Lifting orthogonal representations to spin groups and local root numbers

Representations ofD _k ^* k ^* for a quaternion division algebraD _k over a local fieldk are orthogonal representations. In this note we investigate when these orthogonal representations can be lifted to the corresponding spin group. The results are expressed in terms of local root number of the representation.     

L p-multipliers for the Hilbert space valued functions on the Heisenberg group

It is well known that if m is an L ^p -multiplier for the Fourier transform on \mathbbRⁿ{\mathbb{R}^n} , (1 < p < ∞) then there exists a pseudomeasure σ such that T _m f = σ * f . A similar problem is discussed for the L ^p −Fourier multipliers for H{\mathcal{H}} -valued functions on the Heisenberg group, where H{\mathcal{H}} is a separable Hilbert space.     

Minimizing submodular functions over families of sets

We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results.Research partially supported by NSF contract 9302476-CCR, Air Force contract F49620-92-J-0125 and DARPA contract N00014-92-J-1799.     

Multi-fuzzy sets: An extension of fuzzy sets

In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic fuzzy set theory and L-fuzzy set theory.     

Stability criteria with less LMI variables for linear system with additive time-delays

In this technical note, equivalent stability criterion with minimal number of variables for three recently reported stability criteria is proposed for a class of linear systems with additive time-varying delays. The existing delay-dependent stability criteria for additive time-delay systems have more number of matrix variables in the LMI; and hence, they require more computational cost. The proposed equivalent criteria, unlike the original ones, encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criteria mathematically less complex and computationally more attractive. The complexity involved in the existing stability criteria is attributed to the fact the cross-terms that emanate from the time-derivative of the Lyapunov-Krasovskii functional are dealt with free-weighting matrices. Hence, apart from the matrix variables that are associated in the corresponding Lyapunov-Krasovskii functional, the existing criteria also have additional matrix variables in them. In this paper, we have devised techniques to eliminate the free-weighting matrices in the existing stability criteria without sacrificing the conservatism. The resulting equivalent stability criteria, therefore, have least possible number of variables in the LMI; and hence, have minimum computational burden. The effectiveness of the proposed equivalent criteria is validated on a numerical example.     

Peak effect studies in single crystals CeRu2 and 2H-NbS2

We have studied the peak effect (PE) phenomenon in single crystals of weakly pinned superconductors CeRu₂ and 2H-NbS₂. 2H-NbS₂ is iso-structural and iso-electronic to 2H-NbSe₂, whose similarity with CeRu₂ as regards the PE representing the order-to-disorder transformation of the flux line lattice was claimed some time ago. We report on the step change in equilibrium magnetization across the peak effect in CeRu₂. We also present the vortex phase diagram of 2H-NbS₂ obtained from the magnetization data, and compare the PE phenomenon in 2H-NbS₂ and 2H-NbSe₂.     

Composite MR image reconstruction and unaliasing for general trajectories using neural networks

In rapid parallel magnetic resonance imaging, the problem of image reconstruction is challenging. Here, a novel image reconstruction technique for data acquired along any general trajectory in neural network framework, called “Composite Reconstruction And Unaliasing using Neural Networks” (CRAUNN), is proposed. CRAUNN is based on the observation that the nature of aliasing remains unchanged whether the undersampled acquisition contains only low frequencies or includes high frequencies too. Here, the transformation needed to reconstruct the alias-free image from the aliased coil images is learnt, using acquisitions consisting of densely sampled low frequencies. Neural networks are made use of as machine learning tools to learn the transformation, in order to obtain the desired alias-free image for actual acquisitions containing sparsely sampled low as well as high frequencies. CRAUNN operates in the image domain and does not require explicit coil sensitivity estimation. It is also independent of the sampling trajectory used, and could be applied to arbitrary trajectories as well. As a pilot trial, the technique is first applied to Cartesian trajectory-sampled data. Experiments performed using radial and spiral trajectories on real and synthetic data, illustrate the performance of the method. The reconstruction errors depend on the acceleration factor as well as the sampling trajectory. It is found that higher acceleration factors can be obtained when radial trajectories are used. Comparisons against existing techniques are presented. CRAUNN has been found to perform on par with the state-of-the-art techniques. Acceleration factors of up to 4, 6 and 4 are achieved in Cartesian, radial and spiral cases, respectively.     

Preferential Solvation Studies of 1, 5 Diamino Anthraquinone in Binary Liquid Mixtures

The absorption and fluorescence spectra of 1,5-diaminoanthraquinone(1,5-DAAQ) have been investigated in organic solvents-Benzene(BZ), Ethanol (ETOH), Acetonitrile (AN), Dimethylformamide (DMF) and Dimethyl sulfoxide (DMSO). There is an intra molecular hydrogen bond formed between quinoid oxygen and the substituents NH₂ [C = O...H-N]. The interaction of the hydrogen atom of - NH₂ leads to red shift in both absorption and fluorescence spectra. The dipole moment ratio of 1,5 DAAQ in ground and excited states was calculated from stokes shift obtained from optical absorption and fluorescence spectra. Photo physical properties of 1,5-DAAQ dye was studied using this absorption and fluorescence spectroscopy techniques in binary liquid mixtures(AN + DMF, AN + DMSO, AN + ETOH and BZ + ETOH).     

Binary mixture of p‐methylbenzaldehyde with polar and nonpolar solvents

In this work, a combined theoretical and experimental study of binary mixture of liquid p‐methylbenzaldehyde (PMBz) is reported using ab initio calculations as well as Raman and IR spectroscopies. The purpose of this study was twofold: firstly, to describe the interaction of PMBz in terms of bonding energies and preferred geometries; and secondly, to characterize the spectroscopic effects on the vibrational modes of PMBz in the binary mixture of different polar and nonpolar solvents. The three vibrational modes, namely, carbonyl stretching, ν(C CH₃) and aldehydic (C H) vibrations have been analyzed in all the three solvents in different concentrations. The dependence of Raman linewidth on the concentration of PMBz of these modes was also taken into account. By analyzing the peak position and linewidth of these modes, it is seen that the solute–solvent interaction is stronger in BuOH and 1,2 dichloroethane (DCE) because of the hydrogen‐bonding interaction between these molecules. The formation of C H···O hydrogen bonds in liquid p‐methylbenzaldehyde is also investigated by Gaussian fitting. The ab initio calculations suggest several possible dimer configurations. Copyright © 2008 John Wiley & Sons, Ltd.     

Magnetic-Field-Controlled Quantum Critical Points in the Triangular Antiferromagnetic Cs2CuCl4-xBrx Mixed System

The triangular antiferromagnetic Cs₂CuCl_4-xBr_x mixed system is studied by neutron single-crystal diffraction in magnetic field. It shows a rich magnetic phase diagram consisting of four regimes depending on the Br concentration and is characterized by different exchange coupling mechanisms. For the investigated compositions from regime I (0 < x ≤ 1.5), a critical magnetic field B_c is found for a Br concentration x = 0.8 at B_c = 8.10(1) T and for x = 1.1 at B_c = 7.73(1) T and from regime IV (3.2 < x < 4) for x = 3.3 at B_c = 0.99(3) T. For magnetic fields larger than the respective B_c, magnetic superlattice reflections of these compounds are not found. The incommensurate magnetic wave vector q = (0, 0.470, 0) appears below the ordering temperature T_N = 0.51(1) K for Cs₂CuCl_3.2Br_0.8, and q = (0, 0.418, 0) below T_N = 1.00(6) K for Cs₂CuCl_0.3Br_3.7. Neutron diffraction experiments at around 60 mK for x = 3.7 in a magnetic field show the critical magnetic field at B_c = 7.94(16) T and the formation of the second magnetic phase at around 8.5 T depending on the temperature. Inelastic neutron scattering experiments for the compound from regime III (2 < x ≤ 3.2) with x = 2.2 show dynamical correlations at a temperature around 50 mK giving evidence for a spin liquid phase.