Topology

The charged quantum geometry of mass-ENERGY-Matter - developed from the foundational postulate that quantised angular momenta of Planck's constant is in fact reflective of an equilateral mass-energy geometry from which all 2d immaterial EM fields and 3D material particles are created.

Özet
Matematiğin mimarlık dahil olmak üzere farklı disiplinlerle girdiği sıkı ilişki ve teknolojinin gün geçtikçe gelişmesiyle kullanım alanı artan bilgisayar destekli tasarım teknolojisi sayesinde tasarım sürecinde farklı matematiksel modellerin kullanılması mümkün olmuştur. Matematiksel modellerle strüktür tasarımı, geometri ve malzeme parametrelerini ön plana çıkarmıştır. 
Karmaşıklık kuramının sistemdeki dinamiklerin modellenmesi açısından strüktür tasarımındaki rolü önemlidir. Birbirinden farklı birçok parametrenin olması ve bunlar arasındaki ilişkilerin keşif süreci taşıyıcı sistemi tasarlanabilir bir sistem yapmıştır.  Geometri, bu sistemin formunu oluşturur ve ilk dikkat çeken parametredir. Yaratılan her form bir geometri içerir ve formun ayakta durabilmesi için de strüktür tasarımına ihtiyaç vardır. Mimarlıkta geometriyle birlikte malzeme, tasarımın dokusunun, biçiminin ve binanın görünümünün oluşmasında temel bileşenlerdendir.
Strüktür tasarımında en temel yöntem olan sonlu elemanlar analizi ışığında, arup optimizeri, dinamik rahatlama, evrimsel şekil optimizeri ve evrimsel strüktür optimizeri incelenmiştir. Bu analizler sonucu ortaya çıkan zincir eğrisi, bükülme, minimal yüzey ve nurbs modelleri araştırılmıştır. Arup optimizeri, tüm sistemde kendi kendini organize etmesini sağlayacak en uygun tekrar elemanlarını seçer ve bu elemanları tek tek analiz eder. Dinamik rahatlama, malzemenin yerçekimi ile kendiliğinden şekil almasını sağlayan topolojik şekildeki kemer yapının optimizasyonunu sağlar. Evrimsel şekil optimizeri ise serbest forma en uygun alanı seçmek için en az deplasman yaptıracak strüktürel eleman yerleşmesini analiz eder. Evrimsel strüktür optimizeri ise sistemde vektörel gerilimi azaltmaya yönelik analizler yapar.
Strüktür modellerinden zincir eğrisi modelinde zincir, yerçekimine karşı oluşan eğrinin formunu alır. Bükülme, malzemenin kırılma noktasının gelişen teknoloji ve yeni malzemelerle eşik değerinin artması sonucunda, eski kırılma noktasının bükülmesiyle oluşan formdur. Minimal yüzeyler, minimum yüzey-gerilim potansiyel enerjisine sahip ve alan olarak da minimum olan formlardır. Nurbs ise üniform olmayan çizgiler eğrisidir ve bu eğriler, bir strüktür modelinde geometrinin haritalamasını yaparak serbest form yapıların strüktüre referans olabilecek olası çizgi ve yüzey ilşikilerinin hesaplanmasında kullanılırlar.
Matematiğin bir model oluşturduğu bu strüktür sistemlerinde, bilgisayar ortamında oluşan simülasyon, geçmişin sıkıcı ve anlaması zor olan hesaplamalarını geride bırakıp mimar ve mühendislere ortak olarak kullanabilecekleri bir ara yüz oluşturmuştur.

          Anahtar Kelimeler: Strüktür Tasarımı, Karmaşıklık Kuramı, Optimizasyon, Geometri, Kendi kendini Organize Etme, Topoloji

ABSTRACT - Simplicial complexes are extensively used for discretizing digital shapes in two, three, and higher dimensions within a variety of application domains. There have been many proposals of topological data structures, which represent the connectivity information among simplices. We introduce the Mangrove Topological Data Structure (Mangrove TDS) framework, a tool which supports the efficient implementation of data structures for simplicial complexes of any dimension under the same application interface. Our framework is based on a graph-based representation of connectivity relations, that we call the mangrove. It can be customized in order to simulate the content of any topological data structure with a negligible overhead. Thus, the Mangrove TDS framework is extensible, and supports the most diverse modeling needs. We also provide implicit representations of those simplices, which are not directly encoded in a specific topological data structure. Our tests show that these representations, that we call ghost simplices, improve the expressive power and the efficiency of topological queries. In order to prove the validity of our approach, we design two topological data structures, specific for non-manifold complexes, within our framework. We perform comparisons with some widely-used representations in the literature as well as with libraries available in the public domain.

Abstract—Some in-parallel robots, such as the 3-2-1 and the 3/2 manipulators, have attracted attention because their forward kinematics can be solved by three consecutive trilaterations. In this paper, we identify a class of these robots, which we call flagged manipulators, whose singularity loci admit a well-behaved decomposition, i.e., a stratification, derived from that of the flag manifold. Two remarkable properties must be highlighted. First, the decomposition has the same topology for all members in the class, irrespective of the metric details of each particular robot instance. Thus, we provide explicitly all the singular strata and their connectivity, which apply to all flagged manipulators without any tailoring. Second, the strata can be easily characterized geometrically, because it is possible to assign local coordinates to each stratum (in the configuration space of the manipulator) that correspond to uncoupled rotations and/or translations in the workspace. Index Terms—...

The key issue of the localization study is that how we can minimize the energy consumption of devices with guaranteeing high degree of accuracy. In this paper, we show that the collaboration among proxy devices with short range communication is helpful to energy-efficiently localize their locations in time-average sense by analyzing the device proximity including real GPS trace of students in KAIST and NCSU campuses. Next, we deliberate what is the best method for selfish mobile users to collaborate for the energy-efficient localization, and formulate an optimization problem which considers the energy efficiency and/or user fairness. However, optimizing this problem is tricky since it requires a global knowledge of sets of proxy devices and also solving a NP-hard problem to select devices which directly measure locations. This paper makes a contribution towards presenting a practical and fully distributed location sharing protocol based on competition for turning off GPS, and an opt...

We introduce a new class of functions called almost strongly Θ-b-continuous function which is a generalization of strongly Θ-continuous functions and strongly Θ-b- continuous functions. Some characterizations and several properties concerning almost strongly Θ-b-continuous function are obtained.

This paper presents the selection process of the best suited topology for a bidirectional charger, intended to be economically implemented for a small electric vehicle with a 16 kWh battery package. The first stage is a State-of-the-Art revision, whose results are a reduced number of topologies pre-selected. Second stage is the evaluation through Multisim-NI Simulation of the pre-selected topologies; looking for the better relation: number of semiconductor devices, stresses to which semiconductor devices are subjected, number of control signals needed with its associated measurement devices, passive elements size and total losses.

Chaos has usually been studied in terms of the properties of systems by which the condition is observed. Different properties or routes are observed in systems deemed to be chaotic. A form of chaos could be equivalent to another based on these routes. A form of chaos could be considered as either stronger or weaker based on the strength of the routes considered and the type of map. Li-Yorke sensitivity is a stronger form of sensitivity.

A planetary trains for multi-speed is mainly used for automation in industries of automobile. A planetary
gear train is represented by a graph. It is identified by (i) number of vertices and their connectivity (ii) number of edges and their types and values (iii) fundamental circuits, their size and adjancy. Connectivity of individual link is a property characteristic of kinematic chain. It is possible to identify a planetary gear,therefore of using sets of labele (decimal numbers representing connectivity ) of individual link. The
connectivity of vertices , edges values and circuit values, related to design invariants which in turn indicates the possible behavior of the gear train ( for example capacity of power transmission, speed ratio and power carculation). For a specified degree – of – freedom a number of planetary gear kinematic chain (PGKCs) are selected and hence planetary gear trains (PGTs) can be formed with a given number of links
and joints so that designer must be able to select to select the best train from the view point of say velocity ratio and capacity of power transmission, space requirements etc. Synthesis of planetary gear kinematic chain and planetary gear trains has been studied(1-9). Almost all reported work deals with only
identification of distinct chains. Besides providing an atlus of chains, this in itself does not provide any help to designer in the selection of best possible gear train. In the present paper a simple method based of circuit property ( based on link-link shortest path distance and degree of links) is presented to determine the topology values of power transmission efficiency and topology power transmission capacity of five-links PGKCs and their distinct inversions

The present work proposes new styles of rough sets by using different neighborhoods which are made from a general binary relation. The proposed approximations represent a generalization to Pawlak's rough sets and some of its generalizations, where the accuracy of these approximations is enhanced significantly. Comparisons are obtained between the methods proposed and the previous ones. Moreover, we extend the notion of "nano-topology", which have introduced by Thivagar and Richard [49], to any binary relation. Besides, to demonstrate the importance of the suggested approaches for deciding on an effective tool for diagnosing lung cancer diseases, we include a medical application of lung cancer disease to identify the most risk factors for this disease and help the doctor in decision-making. Finally, two algorithms are given for decision-making problems. These algorithms are tested on hypothetical data for comparison with already existing methods.

In cloud computing, instead of building their own network and facilities, companies can allocate resources from network operators, thus reducing hardware investment and maintenance cost. The company's IT infrastructure can be designed as an abstract virtual graph of services to be mapped into the substrate network of the operator. In this paper, we refer to the virtual graph mapping problem

We present a hybrid neural-network for human face recognition which compares favourably with other methods. The system combines local image sampling, a self-organizing map (SOM) neural network, and a convolutional neural network. The SOM provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space, thereby providing dimensionality reduction and invariance to minor changes in the image sample, and the convolutional neural network provides partial invariance to translation, rotation, scale, and deformation. The convolutional network extracts successively larger features in a hierarchical set of layers. We present results using the Karhunen-Loeve transform in place of the SOM, and a multilayer perceptron (MLP) in place of the convolutional network for comparison. We use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression, pose, and facial details. We analyze the computational complexity and discuss how new classes could be added to the trained recognizer

A new 3-phase buck-boost unity power factor rectifier consisting of a 3-phase bridge buck PFC rectifier and two boost dc-dc converters connected in series is proposed for an industrial application where two independent output voltages need to be controlled. This paper presents the proposed topology and the requirements for this application. The proposed and alternative topologies are briefly compared. Through this comparison, it is shown that the proposed topology offers the best solution in terms of simplicity and functionality. The operation of the new topology is described in detail and then the control strategy including PWM calculations to obtain the best performance is given. The validity of the theory and practicality of the new rectifier system is confirmed through simulation and experimental results obtained from a 5 kW prototype.

It is well-known that the Voronoi diagram of points and the power diagram for weighted points, such as spheres, are cell complexes, and their respective dual structures, i.e. the Delaunay triangulation and the regular triangulation, are simplicial complexes. Hence, the topologies of these diagrams are usually stored in their dual complexes,using a very compact,data structure of arrays. The topology