities as well. At the end, some useful applications in information theory of the obtained results are given. The idea used in this paper may inculcate further research.     

Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations

We introduce a proximal bundle method for the numerical minimization of a nonsmooth difference-of-convex (DC) function. Exploiting some classic ideas coming from cutting-plane approaches for the convex case, we iteratively build two separate piecewise-affine approximations of the component functions, grouping the corresponding information in two separate bundles. In the bundle of the first component, only information related to points close to the current iterate are maintained, while the second bundle only refers to a global model of the corresponding component function. We combine the two convex piecewise-affine approximations, and generate a DC piecewise-affine model, which can also be seen as the pointwise maximum of several concave piecewise-affine functions. Such a nonconvex model is locally approximated by means of an auxiliary quadratic program, whose solution is used to certify approximate criticality or to generate a descent search-direction, along with a predicted reduction, that is next explored in a line-search setting. To improve the approximation properties at points that are far from the current iterate a supplementary quadratic program is also introduced to generate an alternative more promising search-direction. We discuss the main convergence issues of the line-search based proximal bundle method, and provide computational results on a set of academic benchmark test problems.     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.     

EXPERIMENTAL STUDY OF TURBULENT NATURAL CONVECTION IN A TALL AIR CAVITY

Abstract

This article describes an experimental study of turbulent natural convection in an air cavity with an aspect ratio of 28.6. The study provides data for the velocities and temperatures at a Rayleigh number based on cavity width of 0.83 × 10⁶, which is useful in validating computational and theoretical results. A laser Doppler anemometer was used for velocity measurements, while fine thermocouples were used for temperature measurements. Heal transfer rates and heat losses from the cell are evaluated. Further, the experimental data in the central portion of the tall cavity have been averaged to simulate an antisymmetric, Boussinesq, fully developed flow in an infinitely tall air cavity. Causes of asymmetry of the data, including radiation absorption, are also assessed.     

Nonsmooth nonconvex optimization approach to clusterwise linear regression problems

Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis.     

CuSO4/sodium ascorbate catalysed synthesis of benzosuberone and 1,2,3-triazole conjugates: Design,synthesis and in vitro anti-proliferative activity

A novel series of conjugates of benzosuberone and 1,2,3-triazole i.e. 3-(4-phenyl-1H-1,2,3-triazol-1-yl)propyl-9-chloro-2,3-dimethyl-6,7-dihydro-5H-benzo[7]annulene-8-carboxylic acids (8a-j) were synthesized in good to excellent yields catalysed by CuSO₄ under milder reaction conditions and evaluated for their anti-proliferative activity. The structural elucidation of the prepared compounds was carried out using IR, ¹H NMR, ¹³C NMR and Mass spectral analysis. The newly synthesized derivatives (8a-j) were evaluated for their anti-proliferative activity against four human cell lines and the novel derivatives showed moderate to excellent activity. The obtained results suggest that these compounds can be considered as new hits for anti-proliferative drug development programme and further SAR studies can help obtain better anticancer agents.