**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1399

# Search results for: computer algebra.

##### 1399 On the Invariant Uniform Roe Algebra as Crossed Product

**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.

##### 1398 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial 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.

##### 1397 Deduction of Fuzzy Autocatalytic Set to Omega Algebra and Transformation Semigroup

**Authors:**
Liew Siaw Yee,
Tahir Ahmad

**Abstract:**

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

##### 1396 How are Equalities Defined, Strong or Weak on a Multiple Algebra?

**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.

##### 1395 1−Skeleton Resolution of Free Simplicial Algebras with Given CW−Basis

**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.

##### 1394 Query Algebra for Semistuctured Data

**Authors:**
Ei Ei Myat,
Ni Lar Thein

**Abstract:**

**Keywords:**
Algebra,
Semistructured data,
Query Algebra.

##### 1393 Generalized π-Armendariz Authentication Cryptosystem

**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.

##### 1392 Expressive Modes and Species of Language

**Authors:**
Richard Elling Moe

**Abstract:**

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

##### 1391 Multiplicative Functional on Upper Triangular Fuzzy Matrices

**Authors:**
Liu Ping

**Abstract:**

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

##### 1390 Algebraic Quantum Error Correction Codes

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

**Abstract:**

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

##### 1389 An Algebra for Protein Structure Data

**Authors:**
Yanchao Wang,
Rajshekhar Sunderraman

**Abstract:**

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

##### 1388 Fixed Point Equations Related to Motion Integrals in Renormalization Hopf Algebra

**Authors:**
Ali Shojaei-Fard

**Abstract:**

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

##### 1387 Computational Algorithm for Obtaining Abelian Subalgebras in Lie Algebras

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

**Abstract:**

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

##### 1386 Formex Algebra Adaptation into Parametric Design Tools: Dome Structures

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

**Abstract:**

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

##### 1385 Non Approximately Inner Tensor Product of C*—Algebras

**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.

##### 1384 A Generalised Relational Data Model

**Authors:**
Georgia Garani

**Abstract:**

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

##### 1383 Theory of Fractions in College Algebra Course

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

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

##### 1382 Fractal Shapes Description with Parametric L-systems and Turtle Algebra

**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.

##### 1381 Assessing the Relation between Theory of Multiple Algebras and Universal Algebras

**Authors:**
Mona Taheri

**Abstract:**

**Keywords:**
multiple algebras ,
universal algebras

##### 1380 Delay-independent Stabilization of Linear Systems with Multiple Time-delays

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

**Abstract:**

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

##### 1379 Equalities in a Variety of Multiple Algebras

**Authors:**
Mona Taheri

**Abstract:**

**Keywords:**
hypergroup,
multiple algebras

##### 1378 A P-SPACE Algorithm for Groebner Bases Computation in Boolean Rings

**Authors:**
Quoc-Nam Tran

**Abstract:**

**Keywords:**
Algorithm,
Complexity,
Groebner basis,
Applications
of Computer Science.

##### 1377 Groebner Bases Computation in Boolean Rings is P-SPACE

**Authors:**
Quoc-Nam Tran

**Abstract:**

**Keywords:**
Algorithm,
Complexity,
Groebner basis,
Applications of Computer Science.

##### 1376 Analyzing Periurban Fringe with Rough Set

**Authors:**
Benedetto Manganelli,
Beniamino Murgante

**Abstract:**

The distinction among urban, periurban and rural areas represents a classical example of uncertainty in land classification. Satellite images, geostatistical analysis and all kinds of spatial data are very useful in urban sprawl studies, but it is important to define precise rules in combining great amounts of data to build complex knowledge about territory. Rough Set theory may be a useful method to employ in this field. It represents a different mathematical approach to uncertainty by capturing the indiscernibility. Two different phenomena can be indiscernible in some contexts and classified in the same way when combining available information about them. This approach has been applied in a case of study, comparing the results achieved with both Map Algebra technique and Spatial Rough Set. The study case area, Potenza Province, is particularly suitable for the application of this theory, because it includes 100 municipalities with different number of inhabitants and morphologic features.

**Keywords:**
Land Classification,
Map Algebra,
Periurban Fringe,
Rough Set,
Urban Planning,
Urban Sprawl.

##### 1375 Computing Center Conditions for Non-analytic Vector Fields with Constant Angular Speed

**Authors:**
Li Feng

**Abstract:**

We investigate the planar quasi-septic non-analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The system could be changed into an analytic system by two transformations, with the help of computer algebra system MATHEMATICA, the conditions of uniform isochronous center are obtained.

**Keywords:**
Non-analytic,
center–focus problem,
Lyapunov constant,
uniform isochronous center.

##### 1374 Some Investigations on Higher Mathematics Scores for Chinese University Student

**Authors:**
Xun Ge,
Jingju Qian

**Abstract:**

To investigate some relations between higher mathe¬matics scores in Chinese graduate student entrance examination and calculus (resp. linear algebra, probability statistics) scores in subject's completion examination of Chinese university, we select 20 students as a sample, take higher mathematics score as a decision attribute and take calculus score, linear algebra score, probability statistics score as condition attributes. In this paper, we are based on rough-set theory (Rough-set theory is a logic-mathematical method proposed by Z. Pawlak. In recent years, this theory has been widely implemented in the many fields of natural science and societal science.) to investigate importance of condition attributes with respective to decision attribute and strength of condition attributes supporting decision attribute. Results of this investigation will be helpful for university students to raise higher mathematics scores in Chinese graduate student entrance examination.

**Keywords:**
Rough set,
higher mathematics scores,
decision attribute,
condition attribute.

##### 1373 An Ontology for Knowledge Representation and Applications

**Authors:**
Nhon Do

**Abstract:**

**Keywords:**
Artificial intelligence,
knowledge representation,
knowledge base system,
ontology.

##### 1372 Identification of Configuration Space Singularities with Local Real Algebraic Geometry

**Authors:**
Marc Diesse,
Hochschule Heilbronn

**Abstract:**

**Keywords:**
Linkages,
configuration space singularities,
real
algebraic geometry,
analytic geometry,
computer algebra.

##### 1371 Further Investigations on Higher Mathematics Scores for Chinese University Students

**Authors:**
Xun Ge

**Abstract:**

Recently, X. Ge and J. Qian investigated some relations between higher mathematics scores and calculus scores (resp. linear algebra scores, probability statistics scores) for Chinese university students. Based on rough-set theory, they established an information system S = (U,CuD,V, f). In this information system, higher mathematics score was taken as a decision attribute and calculus score, linear algebra score, probability statistics score were taken as condition attributes. They investigated importance of each condition attribute with respective to decision attribute and strength of each condition attribute supporting decision attribute. In this paper, we give further investigations for this issue. Based on the above information system S = (U, CU D, V, f), we analyze the decision rules between condition and decision granules. For each x E U, we obtain support (resp. strength, certainty factor, coverage factor) of the decision rule C —>x D, where C —>x D is the decision rule induced by x in S = (U, CU D, V, f). Results of this paper gives new analysis of on higher mathematics scores for Chinese university students, which can further lead Chinese university students to raise higher mathematics scores in Chinese graduate student entrance examination.

**Keywords:**
Rough set,
support,
strength,
certainty factor,
coverage factor.

##### 1370 Intuitionistic T-S Fuzzy Subalgebras and Ideals in BCI-algebras

**Authors:**
Shaoquan Sun,
Qianqian Li

**Abstract:**

The aim of this paper is to introduce the notions of intuitionistic T-S fuzzy subalgebras and intuitionistic T-S fuzzy ideals in BCI-algebras, and then to investigate their basic properties.

**Keywords:**
BCI-algebra,
intuitionistic T-S fuzzy subalgebra,
intuitionistic T-S fuzzy ideal,
norm intersection,
direct product,
epimorphism,
isomorphism.