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.
Abstract: Modeling of a heterogeneous industrial fixed bed
reactor for selective dehydrogenation of heavy paraffin with Pt-Sn-
Al2O3 catalyst has been the subject of current study. By applying
mass balance, momentum balance for appropriate element of reactor
and using pressure drop, rate and deactivation equations, a detailed
model of the reactor has been obtained. Mass balance equations have
been written for five different components. In order to estimate
reactor production by the passage of time, the reactor model which is
a set of partial differential equations, ordinary differential equations
and algebraic equations has been solved numerically.
Paraffins, olefins, dienes, aromatics and hydrogen mole percent as
a function of time and reactor radius have been found by numerical
solution of the model. Results of model have been compared with
industrial reactor data at different operation times. The comparison
successfully confirms validity of proposed model.
Abstract: Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the well-known Quine-McCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the Quine-McCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the Quine-McCluskey method and show that it represents a set covering problem that, unfortunately, is an NP-hard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings.
Abstract: In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.
Abstract: The notions of I-vague groups with membership and
non-membership functions taking values in an involutary dually
residuated lattice ordered semigroup are introduced which generalize
the notions with truth values in a Boolean algebra as well as those
usual vague sets whose membership and non-membership functions
taking values in the unit interval [0, 1]. Moreover, various operations
and properties are established.
Abstract: This paper discusses a new, systematic approach to
the synthesis of a NP-hard class of non-regenerative Boolean
networks, described by FON[FOFF]={mi}[{Mi}], where for every
mj[Mj]∈{mi}[{Mi}], there exists another mk[Mk]∈{mi}[{Mi}], such
that their Hamming distance HD(mj, mk)=HD(Mj, Mk)=O(n), (where
'n' represents the number of distinct primary inputs). The method
automatically ensures exact minimization for certain important selfdual
functions with 2n-1 points in its one-set. The elements meant for
grouping are determined from a newly proposed weighted incidence
matrix. Then the binary value corresponding to the candidate pair is
correlated with the proposed binary value matrix to enable direct
synthesis. We recommend algebraic factorization operations as a post
processing step to enable reduction in literal count. The algorithm
can be implemented in any high level language and achieves best
cost optimization for the problem dealt with, irrespective of the
number of inputs. For other cases, the method is iterated to
subsequently reduce it to a problem of O(n-1), O(n-2),.... and then
solved. In addition, it leads to optimal results for problems exhibiting
higher degree of adjacency, with a different interpretation of the
heuristic, and the results are comparable with other methods.
In terms of literal cost, at the technology independent stage, the
circuits synthesized using our algorithm enabled net savings over
AOI (AND-OR-Invert) logic, AND-EXOR logic (EXOR Sum-of-
Products or ESOP forms) and AND-OR-EXOR logic by 45.57%,
41.78% and 41.78% respectively for the various problems.
Circuit level simulations were performed for a wide variety of
case studies at 3.3V and 2.5V supply to validate the performance of
the proposed method and the quality of the resulting synthesized
circuits at two different voltage corners. Power estimation was
carried out for a 0.35micron TSMC CMOS process technology. In
comparison with AOI logic, the proposed method enabled mean
savings in power by 42.46%. With respect to AND-EXOR logic, the
proposed method yielded power savings to the tune of 31.88%, while
in comparison with AND-OR-EXOR level networks; average power
savings of 33.23% was obtained.
Abstract: Trust is essential for further and wider acceptance of
contemporary e-services. It was first addressed almost thirty years
ago in Trusted Computer System Evaluation Criteria standard by
the US DoD. But this and other proposed approaches of that
period were actually solving security. Roughly some ten years ago,
methodologies followed that addressed trust phenomenon at its core,
and they were based on Bayesian statistics and its derivatives, while
some approaches were based on game theory. However, trust is a
manifestation of judgment and reasoning processes. It has to be dealt
with in accordance with this fact and adequately supported in cyber
environment. On the basis of the results in the field of psychology
and our own findings, a methodology called qualitative algebra has
been developed, which deals with so far overlooked elements of trust
phenomenon. It complements existing methodologies and provides a
basis for a practical technical solution that supports management of
trust in contemporary computing environments. Such solution is also
presented at the end of this paper.
Abstract: The design of a steam turbine is a very complex
engineering operation that can be simplified and improved thanks to
computer-aided multi-objective optimization. This process makes use
of existing optimization algorithms and losses correlations to identify
those geometries that deliver the best balance of performance (i.e.
Pareto-optimal points).
This paper deals with a one-dimensional multi-objective and
multi-point optimization of a single-stage steam turbine. Using a
genetic optimization algorithm and an algebraic one-dimensional
ideal gas-path model based on loss and deviation correlations, a code
capable of performing the optimization of a predefined steam turbine
stage was developed. More specifically, during this study the
parameters modified (i.e. decision variables) to identify the best
performing geometries were solidity and angles both for stator and
rotor cascades, while the objective functions to maximize were totalto-
static efficiency and specific work done.
Finally, an accurate analysis of the obtained results was carried
out.
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.
Abstract: In the present study, a procedure was developed to
determine the optimum reaction rate constants in generalized
Arrhenius form and optimized through the Nelder-Mead method. For
this purpose, a comprehensive mathematical model of a fixed bed
reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3
catalyst was developed. Utilizing appropriate kinetic rate expressions
for the main dehydrogenation reaction as well as side reactions and
catalyst deactivation, a detailed model for the radial flow reactor was
obtained. The reactor model composed of a set of partial differential
equations (PDE), ordinary differential equations (ODE) as well as
algebraic equations all of which were solved numerically to
determine variations in components- concentrations in term of mole
percents as a function of time and reactor radius. It was demonstrated
that most significant variations observed at the entrance of the bed
and the initial olefin production obtained was rather high. The
aforementioned method utilized a direct-search optimization
algorithm along with the numerical solution of the governing
differential equations. The usefulness and validity of the method was
demonstrated by comparing the predicted values of the kinetic
constants using the proposed method with a series of experimental
values reported in the literature for different systems.
Abstract: The present contribution deals with the
thermophoretic deposition of nanoparticles over a rapidly rotating
permeable disk in the presence of partial slip, magnetic field, thermal
radiation, thermal-diffusion, and diffusion-thermo effects. The
governing nonlinear partial differential equations such as continuity,
momentum, energy and concentration are transformed into nonlinear
ordinary differential equations using similarity analysis, and the
solutions are obtained through the very efficient computer algebra
software MATLAB. Graphical results for non-dimensional
concentration and temperature profiles including thermophoretic
deposition velocity and Stanton number (thermophoretic deposition
flux) in tabular forms are presented for a range of values of the
parameters characterizing the flow field. It is observed that slip
mechanism, thermal-diffusion, diffusion-thermo, magnetic field and
radiation significantly control the thermophoretic particles deposition
rate. The obtained results may be useful to many industrial and
engineering applications.
Abstract: In this paper is investigated a possible
optimization of some linear algebra problems which can be
solved by parallel processing using the special arrays called
systolic arrays. In this paper are used some special types of
transformations for the designing of these arrays. We show
the characteristics of these arrays. The main focus is on
discussing the advantages of these arrays in parallel
computation of matrix product, with special approach to the
designing of systolic array for matrix multiplication.
Multiplication of large matrices requires a lot of
computational time and its complexity is O(n3 ). There are
developed many algorithms (both sequential and parallel) with
the purpose of minimizing the time of calculations. Systolic
arrays are good suited for this purpose. In this paper we show
that using an appropriate transformation implicates in finding
more optimal arrays for doing the calculations of this type.
Abstract: Ontology is a terminology which is used in artificial
intelligence with different meanings. Ontology researching has an
important role in computer science and practical applications,
especially distributed knowledge systems. In this paper we present an
ontology which is called Computational Object Knowledge Base
Ontology. It has been used in designing some knowledge base
systems for solving problems such as the system that supports
studying knowledge and solving analytic geometry problems, the
program for studying and solving problems in Plane Geometry, the
knowledge system in linear algebra.
Abstract: In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.
Abstract: In this paper, we derive some algebraic identities on
right and left neighbors R(F) and L(F) of an indefinite binary
quadratic form F = F(x, y) = ax2 + bxy + cy2 of discriminant
Δ = b2 -4ac. We prove that the proper cycle of F can be given by
using its consecutive left neighbors. Also we construct a connection
between right and left neighbors of F.
Abstract: The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.
Abstract: In this study, a reformer model simulation to use
refinery (Farashband refinery, Iran) waste natural gas. In the
petroleum and allied sectors where natural gas is being encountered
(in form of associated gas) without prior preparation for its positive
use, its combustion (which takes place in flares, an equipment through
which they are being disposed) has become a great problem because
of its associated environmental problems in form of gaseous emission.
The proposed model is used to product syngas from waste natural gas.
A detailed steady model described by a set of ordinary differential and
algebraic equations was developed to predict the behavior of the
overall process. The proposed steady reactor model was validated
against process data of a reformer synthesis plant recorded and a good
agreement was achieved. H2/CO ratio has important effect on Fischer-
Tropsch synthesis reactor product and we try to achieve this parameter
with best designing reformer reactor. We study different kind of
reformer reactors and then select auto thermal reforming process of
natural gas in a fixed bed reformer that adjustment H2/CO ratio with
CO2 and H2O injection. Finally a strategy was proposed for prevention
of extra natural gas to atmosphere.
Abstract: In this paper 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 (o--algebras, probability spaces and condi¬tional 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 paper 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 crypto-graphic research, if the corresponding basic mathematical knowledge is available in a database.
Abstract: One of the main image representations in Mathematical Morphology is the 3D Shape Decomposition Representation, useful for Image Compression and Representation,and Pattern Recognition. The 3D Morphological Shape Decomposition representation can be generalized a number of times,to extend the scope of its algebraic characteristics as much as possible. With these generalizations, the Morphological Shape Decomposition 's role to serve as an efficient image decomposition tool is extended to grayscale images.This work follows the above line, and further develops it. Anew evolutionary branch is added to the 3D Morphological Shape Decomposition's development, by the introduction of a 3D Multi Structuring Element Morphological Shape Decomposition, which permits 3D Morphological Shape Decomposition of 3D binary images (grayscale images) into "multiparameter" families of elements. At the beginning, 3D Morphological Shape Decomposition representations are based only on "1 parameter" families of elements for image decomposition.This paper addresses the gray scale inter frame interpolation by means of mathematical morphology. The new interframe interpolation method is based on generalized morphological 3D Shape Decomposition. This article will present the theoretical background of the morphological interframe interpolation, deduce the new representation and show some application examples.Computer simulations could illustrate results.