Extended Graph of the Fuzzy Topographic Topological Mapping Model

Fuzzy topological topographic mapping (FTTM) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, FTTMn, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of FTTM, namely the homeomorphisms between its components, allows the generation of new FTTM. The generated FTTMs can be represented as pseudo graphs. A graph of pseudo degree zero is a special type of graph where each of the FTTM components differs from the one adjacent to it. Previous researchers have investigated and conjectured the number of generated FTTM pseudo degree zero with respect to n number of components and k number of versions. In this paper, the conjecture is proven analytically for the first time using a newly developed grid-based method. Some definitions and properties of the novel grid-based method are introduced and developed along the way. The developed definitions and properties of the method are then assembled to prove the conjecture. The grid-based technique is simple yet offers some visualization features of the conjecture.

A Composite Initialization Method for Phase Retrieval

Phase retrieval is a classical inverse problem with respect to recovering a signal from a system of phaseless constraints. Many recently proposed methods for phase retrieval such as PhaseMax and gradient-descent algorithms enjoy benign theoretical guarantees on the condition that an elaborate estimate of true solution is provided. Current initialization methods do not perform well when number of measurements are low, which deteriorates the success rate of current phase retrieval methods. We propose a new initialization method that can obtain an estimate of the original signal with uniformly higher accuracy which combines the advantages of the null vector method and maximal correlation method. The constructed spectral matrix for the proposed initialization method has a simple and symmetrical form. A lower error bound is proved theoretically as well as verified numerically.

Spectral Norm Regularization for Blind Image Deblurring

Blind image deblurring is a well-known ill-posed inverse problem in the computer vision field. To make the problem well-posed, this paper puts forward a plain but effective regularization method, namely spectral norm regularization (SN), which can be regarded as the symmetrical form of the spectral norm. This work is inspired by the observation that the SN value increases after the image is blurred. Based on this observation, a blind deblurring algorithm (BDA-SN) is designed. BDA-SN builds a deblurring estimator for the image degradation process by investigating the inherent properties of SN and an image gradient. Compared with previous image regularization methods, SN shows more vital abilities to differentiate clear and degraded images. Therefore, the SN of an image can effectively help image deblurring in various scenes, such as text, face, natural, and saturated images. Qualitative and quantitative experimental evaluations demonstrate that BDA-SN can achieve favorable performances on actual and simulated images, with the average PSNR reaching 31.41, especially on the benchmark dataset of Levin et al.

Analysis of Bandwidth and Working Frequency of Bi-circular Antenna

This paper discusses the analysis results of determining the bandwidth and working frequency of a bi-circular antenna design. The analysis was carried out using three approaches, namely the FDTD simulation method, the measurement method using a network analyzer on the fabrication results of the antenna design, and the method of applying the bi-polygonal antenna model to the bi-circular antenna design. The novelty in this research is the application of the bi-polygonal antenna model and the comparison of the results of determining the bandwidth and working frequency of a bi-circular antenna with these three methods. Based on the results of the analysis using these three methods, it was found that different bandwidth values and the same antenna working frequency value were 2.45 GHz. The modeling results give a narrow and symmetrical form of return loss vs. frequency curve, the simulation results give a wide and slightly symmetrical form of return loss vs. frequency curve, and the measurement results give a wide and asymmetrical shape of return loss vs. frequency curve.

USING THE DUALITY PRINCIPLE WHEN CONSTRUCTING EXERCISES AT THE GEOMETRY LESSONS

Geometry is one of the complex disciplines where many facts are interconnected. It is possible to develop the idea of facts interrelations through correlation using the duality principle. The duality principle is known in projective geometry, mathematical logic. This principle is clearly pronounced in one of the theorems of new triangle geometry. The traditional analytical geometry course does not study the facts of new triangle geometry. To reinforce many topics of the analytical geometry course, for example, “The distance between two points”, “The symmetrical form of the equation of a line”, “The angle between two lines”, it is reasonable to consider some facts from the new triangle geometry in the Cartesian coordinate system. Thus, an element of novelty is introduced to the reviewed material. The guidebooks on triangle geometry solve tasks through classical approaches or applying barycentric coordinates not using analytical geometry formulas. The paper proposes the constructing technique for the couples of exercises using the duality principle in the plane geometry teaching methods. Tasks are constructed for the Cartesian coordinate system as this allows demonstrating the duality of points in the drawings. In the composed exercises, two drawings are constructed in parallel columns. In different cases, the points can be the triangle-apexes, an orthocenter, or a height base. The initial triangle sides are located on the axes of coordinates, and their side lengths set up Pythagorean triple for better understanding the task-solving algorithm by the students. The symmetrical form of the equation of a line shows the necessity of analytical study since it is difficult to check the distance from the orthocenter to the orthotriangle sides in the drawings due to the small value. For many such information units, the aggregation relationships (whole-part) are set up, reflecting the geometric embedding of components.

Síndrome de Guillain Barré: perfil clínico epidemiológico e assistência de enfermagem

Introducción: El Síndrome de Guillain-Barré (SGB) se considera una polineuropatía inflamatoria aguda.Objetivo: Conocer las características sociodemográficas, clínicas epidemiológicas y asistenciales de pacientes internados con SGB en un hospital escolar del Oeste de Paraná.Metodología: Se trata de una investigación cuantitativa, retrospectiva acerca de la caracterización sociodemográfica, clínica epidemiológica y asistencial de pacientes internados con SGB en un hospital escolar en el período de 2013 a 2017. Totalizando 23 pacientes cuyos prontuarios electrónicos fueron analizados.Todos los análisis estadísticos se realizaron en el programa XLStat (2010).Resultados: La mayoría de los pacientes presentó edades entre 51 y 60 años (31,12%), seguidas de las edades de 41 a 50 años (13,04%) y menores de 15 años (13,04%), sexo masculino (60, 87), con gran parte presentando síntomas infecciosos previos como mialgia, cefalea, fiebre, diarrea. Los síntomas referentes a SGB presentados en el período de 4 a 9 días antes de la internación englobó la forma ascendente, simétrica, con disminución de la fuerza muscular. Durante la internación fueron sometidos a procedimientos como cateterismo vesical y punción venosa periférica. Entre los exámenes de laboratorio se destacó el hemograma y diagnóstico a la electroneuromiografía. El tratamiento principal fue la inmunoglobulina. La mayoría de los pacientes presentó alta dependencia de asistencia de enfermería conforme sistema de clasificación de pacientes de Fugulin.Conclusión: El desarrollo de estudios que propician el conocimiento de la caracterización de un grupo específico de pacientes atacados por una enfermedad considerada rara, se constituyen en instrumentos para la planificación en salud. Introduction: Guillain-Barré syndrome (GBS) is considered an acute inflammatory polyneuropathy. Objective: To know the socio-demographic, clinical epidemiological and care characteristics of patients hospitalized with GBS in a school hospital in the West of Paraná. Methodology: This is a quantitative, retrospective study about the socio-demographic characterization, clinical epidemiology and care of hospitalized patients with GBS in a school hospital from 2013 to 2017. Totaling 23 patients whose electronic records were analyzed. All statistical analyzes were performed in the XLStat program (2010). Results: The majority of the patients presented ages ranging from 51 to 60 years (31.12%), followed by ages 41 to 50 (13.04%) and under 15 (13.04%), male (60.87) , with most presenting previous infectious symptoms such as myalgia, headache, fever, diarrhea. The symptoms related to GBS presented in the period from four to nine days before admission included the ascending, symmetrical form with a decrease in muscle strength. During the hospitalization they underwent procedures such as bladder catheterization and peripheral venous puncture. Among the laboratory exams, the blood test and diagnosis of electro-urography were highlighted. The main treatment was immunoglobulin. Most of the patients presented high dependence for nursing care according to Fugulin's patient classification system. Conclusion: The development of studies that allow the knowledge of the characterization of a specific group of patients affected by a disease considered rare, constitute instruments for health planning. Introdução: A Síndrome de Guillain-Barré (SGB) é considerada uma polineuropatia inflamatória aguda. Objetivo: Conhecer as características sócio demográficas, clínica epidemiológicas e assistenciais de pacientes internados com SGB em um hospital escola do Oeste do Paraná. Metodologia: Trata-se de uma pesquisa quantitativa, retrospectiva acerca da caracterização sócio demográfica, clínica epidemiológica e assistencial de pacientes internados com SGB em um hospital escola no período de 2013 a 2017. Totalizando 23 pacientes cujos prontuários eletrônicos foram analisados. Todas as análises estatísticas foram realizadas no programa XLStat (2010). Resultados: A maioria dos pacientes apresentou idades entre 51 e 60 anos (31,12%), seguidas das idades 41 a 50 anos (13,04%) e menores de 15 anos (13,04%), sexo masculino (60,87), com grande parte apresentando sintomas infecciosos prévios como mialgia, cefaleia, febre, diarreia. Os sintomas referentes a SGB apresentados no período de 4 a 9 dias antes da internação englobou a forma ascendente, simétrica, com diminuição da força muscular. Durante a internação foram submetidos a procedimentos como cateterismo vesical e punção venosa periférica. Entre os exames laboratoriais destacou-se o hemograma e diagnóstico a eletroneuromiografia. O tratamento principal foi a imunoglobulina. A maioria dos pacientes apresentou alta dependência para assistência de enfermagem conforme sistema de classificação de pacientes de Fugulin. Conclusão: O desenvolvimento de estudos que propiciam o conhecimento da caracterização de um grupo específico de pacientes acometidos por uma doença considerada rara, constituem-se em instrumentos para o planejamento em saúde.

A problem of measuring quantity of liquid inside moving tank and possible ways to resolve it

The article describes a problem of measuring quantity of liquid substance inside moving tank. The problem consists in low accuracy in this type of measurement that is significantly lower than accuracy of such measurements provided in unmovable fixed tanks. Mostly, this problem is spread in transport: aviation, sea vessels, space rockets and automobiles, and it refers for measuring fuel in tanks, coolant volume, amount of various liquid substance under transportation etc. Low accuracy of obtained measurement data affects vehicle technical performance, leads to financial losses and even provokes some safety issues. There are several factors that increase measurement error during measuring inside a tank that is being under dimensional and angular motion. All of them change shape and position of liquid surface and make measuring process more complicated. Influence of some of these factors could be eliminated if the tank has symmetrical form, level sensor is installed along tank axe, and measurements are provided at middle part of tank height. If there are no such conditions, we face the discussed problem. The abovementioned factors are: tank inclination, tank acceleration, free motion of liquid surface, drastic changes in the shape of the liquid surface in case if the liquid surface position is shifting while it is located at nearby tank top or bottom area.Author made a review with the aim to analyze how this problem is treated in various transportation systems. The review shows that the problem of measuring quantity of liquid substance inside moving tank is not resolved in general. Some partial solutions are presented, in particular, for measuring fuel quantity inside tanks of swinging sea-based launch vehicle. But it is still needed to find a general solution.The problem couldn't be solved only by instrumental methods. Some published papers indicate the possible ways to resolve the problem. They are related to computational methods of data processing. Thus, development of this methods and creation of the corresponding information and measuring technology should be recognized as a most perspective way to resolve the problem of measuring quantity of liquid inside moving tank.

More on algebraic properties of the discrete Fourier transform raising and lowering operators

In the present work, we discuss some additional findings concerning algebraic properties of the N-dimensional discrete Fourier transform (DFT) raising and lowering difference operators, recently introduced in [Atakishiyeva MK, Atakishiyev NM (2015), J Phys: Conf Ser 597, 012012; Atakishiyeva MK, Atakishiyev NM (2016), Adv Dyn Syst Appl 11, 81–92]. In particular, we argue that the most authentic symmetrical form of discretization of the integral Fourier transform may be constructed as the discrete Fourier transforms based on the odd points N only, while in the discrete Fourier transforms on the even points N this symmetry is spontaneously broken. This heretofore undetected distinction between odd and even dimensions is shown to be intimately related with the newly revealed algebraic properties of the above-mentioned DFT raising and lowering difference operators and, of course, is very consistent with the well-known formula for the multiplicities of the eigenvalues, associated with the N-dimensional DFT. In addition, we propose a general approach to deriving the eigenvectors of the discrete number operators N(N), that avoids the above-mentioned pitfalls in the structure of each even-dimensional case N = 2L.

Symmetries in Spaces, Symmetries in Listening

Based on the importance of the concept of symmetry in French sociological aesthetics circa 1900, this chapter analyzes the convergence of theaters, musical form, and musical understanding. The analysis focuses on architectural shape, audience response, and the musical repertoire in the new theaters built in Barcelona (1847), Paris (1862), and Rome (1880). While these theaters were fashioned after the baroque form of the “teatro all’italiana” that prevailed in Italy, France, and Spain during the late nineteenth century, they provided huge spaces accommodating a socially mixed audience within an architecturally symmetrical form. Music critics often aligned acoustic sound waves with actual visibility in the auditorium, and semicircular structures in the scenography on stage may have affected the reception of the musical performance. The newly built theaters arrived at a time when the “classical” music scene and a certain canon was developed, opposing the more “intellectual” audiences and repertories of contemporary music.

A new approach on electromagnetism with dual number coefficient octonion algebra

Dual number coefficient octonion (DNCO) is one of the kind of octonion, it has 16 components with an additional dual unit [Formula: see text]. Starting with DNCO algebra, we develop the generalized electromagnetic field equations of dyons regarding the DNCOS spaces, which has two octonionic space-times namely the octonionic internal space-time and the octonionic external space-time. Besides, the generalized four-potential components of dyons have been expressed with respect to the dual octonion form. Furthermore, we obtain the symmetrical form of Dirac–Maxwell equations, and the generalized potential wave equations for dyons in terms of the dual octonion. Finally, we conclude that dual octonion formulation is compact and simpler like octonion formulation.