Search results for: characteristic triangle

Authors: Wajdi Mohamed Ratemi

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The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: pascal’s triangle, generalized pascal’s triangle, polynomial expansion, sierpinski’s triangle, combinatorics, probabilities

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

Keywords: Malfatti’s problem, geometric constraint solver, computer-aided geometric design, circle packing, data visualization

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Authors: Alexander Glebovskiy

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Practitioners charged with fraud prevention and investigation strongly rely on the Fraud Triangle framework developed by Joseph T. Wells in 1997 while analyzing the causes of fraud at business organizations. The Fraud Triangle model explains fraud by elements such as pressure, opportunity, and rationalization. This view is not fully suitable for effective fraud prevention as the Fraud Triangle model provides limited insight into the causation of fraud. Fraud is a multifaceted phenomenon, the contextual factors of which may not fit into any framework. Employee criminal behavior in business organizations is influenced by environmental, individual, and organizational aspects. Therefore, further criminogenic factors and processes facilitating fraud in organizational settings need to be considered in the root-cause analysis: organizational culture, leadership style, groupthink effect, isomorphic behavior, crime of obedience, displacement of responsibility, lack of critical thinking and unquestioning conformity and loyalty.

Keywords: criminogenesis, fraud triangle, fraud prevention, organizational culture

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Authors: Jian Zheng, Jinfeng Yu, Xinhua Ni

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The limiting fracture stress predicting model of composite ceramics with symmetric triangle eutectic was established based on its special microscopic structure. The symmetric triangle eutectic is consisted of matrix, the strong constraint inter-phase and reinforced fiber inclusions which are 120 degrees uniform symmetrical distribution. Considering the conditions of the rupture of the cohesive bond between matrix and fibers in eutectic and the stress concentration effect at the fiber end, the intrinsic fracture stress of eutectic was obtained. Based on the biggest micro-damage strain in eutectic, defining the load function, the macro-damage fracture stress of symmetric triangle eutectic was determined by boundary conditions. Introducing the conception of critical zone, the theoretical limiting fracture stress forecasting model of composite ceramics was got, and the stress was related to the fiber size and fiber volume fraction in eutectic. The calculated results agreed with the experimental results in the literature.

Keywords: symmetric triangle eutectic, composite ceramics, limiting stress, intrinsic fracture stress

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Authors: Zuraidasahana Zulkarnain, Mohd Shafry Mohd Rahim, Nor Anita Fairos Ismail, Mohd Azhar M. Arsad

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Handwritten signature is accepted widely as a biometric characteristic for personal authentication. The use of appropriate features plays an important role in determining accuracy of signature verification; therefore, this paper presents a feature based on the geometrical concept. To achieve the aim, triangle attributes are exploited to design a new feature since the triangle possesses orientation, angle and transformation that would improve accuracy. The proposed feature uses triangulation geometric set comprising of sides, angles and perimeter of a triangle which is derived from the center of gravity of a signature image. For classification purpose, Euclidean classifier along with Voting-based classifier is used to verify the tendency of forgery signature. This classification process is experimented using triangular geometric feature and selected global features. Based on an experiment that was validated using Grupo de Senales 960 (GPDS-960) signature database, the proposed triangular geometric feature achieves a lower Average Error Rates (AER) value with a percentage of 34% as compared to 43% of the selected global feature. As a conclusion, the proposed triangular geometric feature proves to be a more reliable feature for accurate signature verification.

Keywords: biometrics, euclidean classifier, features extraction, offline signature verification, voting-based classifier

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Authors: M. Bevilacqua, F. E. Ciarapica, G. Marcucci

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Supply Chain Resilience has been broadly studied during the last decade, focusing the research on many aspects of Supply Chain performance. Consequently, different definitions of Supply Chain Resilience have been developed by the research community, drawing inspiration also from other fields of study such as ecology, sociology, psychology, economy et al. This way, the definitions so far developed in the extant literature are therefore very heterogeneous, and many authors have pointed out a lack of consensus in this field of analysis. The aim of this research is to find common points between these definitions, through the development of a framework of study: the Resilience Triangle. The Resilience Triangle is a tool developed in the field of civil engineering, with the objective of modeling the loss of resilience of a given structure during and after the occurrence of a disruption such as an earthquake. The Resilience Triangle is a simple yet powerful tool: in our opinion, it can summarize all the features that authors have captured in the Supply Chain Resilience definitions over the years. This research intends to recapitulate within this framework all these heterogeneities in Supply Chain Resilience research. After collecting a various number of Supply Chain Resilience definitions present in the extant literature, the methodology approach provides a taxonomy step with the scope of collecting and analyzing all the data gathered. The next step provides the comparison of the data obtained with the plotting of a disruption profile, in order to contextualize the Resilience Triangle in the Supply Chain context. The tool and the results developed in this research will allow to lay the foundation for future Supply Chain Resilience modeling and measurement work.

Keywords: supply chain resilience, resilience definition, supply chain resilience triangle

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Authors: Lingge Tan, Hongpeng Xu, Jieun Yang, Maarten Hornikx

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Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper provides a type of modular diffuser based on the Sierpinski Triangle of the plane and combines it with fractal theory to expand the effective frequency range. In numerical calculations and full-scale model experiments, the effect of fractal design elements on normal-incidence diffusion coefficients is examined. It is demonstrated the reasonable times of iteration of modules is three, and the coverage density is 58.4% in the design frequency from 125Hz to 4kHz.

Keywords: acoustic diffuser, fractal, Sierpinski-triangle, diffusion coefficient

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Authors: Ashwin Rai, Rajalakshmi Rai, Rajanigandha Vadgoankar

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Lingual artery is the chief artery of the tongue and the neighboring structures pertaining to the oral cavity. At the carotid triangle, this artery arises from the external carotid artery opposite to the tip of greater cornua of hyoid bone, undergoes a tortuous course with its first part being crossed by the hypoglossal nerve and runs beneath the digastric muscle. Then it continues to supply the tongue as the deep lingual artery. The aim of this study is to draw surgeon's attention to the course of lingual artery in this area since it can be accidentally lesioned causing an extensive hemorrhage in certain surgical or dental procedures. The study was conducted on 44 formalin fixed head and neck specimens focusing on the anatomic relations of lingual artery. In this study, we found that the lingual artery is located inferior to the digastric muscle and the hypoglossal nerve contradictory to the classical description. This data would be useful during ligation of lingual artery to avoid injury to the hypoglossal nerve in surgeries related to the anterior triangle of neck.

Keywords: anterior triangle, digastric muscle, hypoglossal nerve, lingual artery

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Authors: Jalalludin Abdul Malek, Zurinah Tahir

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When the Multimedia Super Corridor (MSC) was launched in 1995, it became the catalyst for the implementation of the intelligent city concept, an area that covers about 15 x 50 kilometres from Kuala Lumpur City Centre (KLCC), Putrajaya and Kuala Lumpur International Airport (KLIA). The concept of intelligent city means that the city has an advanced infrastructure and infostructure such as information technology, advanced telecommunication systems, electronic technology and mechanical technology to be utilized for the development of urban elements such as industries, health, services, transportation and communications. For example, the Golden Triangle of Kuala Lumpur has also many intelligent buildings developed by the private sector such as the KLCC Tower to implement the intelligent city concept. Consequently, the intelligent buildings in the Golden Triangle can be linked directly to the Putrajaya Intelligent City and Cyberjaya Intelligent City within the confines of the MSC. However, the reality of the situation is that there are not many intelligent buildings within the Golden Triangle Kuala Lumpur scope which can be considered of high-standard intelligent buildings as referred to by the Intelligence Quotient (IQ) building standard. This increases the need to implement the real ‘intelligent city’ concept. This paper aims to show the strengths and weaknesses of the intelligent buildings in the Golden Triangle by taking into account aspects of 'intelligence' in the areas of technology and infrastructure of buildings.

Keywords: intelligent city concepts, intelligent building, Golden Triangle, Kuala Lumpur

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Authors: Reskino Resky

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This research purposes to create a model to detecting financial statement fraud. This research examines the variable of fraud triangle and auditor industry specialization with financial statement fraud. This research used sample of company which is listed in Indonesian Stock Exchange that have sanctions and cases by Financial Services Authority in 2011-2013. The number of company that were became in this research were 30 fraud company and 30 non-fraud company. The method of determining the sample is by using purposive sampling method with judgement sampling, while the data processing methods used by researcher are mann-whitney u and discriminants analysis. This research have two from five variable that can be process with discriminant analysis. The result shows the financial targets can be detect financial statement fraud, while financial stability can’t be detect financial statement fraud.

Keywords: fraud triangle analysis, financial targets, financial stability, auditor industry specialization, financial statement fraud

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Authors: Yuji Kageyama, Shin Nagata, Tatsuya Takino, Izuru Nomura, Hiroyuki Kamata

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In previous study, technique to estimate a self-location by using a lunar image is proposed. We consider the improvement of the conventional method in consideration of FPGA implementation in this paper. Specifically, we introduce Artificial Bee Colony algorithm for reduction of search time. In addition, we use fixed point arithmetic to enable high-speed operation on FPGA.

Keywords: SLIM, Artificial Bee Colony Algorithm, location estimate, evolutional triangle similarity

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Authors: Sonia Hirt

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The Planner's Triangle, an oft-cited model that visually defined planning as the search for sustainability to balance the three basic priorities of equity, economy, and environment, has influenced planning theory and practice for a quarter of a century. In this essay, we argue that the triangle requires updating and expansion. Even if planners keep sustainability as their key core aspiration at the center of their imaginary geometry, the triangle's vertices have to be rethought. Planners should move on to a 21st-century concept. We propose a Planner's Pentangle with five basic priorities as vertices of a new conceptual polygon. These five priorities are Wellbeing, Equity, Economy, Environment, and Esthetics (WE⁴). The WE⁴ concept more accurately and fully represents planning’s history. This is especially true in the United States, where public art and public health played pivotal roles in the establishment of the profession in the late 19th and early 20th centuries. It also more accurately represents planning’s future. Both health/wellness and aesthetic concerns are becoming increasingly important in the 21st century. The pentangle can become an effective tool for understanding and visualizing planning's history and present. Planning has a long history of representing urban presents and future as conceptual models in visual form. Such models can play an important role in understanding and shaping practice. For over two decades, one such model, the Planner's Triangle, stood apart as the expression of planning's pursuit for sustainability. But if the model is outdated and insufficiently robust, it can diminish our understanding of planning practice, as well as the appreciation of the profession among non-planners. Thus, we argue for a new conceptual model of what planners do.

Keywords: sustainable development, planning for sustainable development, planner's triangle, planner's pentangle, planning and health, planning and art, planning history

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Authors: Neda Nabid, Iman Hajirasouliha, Sanaz Shirinbar

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One of the most challenging issues in earthquake engineering is to find effective ways to reduce earthquake forces and damage to structural and non-structural elements under strong earthquakes. While friction dampers are the most efficient systems to improve the seismic performance of substandard structures, their optimum design is a challenging task. This research aims to find more appropriate slip load distribution pattern for efficient design of friction panels. Non-linear dynamic analyses are performed on 3, 5, 10, 15, and 20-story RC frame using Drain-2dx software to find the appropriate range of slip loads and investigate the effects of different distribution patterns (cantilever, uniform, triangle, and reverse triangle) under six different earthquake records. The results indicate that using triangle load distribution can significantly increase the energy dissipation capacity of the frame and reduce the maximum inter-storey drift, and roof displacement.

Keywords: friction panels, slip load, distribution patterns, RC frames, energy dissipation

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Authors: P. Booma Devi, Dilip A. Shah

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This paper seeks the potentials of studying aerodynamic characteristics of inward cavities called dimples, as an alternative to the classical vortex generators. Increasing stalling angle is a greater challenge in wing design. But our examination is primarily focused on increasing lift. In this paper, enhancement of lift is mainly done by introduction of dimple or cavity in a wing. In general, aircraft performance can be enhanced by increasing aerodynamic efficiency that is lift to drag ratio of an aircraft wing. Efficiency improvement can be achieved by improving the maximum lift co-efficient or by reducing the drag co-efficient. At the time of landing aircraft, high angle of attack may lead to stalling of aircraft. To avoid this kind of situation, increase in the stalling angle is warranted. Hence, improved stalling characteristic is the best way to ease landing complexity. Computational analysis is done for the wing segment made of NACA 0012. Simulation is carried out for 30 m/s free stream velocity over plain airfoil and different types of cavities. The wing is modeled in CATIA V5R20 and analyses are carried out using ANSYS CFX. Triangle and square shapes are used as cavities for analysis. Simulations revealed that cavity placed on wing segment shows an increase of maximum lift co-efficient when compared to normal wing configuration. Flow separation is delayed at downstream of the wing by the presence of cavities up to a particular angle of attack.

Keywords: lift, drag reduce, square dimple, triangle dimple, enhancement of stall angle

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Authors: Huang Yong, Chen Qianting, Zhao Shurong

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In order to identify the role and effect of Characteristic Towns as an important means to promote urban-rural integration, this paper uses Flow Theory and complex network analysis methods to jointly construct the identification path of urban-rural integration capabilities of Characteristic Towns. Take the National Characteristic Towns of Yunnan Province as the empirical objects to identify their role laws. The study found that in the implementation of the National Characteristic Town Project in Yunnan Province, (1) the population is more susceptible to the impact of the Characteristic Town Project than the technical elements, but the stability is poor; (2) The flow capacity of urban and rural technical elements is weak, and the quality of the enterprise cooperation network in general; (3) Compared with the batch of Characteristic Towns in 2016, its ability to promote urban-rural integration is higher in 2017; (4) The role of the Characteristic Town Project on urban-rural integration focuses on the improvement of the number of urban and rural flow elements. This paper analyzes the mode of the role of Characteristic Towns on urban-rural integration from the perspective of ‘flow,’ establishes a research paradigm for evaluating the role of Characteristic Towns in urban-rural integration capabilities, and builds a path for the application of Characteristic Towns to support the realization of urban-rural integration goals.

Keywords: characteristic town, urban-rural integration, flow theory, complex network analysis

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Authors: Sanaz Ahmadzadeh Siyahrood, Arghavan Ebrahimi, Mohammadjavad Mahdavinejad

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Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.

Keywords: angle, equal triangle, square, structural hierarchy

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Authors: I. Zahraoui, J. Terhzaz, A. Errkik, El. H. Abdelmounim, A. Tajmouati, L. Abdellaoui, N. Ababssi, M. Latrach

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This paper presents a novel design of a microstrip fractal antenna based on the use of Sierpinski triangle shape, it’s designed and simulated by using FR4 substrate in the operating frequency bands (GPS, WiMAX), the design is a fractal antenna with a modified ground structure. The proposed antenna is simulated and validated by using CST Microwave Studio Software, the simulated results presents good performances in term of radiation pattern and matching input impedance.

Keywords: dual-band antenna, fractal antenna, GPS band, modified ground structure, sierpinski triangle, WiMAX band

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Authors: Vladimir S. Timofeev

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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation

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Authors: Konstantin Nefedev, Petr Andriushchenko

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Usually under the frustrated magnetics, it understands such materials, in which ones the interaction between located magnetic moments or spins has competing character, and can not to be satisfied simultaneously. The most well-known and simplest example of the frustrated system is antiferromagnetic Ising model on the triangle. Physically, the existence of frustrations means, that one cannot select all three pairs of spins anti-parallel in the basic unit of the triangle. In physics of the interacting particle systems, the vector models are used, which are constructed on the base of the pair-interaction law. Each pair interaction energy between one-component vectors can take two opposite in sign values, excluding the case of zero. Mathematically, the existence of frustrations in system means that it is impossible to have all negative energies of pair interactions in the Hamiltonian even in the ground state (lowest energy). In fact, the frustration is the excitation, which leaves in system, when thermodynamics does not work, i.e. at the temperature absolute zero. The origin of the frustration is the presence at least of one ''unsatisfied'' pair of interacted spins (magnetic moments). The minimal relative quantity of these excitations (relative quantity of frustrations in ground state) can be used as parameter of frustration. If the energy of the ground state is Egs, and summary energy of all energy of pair interactions taken with a positive sign is Emax, that proposed frustration parameter pf takes values from the interval [0,1] and it is defined as pf=(Egs+Emax)/2Emax. For antiferromagnetic Ising model on the triangle pf=1/3. We calculated the parameters of frustration in thermodynamic limit for different 2D periodical structures of Ising dipoles, which were on the ribs of the lattice and interact by means of the long-range dipolar interaction. For the honeycomb lattice pf=0.3415, triangular - pf=0.2468, kagome - pf=0.1644. All dependencies of frustration parameter from 1/N obey to the linear law. The given frustration parameter allows to consider the thermodynamics of all magnetic systems from united point of view and to compare the different lattice systems of interacting particle in the frame of vector models. This parameter can be the fundamental characteristic of frustrated systems. It has no dependence from temperature and thermodynamic states, in which ones the system can be found, such as spin ice, spin glass, spin liquid or even spin snow. It shows us the minimal relative quantity of excitations, which ones can exist in system at T=0.

Keywords: frustrations, parameter of order, statistical physics, magnetism

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Authors: Axel Priambodo, Dwiharso Nugroho

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Studies conducted to map the reservoir properties based on facies architecture in which to determine the distribution of the petrophysical properties and calculate hydrocarbon reserves in study interval. Facies Architecture analysis begins with stratigraphic correlation that indicates the area is divided into different system tracts. The analysis of distribution patterns and compiling core analysis with facies architecture model show that there are three estuarine facies appear. Formation evaluation begins with shale volume calculation using Asquith-Krygowski and Volan Triangle Method. Proceed to the calculation of the total and effective porosity using the Bateman-Konen and Volan Triangle Method. After getting the value of the porosity calculation was continued to determine the effective water saturation and non-effective by including parameters of water resistivity and resistivity clay. The results of the research show that the Facies Architecture on the field in divided into three main facies which are Estuarine Channel, Estuarine Sand Bar, and Tidal Flat. The petrophysics analysis are done by comparing different methods also shows that the Volan Triangle Method does not give a better result of the Volume Shale than the Gamma Ray Method, but on the other hand, the Volan Triangle Methode is better on calculating porosity compared to the Bateman-Konen Method. The effective porosity distributions are affected by the distribution of the facies. Estuarine Sand Bar has a low porosity number and Estuarine Channel has a higher number of the porosity. The effective water saturation is controlled by structure where on the closure zone the water saturation is lower than the area beneath it. It caused by the hydrocarbon accumulation on the closure zone.

Keywords: petrophysics, geology, petroleum, reservoir

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Authors: Yeonjune Kang

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A triangulation of a planar region is a partition of that region into triangles. In the finite element method, triangulations are often used as the grid underlying a computation. In order to be suitable as a finite element mesh, a triangulation must have well-shaped triangles, according to criteria that depend on the details of the particular problem. For instance, most methods require that all triangles be small and as close to the equilateral shape as possible. Stated differently, one wants to avoid having either thin or flat triangles in the triangulation. There are many triangulation procedures, a particular one being the one known as the longest edge bisection algorithm described below. Starting with a given triangle, locate the midpoint of the longest edge and join it to the opposite vertex of the triangle. Two smaller triangles are formed; apply the same bisection procedure to each of these triangles. Continuing in this manner after n steps one obtains a triangulation of the initial triangle into 2n smaller triangles. The longest edge algorithm was first considered in the late 70’s. It was shown by various authors that this triangulation has the desirable properties for the finite element method: independently of the number of iterations the angles of these triangles cannot get too small; moreover, the size of the triangles decays exponentially. In the present paper we consider a related triangulation algorithm we refer to as the largest angle bisection procedure. As the name suggests, rather than bisecting the longest edge, at each step we bisect the largest angle. We study the properties of the resulting triangulation and prove that, while the general behavior resembles the one in the longest edge bisection algorithm, there are several notable differences as well.

Keywords: angle bisectors, geometry, triangulation, applied mathematics

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Authors: Chondrogianni Dimitra, Yorgos J. Stephanedes

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The impact of the economic crisis, coupled with the aging of the city's old core, is reflected in central Athens. Public and private users, residents, employees, visitors desire the quality upgrading of abandoned buildings and public spaces through environmental upgrading and sustainable mobility, and promotion of the international metropolitan character of the city. In the study, a strategy for reshaping the character and function of the historic Athenian triangle is proposed, aiming at its economic, environmental, and social sustainable development through feasible, meaningful, and non-landscaping solutions of low cost and high positive impact. Sustainable mobility is the main principle in re-planning the study area and transforming it into a “Low Pollution and Limited Vehicle Traffic Zone” is the main strategy. Τhe proposed measures include the development of pedestrian mobility networks by expanding the pedestrian roads and limited-traffic routes, of bicycle networks based on the approved Metropolitan Bicycle Route of Athens, of public transportation networks with new lines of electric mini-buses, and of new regulations for vehicle mobility in the historic triangle. In addition, complementary actions are proposed regarding the provision of Wi-Fi on fixed track media, development of applications that facilitate combined travel and provide real-time data, integration of micromobility (roller skates, Segway, Hoverboard), and its enhancement as a flexible means of personal mobility, and development of car-sharing, ride-sharing and dynamic carpooling initiatives.

Keywords: regeneration plans, sustainable mobility, environmental upgrading, athens historical triangle

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Authors: Remus Titiriga

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The paper focuses on Pascal's indivisibles evolving to Leibniz's infinitesimals. It starts with parallel developments by the two savants in Combinatorics (triangular numbers for Pascal and harmonic triangles for Leibniz) and their implication in determining the sum of mathematical series. It follows with a focus on the geometrical contributions of Pascal. He considered the cycloid and other mechanical curves the epitome of geometric comprehensibility in a series of challenging problems he posed to the mathematical world. Pascal provided the solutions in 1658, in a volume published under the pseudonym of Dettonville, using indivisibles and ratios between curved and straight lines. In the third part, the research follows the impact of this volume on Leibniz as the initial impetus for the elaboration of modern calculus as an algorithmic method disjoint of geometrical intuition. Then paper analyses the further steps and proves that Leibniz's developments relate to his philosophical frame (the search for a characteristic Universalis, the consideration of principle of continuity or the rule of sufficient reason) different from Pascal's and impacting mathematical problems and their solutions. At this stage in Leibniz's evolution, the infinitesimals replaced the indivisibles proper. The last part of the paper starts with speculation around "What if?". Could Pascal, if he lived more, accomplish the same feat? The document uses Pascal's reconstructed philosophical frame to formulate a positive answer. It also proposes to teach calculus with indivisibles and infinitesimals mimicking Pascal and Leibniz's achievements.

Keywords: indivisibles, infinitesimals, characteristic triangle, the principle of continuity

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Authors: Xiaohan Ye

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Under the new normal situation, some urban spaces with the industrial base and regional features in Zhejiang, China have been selected to build a characteristic town, a kind of environmentally-friendly development platform with city-industry integrated, in an attempt to achieve the most optimized layout of productivity with the least space resource. After analysis on the connotation, mechanism and mode of characteristic town in Zhejiang, it is suggested in this paper that characteristic town should take improving the regional ecological environment as an important object in planning strategy from the perspective of ecological concept. Improved environmental quality, optimized resource allocation, and compact industrial distribution should be realized so as to drive the regional green and sustainable development. Finally, this paper analyzes location selection, industrial distribution, spatial organization and environment construction based on the exploration of the dream town of Zhejiang province, the first batch of provincial-level characteristic towns to demonstrate how to apply the ecological concept to the design of characteristic town.

Keywords: characteristic town, ecological concept, Hangzhou dream town, planning strategy

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Authors: Zongjie Wang, Zhizhong Guo

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While the regular optimal power flow model focuses on a single time scan, the optimization of power systems is typically intended for a time duration with respect to a desired objective function. In this paper, a temporal optimal power flow model for a time period is proposed. To reduce the computation burden needed for calculating temporal optimal power flow, a characteristic optimal power flow model is proposed, which employs different characteristic load patterns to represent the objective function and security constraints. A numerical method based on the interior point method is also proposed for solving the characteristic optimal power flow model. Both the temporal optimal power flow model and characteristic optimal power flow model can improve the systems’ desired objective function for the entire time period. Numerical studies are conducted on the IEEE 14 and 118-bus test systems to demonstrate the effectiveness of the proposed characteristic optimal power flow model.

Keywords: optimal power flow, time period, security, economy

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Authors: Yu-Han Tao, Hui-Qin Xu

Abstract:

The present study aimed to explain the protective effect of Cornus officinalis characteristic components, under AGEs damage to HUVEC. After cultured HUVEC adhered, Cornus officinalis characteristic components such as loganin, morroniside, oleanolic acid, ursolic acid and aminoguanidine (positive control dug) hatched, after 1h the AGEs (200 mg/L) were added. After 24h, LDH, SOD, MDA, NO, ET, and AngⅡ, TGF-β, IL-1β, ROS in the supernatant were determined. The results showed the Cornus officinalis characteristic compounds could improve vitality of SOD, NO, reduce the MDA, ET, AngⅡ, TGF-β, IL-1β, ROS significantly when compared with the model groug. Loganin, oleanic acid, ursolic acid, had significant protective effect on AGEs injured HUVEC. As a conclusion, characteristic components in Cornus officinalis had a positive effect after HUVEC injured by AGEs.

Keywords: Cornus officinalis, morroniside, oganin, oleanolic acid, ursolic acid

Procedia PDF Downloads 359

Authors: Thomas Odaker, Dieter Kranzlmueller, Jens Volkert

Abstract:

We present an approach to triangle mesh simplification designed to be executed on the GPU. We use a quadric error metric to calculate an error value for each vertex of the mesh and order all vertices based on this value. This step is followed by the parallel removal of a number of vertices with the lowest calculated error values. To allow for the parallel removal of multiple vertices we use a set of per-vertex boundaries that prevent mesh foldovers even when simplification operations are performed on neighbouring vertices. We execute multiple iterations of the calculation of the vertex errors, ordering of the error values and removal of vertices until either a desired number of vertices remains in the mesh or a minimum error value is reached. This parallel approach is used to speed up the simplification process while maintaining mesh topology and avoiding foldovers at every step of the simplification.

Keywords: computer graphics, half edge collapse, mesh simplification, precomputed simplification, topology preserving

Procedia PDF Downloads 349

Authors: Muhammad Luqman, Yusuf Kurniawan

Abstract:

S-Boxes is one of the linear parts of the cryptographic algorithm. The existence of S-Box in the cryptographic algorithm is needed to maintain non-linearity of the algorithm. Nowadays, modern cryptographic algorithms use an S-Box as a part of algorithm process. Despite the fact that several cryptographic algorithms today reuse theoretically secure and carefully constructed S-Boxes, there is an evaluation characteristic that can measure security properties of S-Boxes and hence the corresponding primitives. Analysis of an S-Box usually is done using manual mathematics calculation. Several S-Boxes are presented as a Truth Table without any mathematical background algorithm. Then, it’s rather difficult to determine the strength of Truth Table S-Box without a mathematical algorithm. A comprehensive analysis should be applied to the Truth Table S-Box to determine the characteristic. Several important characteristics should be owned by the S-Boxes, they are Nonlinearity, Balancedness, Algebraic degree, LAT, DAT, differential delta uniformity, correlation immunity and global avalanche criterion. Then, a comprehensive tool will be present to automatically calculate the characteristics of S-Boxes and determine the strength of S-Box. Comprehensive analysis is done on a deterministic process to produce a sequence of S-Boxes characteristic and give advice for a better S-Box construction.

Keywords: cryptographic properties, Truth Table S-Boxes, S-Boxes characteristic, deterministic process

Procedia PDF Downloads 347

Authors: Phuoc Si Nguyen

Abstract:

Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: frequency transformation, bilinear z-transformation, pre-warping frequency, digital filters, analog filters, pascal’s triangle

Procedia PDF Downloads 530