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.
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.
Abstract: In this paper zero-dissipative explicit Runge-Kutta
method is derived for solving second-order ordinary differential
equations with periodical solutions. The phase-lag and dissipation
properties for Runge-Kutta (RK) method are also discussed. The new
method has algebraic order three with dissipation of order infinity.
The numerical results for the new method are compared with existing
method when solving the second-order differential equations with
periodic solutions using constant step size.
Abstract: Let X be a connected space, X be a space, let p : X -→ X be a continuous map and let (X, p) be a covering space of X. In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X, p) of X and also their automorphism groups A(X, p).
Abstract: This paper proposes a new technique for improving
the efficiency of software testing, which is based on a conventional
attempt to reduce test cases that have to be tested for any given
software. The approach utilizes the advantage of Regression Testing
where fewer test cases would lessen time consumption of the testing
as a whole. The technique also offers a means to perform test case
generation automatically. Compared to one of the techniques in the
literature where the tester has no option but to perform the test case
generation manually, the proposed technique provides a better
option. As for the test cases reduction, the technique uses simple
algebraic conditions to assign fixed values to variables (Maximum,
minimum and constant variables). By doing this, the variables values
would be limited within a definite range, resulting in fewer numbers
of possible test cases to process. The technique can also be used in
program loops and arrays.
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.
Abstract: Over the years, many implementations have been
proposed for solving IA networks. These implementations are
concerned with finding a solution efficiently. The primary goal of
our implementation is simplicity and ease of use.
We present an IA network implementation based on finite domain
non-binary CSPs, and constraint logic programming. The
implementation has a GUI which permits the drawing of arbitrary IA
networks. We then show how the implementation can be extended to
find all the solutions to an IA network. One application of finding all
the solutions, is solving probabilistic IA networks.
Abstract: The security of power systems against malicious cyberphysical
data attacks becomes an important issue. The adversary
always attempts to manipulate the information structure of the power
system and inject malicious data to deviate state variables while
evading the existing detection techniques based on residual test. The
solutions proposed in the literature are capable of immunizing the
power system against false data injection but they might be too costly
and physically not practical in the expansive distribution network.
To this end, we define an algebraic condition for trustworthy power
system to evade malicious data injection. The proposed protection
scheme secures the power system by deterministically reconfiguring
the information structure and corresponding residual test. More
importantly, it does not require any physical effort in either microgrid
or network level. The identification scheme of finding meters being
attacked is proposed as well. Eventually, a well-known IEEE 30-bus
system is adopted to demonstrate the effectiveness of the proposed
schemes.
Abstract: In this paper, a numerical solution based on nonpolynomial
cubic spline functions is used for finding the solution of
boundary value problems which arise from the problems of calculus
of variations. This approximation reduce the problems to an explicit
system of algebraic equations. Some numerical examples are also
given to illustrate the accuracy and applicability of the presented
method.
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.
Abstract: In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.
Abstract: One major difficulty that faces developers of
concurrent and distributed software is analysis for concurrency based
faults like deadlocks. Petri nets are used extensively in the
verification of correctness of concurrent programs. ECATNets are a
category of algebraic Petri nets based on a sound combination of
algebraic abstract types and high-level Petri nets. ECATNets have
'sound' and 'complete' semantics because of their integration in
rewriting logic and its programming language Maude. Rewriting
logic is considered as one of very powerful logics in terms of
description, verification and programming of concurrent systems We
proposed previously a method for translating Ada-95 tasking
programs to ECATNets formalism (Ada-ECATNet) and we showed
that ECATNets formalism provides a more compact translation for
Ada programs compared to the other approaches based on simple
Petri nets or Colored Petri nets. We showed also previously how the
ECATNet formalism offers to Ada many validation and verification
tools like simulation, Model Checking, accessibility analysis and
static analysis. In this paper, we describe the implementation of our
translation of the Ada programs into ECATNets.
Abstract: In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.
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.
Abstract: In this article we explore the application of a formal
proof system to verification problems in cryptography. Cryptographic
properties concerning correctness or security of some cryptographic
algorithms are of great interest. Beside some basic lemmata, we
explore an implementation of a complex function that is used in
cryptography. More precisely, we describe formal properties of this
implementation that we computer prove. We describe formalized
probability distributions (σ-algebras, probability spaces and conditional
probabilities). These are given in the formal language of the
formal proof system Isabelle/HOL. Moreover, we computer prove
Bayes- Formula. Besides, we describe an application of the presented
formalized probability distributions to cryptography. Furthermore,
this article shows that computer proofs of complex cryptographic
functions are possible by presenting an implementation of the Miller-
Rabin primality test that admits formal verification. Our achievements
are a step towards computer verification of cryptographic primitives.
They describe a basis for computer verification in cryptography.
Computer verification can be applied to further problems in cryptographic
research, if the corresponding basic mathematical knowledge
is available in a database.
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.
Abstract: Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated.Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds for the moduli of the zeros of complex polynomials. That means, we provide disks in the complex plane where all zeros of a complex polynomial are situated. Such bounds are extremely useful for obtaining a priori assertations regarding the location of zeros of polynomials. Based on the proven bounds and a test set of polynomials, we present an experimental study to examine which bound is optimal.
Abstract: Modeling transfer phenomena in several chemical
engineering operations leads to the resolution of partial differential
equations systems. According to the complexity of the operations
mechanisms, the equations present a nonlinear form and analytical
solution became difficult, we have then to use numerical methods
which are based on approximations in order to transform a
differential system to an algebraic one.Finite element method is one
of numerical methods which can be used to obtain an accurate
solution in many complex cases of chemical engineering.The packed
columns find a large application like contactor for liquid-liquid
systems such solvent extraction. In the literature, the modeling of this
type of equipment received less attention in comparison with the
plate columns.A mathematical bidimensionnal model with radial and
axial dispersion, simulating packed tower extraction behavior was
developed and a partial differential equation was solved using the
finite element method by adopting the Galerkine model. We
developed a Mathcad program, which can be used for a similar
equations and concentration profiles are obtained along the column.
The influence of radial dispersion was prooved and it can-t be
neglected, the results were compared with experimental concentration
at the top of the column in the extraction system:
acetone/toluene/water.
Abstract: The paper presents the virtual model of the active
suspension system used for improving the dynamic behavior of a
motor vehicle. The study is focused on the design of the control
system, the purpose being to minimize the effect of the road
disturbances (which are considered as perturbations for the control
system). The analysis is performed for a quarter-car model, which
corresponds to the suspension system of the front wheel, by using the
DFC (Design for Control) software solution EASY5 (Engineering
Analysis Systems) of MSC Software. The controller, which is a PIDbased
device, is designed through a parametric optimization with the
Matrix Algebra Tool (MAT), considering the gain factors as design
variables, while the design objective is to minimize the overshoot of
the indicial response.
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.