K1-xLaxCa2-xNb3O10, a Layered Perovskite Series with Variable Interlayer Cation Density, and LaCaNb3O10, a Novel Layered Perovskite Oxide with No Interlayer Cations

A series of layered perovskite oxides of the formula K1-xLaxCa2-xNb3O10 for 0 < x ≤ 1.0 have been prepared. All the members are isostructural, possessing the structure of KCa2Nb3O10. The interlayer potassium ions in the new series can be ion-exchanged with protons to give H1-xLaxCa2-xNb3O10. The latter readily forms intercalation compounds of the formula (CnH2n+1NH3)1-x LaxCa2-xNb3O10, just as the parent solid acid HCa2Nb3O10. The end member LaCaNb3O10 containing no interlayer cations is a novel layered perovskite oxide, being a n = 3 member of the series An-1BnX3n+1.

Evolution in the time series of vortex velocity fluctuations across different regimes of vortex flow

Investigations of vortex velocity fluctuation in time domain have revealed a presence of low frequency velocity fluctuations which evolve with the different driven phases of the vortex state in a single crystal of 2H-NbSe2. The observation of velocity fluctuations with a characteristic low frequency is associated with the onset of nonlinear nature of vortex flow deep in the driven elastic vortex state. (C) 2009 Elsevier B.V. All rights reserved.

Synthesis of Layered Perovskite Oxides, ACa2-xLaxNb3-xTix010 (A = K, Rb, Cs), and Characterization of New Solid Acids, HCa2-xLaxNb3-xTixOlo (0 < x d 2), Exhibiting Variable Bronsted Acidity?

Layered perovskite oxides of the formula ACa~,La,Nb3-,Ti,010 (A = K, Rb, Cs and 0 < x d 2) have been prepared. The members adopt the structures of the parent ACazNb3010. Interlayer alkali cations in the niobium-titanium oxide series can be ion-exchanged with Li+, Na+, NH4+, or H+ to give new derivatives. Intercalation of the protonated derivatives with organic bases reveals that the Bronsted acidity of the solid solution series, HC~ ~ , L ~ ,N~ ~ , T ~ ,dOep~eOnd, s on the titanium content. While the x = 1 member (HCaLaNbzTiOlo) is nearly as acidic as the parent HCazNb3010, the x = 2 member (HLazNbTizOlo) is a weak acid hardly intercalating organic bases with pKa - 11.3. The variation of acidity is probably due to an ordering of Nb/Ti atoms in the triple octahedral perovskite slabs, [Ca~,La,Nb~,Ti,0~0], such that protons are attached to NbO6 octahedra in the x = 1 member and to Ti06 octahedra in the x = 2 member.

Support vector machine for evaluating seismic-liquefaction potential using shear wave velocity

The use of the shear wave velocity data as a field index for evaluating the liquefaction potential of sands is receiving increased attention because both shear wave velocity and liquefaction resistance are similarly influenced by many of the same factors such as void ratio, state of stress, stress history and geologic age. In this paper, the potential of support vector machine (SVM) based classification approach has been used to assess the liquefaction potential from actual shear wave velocity data. In this approach, an approximate implementation of a structural risk minimization (SRM) induction principle is done, which aims at minimizing a bound on the generalization error of a model rather than minimizing only the mean square error over the data set. Here SVM has been used as a classification tool to predict liquefaction potential of a soil based on shear wave velocity. The dataset consists the information of soil characteristics such as effective vertical stress (sigma'(v0)), soil type, shear wave velocity (V-s) and earthquake parameters such as peak horizontal acceleration (a(max)) and earthquake magnitude (M). Out of the available 186 datasets, 130 are considered for training and remaining 56 are used for testing the model. The study indicated that SVM can successfully model the complex relationship between seismic parameters, soil parameters and the liquefaction potential. In the model based on soil characteristics, the input parameters used are sigma'(v0), soil type. V-s, a(max) and M. In the other model based on shear wave velocity alone uses V-s, a(max) and M as input parameters. In this paper, it has been demonstrated that Vs alone can be used to predict the liquefaction potential of a soil using a support vector machine model. (C) 2010 Elsevier B.V. All rights reserved.

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

Popular matchings with variable item copies

We consider the problem of matching people to items, where each person ranks a subset of items in an order of preference, possibly involving ties. There are several notions of optimality about how to best match a person to an item; in particular, popularity is a natural and appealing notion of optimality. A matching M* is popular if there is no matching M such that the number of people who prefer M to M* exceeds the number who prefer M* to M. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not admit popular matchings. This motivates the following extension of the popular matchings problem: Given a graph G = (A U 3, E) where A is the set of people and 2 is the set of items, and a list < c(1),...., c(vertical bar B vertical bar)> denoting upper bounds on the number of copies of each item, does there exist < x(1),...., x(vertical bar B vertical bar)> such that for each i, having x(i) copies of the i-th item, where 1 <= xi <= c(i), enables the resulting graph to admit a popular matching? In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c(i) is 1 or 2. We show a polynomial time algorithm for a variant of the above problem where the total increase in copies is bounded by an integer k. (C) 2011 Elsevier B.V. All rights reserved.

Symmetry Properties of the Large-Deviation Function of the Velocity of a Self-Propelled Polar Particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.

Variable Elimination in Linear Constraints

Gauss and Fourier have together provided us with the essential techniques for symbolic computation with linear arithmetic constraints over the reals and the rationals. These variable elimination techniques for linear constraints have particular significance in the context of constraint logic programming languages that have been developed in recent years. Variable elimination in linear equations (Guassian Elimination) is a fundamental technique in computational linear algebra and is therefore quite familiar to most of us. Elimination in linear inequalities (Fourier Elimination), on the other hand, is intimately related to polyhedral theory and aspects of linear programming that are not quite as familiar. In addition, the high complexity of elimination in inequalities has forces the consideration of intricate specializations of Fourier's original method. The intent of this survey article is to acquaint the reader with these connections and developments. The latter part of the article dwells on the thesis that variable elimination in linear constraints over the reals extends quite naturally to constraints in certain discrete domains.

Improved velocity method for the determination of coefficient of consolidation

Parkin (1978) suggested the velocity method based on the observation that the theoretical rate of consolidation and time factor plot on a log-log scale yields an initial slope of 1:2 up to 50% consolidation. A new method is proposed that is an improvement over Parkin's velocity method because it minimizes the problems encountered in using that method. The results obtained agree with the other methods in use.

Identification of Local Conformational Similarity in Structurally Variable Regions of Homologous Proteins Using Protein Blocks

Structure comparison tools can be used to align related protein structures to identify structurally conserved and variable regions and to infer functional and evolutionary relationships. While the conserved regions often superimpose well, the variable regions appear non superimposable. Differences in homologous protein structures are thought to be due to evolutionary plasticity to accommodate diverged sequences during evolution. One of the kinds of differences between 3-D structures of homologous proteins is rigid body displacement. A glaring example is not well superimposed equivalent regions of homologous proteins corresponding to a-helical conformation with different spatial orientations. In a rigid body superimposition, these regions would appear variable although they may contain local similarity. Also, due to high spatial deviation in the variable region, one-to-one correspondence at the residue level cannot be determined accurately. Another kind of difference is conformational variability and the most common example is topologically equivalent loops of two homologues but with different conformations. In the current study, we present a refined view of the ``structurally variable'' regions which may contain local similarity obscured in global alignment of homologous protein structures. As structural alphabet is able to describe local structures of proteins precisely through Protein Blocks approach, conformational similarity has been identified in a substantial number of `variable' regions in a large data set of protein structural alignments; optimal residue-residue equivalences could be achieved on the basis of Protein Blocks which led to improved local alignments. Also, through an example, we have demonstrated how the additional information on local backbone structures through protein blocks can aid in comparative modeling of a loop region. In addition, understanding on sequence-structure relationships can be enhanced through our approach. This has been illustrated through examples where the equivalent regions in homologous protein structures share sequence similarity to varied extent but do not preserve local structure.

Variable density approach for rotating shallow shell of variable thickness

A new approach based on variable density in conjunction with shallow shell theory is proposed to analyse rotating shallow shell of variable thickness. Coupled non-linear ordinary differential equations governing shallows shells of variable thickness are first derived before applying the variable density approach. Results obtained from the new approach compare well with FEM calculation for a wide range of profiles considered in this paper.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Combined convection in power-law fluids along a nonisothermal vertical plate in a porous medium

The problem of combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5 to 2.0.

Variable Sparsity Kernel Learning

This paper(1) presents novel algorithms and applications for a particular class of mixed-norm regularization based Multiple Kernel Learning (MKL) formulations. The formulations assume that the given kernels are grouped and employ l(1) norm regularization for promoting sparsity within RKHS norms of each group and l(s), s >= 2 norm regularization for promoting non-sparse combinations across groups. Various sparsity levels in combining the kernels can be achieved by varying the grouping of kernels-hence we name the formulations as Variable Sparsity Kernel Learning (VSKL) formulations. While previous attempts have a non-convex formulation, here we present a convex formulation which admits efficient Mirror-Descent (MD) based solving techniques. The proposed MD based algorithm optimizes over product of simplices and has a computational complexity of O (m(2)n(tot) log n(max)/epsilon(2)) where m is no. training data points, n(max), n(tot) are the maximum no. kernels in any group, total no. kernels respectively and epsilon is the error in approximating the objective. A detailed proof of convergence of the algorithm is also presented. Experimental results show that the VSKL formulations are well-suited for multi-modal learning tasks like object categorization. Results also show that the MD based algorithm outperforms state-of-the-art MKL solvers in terms of computational efficiency.