Abstract: As there are also graph methods of circuit analysis in
addition to algebraic methods, it is, in theory, clearly possible to
carry out an analysis of a whole switched circuit in two-phase
switching exclusively by the graph method as well. This article deals
with two methods of full-graph solving of switched circuits: by
transformation graphs and by two-graphs. It deals with the circuit
switched capacitors and the switched current, too. All methods are
presented in an equally detailed steps to be able to compare.
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 [2] 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 [12] and its programming language Maude [13].
Rewriting logic is considered as one of very powerful logics in terms
of description, verification and programming of concurrent systems.
We proposed in [4] a method for translating Ada-95 tasking
programs to ECATNets formalism (Ada-ECATNet). In this paper,
we show 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 (CPNs). Such translation
doesn-t reduce only the size of program, but reduces also the number
of program states. We show also, how this compact Ada-ECATNet
may be reduced again by applying reduction rules on it. This double
reduction of Ada-ECATNet permits a considerable minimization of
the memory space and run time of corresponding Maude program.
Abstract: Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.
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.
Abstract: There is a world-wide need for the development of sustainable management strategies to control pest infestation and the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters, such as mortality. Concentration and time of exposure are both important in determining mortality in response to a toxic agent. Recent research indicated the existence of two resistance phenotypes in R. dominica in Australia, weak and strong, and revealed that the presence of resistance alleles at two loci confers strong resistance, thus motivating the construction of a two-locus model of resistance. Experimental data sets on purified pest strains, each corresponding to a single genotype of our two-locus model, were also available. Hence it became possible to explicitly include mortalities of the different genotypes in the model. In this paper we described how we used two generalized linear models (GLM), probit and logistic models, to fit the available experimental data sets. We used a direct algebraic approach generalized inverse matrix technique, rather than the traditional maximum likelihood estimation, to estimate the model parameters. The results show that both probit and logistic models fit the data sets well but the former is much better in terms of small least squares (numerical) errors. Meanwhile, the generalized inverse matrix technique achieved similar accuracy results to those from the maximum likelihood estimation, but is less time consuming and computationally demanding.
Abstract: In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web-pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.
Abstract: This paper presents unified theory for local (Savitzky-
Golay) and global polynomial smoothing. The algebraic framework
can represent any polynomial approximation and is seamless from
low degree local, to high degree global approximations. The representation
of the smoothing operator as a projection onto orthonormal
basis functions enables the computation of: the covariance matrix
for noise propagation through the filter; the noise gain and; the
frequency response of the polynomial filters. A virtually perfect Gram
polynomial basis is synthesized, whereby polynomials of degree
d = 1000 can be synthesized without significant errors. The perfect
basis ensures that the filters are strictly polynomial preserving. Given
n points and a support length ls = 2m + 1 then the smoothing
operator is strictly linear phase for the points xi, i = m+1. . . n-m.
The method is demonstrated on geometric surfaces data lying on an
invariant 2D lattice.
Abstract: The theory of Groebner Bases, which has recently been
honored with the ACM Paris Kanellakis Theory and Practice Award,
has become a crucial building block to computer algebra, and is
widely used in science, engineering, and computer science. It is wellknown
that Groebner bases computation is EXP-SPACE in a general
polynomial ring setting.
However, for many important applications in computer science
such as satisfiability and automated verification of hardware and
software, computations are performed in a Boolean ring. In this paper,
we give an algorithm to show that Groebner bases computation is PSPACE
in Boolean rings. We also show that with this discovery,
the Groebner bases method can theoretically be as efficient as
other methods for automated verification of hardware and software.
Additionally, many useful and interesting properties of Groebner
bases including the ability to efficiently convert the bases for different
orders of variables making Groebner bases a promising method in
automated verification.
Abstract: Sinc-collocation scheme is one of the new techniques
used in solving numerical problems involving integral equations. This
method has been shown to be a powerful numerical tool for finding
fast and accurate solutions. So, in this paper, some properties of the
Sinc-collocation method required for our subsequent development
are given and are utilized to reduce integral equation of the first
kind to some algebraic equations. Then convergence with exponential
rate is proved by a theorem to guarantee applicability of numerical
technique. Finally, numerical examples are included to demonstrate
the validity and applicability of the technique.
Abstract: Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.
Abstract: Nowadays there are many methods for representing
knowledge such as semantic network, neural network, and conceptual
graphs. Nonetheless, these methods are not sufficiently efficient
when applied to perform and deduce on knowledge domains about
supporting in general education such as algebra, analysis or plane
geometry. This leads to the introduction of computational network
which is a useful tool for representation knowledge base, especially
for computational knowledge, especially knowledge domain about
general education. However, when dealing with a practical problem,
we often do not immediately find a new solution, but we search
related problems which have been solved before and then proposing
an appropriate solution for the problem. Besides that, when finding
related problems, we have to determine whether the result of them
can be used to solve the practical problem or not. In this paper, the
extension model of computational network has been presented. In this
model, Sample Problems, which are related problems, will be used
like the experience of human about practical problem, simulate the
way of human thinking, and give the good solution for the practical
problem faster and more effectively. This extension model is applied
to construct an automatic system for solving algebraic problems in
middle school.
Abstract: Measuring the complexity of software has been an
insoluble problem in software engineering. Complexity measures can
be used to predict critical information about testability, reliability,
and maintainability of software systems from automatic analysis of
the source code. During the past few years, many complexity
measures have been invented based on the emerging Cognitive
Informatics discipline. These software complexity measures,
including cognitive functional size, lend themselves to the approach
of the total cognitive weights of basic control structures such as loops
and branches. This paper shows that the current existing calculation
method can generate different results that are algebraically
equivalence. However, analysis of the combinatorial meanings of this
calculation method shows significant flaw of the measure, which also
explains why it does not satisfy Weyuker's properties. Based on the
findings, improvement directions, such as measures fusion, and
cumulative variable counting scheme are suggested to enhance the
effectiveness of cognitive complexity measures.
Abstract: Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.
Abstract: The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.
Abstract: Quasigroups are algebraic structures closely related to
Latin squares which have many different applications. The
construction of block cipher is based on quasigroup string
transformation. This article describes a block cipher based
Quasigroup of order 256, suitable for fast software encryption of
messages written down in universal ASCII code. The novelty of this
cipher lies on the fact that every time the cipher is invoked a new set
of two randomly generated quasigroups are used which in turn is
used to create a pair of quasigroup of dual operations. The
cryptographic strength of the block cipher is examined by calculation
of the xor-distribution tables. In this approach some algebraic
operations allows quasigroups of huge order to be used without any
requisite to be stored.
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.
Abstract: This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.
Abstract: According to celebrated Hurwitz theorem, there exists
four division algebras consisting of R (real numbers), C (complex
numbers), H (quaternions) and O (octonions). Keeping in view
the utility of octonion variable we have tried to extend the three
dimensional vector analysis to seven dimensional one. Starting with
the scalar and vector product in seven dimensions, we have redefined
the gradient, divergence and curl in seven dimension. It is shown
that the identity n(n - 1)(n - 3)(n - 7) = 0 is satisfied only
for 0, 1, 3 and 7 dimensional vectors. We have tried to write all
the vector inequalities and formulas in terms of seven dimensions
and it is shown that same formulas loose their meaning in seven
dimensions due to non-associativity of octonions. The vector formulas
are retained only if we put certain restrictions on octonions and split
octonions.
Abstract: If there exists a nonempty, proper subset S of the set of all (n+1)(n+2)/2 inertias such that S Ôèå i(A) is sufficient for any n×n zero-nonzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zero-nonzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In [Kim, Olesky and Driessche, Critical sets of inertias for matrix patterns, Linear and Multilinear Algebra, 57 (3) (2009) 293-306], identifying all minimal critical sets of inertias for n×n zero-nonzero patterns with n ≥ 3 and the minimum cardinality of such a set are posed as two open questions by Kim, Olesky and Driessche. In this note, the minimum cardinality of all critical sets of inertias for 4 × 4 irreducible zero-nonzero patterns is identified.
Abstract: A dual-reciprocity boundary element method is presented
for the numerical solution of a class of axisymmetric elastodynamic
problems. The domain integrals that arise in the integrodifferential
formulation are converted to line integrals by using the
dual-reciprocity method together suitably constructed interpolating
functions. The second order time derivatives of the displacement
in the governing partial differential equations are suppressed by
using Laplace transformation. In the Laplace transform domain, the
problem under consideration is eventually reduced to solving a system
of linear algebraic equations. Once the linear algebraic equations are
solved, the displacement and stress fields in the physical domain can
be recovered by using a numerical technique for inverting Laplace
transforms.