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ON DAVIDSON'S PROBLEM IN THE COLLECTIVE RISK THEORY
Get PDFIn this paper Davidson's classic problem concerning the solution of an integrodifferential equation regarding the collective risk theory with the aim of examining the probability of the failure of an insurance company is further analysed. The validity of a new representation’s formula to the solution of the problem is demonstrated after having discussed the question of the existence of that solution
DYNAMIC PROGRAMMING APPROACH TO TESTING RESOURCE ALLOCATION PROBLEM FOR MODULAR SOFTWARE
Get PDFTesting phase of a software begins with module testing. During this period modules are tested independently to remove maximum possible number of faults within a specified time limit or testing resource budget. This gives rise to some interesting optimization problems, which are discussed in this paper. Two Optimization models are proposed for optimal allocation of testing resources among the modules of a Software. In the first model, we maximize the total fault removal, subject to budgetary Constraint. In the second model, additional constraint representing aspiration level for fault removals for each module of the software is added. These models are solved using dynamic programming technique. The methods have been illustrated through numerical examples
Chemical Examples in Hypergroups
Get PDFHypergroups first were introduced by Marty in 1934. Up to now many researchers have been working on this field of modern algebra and developed it. It is purpose of this paper to provide examples of hypergroups associated with chemistry. The examples presented are connected to construction from chain reactions
KALMAN FILTERS AND ARMA MODELS
Get PDFThe Kalman filter is the celebrated algorithm giving a recursive solution of the prediction problem for time series. After a quite general formulation of the prediction problem, the contributions of its solution by the great mathematicians Kolmogorov and Wiener are shorthly recalled and it is showed as Kalman filter furnishes the optimal predictor, in the sense of least squares, for processes which satisfy the linear models with a finite number of parameters, that are the ARMA models
Homomorphic relation on hyperingoinds and join hyperrings
No full textThis paper is a study of the Join Hyperringoid, which is a hypercompositional structure that has appeared recently. Here appear the homomorphic relations and a special type of such relations, the congruence ones. Moreover, the homomorphisms of the join hyperringoids are being studied, along with the homomorphisms of the Fortified Join Hyperringoids
ON SOME APPLICATIONS OF FUZZY SETS AND COMMUTATIVE HYPERGROUPS TO EVALUATION IN ARCHITECTURE AND TOWN-PLANNING
No full textIn some recent laws about the determination of the rents and of the estimated income of properties, it is required a subdivision of the municipal area in homogeneous zones on the basis of assigned criteria. For this reason in many cities, as it also appeared in some daily newspapers, it has been made a crisp classification of the set of buildings. In some our papers we have observed that the peculiarities of the buildings change in a "not sharp" way and so a fuzzy classification seems more suitable.In this paper, starting from the concept of join space associated to a fuzzy set, we study the relations between fuzzy partitions and commutative hypergroups. More in general, we introduce the concepts of "qualitative linear fuzzy set" and we show the relations among the families of these sets, fuzzy partitions and commutative hypergroups. The aim of the study is to show that the commutative hypergroups are a useful tool to study problems on the evaluation in town-planning. In particular, from the blocks associated to a suitable commutative hypergroup, we single out "almost homogeneous" areas and we can determine, in such areas, the fluctuation of the rents and of the values of the buildings
HYPERCOMPOSITIONAL STRUCTURES FROM THE COMPUTER THEORY
No full textAbstract This paper presents the several types of hypercompositional structures that have been introduced and used for the approach and solution of problems in the theory of languages and automata
Ideals in a semihypergroup and Green's relations
No full textThe concept of ideal in a right (left) semihypergroup is defined. Then some connections between ideals and the hyper versions of Green's relations are discussed
OVER THE CONSTRUCTION OF AN HYPERSTRUCTURE OF QUOTIENTS FOR A MULTIPLICATIIVE HYPERRING
No full textIn this paper we construct a weak hyperfield of quotients for a class of multiplicative hyperrings
PROPERTIES OF HYPERPRODUCTS AND THE RELATION β IN QUASIHYPERGROUPS
No full textSome properties of the complete parts in hyper-groupoids are established. Applying these properties to the case of quasihypergroups H for which H/β*. is a quasigroup, a necessary and sufficient condition for the transitivity of the relation β is proved. Consequently, several classes of quasihypergroups in which β is transitive are obtained (for instance, in any finite quasihypergroup with identity β is a transitive relation). Then, in the case of quasihypergroups having underlying groups, the relation β is completely de-termined