Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Pionic branches in neutron matter and the problem of pion condensation

The pion spectrum for charged and neutral pions is investigated in pure neutron matter, by letting the pions interact with a neutron Fermi sea in a self-consistent scheme that renormalizes simultaneously the mesons, considered the source of the interaction, and the nucleons. The possibility of obtaining different kinds of pion condensates is investigated with the result that they cannot be reached even for values of the spin-spin correlation parameter, g', far below the range commonly accepted.

The Fishing Industry in Kerala - Problem and Potentials

importance of fishing and other allied industries in the economy was realised only very recently. Consequently only very few studies are available on the subject. Here an attempt is made to survey the available literature on the subject.

On the generalized obnoxious center problem: antimedian subsets

The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

Reinforcement Learning approaches to Economic Dispatch problem

This paper presents Reinforcement Learning (RL) approaches to Economic Dispatch problem. In this paper, formulation of Economic Dispatch as a multi stage decision making problem is carried out, then two variants of RL algorithms are presented. A third algorithm which takes into consideration the transmission losses is also explained. Efficiency and flexibility of the proposed algorithms are demonstrated through different representative systems: a three generator system with given generation cost table, IEEE 30 bus system with quadratic cost functions, 10 generator system having piecewise quadratic cost functions and a 20 generator system considering transmission losses. A comparison of the computation times of different algorithms is also carried out.

Reinforcement Learning Solution for Unit Commitment Problem Considering Minimum Start Up and Shut Down Times

Unit Commitment Problem (UCP) in power system refers to the problem of determining the on/ off status of generating units that minimize the operating cost during a given time horizon. Since various system and generation constraints are to be satisfied while finding the optimum schedule, UCP turns to be a constrained optimization problem in power system scheduling. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision making task and an efficient Reinforcement Learning solution is formulated considering minimum up time /down time constraints. The correctness and efficiency of the developed solutions are verified for standard test systems

Reinforcement Learning solution for Unit Commitment Problem through pursuit method

Unit commitment is an optimization task in electric power generation control sector. It involves scheduling the ON/OFF status of the generating units to meet the load demand with minimum generation cost satisfying the different constraints existing in the system. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision task and Reinforcement Learning solution is formulated through one efficient exploration strategy: Pursuit method. The correctness and efficiency of the developed solutions are verified for standard test systems

Testing Isotropy and a related Random Walk problem

One comes across directions as the observations in a number of situations. The first inferential question that one should answer when dealing with such data is, “Are they isotropic or uniformly distributed?” The answer to this question goes back in history which we shall retrace a bit and provide an exact and approximate solution to this so-called “Pearson’s Random Walk” problem.

Employment Realm in Technical Education in Kerala-A Study on the Problem of Unemployment among Engineers

The The The The growing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demandgrowing demand for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of for the expansion of the the the the publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system publicly funded system of education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goodof education as merit and free goods emphasized emphasized emphasized emphasized emphasized emphasized emphasized emphasized emphasized emphasized on large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation large allocation of funds on of funds on of funds on of funds on of funds on of funds on of funds on of funds on of funds on of funds on of funds for promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting educationfor promoting education. Compared to . Compared to . Compared to . Compared to . Compared to . Compared to . Compared to . Compared to . Compared to . Compared to . Compared to . Compared to . Compared to the rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of Indiathe rest of India, Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead , Kerala is far ahead in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect in this respect primarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the eprimarily because of the earlierarlierarlierarlierarlierarlier political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social political and social compulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions ofcompulsions of the state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The prethe state. The presumption of sumption of sumption of sumption of sumption of sumption of sumption of sumption of sumption of sumption of sumption of assured assured assured assured assured assured assured assured and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed and guaranteed employment in employment in employment in employment in employment in employment in employment in employment in employment in employment in employment in employment in the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East the Middle East and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other and also in other countries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased furthecountries increased further the scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher educationthe scope of higher education in KeralaKeralaKeralaKeralaKeralaKerala, particularparticularparticularparticularparticularparticularparticularparticularparticularparticularly the technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe technical educationthe

Research through DESIGN through research - a problem statement and a conceptual sketch

This paper re-addresses the issue of a lacking genuine design research paradigm. It tries to sketch an operational model of such a paradigm, based upon a generic design process model, which is derived from basic notions of evolution and learning in different domains of knowing (and turns out to be not very different from existing ones). It does not abandon the scientific paradigm but concludes that the latter has to be embedded into / subordinated under a design paradigm.

A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

The problem of noncharacteristic quasimolecular X-rays in heavy ion collision

Quasi-molecular X-rays observed in heavy ion collisions are interpreted within a relativistic calculation of correlation diagrams using the Dirac-Slater model. A semiquantitative description of noncharacteristic M X rays is given for the system Au-I.