Abstract: On path space kQ, there is a trivial kQa-module structure determined by the multiplication of path algebra kQa and a trivial kQc-comodule structure determined by the comultiplication of path coalgebra kQc. In this paper, on path space kQ, a nontrivial kQa-module structure is defined, and it is proved that this nontrivial left kQa-module structure is isomorphic to the dual module structure of trivial right kQc-comodule. Dually, on path space kQ, a nontrivial kQc-comodule structure is defined, and it is proved that this nontrivial right kQc-comodule structure is isomorphic to the dual comodule structure of trivial left kQa-module. Finally, the trivial and nontrivial module structures on path space are compared from the aspect of submodule, and the trivial and nontrivial comodule structures on path space are compared from the aspect of subcomodule.
Abstract: This article presents a numerical method to find the
heat flux in an inhomogeneous inverse heat conduction problem with
linear boundary conditions and an extra specification at the terminal.
The method is based upon applying the satisfier function along with
the Ritz-Galerkin technique to reduce the approximate solution of the
inverse problem to the solution of a system of algebraic equations.
The instability of the problem is resolved by taking advantage of
the Landweber’s iterations as an admissible regularization strategy.
In computations, we find the stable and low-cost results which
demonstrate the efficiency of the technique.
Abstract: The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.
Abstract: In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.
Abstract: The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.
Abstract: The aim of this paper is to introduce the notion of
intuitionistic fuzzy positive implicative ideals with thresholds (λ, μ) of
BCI-algebras and to investigate its properties and characterizations.
Abstract: This paper deals with using of prevailing operation
system MS Office (SmartArt...) for mathematical models, using
DYVELOP (Dynamic Vector Logistics of Processes) method. It
serves for crisis situations investigation and modelling within the
organizations of critical infrastructure. In first part of paper, it will be
introduced entities, operators, and actors of DYVELOP method. It
uses just three operators of Boolean algebra and four types of the
entities: the Environments, the Process Systems, the Cases, and the
Controlling. The Process Systems (PrS) have five “brothers”:
Management PrS, Transformation PrS, Logistic PrS, Event PrS and
Operation PrS. The Cases have three “sisters”: Process Cell Case,
Use Case, and Activity Case. They all need for the controlling of
their functions special Ctrl actors, except ENV – it can do without
Ctrl. Model´s maps are named the Blazons and they are able
mathematically - graphically express the relationships among entities,
actors and processes. In second part of this paper, the rich blazons of
DYVELOP method will be used for the discovering and modelling of
the cycling cases and their phases. The blazons need live PowerPoint
presentation for better comprehension of this paper mission. The
crisis management of energetic crisis infrastructure organization is
obliged to use the cycles for successful coping of crisis situations.
Several times cycling of these cases is necessary condition for the
encompassment for both emergency events and the mitigation of
organization´s damages. Uninterrupted and continuous cycling
process brings for crisis management fruitfulness and it is good
indicator and controlling actor of organizational continuity and its
sustainable development advanced possibilities. The research reliable
rules are derived for the safety and reliable continuity of energetic
critical infrastructure organization in the crisis situation.
Abstract: In this paper, for an arbitrary multiplicative functional
f from the set of all upper triangular fuzzy matrices to the fuzzy
algebra, we prove that there exist a multiplicative functional F and a
functional G from the fuzzy algebra to the fuzzy algebra such that the
image of an upper triangular fuzzy matrix under f can be represented
as the product of all the images of its main diagonal elements under
F and other elements under G.
Abstract: The present research investigated whether gender
differences affect performance in a simple math quiz in statistics
course. Participants of this study comprised a sample of 567 statistics
students in two different universities in Lebanon. Data were collected
through a simple math quiz. Analysis of quantitative data indicated
that there wasn’t a significant difference in math performance
between males and females. The results suggest that improvements in
student performance may depend on improved mastery of basic
algebra especially for females. The implications of these findings and
further recommendations were discussed.
Abstract: In this paper, the notion of rank−k numerical range
of rectangular complex matrix polynomials are introduced. Some
algebraic and geometrical properties are investigated. Moreover, for
Є > 0, the notion of Birkhoff-James approximate orthogonality
sets for Є−higher rank numerical ranges of rectangular matrix
polynomials is also introduced and studied. The proposed definitions
yield a natural generalization of the standard higher rank numerical
ranges.
Abstract: EEG correlates of mathematical and trait anxiety level
were studied in 52 healthy Russian-speakers during execution of
error-recognition tasks with lexical, arithmetic and algebraic
conditions. Event-related spectral perturbations were used as a
measure of brain activity. The ERSP plots revealed alpha/beta
desynchronizations within a 500-3000 ms interval after task onset
and slow-wave synchronization within an interval of 150-350 ms.
Amplitudes of these intervals reflected the accuracy of error
recognition, and were differently associated with the three conditions.
The correlates of anxiety were found in theta (4-8 Hz) and beta2 (16-
20 Hz) frequency bands. In theta band the effects of mathematical
anxiety were stronger expressed in lexical, than in arithmetic and
algebraic condition. The mathematical anxiety effects in theta band
were associated with differences between anterior and posterior
cortical areas, whereas the effects of trait anxiety were associated
with inter-hemispherical differences. In beta1 and beta2 bands effects
of trait and mathematical anxiety were directed oppositely. The trait
anxiety was associated with increase of amplitude of
desynchronization, whereas the mathematical anxiety was associated
with decrease of this amplitude. The effect of mathematical anxiety
in beta2 band was insignificant for lexical condition but was the
strongest in algebraic condition. EEG correlates of anxiety in theta
band could be interpreted as indexes of task emotionality, whereas
the reaction in beta2 band is related to tension of intellectual
resources.
Abstract: A cyclostationary Gaussian linearization method is
formulated for investigating the time average response of nonlinear
system under sinusoidal signal and white noise excitation. The
quantitative measure of cyclostationary mean, variance, spectrum of
mean amplitude, and mean power spectral density of noise are
analyzed. The qualitative response behavior of stochastic jump and
bifurcation are investigated. The validity of the present approach in
predicting the quantitative and qualitative statistical responses is
supported by utilizing Monte Carlo simulations. The present analysis
without imposing restrictive analytical conditions can be directly
derived by solving non-linear algebraic equations. The analytical
solution gives reliable quantitative and qualitative prediction of mean
and noise response for the Duffing system subjected to both sinusoidal
signal and white noise excitation.
Abstract: Subspace channel estimation methods have been
studied widely, where the subspace of the covariance matrix is
decomposed to separate the signal subspace from noise subspace. The
decomposition is normally done by using either the eigenvalue
decomposition (EVD) or the singular value decomposition (SVD) of
the auto-correlation matrix (ACM). However, the subspace
decomposition process is computationally expensive. This paper
considers the estimation of the multipath slow frequency hopping
(FH) channel using noise space based method. In particular, an
efficient method is proposed to estimate the multipath time delays by
applying multiple signal classification (MUSIC) algorithm which is
based on the null space extracted by the rank revealing LU (RRLU)
factorization. As a result, precise information is provided by the
RRLU about the numerical null space and the rank, (i.e., important
tool in linear algebra). The simulation results demonstrate the
effectiveness of the proposed novel method by approximately
decreasing the computational complexity to the half as compared
with RRQR methods keeping the same performance.
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.
Abstract: This paper describes the problem of building secure
computational services for encrypted information in the Cloud
Computing without decrypting the encrypted data; therefore, it meets
the yearning of computational encryption algorithmic aspiration
model that could enhance the security of big data for privacy,
confidentiality, availability of the users. The cryptographic model
applied for the computational process of the encrypted data is the
Fully Homomorphic Encryption Scheme. We contribute a theoretical
presentations in a high-level computational processes that are based
on number theory and algebra that can easily be integrated and
leveraged in the Cloud computing with detail theoretic mathematical
concepts to the fully homomorphic encryption models. This
contribution enhances the full implementation of big data analytics
based cryptographic security algorithm.
Abstract: This paper presents small signal stability study carried
over the 140-Bus, 31-Machine, 5-Area MEPE system and validated
on free and open source software: PSAT. Well-established linearalgebra
analysis, eigenvalue analysis, is employed to determine the
small signal dynamic behavior of test system. The aspects of local
and interarea oscillations which may affect the operation and
behavior of power system are analyzed. Eigenvalue analysis is carried
out to investigate the small signal behavior of test system and the
participation factors have been determined to identify the
participation of the states in the variation of different mode shapes.
Also, the variations in oscillatory modes are presented to observe the
damping performance of the test system.
Abstract: This study is used as a definition method to the value
and function in manufacturing sector. In concurrence of discussion
about present condition of modeling method, until now definition of
1D-CAE is ambiguity and not conceptual. Across all the physic fields,
those methods are defined with the formulation of differential
algebraic equation which only applied time derivation and simulation.
At the same time, we propose semi-acausal modeling concept and
differential algebraic equation method as a newly modeling method
which the efficiency has been verified through the comparison of
numerical analysis result between the semi-acausal modeling
calculation and FEM theory calculation.
Abstract: Supply chain (SC) is an operational research (OR)
approach and technique which acts as catalyst within central nervous
system of business today. Without SC, any type of business is at
doldrums, hence entropy. SC is the lifeblood of business today
because it is the pivotal hub which provides imperative competitive
advantage. The paper present a conceptual framework dubbed as
Homomorphic Conceptual Framework for Effective Supply Chain
Strategy (HCEFSC).The term Homomorphic is derived from abstract
algebraic mathematical term homomorphism (same shape) which
also embeds the following mathematical application sets:
monomorphisms, isomorphism, automorphisms, and endomorphism.
The HCFESC is intertwined and integrated with wide and broad sets
of elements.
Abstract: Guided by the theory of learning styles, this study is
based on the development of a multimedia learning application for
students with mastery learning style. The learning material was
developed by applying a graduated difficulty learning strategy.
Algebra was chosen as the learning topic for this application. The
effectiveness of this application in helping students learn is measured
by giving a pre- and post-test. The result shows that students who
learn using the learning material that matches their preferred learning
style perform better than the students with a non-personalized
learning material.
Abstract: Distributed Generation (DG) can help in reducing the
cost of electricity to the costumer, relieve network congestion and
provide environmentally friendly energy close to load centers. Its
capacity is also scalable and it provides voltage support at distribution
level. Hence, DG placement and penetration level is an important
problem for both the utility and DG owner. DG allocation and capacity
determination is a nonlinear optimization problem. The objective
function of this problem is the minimization of the total loss of the
distribution system. Also high levels of penetration of DG are a new
challenge for traditional electric power systems. This paper presents a
new methodology for the optimal placement of DG and penetration
level of DG in distribution system based on General Algebraic
Modeling System (GAMS) and Genetic Algorithm (GA).