Search results for: Exterior algebra

Authors: Z. Altawallbeh

Abstract:

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

Keywords: Exterior algebra, free resolution, free and projective modules, Hochschild homology, homotopic function, symmetric algebra.

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Authors: Kankeyanathan Kannan

Abstract:

The uniform Roe C*-algebra (also called uniform translation)C^*- algebra provides a link between coarse geometry and C^*- algebra theory. The uniform Roe algebra has a great importance in geometry, topology and analysis. We consider some of the elementary concepts associated with coarse spaces. 

Keywords: Invariant Approximation Property, Uniform Roe algebras.

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Authors: Liew Siaw Yee, Tahir Ahmad

Abstract:

In this paper, the Fuzzy Autocatalytic Set (FACS) is composed into Omega Algebra by embedding the membership value of fuzzy edge connectivity using the property of transitive affinity. Then, the Omega Algebra of FACS is a transformation semigroup which is a special class of semigroup is shown.

Keywords: Fuzzy autocatalytic set, omega algebra, semigroup, transformation semigroup.

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Authors: Mona Taheri

Abstract:

For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.

Keywords: Multiple algebra, mathematics, universal algebra.

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Authors: Ali Mutlu, Berrin Mutlu

Abstract:

In this paper we use the definition of CW basis of a free simplicial algebra. Using the free simplicial algebra, it is shown to construct free or totally free 2−crossed modules on suitable construction data with given a CW−basis of the free simplicial algebra. We give applications free crossed squares, free squared complexes and free 2−crossed complexes by using of 1(one) skeleton resolution of a step by step construction of the free simplicial algebra with a given CW−basis.

Keywords: Free crossed square, Free 2−crossed modules, Free simplicial algebra, Free square complexes, Free 2−crossed complexes CW−basis, 1−skeleton. A. M. S.Classification:[2000] 18D35, 18G30, 18G50, 18G55, 55Q05, 55Q20.

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Authors: Ei Ei Myat, Ni Lar Thein

Abstract:

With the tremendous growth of World Wide Web (WWW) data, there is an emerging need for effective information retrieval at the document level. Several query languages such as XML-QL, XPath, XQL, Quilt and XQuery are proposed in recent years to provide faster way of querying XML data, but they still lack of generality and efficiency. Our approach towards evolving a framework for querying semistructured documents is based on formal query algebra. Two elements are introduced in the proposed framework: first, a generic and flexible data model for logical representation of semistructured data and second, a set of operators for the manipulation of objects defined in the data model. In additional to accommodating several peculiarities of semistructured data, our model offers novel features such as bidirectional paths for navigational querying and partitions for data transformation that are not available in other proposals.

Keywords: Algebra, Semistructured data, Query Algebra.

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Authors: Chih-Yuan Chang, Jin-Chiuan Chang, San-Shan Hung, Cheng-Jui Hsu

Abstract:

The heat storage capacity of concrete in building shells is a major reason for excessively large electricity consumption induced by indoor air conditioning. In this research, the previously developed Smart Temperature Information Material (STIM) is embedded in two groups of exterior wall specimens (the control group contains reinforced concrete exterior walls and the experimental group consists of tiled exterior walls). Long term temperature measurements within the concrete are taken by the embedded STIM. Temperature differences between the control group and the experimental group in walls facing the four cardinal directions (east, west, south, and north) are evaluated. This study aims to provide a basic reference for the design of exterior walls and the selection of heat insulation materials.

Keywords: building envelope, sensor, energy, thermal insulation, reinforced concrete

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Authors: Troy L. Story

Abstract:

A mathematical model for the Dynamics of Economic Profit is constructed by proposing a characteristic differential oneform for this dynamics (analogous to the action in Hamiltonian dynamics). After processing this form with exterior calculus, a pair of characteristic differential equations is generated and solved for the rate of change of profit P as a function of revenue R (t) and cost C (t). By contracting the characteristic differential one-form with a vortex vector, the Lagrangian is obtained for the Dynamics of Economic Profit.

Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics, economic functions, and dynamics

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Authors: Liu Ping

Abstract:

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal elements under F and other elements under G.

Keywords: Multiplicative functional, triangular fuzzy matrix, fuzzy addition operation, fuzzy multiplication operation.

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Authors: Troy L. Story

Abstract:

Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics.

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Authors: Ming-Chung Tsai, Kuan-Peng Chen, Zheng-Yao

Abstract:

A systematic and exhaustive method based on the group structure of a unitary Lie algebra is proposed to generate an enormous number of quantum codes. With respect to the algebraic structure, the orthogonality condition, which is the central rule of generating quantum codes, is proved to be fully equivalent to the distinguishability of the elements in this structure. In addition, four types of quantum codes are classified according to the relation of the codeword operators and some initial quantum state. By linking the unitary Lie algebra with the additive group, the classical correspondences of some of these quantum codes can be rendered.

Keywords: Quotient-Algebra Partition, Codeword Spinors, Basis Codewords, Syndrome Spinors

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Authors: Yanchao Wang, Rajshekhar Sunderraman

Abstract:

This paper presents an algebraic approach to optimize queries in domain-specific database management system for protein structure data. The approach involves the introduction of several protein structure specific algebraic operators to query the complex data stored in an object-oriented database system. The Protein Algebra provides an extensible set of high-level Genomic Data Types and Protein Data Types along with a comprehensive collection of appropriate genomic and protein functions. The paper also presents a query translator that converts high-level query specifications in algebra into low-level query specifications in Protein-QL, a query language designed to query protein structure data. The query transformation process uses a Protein Ontology that serves the purpose of a dictionary.

Keywords: Domain-Specific Data Management, Protein Algebra, Protein Ontology, Protein Structure Data.

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Authors: Ali Shojaei-Fard

Abstract:

In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.

Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.

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Authors: I. Fathollahi, J. Hesari, S. Azadmard, S. Oustan

Abstract:

The relationships between Proteolysis and soluble calcium levels with hardness of cheese texture were investigated in Iranian UF white cheese during 90 d ripening. Cheeses were sampled in interior and exterior. Results showed that levels of proteolysis, soluble calcium and hardness of cheese texture changed significantly (p< 0.05) over ripening. Levels of proteolysis and hardness were significantly (p< 0.05) different in interior and exterior zones of cheeses. External zones of cheeses became softer and had higher levels of proteolysis compared to internal zones during ripening. The highest correlation coefficient (r2= 0.979; p<0.01) was observed between hardness and levels of pH 4.6-soluble nitrogen in exterior zones of cheese. These result showed that proteolysis can contribute to textural softening during ripening of Iranian UF white cheese.

Keywords: Calcium, Proteolysis, Softening, Ultrafiltration, White cheese.

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Authors: Manuel Ceballos, Juan Nunez, Angel F. Tenorio

Abstract:

The set of all abelian subalgebras is computationally obtained for any given finite-dimensional Lie algebra, starting from the nonzero brackets in its law. More concretely, an algorithm is described and implemented to compute a basis for each nontrivial abelian subalgebra with the help of the symbolic computation package MAPLE. Finally, it is also shown a brief computational study for this implementation, considering both the computing time and the used memory.

Keywords: Solvable Lie algebra, maximal abelian dimension, algorithm.

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Authors: Réka Sárközi, Péter Iványi, Attila B. Széll

Abstract:

The aim of this paper is to present the adaptation of the dome construction tool for formex algebra to the parametric design software Grasshopper. Formex algebra is a mathematical system, primarily used for planning structural systems such like truss-grid domes and vaults, together with the programming language Formian. The goal of the research is to allow architects to plan truss-grid structures easily with parametric design tools based on the versatile formex algebra mathematical system. To produce regular structures, coordinate system transformations are used and the dome structures are defined in spherical coordinate system. Owing to the abilities of the parametric design software, it is possible to apply further modifications on the structures and gain special forms. The paper covers the basic dome types, and also additional dome-based structures using special coordinate-system solutions based on spherical coordinate systems. It also contains additional structural possibilities like making double layer grids in all geometry forms. The adaptation of formex algebra and the parametric workflow of Grasshopper together give the possibility of quick and easy design and optimization of special truss-grid domes.

Keywords: Parametric design, structural morphology, space structures, spherical coordinate system.

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Authors: Rasoul Abazari

Abstract:

In this paper, we show that C*-tensor product of an arbitrary C*-algebra A, (not unital necessary) and C*-algebra B without ground state, have no approximately inner strongly continuous one-parameter group of *-automorphisms.

Keywords: One–parameter group, C*– tensor product, Approximately inner, Ground state.

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Authors: Matthew D. Baffa

Abstract:

Infrared thermography is a non-destructive test method used to estimate surface temperatures based on the amount of electromagnetic energy radiated by building envelope components. These surface temperatures are indicators of various qualitative building envelope deficiencies such as locations and extent of heat loss, thermal bridging, damaged or missing thermal insulation, air leakage, and moisture presence in roof, floor, and wall assemblies. Although infrared thermography is commonly used for qualitative deficiency detection in buildings, this study assesses its use as a quantitative method to estimate the overall thermal conductance value (U-value) of the exterior above-grade walls of a study home. The overall U-value of exterior above-grade walls in a home provides useful insight into the energy consumption and thermal comfort of a home. Three methodologies from the literature were employed to estimate the overall U-value by equating conductive heat loss through the exterior above-grade walls to the sum of convective and radiant heat losses of the walls. Outdoor infrared thermography field measurements of the exterior above-grade wall surface and reflective temperatures and emissivity values for various components of the exterior above-grade wall assemblies were carried out during winter months at the study home using a basic thermal imager device. The overall U-values estimated from each methodology from the literature using the recorded field measurements were compared to the nominal exterior above-grade wall overall U-value calculated from materials and dimensions detailed in architectural drawings of the study home. The nominal overall U-value was validated through calendarization and weather normalization of utility bills for the study home as well as various estimated heat loss quantities from a HOT2000 computer model of the study home and other methods. Under ideal environmental conditions, the estimated overall U-values deviated from the nominal overall U-value between ±2% to ±33%. This study suggests infrared thermography can estimate the overall U-value of exterior above-grade walls in low-rise residential homes with a fair amount of accuracy.

Keywords: Emissivity, heat loss, infrared thermography, thermal conductance.

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Authors: Georgia Garani

Abstract:

A generalised relational data model is formalised for the representation of data with nested structure of arbitrary depth. A recursive algebra for the proposed model is presented. All the operations are formally defined. The proposed model is proved to be a superset of the conventional relational model (CRM). The functionality and validity of the model is shown by a prototype implementation that has been undertaken in the functional programming language Miranda.

Keywords: nested relations, recursive algebra, recursive nested operations, relational data model.

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Authors: Alexander Y. Vaninsky

Abstract:

The paper compares the treatment of fractions in a typical undergraduate college curriculum and in abstract algebra textbooks. It stresses that the main difference is that the undergraduate curriculum treats equivalent fractions as equal, and this treatment eventually leads to paradoxes and impairs the students- ability to perceive ratios, proportions, radicals and rational exponents adequately. The paper suggests a simplified version of rigorous theory of fractions suitable for regular college curriculum.

Keywords: Fractions, mathematics curriculum, mathematics education, teacher preparation

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Authors: Ikbal Zammouri, Béchir Ayeb

Abstract:

In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between l-systems and IFS.

Keywords: Fractal shapes, IFS, parametric l-systems, turtlealgebra.

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Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

Abstract:

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: Cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol.

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Authors: Liu Ying-jie, Lu Wen-bo, Peng Cheng-jian

Abstract:

With the development of the automotive technology and electric vehicle, the contribution of the wind noise on the interior noise becomes the main source of noise. The main transfer path which the exterior excitation is transmitted through is the greenhouse panels and side windows. Simulating the wind noise transmitted into the vehicle accurately in the early development stage can be very challenging. The basic methodologies of this study were based on the Lighthill analogy; the exterior flow field around a passenger car was computed using unsteady Computational Fluid Dynamics (CFD) firstly and then a Finite Element Method (FEM) was used to compute the interior acoustic response. The major findings of this study include: 1) The Sound Pressure Level (SPL) response at driver’s ear locations is mainly induced by the turbulence pressure fluctuation; 2) Peaks were found over the full frequency range. It is found that the methodology used in this study could predict the interior wind noise induced by the exterior aerodynamic excitation in industry.

Keywords: Wind noise, computational fluid dynamics, finite element method, passenger car.

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Authors: Richard Elling Moe

Abstract:

Computer languages are usually lumped together into broad -paradigms-, leaving us in want of a finer classification of kinds of language. Theories distinguishing between -genuine differences- in language has been called for, and we propose that such differences can be observed through a notion of expressive mode. We outline this concept, propose how it could be operationalized and indicate a possible context for the development of a corresponding theory. Finally we consider a possible application in connection with evaluation of language revision. We illustrate this with a case, investigating possible revisions of the relational algebra in order to overcome weaknesses of the division operator in connection with universal queries.

Keywords: Expressive mode, Computer language species, Evaluation of revision, Relational algebra, Universal database queries

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Authors: Jafreezal Jaafar, Hasiah Mohamed, Hazida Razali

Abstract:

This paper focuses on the 3D reconstruction of the architectural design of Darul Ridzuan Museum. It has concentrated on designing exterior part of the building according to colored digital photo of the real museum. Besides viewing the architecture, walkthroughs are generated for the user to control it in an easier way. User can travel through the museum to get the feel of the environment and to explore the design of the museum as a whole; both exterior and interior. The result has shown positive result in terms of realism, navigation, collision detection, suitability, usability and user-s acceptance. In brief, the 3D virtual museum has provided an alternative to present a real museum.

Keywords: Virtual Heritage, 3D Modelling, Virtual Museum, Usability Evaluation

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Authors: Mona Taheri

Abstract:

In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the basic relation and the fundamental algebra in question. In this study, by stating the characteristic theorem of multiple algebras, we show that the theory of multiple algebras is a natural extension of the theory of universal algebras.

Keywords: multiple algebras , universal algebras

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Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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Authors: Mona Taheri

Abstract:

The purpose of this research is to study the concepts of multiple Cartesian product, variety of multiple algebras and to present some examples. In the theory of multiple algebras, like other theories, deriving new things and concepts from the things and concepts available in the context is important. For example, the first were obtained from the quotient of a group modulo the equivalence relation defined by a subgroup of it. Gratzer showed that every multiple algebra can be obtained from the quotient of a universal algebra modulo a given equivalence relation. The purpose of this study is examination of multiple algebras and basic relations defined on them as well as introduction to some algebraic structures derived from multiple algebras. Among the structures obtained from multiple algebras, this article studies submultiple algebras, quotients of multiple algebras and the Cartesian product of multiple algebras.

Keywords: hypergroup, multiple algebras

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Authors: Abdallah F. Abd El-Mohsen, Ahmed A. Abdelsamee, Nouby M. Ghazaly

Abstract:

Engine exhaust noise is considered one of the largest sources of vehicle exterior noise. Further reduction of noise from the vehicle exhaust system will be required, as the vehicle exterior noise regulations become stricter. Therefore, the present study has been carried out to illustrate the role of engine operating parameters and exhaust system construction factors on exhaust noise emitted. The measurements carried out using different exhaust systems, which are mainly used in today’s vehicle. The effect of engine speed on the spectra level of exhaust noise is recorded at engine speeds of 900 rpm, 1800 rpm, 2700, rpm 3600 rpm and 4500 rpm. The results indicate that the increase of engine speed causes a significant increase in the spectrum level of exhaust noise. The increase in the number of the outlet of the expansion chamber also reduces the overall level of exhaust noise.

Keywords: Exhaust system, engine speed, expansion chamber.

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Authors: Marko Spasojevic, Ying Hei Chui, Yuxiang Chen

Abstract:

Increasing the level of exterior insulation in residential buildings is a popular way for improving the thermal characteristic of building enclosure and reducing heat loss. However, the layout and properties of materials composing the wall have a great effect on moisture accumulation within the wall cavity, long-term durability of a wall as well as the structural performance. A one-dimensional hygrothermal modeling has been performed to investigate moisture condensation risks and the drying capacity of standard 2×4 and 2×6 light wood-frame wall assemblies including exterior low-permeance extruded polystyrene (XPS) insulation. The analysis considered two different wall configurations whereby the rigid insulation board was placed either between Oriented Strand Board (OSB) sheathing and the stud or outboard to the structural sheathing. The thickness of the insulation varied between 0 mm and 50 mm and the analysis has been conducted for eight different locations in Canada, covering climate zone 4 through zone 8. Results show that the wall configuration with low-permeance insulation inserted between the stud and OSB sheathing accumulates more moisture within the stud cavity, compared to the assembly with the same insulation placed exterior to the sheathing. On the other hand, OSB moisture contents of the latter configuration were markedly higher. Consequently, the analysis of hygrothermal performance investigated and compared moisture accumulation in both the OSB and stud cavity. To investigate the structural performance of the wall and the effect of soft insulation layer inserted between the sheathing and framing, forty nail connection specimens were tested. Results have shown that both the connection strength and stiffness experience a significant reduction as the insulation thickness increases. These results will be compared with results from a full-scale shear wall tests in order to investigate if the capacity of shear walls with insulated sheathing would experience a similar reduction in structural capacities.

Keywords: Hygrothermal analysis, insulated sheathing, moisture performance, nail joints, wood shear wall.

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