Deriving crisp and consistent priorities for fuzzy AHP-based multicriteria systems using non-linear constrained optimization

Fuzzy optimization models are used to derive crisp weights (priority vectors) for the fuzzy analytic hierarchy process (AHP) based multicriteria decision making systems. These optimization models deal with the imprecise judgements of decision makers by formulating the optimization problem as the system of constrained non linear equations. Firstly, a Genetic Algorithm based heuristic solution for this optimization problem is implemented in this paper. It has been found that the crisp weights derived from this solution for fuzzy-AHP system, sometimes lead to less consistent or inconsistent solutions. To deal with this problem, we have proposed a consistency based constraint for the optimization models. A decision maker can set the consistency threshold value and if the solution exists for that threshold value then crisp weights can be derived, otherwise it can be concluded that the fuzzy comparison matrix for AHP is not consistent for the given threshold. Three examples are considered to demonstrate the effectiveness of the proposed method. Results with the proposed constraint based fuzzy optimization model are more consistent than the existing optimization models.     

Polynomial approximation, local polynomial convexity, and degenerate CR singularities

We begin with the following question: given a closed disc and a complex-valued function , is the uniform algebra on generated by z and F equal to ? When F∈C¹(D), this question is complicated by the presence of points in the surface that have complex tangents. Such points are called CR singularities. Let p∈S be a CR singularity at which the order of contact of the tangent plane with S is greater than 2; i.e. a degenerate CR singularity. We provide sufficient conditions for S to be locally polynomially convex at the degenerate singularity p. This is useful because it is essential to know whether S is locally polynomially convex at a CR singularity in order to answer the initial question. To this end, we also present a general theorem on the uniform algebra generated by z and F, which we use in our investigations. This result may be of independent interest because it is applicable even to non-smooth, complex-valued F.     

A modified Brent’s method for finding zeros of functions

Brent’s method, also known as zeroin, has been the most popular method for finding zeros of functions since it was developed in 1972. This method usually converges very quickly to a zero; for the occasional difficult functions encountered in practice, it typically takes $O(n)$ iterations to converge, where $n$ is the number of steps required for the bisection method to find the zero to approximately the same accuracy. While it has long been known that in theory Brent’s method could require as many as $O(n^2)$ iterations to find a zero, such behavior had never been observed in practice. In this paper, we first show that Brent’s method can indeed take $O(n^2)$ iterations to converge, by explicitly constructing such worst case functions. In particular, for double precision accuracy, Brent’s method takes $2{,}914$ iterations to find the zero of our function, compared to the $77$ iterations required by bisection. Secondly, we present a modification of Brent’s method that places a stricter complexity bound of $O(n)$ on the search for a zero. In our extensive testing, this modification appears to behave very similarly to Brent’s method for all the common functions, yet it remains at worst five times slower than the bisection method for all difficult functions, in sharp contrast to Brent’s method.     

A Finite Deformation Microsphere Model for Magneto-Visco-Elastic Response in Magnetorheological Elastomers

In this work we present a novel approach to the modeling of magnetorheological elastomers (MREs) for finite deformations. Keeping in mind the composite nature at the microscale, we employ the microsphere model as an effective tool to capture the constitutive response of the material. The microsphere model has been successfully applied to the modelling of rubber-like materials. Here, we extend this approach by taking into account the effect of the magnetic dipole-dipole interactions on the orientation of the polymer chains. Thus, the presented microsphere model is directly motivated by considering the underlying phenomena at the microscale level. Finally the material model is embedded in a finite element framework and the results of a boundary value problems is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

From a Binary to a Quaternary Cocrystal: An Unusual Supramolecular Synthon

Formation of a stoichiometric quaternary cocrystal consisting of resorcinol ( RES ), tetramethylpyrazine ( TMP ), phenazine ( PHE ) and pyrene ( PYR ) is described. A closed tetrameric resorcinol‐heterocycle synthon, unusual in that it has two different linker bases rather than just one, is observed in this four‐component solid. The tetrameric synthon is formed by two RES molecules and the two pyridine bases TMP and PHE . The stoichiometric quaternary cocrystal grows in an epitaxial fashion on the surfaces of a RES.PHE binary cocrystal which is initially obtained from the mother liquor. By indexing the common crystal faces of the binary and quaternary cocrystals, and noting that no ternary solid is obtained, a plausible mechanism has been proposed for the formation of this rare supramolecular architecture.     

Evolution of absorption energy per unit thickness of damaged sandstone

Journal of Thermal Analysis and Calorimetry - This paper experimentally studies the evolution of absorption energy characteristics per unit thickness of Jhiri sandstone at variable temperatures...     

Rotational dynamics of propylene inside Na-Y zeolite cages

We report here the quasielastic neutron scattering (QENS) studies on the dynamics of propylene inside Na-Y zeolite using triple axis spectrometer (TAS) at Dhruva reactor, Trombay. Molecular dynamics (MD) simulations performed on the system had shown that the rotational motion involves energy larger than that involved in the translational motion. Therefore, rotational motion was not observed in our earlier QENS studies on propylene adsorbed Na-Y zeolite using a higher resolution spectrometer at Dhruva. Analysis of the TAS spectra revealed that the quasielastic broadening observed in propylene-loaded zeolite spectra is due to the rotational motion of the propylene molecules. This is consistent with our simulation result. Further, the rotational motion is found to be isotropic. The rotational diffusion coefficient has been obtained.      

Unravelling the Role of Water in Ultrafast Excited-State Relaxation Dynamics within Nano-Architectures of Chlorophyll a

Water plays a pivotal role in structural stability of supramolecular pigment assemblies designed for natural light harvesting (for example, chlorosome antenna complex) as well as their artificial analogs. However, the dynamic role of water in the context of excite-state relaxation has not been explored till date, which we report here. Using femtosecond transient absorption spectroscopy, we investigate the excited-state dynamics of two types of nano-scale assemblies of chlorophyll a with different structural motifs, rod-shaped and micellar assemblies, that depend on the water content. We show how water participates in excess energy dissipation by vibrational cooling of the non-thermally populated Q_y band at different rates in different types of clusters but exhibits no polar solvation dynamics. For the micelles, we observe a bifurcation of stimulated emission line shape, whereas a positive-to-negative switching of differential absorption is observed for the rods; both these observations are correlated with their specific structural aspects. Density functional theory calculations reveal two possible stable ground state geometries of dimers, accounting for the bifurcation of line shape in micelles. Thus, our study elucidates water-mediated structure–function relationship within these pigment assemblies.     

Design and Synthesis of Imidazole and Triazole Pyrazoles as Mycobacterium Tuberculosis CYP121A1 Inhibitors

The emergence of untreatable drug-resistant strains of Mycobacterium tuberculosis is a major public health problem worldwide, and the identification of new efficient treatments is urgently needed. Mycobacterium tuberculosis cytochrome P450 CYP121A1 is a promising drug target for the treatment of tuberculosis owing to its essential role in mycobacterial growth. Using a rational approach, which includes molecular modelling studies, three series of azole pyrazole derivatives were designed through two synthetic pathways. The synthesized compounds were biologically evaluated for their inhibitory activity towards M. tuberculosis and their protein binding affinity (K_D). Series 3 biarylpyrazole imidazole derivatives were the most effective with the isobutyl ( 10 f ) and tert-butyl ( 10 g ) compounds displaying optimal activity (MIC 1.562 μg/mL, K_D 0.22 μM ( 10 f ) and 4.81 μM ( 10 g )). The spectroscopic data showed that all the synthesised compounds produced a type II red shift of the heme Soret band indicating either direct binding to heme iron or (where less extensive Soret shifts are observed) putative indirect binding via an interstitial water molecule. Evaluation of biological and physicochemical properties identified the following as requirements for activity: LogP >4, H-bond acceptors/H-bond donors 4/0, number of rotatable bonds 5–6, molecular volume >340 ų, topological polar surface area <40 Ų.