Vanishing Component Research Articles

A vacuum transition in the FSM with a possible new take on the horizon problem in cosmology

The framed standard model (FSM), constructed to explain the empirical mass and mixing patterns (including CP phases) of quarks and leptons, in which it has done quite well, gives otherwise the same result as the standard model (SM) in almost all areas in particle physics where the SM has been successfully applied, except for a few specified deviations such as the [Formula: see text] mass and the [Formula: see text] of muons, that is, just where experiment is showing departures from what SM predicts. It predicts further the existence of a hidden sector of particles some of which may function as dark matter. In this paper, we first note that the above results involve, surprisingly, the FSM undergoing a vacuum transition (VTR1) at a scale of around 17[Formula: see text]MeV, where the vacuum expectation values of the colour framons (framed vectors promoted into fields) which are all nonzero above that scale acquire some vanishing components below it. This implies that the metric pertaining to these vanishing components would vanish also. Important consequences should then ensue, but these occur mostly in the unknown hidden sector where empirical confirmation is hard at present to come by, but they give small reflections in the standard sector, some of which may have already been seen. However, one notes that if, going off at a tangent, one imagines colour to be embedded, Kaluza–Klein (KK) fashion, into a higher-dimensional space–time, then this VTR1 would cause 2 of the compactified dimensions to collapse. This might mean then that when the universe cooled to the corresponding temperature of [Formula: see text] K when it was about [Formula: see text] s old, this VTR1 collapse would cause the three spatial dimensions of the universe to expand to compensate. The resultant expansion is estimated, using FSM parameters previously determined from particle physics, to be capable, when extrapolated backwards in time, of bringing the present universe back inside the then horizon, solving thus formally the horizon problem. Besides, VTR1 being a global phenomenon in the FSM, it would switch on and off automatically and simultaneously over all space, thus requiring seemingly no additional strategy for a graceful exit. However, this scenario has not been checked for consistency with other properties of the universe and is to be taken thus not as a candidate solution of the horizon problem but only as an observation from particle physics which might be of interest to cosmologists and experts in the early universe. For particle physicists also, it might serve as an indicator for how relevant this VTR1 can be, even if the KK assumption is not made.

Existence of Controls Insensitizing the Rotational of the Solution of the Navier–Stokes System Having a Vanishing Component

Existence of Controls Insensitizing the Rotational of the Solution of the Navier–Stokes System Having a Vanishing Component

Controllability results for cascade systems of m coupled N-dimensional stokes and Navier-stokes systems by N – 1 scalar controls

In this paper we deal with the controllability properties of a system of m coupled Stokes systems or m coupled Navier-Stokes systems. We show the null-controllability of such systems in the case where the coupling is in a cascade form and when the control acts only on one of the systems. Moreover, we impose that this control has a vanishing component so that we control a m × N state (corresponding to the velocities of the fluids) by N — 1 distributed scalar controls. The proof of the controllability of the coupled Stokes systems is based on a Carleman estimate for the adjoint system. The local null-controllability of the coupled Navier-Stokes systems is then obtained by means of the source term method and a Banach fixed point.

Compact stellar model in higher torsion gravitational theory

In this study, we address the issue of a spherically symmetrical interior solution to the quadratic form of f(T)=T+ϵT2 gravitational theory using a physical tetrad that provides vanishing components of the off-components of the field equation, in contrast to what exists in the current literature. To be able to formulate the resulting differential equation in a closed form, we employ the Krori-Barua (KB) ansatz. Using the KB spacetime form, we derive the analytic form of the energy-density, radial, and tangential pressures and the anisotropic form. All of these quantities are affected by the dimensional parameter ϵ, which causes them to have a noted difference from those given in the frame of Einstein general relativity. The derived model of this study exhibits a non-trivial form of torsion scalar, and it also contains three constants that we drew from the matching of the boundary condition with a line element that also features a non-trivial form of torsion scalar. Having established the physical conditions that are needed for any real stellar, we check our model and show in detail that it bypasses all of these. Finally, we analyze the model's stability utilizing the Tolman-Oppenheimer-Volkoff equation and adiabatic index and show that our model satisfies these.

Transportation dynamics of dielectric particles with the gradient forces in the field of orthogonal standing laser waves

We develop the theory of transportation and localization of a transparent dielectric spherical particle with the gradient forces in the interference field of orthogonally directed standing laser waves Ez(coskz) and Ex(coskx). It is shown that, when the waves Ez and Ex are coherent, the interference radiation field contains two harmonic components with the periods Λ0=π/k and ΛΔ=π/ksin(π/4). The amplitudes of the gradient force components depend on the ratio of the particle radius R to the modulation periods due to inhomogeneity of radiation in the particle volume and are given by the Bessel functions J3/2(2πR/Λ0) and J3/2(2πR/ΛΔ). We find the critical particle radii R0 and RΔ=2R0 defined by the Bessel functions zeros and corresponding to the vanishing components of the gradient forces. In particular, for the radiation with the wavelength λ0=1.064 μm and a particle in water, the smallest critical radii are R0=0.286 μm and 0.492 μm and RΔ=0.404 μm and 0.696 μm, respectively. For a number of special cases, we obtain the analytical solutions of the Newton equations and the particle trajectories that depend on the ratio of wave intensities and the particle radius. The results can be used to study the dynamics of the “optical assembly” of a two-dimensional particles matrix which behaves as a molecular crystal [Mellor and Bain, Chem. Phys. Chem. 7 (2006) 329–332].

Remarks on local controllability for the Boussinesq system with Navier boundary condition

This note deals with the local exact controllability to a particular class of trajectories for the Boussinesq system with nonlinear Navier–slip boundary conditions and internal controls having vanishing components. Briefly speaking, in two dimensions, the local exact controllability property is obtained using only one control in the heat equation, whereas two scalar controls are required in three dimensions.

Classification of Well Log Data Using Vanishing Component Analysis

This study reports the application of the novel supervised learning approach called vanishing component analysis (VCA) for the classification of lithologies from well log signal data. Geophysical well log data is always non-linear due to anisotropy and heterogeneity of the earth. The main purpose of this study is to test the applicability of the VCA algorithm on non-linear geophysical data of Siraj South-01, Middle Indus Basin, Pakistan for classification of lithologies/facies. We demonstrate the performance and stability of the novel approach on a case study before applying it on well log data. Our analysis demonstrates that VCA algorithm is able to linearly separate such a complex non-linear well log data and clearly distinguish between different classes of well log data coming from different rock units. Furthermore, we show that the average accuracies of the classification methods of linear support vector machines, eXtreme gradient boosting, random forest, neural network and linear discriminant analysis on the VCA feature space are much better than the average accuracy obtained by the same methods on the original data.

Deep vanishing component analysis network for pattern classification

Abstract Convolutional neural networks (CNN) have achieved great success in image classification, object detection and semantic segmentation. Generally, CNN is stacked by layers of convolutional filtering, entry-wise nonlinearities, and pooling operators, where convolutional filtering and pooling can be regarded as the operators for feature transformation and dimensionality reduction, respectively. However, CNN was suggested for images and signals, and cannot be used to samples in general vector form. Motivated by the CNN structure, in this paper we propose a deep vanishing component analysis network (DVN) for pattern classification of samples in general vector form. To be specific, vanishing component analysis is utilized for non-linear feature transformation and principal component analysis for dimensionality reduction, while Gentle Adaboost is employed for entry-wise nonlinearities and feature selection. DVN can thus utilize the multi-layer network architecture stacked by VCA, PCA and Gentle Adaboost for pattern classification. Experimental results show that our DVN significantly outperforms the existing surficial learning methods, e.g., SVM, and is comparable or better than several deep learning approaches, e.g., DBN and DBM.

Improvement on the vanishing component analysis by grouping strategy

Vanishing component analysis (VCA) method, as an important method integrating commutative algebra with machine learning, utilizes the polynomial of vanishing component to extract the features of manifold, and solves the classification problem in ideal space dual to kernel space. But there are two problems existing in the VCA method: first, it is difficult to set a threshold of its classification decision function. Second, it is hard to handle with the over-scaled training set and oversized dimension of eigenvector. To address these two problems, this paper improved the VCA method and presented a grouped VCA (GVCA) method by grouping strategy. The classification decision function did not use a predetermined threshold; instead, it solved the values of all polynomials of vanishing component and sorted them, and then used majority voting approach to determine their classes. After that, a strategy of grouping training set was proposed to segment training sets into multiple non-intersecting subsets, which polynomials of vanishing component were later acquired through a VCA method, respectively, and finally combined into an integral set of vanishing component polynomial. What is more important is that it uses the bagging theory in ensemble learning to successfully expound and prove the correctness of the strategy of grouping training sets. It also compares the time complexity for training algorithm with and without grouping training sets, thus demonstrating the effectiveness of the grouping strategy. A series of experiments showed that the GVCA method proposed in the paper has a perfect classification performance with a rapid rate of convergence compared to other statistical learning methods.

Absence of Cyclotron Resonance in the Anomalous Metallic Phase in InO_{x}.

It is observed that many thin superconducting films with not too high disorder level (generally R_{N}/□<2000 Ω) placed in magnetic field show an anomalous metallic phase where the resistance is low but still finite as temperature goes to zero. Here we report in weakly disordered amorphous InO_{x} thin films that this anomalous metal phase possesses no cyclotron resonance and hence non-Drude electrodynamics. The absence of a finite frequency resonant mode can be associated with a vanishing downstream component of the vortex current parallel to the supercurrent and an emergent particle-hole symmetry of this metal, which establishes its non-Fermi-liquid character.

Nonlinear discriminant analysis based on vanishing component analysis

Most kernel-based nonlinear discriminant analysis methods need to compute the kernel distance between test samples and all of the training samples, but this approach consumes large volumes of time and memory, and it may be impractical when there is a large number of training samples. In this study, we propose a vanishing component analysis (VCA) based nonlinear discriminant analysis (VNDA) method. First, VNDA learns nonlinear mapping functions explicitly using the modified VCA method, before employing these functions to map the input feature onto a high-dimensional polynomial feature space, where the linear discriminant analysis (LDA) method is then applied. We prove that principal components analysis plus LDA is a special case of VNDA and that the set of mapping functions learned by VNDA is the best solution to the ratio trace problem in the degree bounded polynomial feature space. Unlike kernel-based methods, VNDA only stores these mapping functions instead of all the training samples in the test step. Experimental results obtained based on four simulated data sets and 15 real data sets demonstrate that the proposed method yields highly competitive test recognition results compared to the state-of-the-art methods, while consuming less memory and time resources.

Двойственные задачи плоских ползущих течений степенной несжимаемой среды

Для уравнений равновесия и совместности, описывающих ползущие плоские течения несжимаемой среды со степенной реологией, рассмотрен класс решений в форме произведения произвольной степени радиальной координаты на произвольную функцию угловой координаты полярной системы координат, покрывающей плоскость. Данный класс решений представляет асимптотику полей вблизи особой точки области, занятой рассматриваемой средой. Показана трансформация друг в друга точечными преобразованиями двух задач для плоскости с клиновидным вырезом, в одной из которых на границах выреза исчезают компоненты вектора поверхностных сил, а в другой - компоненты вектора скоростей. В ходе таких преобразований уравнения равновесия и совместности системы полевых уравнений переходят друг в друга, граничные условия одной задачи переходят в граничные условия другой задачи, а показатель степени реологического уравнения обращается. Для указанных двойственных нелинейных задач на собственные значения были изучены собственные решения и асимптотика полей вблизи вершины выреза в зависимости от показателя степени реологического уравнения и угла раствора выреза. При этом исследовалась ветвь собственных значений, связанная с собственным числом Хатчинсона-Райса-Розенгрена, известным по задаче о распределении напряжений в плоскости с разрезом для степенной среды. Двойственная задача дает распределение скоростей перемещений при течении степенной среды вблизи вершины жесткого клина. Найдены аналитические выражения для еще двух собственных чисел и установлено, что каждое из этих чисел отвечает за определенную простую структуру полей скоростей перемещений или напряжений в каждой из двойственных задач. Одно из этих собственных значений соответствует радиальному характеру течения среды и было обнаружено В. В. Соколовским, а в двойственной задаче отсутствует окружная компонента напряжений. Другое собственное значение соответствует одной ненулевой радиальной компоненте напряжений, а в двойственной задаче поле скоростей тривиально.

RADAR AUTOMATIC TARGET RECOGNITION BASED ON SEQUENTIAL VANISHING COMPONENT ANALYSIS

To reduce the complexity of classifler design in radar automatic target recognition (RATR), a novel RATR method for high range resolution proflle (HRRP) is proposed. Linearly separable features are extracted with sequential vanishing component analysis (SVCA) which is implemented by flnding the generators of each approximately vanishing polynomial set, and target classiflcation is implemented with linear classiflers. Experiments are carried out on simulated vehicle target data and MSTAR database, and the results demonstrate the e-ciency of the proposed method.

ŁOJASIEWICZ INEQUALITY ON NON-COMPACT DOMAINS AND SINGULARITIES AT INFINITY

We give a version of the Łojasiewicz inequality for the real polynomials on non-compact domains. The inequality takes in account not only distance to a fiber, but also distance to a polar set. It improves the recent results of [D. S. Tiep, H. H. Vui and N. T. Thao, Łojasiewicz inequality for polynomial functions on non-compact domains, Int. J. Math.23(4) (2012), Article ID: 1250033, 28 pp., doi:10.1142/S0129167X12500334], since we consider a distance to a smaller set. Then we use this new version of the inequality to obtain a sufficient condition for the existence of a vanishing component at infinity for real polynomials in several variables.

Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count

The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connected graphs are considered. Courant’s well-known nodal domain theorem applies in the present case, and sets an upper bound to the number of nodal domains of eigenvectors: arranging the spectrum as a non-decreasing sequence, and denoting by νn the number of nodal domains of the nth eigenvector, Courant’s theorem guarantees that the nodal deficiency n − νn is non-negative. (The above applies for generic eigenvectors. Special care should be exercised for eigenvectors with vanishing components.) The main result of this work is that the nodal deficiency for generic eigenvectors is equal to a Morse index of an energy functional whose value at its relevant critical points coincides with the eigenvalue. The association of the nodal deficiency to the stability of an energy functional at its critical points was recently discussed in the context of quantum graphs Band et al (2011 Commun. Math. Phys. at press (doi:10.1007/s00220-011-1384-9)) and Dirichlet Laplacian in bounded domains in Berkolaiko et al (2011 arXiv:1107.3489). This work adapts this result to the discrete case. The definition of the energy functional in the discrete case requires a special setting, substantially different from the one used in Band et al and Berkolaiko et al and it is presented here in detail.

Design, Development and Simulations of MHD Equations with its proto type implementations

The equations of motion of conducting fluid in a magnetic field are formulated. These consist of three sets. First is the mass conservation equation, second Navier Stokes equation which is Newton’s second law taking into account the force of magnetic field on moving charges. The electrical field effects are neglected as is usually done in MHD. The third set is Maxwell’s equation especially to monopole condition along with Ampere’s law with the current given by ohm’s law in a moving frame (the frame in which the moving particles of fluid is at rest).The mass conservation equation assuming the fluid to be incompressible leads us to express the velocity field as the curl of a velocity vector potential. The curl of the Navier Stokes equation leads to the elimination of pressure, there by leaving with an equation involving only magnetic field and the fluid velocity field. The curl of the Ampere law equation leads us to another equation relating to the magnetic field to the velocity field. A special case is considered in which the only non vanishing components of the fluid are the x and y components and the only non vanishing component of the magnetic field is z component. In this special case the velocity vector potential only has one non zero component and this is known as stream function. The MHD equation in this reduces to three partial differential equations for the three functions in 2D model. ? stream function embeds and components. Application of MHD system prototype has been worked and presented.

Local null controllability of the two-dimensional Navier–Stokes system in the torus with a control force having a vanishing component

In this paper we deal with the two-dimensional Navier–Stokes system in a torus. The main result establishes the local null controllability with internal controls having one vanishing component. The linearized control system around 0 is not null controllable: the nonlinear term is essential to get this null controllability. Our proof uses the return method together with previous results by Fursikov and Imanuvilov.

Domain walls in Lyra geometry

In this paper we have discussed two models of domain walls within the framework of Lyra geometry. An exact solution is obtained for a thick non static domain wall. The space time is non singular both in its spatial and temporal behavior and the gravitational field experienced by a test particle is attractive. It is found that these exists no particle horizon in our case. Also we have presented a spherical domain wall with non vanishing stress components in the direction perpendicular to the plane of the wall. The gravitational field of the domain wall is shown to be attractive in nature.

Changing Space, Making Race: Distance, Nostalgia, and the Folklorization of Blackness in Puerto Rico

In this article, I critique some of the discursive terms in which blackness is folklorized and celebrated institutionally as part of the nation in Puerto Rico. I examine a government-sponsored housing project that meant to revitalize and stylize the community of San Ant n, in Ponce, as a historic black site. Although government officials tried to preserve what they considered to be traditional aspects of this community, conflict arose because not all residents agreed with this preservationist agenda. I document the controversy, linking the government's approach to racial discourses that represent blackness as a vanishing and distant component of Puerto Rico. I argue that this inclusion and celebration complements ideologies of blanqueamiento (whitening) and race-mixture that distance blackness to the margins of the nation and romanticize black communities as remnants of a past era. I link these dynamics to modernizing State agendas and discourses of authenticity that fuel cultural nationalism worldwide.

Gravitational Field of Spherical Domain Walls

In this paper we have considered a spherically symmetric domain wall with non vanishing stress component in the direction perpendicular to the plane of the wall. The exact solutions are obtained using functional separability of metric coefficients. Also we have studied the motion of the test particles in different situations.