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ABSTRACT: In this paper the author, present a deep survey of analysis of some important properties of an exchange economy core (L. Walras's classical case). Reintroducing the concept of solution uniformly competitive, in- troduced in the literature by Stefanescu , we show as it, under certain conditions, appears to be equivalent to the concept of competitive set of negotiation (also in weak form). The proofs are obtained starting from de�nition of cooperative game with nontransferable utility. A new concept extending the classical notion of core is proposed. A competitive bargain- ing set is a �nite collection of allocations, each of them being supported by a coalition, characterized by internal and external stability. Particu- larly, each core-allocation, together the set of all consumers represents a competitive bargaining set. The existence of the competitive bargaining set is proved for exchange economies if the preferences are represented by continuous monotonic utility functions. [Hide abstract]
ABSTRACT: Recently papers investigating problems on detection of the moment of occurrence of an attack on various systems were published. In particular, they consider "Dos-attacks" or attacks like of "denial of service" in a computing system and subsequent changes of the protocol of processing of input assignments. These studies are actual now. The main difference between the paper and previous works is in selection of another formula for setting the probability of a system destruction as a result of the attack. Another major difference from previous work is the use of beta distribution instead a truncated normal distribution for specifying distribution of a random moment of occurrence of attacks.