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  Journal of Mathematics and System Science

Volume 2, Number 2, February 2012 (Serial Number 3)

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Volume 2, Number 2, February 2012
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On s-Regular Spaces

Halgwrd Mohammed Darwesh and Adil Kadir Jabbar



Abstract: In the present, the authors investigate a new type of separation axioms, which they call it s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of -regularity. However, the authors showed that the s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts of s-regularity and s-regularity are same on the class of anti-locally countable spaces; furthermore, they proved that the three concepts s-regularity, s-regularity and s-regularity are same on the class of extremally disconnected spaces. The authors characterized s-regular T1-spaces by g-open sets, and they proved that the s-regularity is an open hereditary property and it is also a topological property. The s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts s-closure to obtain some characterizations of the s-regular spaces. Behind those, the authors obtained some properties and characterizations of -semi open sets.


Key words: Semi-open set, -semi open set, regular space, s-regular space, s-regular space, locally and anti locally countable space, extremally disconnected space.



Abstract: The electromagnetic field relations are demonstrated on impulse radiating surface and point type sources, which are characterized by first and second order singularities at rest in a Schwartz-Sobolev space setting. The investigation starts with a general introduction to Schwartz-Sobolev distributions, the electromagnetic field equations and various modes of impulsive radiation. This is followed by an outline of temporal distributional relations in arbitrary media and distributional derivative operations on an arbitrary regular surface, all of which are employed in an investigation of impulse radiation mechanism on single and double layer sources. Similar steps are followed in a description of point distributions and investigation of impulse radiation mechanism on electric and magnetic point dipoles.


Key words: Generalized functions, electromagnetic phenomena, single and double layers, point sources, impulse radiation.



Abstract: The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments (i.e. means and variances) of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.


Key words: Double shot noise process, a Cox process, stochastic intensity and time value of claims, aggregate accumulated/discounted claims.




Abstract: This invited paper reviews recent initiatives in teaching about randomized field trials at the graduate level in education research. Reports in a book on randomized trials by Mosteller and Boruch are used as a benchmark. The initiatives have been driven heavily by recent governmental emphasis on evidence based policy in education, criminology, welfare and other sectors. This policy has been backed, in the US at least, by substantial investments in mounting randomized controlled trials to evaluate curriculum packages and programs in grades K-12, crime prevention programs, welfare, and other work. Accelerated growth in randomized trials has entailed cross discipline pre-doctoral and post-doctoral institutes and graduate education programs aimed at enhancing the quality in trial design, execution, and analysis of results. Specific illustrations of graduate education in this area of statistics are taken mainly from experience at the University of Pennsylvanias Graduate School of Education and selected other institutions.


Key words: Randomized controlled trials, quantitative methods, Ph.D. training in quantitative methods, educational research, Institute of Education Sciences.




Abstract: In the traditional theoretical descriptions of microscopic physical systems (typically, atoms and molecules) people strongly relied upon analogies between the classical mechanics and quantum theory. Naturally, such a methodical framework proved limited as it excluded, up to the recent past, multiple, less intuitively accessible phenomenological models from the serious consideration. For this reason, the classical-quantum parallels were steadily weakened, preserving still the basic and robust abstract version of the key Copenhagen-school concept of treating the states of microscopic systems as elements of a suitable linear Hilbert space. Less than 20 years ago, finally, powerful innovations emerged on mathematical side. Various less standard representations of the Hilbert space entered the game. Pars pro toto, one might recall the Dysons representation of the so-called interacting boson model in nuclear physics, or the steady increase of popularity of certain apparently non-Hermitian interactions in field theory. In the first half of the authors present paper the recent heuristic progress as well as phenomenological success of the similar use of non-Hermitian Hamiltonians will be reviewed, being characterized by their self-adjoint form in an auxiliary Krein space K. In the second half of the authors text a further extension of the scope of such a mathematically innovative approach to the physical quantum theory is proposed. The authors key idea lies in the recommendation of the use of the more general versions of the indefinite metrics in the space of states (note that in the Krein-space case the corresponding indefinite metric P is mostly treated as operator of parity). Thus, the author proposes that the operators P should be admitted to represent, in general, the indefinite metric in a Pontryagin space. A constructive version of such a generalized quantization strategy is outlined and found feasible.


Key words: Quantum mechanics, Hermitizations of observables, auxiliary Krein and Pontryagin spaces, Jacobi-matrix Hamiltonians, Dieudonne equation.



Non-Linear Dependence in Oil Price Behavior

Semei Coronado Ramirez, Leonardo Gatica Arreola and Mauricio Ramirez Grajeda



Abstract: In this paper, the authors analyze the adequacy of GARCH-type models to analyze oil price behavior by applying two types of non-parametric tests, the Hinich portmanteau test for non-linear dependence and a frequency-dominant test of time reversibility, the reverse test based on the bispectrum, to explore the high-order spectrum properties of the Mexican oil price series. The results suggest strong evidence of a non-linear structure and time irreversibility. Therefore, it does not comply with the i.i.d (independent and identically distributed) property. The non-linear dependence, however, is not consistent throughout the sample period, as indicated by a windowed test, suggesting episodic nonlinear dependence. The results imply that GARCH models cannot capture the series structure.


Key words: Bispectrum, time reversibility, nonlinearity, asymmetry, oil price.




Abstract: Identifying the causal impact of some intervention in observational studies is a challenging task, and it is even more challenging when one is faced with correlated binary end-points. The statistical literature on analyzing such data is well documented. Dependence between observations from the same study subject in correlated data renders invalid the usual chi-square tests of independence and inflates the variance of parameter estimates. Disaggregated approaches such as hierarchical linear models which are able to adjust for individual level covariates are favoured in the analysis of such data, thereby gaining power over aggregated and individual-level analyses. In this article the authors, therefore, address the issue of analyzing correlated data with dichotomous end-points by using hierarchical logistic regression, a generalization of the standard logistic regression model for independent outcomes.


Key words: Correlated data, observational studies, counterfactual problem, hierarchical models, group randomization, treatment effect.




Abstract: Current trends on CFD (Computational Fluid Dynamics) along with high performance computing are moving towards using modern GPUs (Graphics Processing Units) in order to achieve substantial execution speedup. Consequently, it is definitely crucial to have some understanding about execution time of different computational methods and parallelization procedures. In this study, two GPU accelerated schemes namely LBM (Lattice Boltzmann Method) and SFV (Stream Function-Vorticity) formulation are investigated and comparedfor simulation of flow over a flat plate. The comparisons are based on solvers runtime and speedup and GPU type of structuring. On study the authors found that although the runtime for SFV formulation is less than LBM, LBM has greater potential to obtain higher speedup by using modern GPUs‎ like NVIDIA GTX 480. In addition, a performance sensitivity is done to investigate for different GPU type of structures as a considerable parameter. The difference between GPU runtime in optimum and regular conditions indicates that using one-dimensional structuring can improve the GPU performance about 50 percent.


Key words: LBM, GPU structuring, stream function-vorticity, flat plate.



Abstract: Results of a research about statistical reasoning that six high school teachers developed in a computer environment are presented in this article. A sequence of three activities with the support of software Fathom was presented to the teachers in a course to investigate about the reasoning that teachers develop about the data analysis, particularly about the distribution concept, that involves important concepts such as averages, variability and graphics representations. The design of the activities was planned so that the teachers analyzed quantitative variables separately first, and later made an analysis of a qualitative variable versus a quantitative variable with the objective of establishing comparisons between distributions and use concepts as averages, variability, shape and outliers. The instructions in each activity indicated to the teachers to use all the resources of the software that were necessary to make the complete analysis and respond to certain questions that pretended to capture the type of representations they used to answer. The results indicate that despite the abundance of representations provided by the software, teachers focus on the calculation of averages to describe and compare distributions, rather than on the important properties of data such as variability, shape and outliers. Many teachers were able to build interesting graphs reflecting important properties of the data, but cannot use them to support data analysis. Hence, it is necessary to extend the teachers understanding on data analysis so they can take advantage of the cognitive potential that computer tools to offer.


Key words: Statistical reasoning, data analysis, computer environment to teaching.





Abstract: The paper describes the concept of plaintext encryption by using the Unicode characters. In the case of elliptic curve cryptography, there is not specified rule or algorithm to specify the letters of Tifinagh as well as special characters. So, the paper gives the transformation of characters Tifinagh into points on elliptic curve by using the corresponding characters Latin. The obtained correspondence has been applied in Menezes-Vanstone cryptosystem based on elliptic curve. Therefore, the paper explains in detail its implementation in Maple12.


Key words: Cryptography, elliptic curve, elliptic curve cryptography, Unicode, Tifinagh characters, encryption, decryption, implementation.





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Journal of Mathematics and System Science (Print: ISSN 2159-5291; Online: ISSN 2159-5305), a monthly professional academic and peer-reviewed journal, particularly emphasizes new research results in theory and methodology, in realm of pure mathematics, applied mathematics, computational mathematics, system theory, system control, system engineering, system biology, operations research and management, probability theory, statistics, information processing, etc.. Articles interpreting practical application of up-to-date technology are also welcome.


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