Geometric Point Research Articles

Topological analysis of stability regions of power systems considering global orbits

In this paper, the stability region of power systems is studied from a geometrical point of view. A new method is proposed to obtain the global orbits (GOs) which have the significance for making the stability region be more complete. This method is based on the theory of invariant manifolds and focuses on dynamical behavior at infinity. The boundary of the stability region (BSR) with respect to the stable manifolds of dimension-1 and dimension-2 are given to describe the topological characteristics of the stability region of a multi-machine system. The effect of damping coefficient on the stability region is discussed through the variation of the singularities at infinity. The GOs of the power system when subjected to large disturbance are analyzed with the time domain simulation. The validity of the proposed approach is demonstrated on a 16-machine 68-bus system. The simulation results reveal the types and characteristics of the GOs, which play an important role in the prediction of stability/instability of the postfault system.

Synthetic open cell foams versus a healthy human vertebra: Anisotropy, fluid flow and μ-CT structural studies.

Commercial synthetic open-cell foams are an alternative to human cadaveric bone to simulate in vitro different scenarios of bone infiltration properties. Unfortunately, these artificial foams do not reproduce the anisotropic microstructure of natural bone and, consequently, their suitability in these studies is highly questionable. In order to achieve scaffolds that successfully mimic human bone, microstructural studies of both natural porous media and current synthetic approaches are necessary at different length scales. In this line, the present research was conducted to improve the understanding of local anisotropy in natural vertebral bone and synthetic bone-like porous foams. To attain this objective, small volumes of interest within these materials were reconstructed via micro-computed tomography. The anisotropy of the microstructures was analysed by means of both their main local histomorphometric features and the behaviour of an internal flow computed via computational fluid dynamics. The results showed that the information obtained from each of the micro-volumes of interest could be scaled up to understand not only the macroscopic averaged isotropic and/or anisotropic behaviour of the samples studied, but also to improve the design of macroscopic porous implants better fitting specific local histomorphometric scenarios. The results also clarify the discrepancies in the permeability obtained in the different micro-volumes of interest analysed. STATEMENT OF SIGNIFICANCE: A deep insight comparative study between the porous microstructure of healthy vertebral bone and that of synthetic bone-like open-cell rigid foams used in in vitro permeability studies of bone cement has been performed. The results obtained are of fundamental relevance to computational studies because, in order to achieve convergence values, the computation process should be limited to small computation domains or micro-volumes of interest. This makes the results specific spatial dependent and for this reason computation studies cannot directly capture the macroscopic average behaviour of an anisotropic porous structure such as the one observed in natural bones. The results derived from this study are also important because we have been able to show that the specific spatial information contained in only one healthy vertebra is enough to capture, from a geometric point of view, the same information of "specific surface area vs. porosity" - in other words, the same basic law - that can also be found in other human bones for different patients, even at different biological ages. This is an important finding that, despite the efforts made and the controversies formulated by other authors, should be studied more thoroughly with other bone species and tissues (healthy and/or diseased). Moreover, our results should help to understand that, with the extensive capabilities of current 3D printing technologies, there is an enormous potential in the design of biomimetic porous bone-like scaffolds for bone tissue engineering applications.

New results on orbital resonances.

Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently reexamined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called "low-eccentricity resonant bridges" connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some - though not necessarily entire - resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.

Blt Azumaya algebras and moduli of maximal orders

We study moduli spaces of maximal orders in a ramified division algebra over the function field of a smooth projective surface. As in the case of moduli of stable commutative surfaces, we show that there is a Kollar-type condition giving a better moduli problem with the same geometric points: the stack of blt Azumaya algebras. One virtue of this refined moduli problem is that it admits a compactification with a virtual fundamental class.

К проблеме эволюции пространственных форм архитектуры в контексте научно-технологических достижений

Для архитектурной теории важно изучение фундамен­тальных механизмов формообразования и самой формы в контексте современных данных и концепций различных обла­стей науки. Подходы, используемые классической геометрией и «новыми», неевклидовыми геометриями могут быть в опреде­лённой мере применены для развития пространственного по­тенциала архитектуры и градостроительства. Инновационные пространственные формы возникают и развиваются на стыке науки и искусства, инженерии и зодчества. Рассматриваемая область исследований связана с различными научными обла­стями и специализациями, включающими геоинформатику, био­логию, математику, кристаллографию, инженерную геометрию и компьютерное моделирование. Инновационные технологии и новый инструментарий научной и практической работы проектировщика меняют принципы и концепции построения архитектурного пространства. В частности, проектирование чрезвычайно сложных с геометрической точки зрения кон­струкций было бы невозможным без развития компьютерных технологий. Междисциплинарный подход позволяет выявить спектр неизвестных ранее геометрических форм, вариантов за­полнения и разбиения двумерной поверхности и трёхмерного пространства. Интеграция и конвергенция научных достиже­ний, инженерного искусства и архитектуры нередко ведут к возникновению новаторских форм. Основные геометриче­ские закономерности едины в живой и неживой природе - в естественном и антропогенном мире, включая архитектуру, от микро- до макроуровня; при этом современное экологическое мышление осознаёт земную биосферу как интегрированное целое. Исследования актуализируются наступлением нового технологического уклада и синтезом технологий, размывающим границы между виртуальным и физическим миром. Данная тема носит теоретический характер; потенциально возможно применение результатов в учебной практике и эксперимен­тальном проектировании[1].
 
 [1] Статья подготовлена в рамках выполнения фундаментального научного исследования за счёт средств Государственной программы Российской Федерации «Развитие науки и технологий» на 2013-2020 годы по Плану фундаментальных научных исследований Минстроя России и РААСН, тема 1.4.6. «Технологии и проблемы формообразования в архитектурной теории и учебном процессе».

Analysis and Design of Decision Support System Systems in Choosing the Best Supplier Using the TOPSIS Method at PT. Bintang Putra Mandiri

Analysis and design of a decision support system aims to deal with problems in selecting the best supplier which is a problem at PT. Independent male star. PT. Bintang Putra Mandiri is a company engaged in the subsidized housing contractor and developer. With the existing problems, we need a system that can help companies to help determine the best supplier. Then produced a system that can help companies by using the TOPSIS method. TOPSIS uses the principle that the chosen alternative must have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution from a geometric point of view using the Euclidean distance to determine the relative proximity of an alternative to the optimal solution. As a result, PT. Bintang Putra Mandiri can determine the best supplier precisely. And the TOPSIS method is able to support supplier selection decisions by ranking

Fast and efficient calculations of structural invariants of chirality

Chirality describes the structural properties or configuration of an object, and it plays an important role in fields such as physics, chemistry and biology. It is critical to identify achiral objects and determine symmetry plane of them in shape analysis, and chiral invariants play essential role in above tasks. However, chiral invariants are often complex and time-consuming to calculate in practical applications. In this paper, we present five chiral invariants based on the concept of generating functions. Three of the five chiral invariants decode the expression of a chiral index, and they are the core part of this chiral index. In addition, this paper provides three new chiral invariants. These five chiral invariants have three characteristics: (1) Their results on the shape before and after the reflection transformation are opposite to each other. (2) The five chiral invariants have brief form and low time complexity (O(n)), the order and degree of them are not more than four. (3) They can be used to determine the global symmetry plane of reflection symmetry objects, and they help to deal with false zeros problem. The five chiral invariants give the invariants under reflection transformation from the geometrical point of view, and the experimental results show that they are effective and efficient. In conclusion, our invariants can be used for determining archiral objects and mutual symmetry shape, as well as for determining symmetry plane of reflection symmetry objects.

Three-Dimensional Aberration Analyses of Metasurface Flat Lenses

Three-dimensional analyses of optical aberrations of metasurface flat lenses are presented via ray tracing. The ray tracing is performed on the basis of anomalous refraction/reflection law specialized for metasurface instead of conventional Snell law. Relationship between spherical aberration and working distance, feature of chromatic aberration, astigmatism in meridian, and sagittal directions are analyzed numerically to fully reveal the aberration characteristics. Through the curve descriptions of geometric point spread function (PSF) and the modulation transfer function (MTF), the influence of monochrome aberration on the metasurface flat lenses is fully demonstrated. The results of the design model are instructive for the application of the metasurface flat lense–based high quality optical systems theoretically.

Enhanced understanding of leakage in mechanical seals with elliptical dimples based on CFD simulation

PurposeThe shapes of surface textures have been designed to control the leakage of mechanical seals in recent years. The purpose of this paper is to demonstrate the influence of geometric properties of elliptical dimples on the leakage rate.Design/methodology/approachA new geometric feature point is expressed using an analytical solution to locate the high-pressure zones. Furthermore, a numerical model of the three-dimensional flow field for the mechanical seal with elliptical dimples is developed using ANSYS Fluent to demonstrate the influencing mechanism.FindingsThe location of the proposed geometric converging point coincides with the maximum pressure point under different orientation angles. An inward flow on the leakage section observed from the simulation results is responsible for decreasing the leakage rate.Originality/valueThe influencing mechanism of the elliptical dimple on the leakage rate is demonstrated, which can facilitate the design of surface textures.

A polar coordinate system based on a projection surface for moon-based earth observation images

As a new potential platform for Earth observation, the Moon which is a natural satellite unique to the Earth has been paid more and more attention for its consistent and continuous observation capability of global-scale and macroscopic geoscience phenomena on Earth. Because of the effect of Earth curvature and the Earth–Moon geometric relationship, the geometric correction of the Moon-based Earth observation (MBEO) hemisphere images is more complex than that required for images obtained from low Earth orbit (LEO) platforms and need to be investigated, such as optical images in visible/thermal infrared frequencies or synthetic aperture radar (SAR) images in microwave frequency. In addition, it is also difficult to find the uniformly distributed geometric correction control points on the entire surface of the Earth caused by sea and cloud cover in most regions. In this paper, a polar coordinate system on a projection surface related to the sublunar point is designed to facilitate the geometric correction of MBEO hemisphere images and to try to compensate for the problems of geometrical distortion caused by the shift of the sublunar point, the curvature of the Earth and the terrain fluctuation. Through simulation analysis, the geometric error characteristics and conditions in which the proposed moon-projection polar coordinate system can be used are discussed. This involves considering the Earth model, the projection method, the offset of the sublunar point and the external error. The results show the validity and adaptation of the proposed polar coordinate system and will support the further study of the geometric correction of MEBO images.

Persistent homology of complex networks for dynamic state detection.

In this paper we develop an alternative topological data analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a compressed, multi-scale representation of the graph that can distinguish between dynamic states such as periodic and chaotic behavior. We show the approach for two graph constructions obtained from the time series. In the first approach the time series is embedded into a point cloud which is then used to construct an undirected k-nearest-neighbor graph. The second construct relies on the recently developed ordinal partition framework. In either case, a pairwise distance matrix is then calculated using the shortest path between the graph's nodes, and this matrix is utilized to define a filtration of a simplicial complex that enables tracking the changes in homology classes over the course of the filtration. These changes are summarized in a persistence diagram's two-dimensional summary of changes in the topological features. We then extract existing as well as new geometric and entropy point summaries from the persistence diagram and compare to other commonly used network characteristics. Our results show that persistence-based point summaries yield a clearer distinction of the dynamic behavior and are more robust to noise than existing graph-based scores, especially when combined with ordinal graphs.

Моделирование аппроксимирующего 16-точечного отсека поверхности отклика применительно к решению неоднородного уравнения теплопроводности

The paper proposes a computational method for solving differential equations of mathematical physics by approximating the desired solution using geometric objects of multidimensional space passing through predetermined points. The essence of the method is to simulate an approximating geometric object of a multidimensional affine space constructed on a regular multidimensional network of points. In this case, the response function values satisfying the solution of the original differential equation are calculated at the nodal points of the network. Modeling of approximating geometric object is carried out by means the arcs of algebraic curves passing through predetermined points. It should be noted that taking into account the boundary conditions does not require changes in the geometric algorithm or point equations. It is sufficient to use the necessary coordinates of the nodal boundary points corresponding to the boundary conditions of the solution of the differential equation. To achieve the required accuracy of the solution of differential equations, it is sufficient to compact the reference network of points. Under such conditions, it is possible to use as a single geometric object to approximate the solution of the differential equation, and composite, based on the simulation of multidimensional contours on a regular network of points of multidimensional space. A geometric classification of differential equations depending on the number of parameters determining the approximating geometric object in multidimensional space is proposed. An example of solving the inhomogeneous heat equation by means of an approximating response surface passing through 16 predetermined points is given. In this case, the required approximating compartment of the response surface passes through 3 straight lines that correspond to the boundary conditions and satisfies the solution of the original differential equation at the nodal points of the 16-point network. A comparison of the results of solving the inhomogeneous heat equation approximated by a 16-point compartment of the response surface with the reference compartment of the surface obtained by the method of separating variables is also presented.

Development of the Assembly-Level Monte Carlo Neutron Transport Code M3C for Reactor Physics Calculations

The general geometry continuous-energy Monte Carlo code M3C is currently under development at the Bhabha Atomic Research Centre for reactor physics calculations. The development of the Monte Carlo code M3C for reactor design entails the use of continuous-energy nuclear data and Monte Carlo simulations for each of the neutron interaction processes. This paper describes the current status of the development of the code. The performance and accuracy of the code in application to a variety of problems have been investigated. The important features of this code are treatment of heterogeneous lattices by general geometry, use of point cross sections along with unionized energy grid approach, thermal scattering model for low-energy treatment, probability table treatment in unresolved resonance range, and capability of handling the microscopic fuel particles (TRISO) dispersed randomly, which is very useful in modeling high temperature gas-cooled reactor fuels. Apart from all of the important features in any Monte Carlo code available worldwide, the M3C code has an advanced capability to handle the geometry, which is not described by mathematical equations but only represented by the geometrical points. The code has been validated for its accuracy against a large number of sample problems covering a wide range from simple (like spherical) to complex geometry (like pressurized heavy water reactor lattice) and including randomly dispersed TRISO fuel particle systems. The code is presently restricted to assembly-level calculations.

A new adaptive weighted imbalanced data classifier via improved support vector machines with high-dimension nature

The standard support vector machine (SVM) models are widely used in various fields, but we show that they are not rationally defined from the perspective of geometric point, which is likely to degrade the models’ performances theoretically, especially under the high-dimensional cases. In this paper, we consider a composite penalty and propose an elastic net support vector machine (ENSVM). Unlike the doubly regularized support vector machine (DrSVM, Wang et al. (2006)), we impose the penalty to the slack variables rather than the normal vectors of the hyperplane. Then, we prove that ENSVM is more rationally defined than standard SVM and DrSVM (in section 3.2.1). Moreover, the ENSVM demonstrates a more stable and high-dimension nature inherently, while the simulation results cogently support these merits. Besides, we also combine fused weights with ENSVM and propose an adaptive weighted elastic net support vector machine (AWENSVM), to make the primal model more adaptive and robust to the imbalanced data. Compared with the other popular SVMs, the AWENSVM model proposed in this paper performs better obviously.

Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models

The application of the geometric method of local geoid model determination which requires the fitting of geometric surfaces to known geoid heights to enable geoid heights of new points to be interpolated involves the use of least squares technique for computation of the models' parameters. The selection of polynomial geometric surfaces depends on the size of the study area, the variation of the geoid heights and the number of measurement points. The accuracy of the geometric geoid model increases as the number of observation points approximates the number of geometric surface terms. But in most cases, the number of observation points is not considered. To this effect, this paper presents the relationship between geometric surfaces terms and observation points numbers and effect in the accuracy of geometric geoid models. A total of 23 points of known local gravimetric geoid heights were used. Two polynomial geometric (third and fifth degrees) surfaces were fitted to the geoid heights at various observation point numbers and compared to determine the relationship between the number of model terms and that of observation points and effect in the accuracy of the models. Least squares adjustment technique was applied to obtain the model parameters. The differences between the models and the known geoid heights of the points were computed and used to obtain the RMSEs as well as the accuracy of the models. The obtained results showed that the accuracy of the polynomial geometric geoid models tends to the highest as the number of measurement points approximates the number of the model terms and in a unique solution where the number of observation points is equal to the number of the polynomial geometric model terms, the model accuracy is highest. The paper recommends that the geometric method of local geoid model determination should be strictly applied in small areas. Where the method will be applied in considerable large areas, higher degrees polynomial geometric surfaces with a larger number of terms approximating the number of observation points should be applied. This will enable a proper fit of the polynomial surface to the known geoid heights, as well as high accuracy to be obtained.

PERANCANGAN SPK KELAYAKAN PENERIMA KREDIT PADA DISKOPUKM PROVSU MENGGUNAKAN METODE TOPSIS

The Happy Savings and Loan Cooperative is one of the non-bank financial institutions in the form of cooperatives that serve the needs of its members in lending services with collateral in the form of member deposits, land or building certificates, books for motorized or automobile owners (BPKB) with the aim of providing services and facilities for candidates creditors in the economy. needs Lending funds to prospective creditors must also with the approval of the head of the cooperative / cooperative council. The agreement generally requires considerations such as analyzing the ability to pay prospective creditors. Because each prospective creditor has different economic conditions, it must be observant in making decisions. In determining whether a loan recipient is appropriate or not, there must be an assessment of the criteria established as a reference for decision making. TOPSIS is one of the multi-criteria decision-making methods first introduced by Yoon and Hwang (1981). TOPSIS uses the principle that the chosen alternative must have the shortest distance from the positive ideal solution and the longest distance (the farthest) from the negative ideal solution from a geometric point of view using the Euclidean distance (distance between two points) to determine the relative proximity of an alternative to the optimal solution.
 
 Keywords: TOPSIS, Decision Support System, North Sumatra Cooperative

Measurement of Period Length and Skew Angle Patterns of Textile Cutting Pieces Based on Faster R-CNN

The skew angle and period length of the multi-period pattern are two critical parameters for evaluating the quality of textile cutting pieces. In this paper, a new measurement method of the skew angle and period length is proposed based on Faster region convolutional neural network (R-CNN). First, a dataset containing approximately 5000 unique pattern images was established and annotated in the format of PASCAL VOC 2007. Second, the Faster R-CNN model was used to detect the pattern to determine the approximate location of the pattern (the position of the whole pattern). Third, precise position of the pattern (geometric center points of pattern) are processed based on the approximate position results using the automatic threshold segmentation method. Finally, the four-neighbor method was used to fill the missing center points to obtain a complete center point map, and the skew angle and period length can be measured by the detected center points. The experimental results show that the mean average position (mAP) of the pattern detection reached 84%, the average error of the proposed algorithm was less than 5% compared with the error of the manual measurement.

A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

Conceptual framework for enhancing visual change point analysis in generalized multi-temporal displays

Abstract. Large amounts of point data are being generated and depicted in web maps, in particular promoted by the availability of Volunteered Geographic Information (VGI). This data volume causes usability problems for the visual presentation and exploration, especially by decreasing rendering performance and increasing geometric or semantic point clutter. Typically, generalization techniques are applied in order to overcome these clutter problems. Appropriate constraint-based approaches have been developed for static and single displays.Due to the increasing amount and relevance of multi-temporal point data, the aim of this contribution is to present a so far missing conceptual framework that consists of constraints related to change point analysis. These constraints describe the effects of the generalization on preservation and legibility of change information. Here, different types of change point analysis are differentiated, namely: existential changes, changes of semantic properties, and changes of spatial properties. For this purpose, difference frames between two given frames of the multi-temporal data set are used as a model of the mental representation of change information.The resulting constraints can be used to describe and to compare the suitability of various generalization operations for specific tasks. However, in a later stage they can also trigger the generalization processes as such. This could lead to a new way of thinking, since the optimization of generalization processes should work on difference frames rather than on single views.

Influence of distance between sample surface and geometrical focal point on CN emission intensity from femtosecond laser-induced PMMA plasmas

In this study, a femtosecond laser is used to ablate polymethyl methacrylate and produce plasma with CN molecules to investigate the influence of the distance between the sample surface and geometrical focal point on CN emission intensity in air. The laser wavelength is 800 nm with a pulse width of 50 fs, and the laser energy ranges from 0.1 mJ to 1.5 mJ. It is determined that the spectral characteristics of the CN molecule depend on the distance between the sample surface and geometrical focal point, as well as the energy of the femtosecond laser. At the same energy, the spectral intensity of the CN molecule first increases, and then decreases with an increase in the distance. The position with the strongest spectral emission is not the geometrical focal point of the focusing lens, but away from the geometrical focal point. As the laser energy increases, the position with the strongest spectral emission moves toward the focusing lens. In addition, the vibration temperature and full width at half maximum (FWHM) are also calculated by fitting CN spectral data for specific distances and energies. The vibration temperature and FWHM of CN at the position with strongest emission are the lowest, and the vibration temperature and FWHM at the left side (close to the lens) of the strongest emission position are higher than those at the right side (away from the lens) of the strongest emission position.