Abstract: The Model for Knowledge Base of Computational Objects
(KBCO model) has been successfully applied to represent the
knowledge of human like Plane Geometry, Physical, Calculus. However,
the original model cannot easyly apply in inorganic chemistry
field because of the knowledge specific problems. So, the aim of
this article is to introduce how we extend the Computional Object
(Com-Object) in KBCO model, kinds of fact, problems model, and
inference algorithms to develop a program for solving problems
in inorganic chemistry. Our purpose is to develop the application
that can help students in their study inorganic chemistry at schools.
This application was built successful by using Maple, C# and WPF
technology. It can solve automatically problems and give human
readable solution agree with those writting by students and teachers.
Abstract: In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.
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, 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: A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.
Abstract: Despite the extensive use of eLearning systems, there
is no consensus on a standard framework for evaluating this kind of
quality system. Hence, there is only a minimum set of tools that can
supervise this judgment and gives information about the course
content value. This paper presents two kinds of quality set evaluation
indicators for eLearning courses based on the computational process
of three known metrics, the Euclidian, Hamming and Levenshtein
distances. The “distance" calculus is applied to standard evaluation
templates (i.e. the European Commission Programme procedures vs.
the AFNOR Z 76-001 Standard), determining a reference point in the
evaluation of the e-learning course quality vs. the optimal concept(s).
The case study, based on the results of project(s) developed in the
framework of the European Programme “Leonardo da Vinci", with
Romanian contractors, try to put into evidence the benefits of such a
method.
Abstract: This paper unifies power optimization approaches in
various energy converters, such as: thermal, solar, chemical, and
electrochemical engines, in particular fuel cells. Thermodynamics
leads to converter-s efficiency and limiting power. Efficiency
equations serve to solve problems of upgrading and downgrading of
resources. While optimization of steady systems applies the
differential calculus and Lagrange multipliers, dynamic optimization
involves variational calculus and dynamic programming. In reacting
systems chemical affinity constitutes a prevailing component of an
overall efficiency, thus the power is analyzed in terms of an active
part of chemical affinity. The main novelty of the present paper in the
energy yield context consists in showing that the generalized heat
flux Q (involving the traditional heat flux q plus the product of
temperature and the sum products of partial entropies and fluxes of
species) plays in complex cases (solar, chemical and electrochemical)
the same role as the traditional heat q in pure heat engines.
The presented methodology is also applied to power limits in fuel
cells as to systems which are electrochemical flow engines propelled
by chemical reactions. The performance of fuel cells is determined by
magnitudes and directions of participating streams and mechanism of
electric current generation. Voltage lowering below the reversible
voltage is a proper measure of cells imperfection. The voltage losses,
called polarization, include the contributions of three main sources:
activation, ohmic and concentration. Examples show power maxima
in fuel cells and prove the relevance of the extension of the thermal
machine theory to chemical and electrochemical systems. The main
novelty of the present paper in the FC context consists in introducing
an effective or reduced Gibbs free energy change between products p
and reactants s which take into account the decrease of voltage and
power caused by the incomplete conversion of the overall reaction.
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.
Abstract: Morgan-s refinement calculus (MRC) is one of the
well-known methods allowing the formality presented in the program
specification to be continued all the way to code. On the other hand,
Object-Z (OZ) is an extension of Z adding support for classes and
objects. There are a number of methods for obtaining code from OZ
specifications that can be categorized into refinement and animation
methods. As far as we know, only one refinement method exists
which refines OZ specifications into code. However, this method
does not have fine-grained refinement rules and thus cannot be
automated. On the other hand, existing animation methods do not
present mapping rules formally and do not support the mapping of
several important constructs of OZ, such as all cases of operation
expressions and most of constructs in global paragraph. In this paper,
with the aim of providing an automatic path from OZ specifications
to code, we propose an approach to map OZ specifications into their
counterparts in MRC in order to use fine-grained refinement rules of
MRC. In this way, having counterparts of our specifications in MRC,
we can refine them into code automatically using MRC tools such as
RED. Other advantages of our work pertain to proposing mapping
rules formally, supporting the mapping of all important constructs of
Object-Z, and considering dynamic instantiation of objects while OZ
itself does not cover this facility.
Abstract: Resistance of denial of service attacks is a key security requirement in voting protocols. Acquisti protocol plays an important role in development of internet voting protocols and claims its security without strong physical assumptions. In this study firstly Acquisti protocol is modeled in extended applied pi calculus, and then resistance of denial of service attacks is proved with ProVerif. The result is that it is not resistance of denial of service attacks because two denial of service attacks are found. Finally we give the method against the denial of service attacks.
Abstract: Cognitive Science appeared about 40 years ago,
subsequent to the challenge of the Artificial Intelligence, as common
territory for several scientific disciplines such as: IT, mathematics,
psychology, neurology, philosophy, sociology, and linguistics. The
new born science was justified by the complexity of the problems
related to the human knowledge on one hand, and on the other by the
fact that none of the above mentioned sciences could explain alone
the mental phenomena. Based on the data supplied by the
experimental sciences such as psychology or neurology, models of
the human mind operation are built in the cognition science. These
models are implemented in computer programs and/or electronic
circuits (specific to the artificial intelligence) – cognitive systems –
whose competences and performances are compared to the human
ones, leading to the psychology and neurology data reinterpretation,
respectively to the construction of new models. During these
processes if psychology provides the experimental basis, philosophy
and mathematics provides the abstraction level utterly necessary for
the intermission of the mentioned sciences.
The ongoing general problematic of the cognitive approach
provides two important types of approach: the computational one,
starting from the idea that the mental phenomenon can be reduced to
1 and 0 type calculus operations, and the connection one that
considers the thinking products as being a result of the interaction
between all the composing (included) systems. In the field of
psychology measurements in the computational register use classical
inquiries and psychometrical tests, generally based on calculus
methods. Deeming things from both sides that are representing the
cognitive science, we can notice a gap in psychological product
measurement possibilities, regarded from the connectionist
perspective, that requires the unitary understanding of the quality –
quantity whole. In such approach measurement by calculus proves to
be inefficient. Our researches, deployed for longer than 20 years,
lead to the conclusion that measuring by forms properly fits to the
connectionism laws and principles.
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.