On the problem of algebraic completeness for the invariants of the Riemann tensor. III.

We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.

Purely magnetic locally rotationally symmetric spacetimes

We consider all purely magnetic, locally rotationally symmetric (LRS) spacetimes. It is shown that such spacetimes belong to either LRS class I or III by the Ellis classification. For each class the most general solution is found exhibiting a disposable function and three parameters. A Segré classification of purely magnetic LRS spacetimes is given together with the compatibility requirements of two general energy–momentum tensors. Finally, implicit solutions are obtained, in each class, when the energy–momentum tensor is a perfect fluid.

Probing the flexibility of the DsbA oxidoreductase from Vibrio cholerae - a 15N -1H heteronuclear NMR relaxation analysis of oxidised and reduced forms of DsbA

We have determined the structure of the reduced form of the DsbA oxidoreductase from Vibrio cholerae. The reduced structure shows a high level of similarity to the crystal structure of the oxidized form and is typical of this class of enzyme containing a thioredoxin domain with an inserted α-helical domain. Proteolytic and thermal stability measurements show that the reduced form of DsbA is considerably more stable than the oxidized form. NMR relaxation data have been collected and analyzed using a model-free approach to probe the dynamics of the reduced and oxidized states of DsbA. Akaike's information criteria have been applied both in the selection of the model-free models and the diffusion tensors that describe the global motions of each redox form. Analysis of the dynamics reveals that the oxidized protein shows increased disorder on the pico- to nanosecond and micro- to millisecond timescale. Many significant changes in dynamics are located either close to the active site or at the insertion points between the domains. In addition, analysis of the diffusion data shows there is a clear difference in the degree of interdomain movement between oxidized and reduced DsbA with the oxidized form being the more rigid. Principal components analysis has been employed to indicate possible concerted movements in the DsbA structure, which suggests that the modeled interdomain motions affect the catalytic cleft of the enzyme. Taken together, these data provide compelling evidence of a role for dynamics in the catalytic cycle of DsbA.

On the problem of algebraic completeness for the invariants of the Riemann tensor. II

We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors do not possess a null eigenvector. We show that all cases are completely backsolvable in terms of sets of invariants from CZ. We provide algebraically complete sets for each canonically different space-time.

Syzygies of the polynomial invariants of the Riemann tensor

This thesis introduces a novel way of writing polynomial invariants as network graphs, and applies this diagrammatic notation scheme, in conjunction with graph theory, to derive algorithms for constructing relationships (syzygies) between different invariants. These algorithms give rise to a constructive solution of a longstanding classical problem in invariant theory.

Underdetermined blind source separation by parallel factor analysis in time-frequency domain

This paper presents a new time-frequency approach to the underdetermined blind source separation using the parallel factor decomposition of third-order tensors. Without any constraint on the number of active sources at an auto-term time-frequency point, this approach can directly separate the sources as long as the uniqueness condition of parallel factor decomposition is satisfied. Compared with the existing two-stage methods where the mixing matrix should be estimated at first and then used to recover the sources, our approach yields better source separation performance in the presence of noise. Moreover, the mixing matrix can be estimated at the same time of the source separation process. Numerical simulations are presented to show the superior performance of the proposed approach to some of the existing two-stage blind source separation methods that use the time-frequency representation as well.

Ultra-wideline 14N solid-state NMR as a method for differentiating polymorphs: glycine as a case study

Nitrogen-14 solid-state NMR (SSNMR) is utilized to differentiate three polymorphic forms and a hydrochloride (HCl) salt of the amino acid glycine. Frequency-swept Wideband, Uniform Rate, Smooth Truncated (WURST) pulses were used in conjunction with Carr-Purcell Meiboom-Gill refocusing, in the form of the WURST-CPMG pulse sequence, for all spectral acquisitions. The ¹⁴N quadrupolar interaction is shown to be very sensitive to variations in the local electric field gradients (EFGs) about the ¹⁴N nucleus; hence, differentiation of the samples is accomplished through determination of the quadrupolar parameters CQ and ηQ, which are obtained from analytical simulations of the ¹⁴N SSNMR powder patterns of stationary samples (i.e., static NMR spectra). Additionally, differentiation of the polymorphs is also possible via the measurement of ¹⁴N effective transverse relaxation time constants, T^eff2(¹⁴N). Plane-wave density functional theory (DFT) calculations, which exploit the periodicity of crystal lattices, are utilized to confirm the experimentally determined quadrupolar parameters as well as to determine the orientation of the ¹⁴N EFG tensors in the molecular frames. Several signal-enhancement techniques are also discussed to help improve the sensitivity of the ¹⁴N SSNMR acquisition method, including the use of selective deuteration, the application of the BRoadband Adiabatic INversion Cross-Polarization (BRAIN-CP) technique, and the use of variable-temperature (VT) experiments. Finally, we examine several cases where ¹⁴N VT experiments employing Carr-Purcell-Meiboom-Gill (CPMG) refocusing are used to approximate the rotational energy barriers for RNH3⁺ groups.

Tensor-variate restricted Boltzmann machines

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-order interaction structures. This paper introduces Tensor-variate Restricted Boltzmann Machines (TvRBMs) which generalize RBMs to capture the multiplicative interaction between data modes and the latent variables. TvRBMs are highly compact in that the number of free parameters grows only linear with the number of modes. We demonstrate the capacity of TvRBMs on three real-world applications: handwritten digit classification, face recognition and EEG-based alcoholic diagnosis. The learnt features of the model are more discriminative than the rivals, resulting in better classification performance.

Desenvolvimento de antenas de microfita com Patch em anel utilizando materiais ferrimagnéticos e metamateriais

In general, the materials used as substrates in the project of microstrip antennas are: isotropic, anisotropic dielectrics and ferrimagnetic materials (magnetic anisotropy). The use of ferrimagnetic materials as substrates in microstrip patch antennas has been concentrated on the analysis of antennas with circular and rectangular patches. However, a new class of materials, called metamaterials, has been currently the focus of a great deal of interest. These materials exhibit bianisotropic characteristics, with permittivity and permeability tensors. The main objective of this work is to develop a theoretical and numerical analysis for the radiation characteristics of annular ring microstrip antennas, using ferrites and metamaterials as substrates. The full wave analysis is performed in the Hankel transform domain through the application of the Hertz vector potentials. Considering the definition of the Hertz potentials and imposing the boundary conditions, the dyadic Green s function components are obtained relating the surface current density components at the plane of the patch to the electric field tangential components. Then, Galerkin s method is used to obtain a system of matrix equations, whose solution gives the antenna resonant frequency. From this modeling, it is possible to obtain numerical results for the resonant frequency, radiation pattern, return loss, and antenna bandwidth as a function of the annular ring physical parameters, for different configurations and substrates. The theoretical analysis was developed for annular ring microstrip antennas on a double ferrimagnetic/isotropic dielectric substrate or metamaterial/isotropic dielectric substrate. Also, the analysis for annular ring microstrip antennas on a single ferrimagnetic or metamaterial layer and for suspended antennas can be performed as particular cases

Antena de microfita com substrato metamaterial

This paper presents a theoretical and numerical analysis of the parameters of a rectangular microstrip antenna with metamaterial substrate. The metamaterial (MTM) theory was applied along with Transverse Transmission Line (LTT) method to characterize substrate quantities and obtain the general equations of the electromagnetic fields. A study on metamaterial theory was conducted to obtain the constructive parameters, which were characterized through permittivity and permeability tensors to arrive at a set of electromagnetic equations. Electromagnetic principes are used to obtained parameters such as complex resonance frequency, bandwidth and radiation pattern were then obtained. Different metamaterial and antenna configurations were simulated to miniaturize them physically and increase their bandwidth, the results of which are shown through graphics. The theoretical computational analysis of this work proved to be accurate when compared to other studies, and may be used for other metamaterial devices. Conclusions and suggestions for future work are also proposed

Bianisotropia uniaxial em estruturas irradiantes com multicamadas e supercondutores

This work presents a theoretical and numerical analysis of parameters of a rectangular microstrip antenna with bianisotropic substrate, and including simultaneously the superconducting patch. The full-wave Transverse Transmission Line - TTL method, is used to characterize these antennas. The bianisotropic substrate is characterized by the permittivity and permeability tensors, and the TTL gives the general equations of the electromagnetic fields of the antennas. The BCS theory and the two fluids model are applied to superconductors in these antennas with bianisotropic for first time. The inclusion of superconducting patch is made using the complex resistive boundary condition. The resonance complex frequency is then obtained. Are simulated some parameters of antennas in order to reduce the physical size, and increase the its bandwidth. The numerical results are presented through of graphs. The theoretical and computational analysis these works are precise and concise. Conclusions and suggestions for future works are presented

Caracterização de antenas planares com substrato metamaterial

This work presents a theoretical and numerical analysis for the radiation characteristics of rectangular microstrip antenna using metamaterial substrate. The full wave analysis is performed in the Fourier transform domain through the application of the Transverse Transmission Line - TTL method. A study on metamaterial theory was conducted to obtain the constructive parameters, which were characterized through permittivity and permeability tensors to arrive at a set of electromagnetic equations. The general equations for the electromagnetic fields of the antenna are developed using the Transverse Transmission Line - TTL method. Imposing the boundary conditions, the dyadic Green s function components are obtained relating the surface current density components at the plane of the patch to the electric field tangential components. Then, Galerkin s method is used to obtain a system of matrix equations, whose solution gives the antenna resonant frequency. From this modeling, it is possible to obtain numerical results for the resonant frequency and return loss for different configurations and substrates

An Anisotropic Model of Damage and Unilateral Effect for Brittle Materials

This work deals with the initial applications and formulation of an aniscitropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.

Filtros acústicos em cristais fonônicos

In this work, we have studied the acoustic phonon wave propagation within the periodic and quasiperiodic superlattices of Fibonacci type. These structures are formed by phononic crystals, whose periodicity allows the raise of regions known as stop bands, which prevent the phonon propagation throughout the structure for specific frequency values. This phenomenon allows the construction of acoustic filters with great technological potential. Our theoretical model were based on the method of the transfer matrix, thery acoustics phonons which describes the propagation of the transverse and longitudinal modes within a unit cell, linking them with the precedent cell in the multilayer structure. The transfer matrix is built taking into account the elastic and electromagnetic boundary conditions in the superllatice interfaces, and it is related to the coupled differential equation solutions (elastic and electromagnetic) that describe each model under consideration. We investigated the piezoelectric properties of GaN and AlN the nitride semiconductors, whose properties are important to applications in the semiconductor device industry. The calculations that characterize the piezoelectric system, depend strongly on the cubic (zinc-bend) and hexagonal (wurtzite) crystal symmetries, that are described the elastic and piezoelectric tensors. The investigation of the liquid Hg (mercury), Ga (gallium) and Ar (argon) systems in static conditions also using the classical theory of elasticity. Together with the Euler s equation of fluid mechanics they one solved to the solid/liquid and the liquid/liquid interfaces to obtain and discuss several interesting physical results. In particular, the acoustical filters obtained from these structures are again presented and their features discussed