A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack-McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.
We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.
Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize it as a parabolic inclusion by using the Lagrange multiplier and the nonlinear maximal monotone operator associated with the time differential under time-dependent double obstacles.
In this paper, we give a new approach to the study of Weyl-type theorems. Precisely, we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued functions, we reduce the question of relationship between Weyl-type theorems to the study of the set difference between the parts of the spectrum that are involved. This study solves completely the question of relationship between two spectral valued functions, comparable for one or the other order relation. Then several known results about Weyl-type theorems become corollaries of the results obtained.
The cyber sphere forms a fifth domain of activities were interactions between state and non-state actors could happen. It starts to play an important role within the conflicts and hostilities. Especially in these situations, international society does not have a unified view on the question how to deal with the activities in cyberspace. We could see the different forms of abuse of cyberspace also within the crisis in Ukraine. This crisis is a good example of the complexity of the legal approach and the (non)capability of the legal understanding of cyber operations and attacks. The goal of this article is to highlight this complexity and to determine the status of cyber incidents realized in the Ukraine from the perspective of international law., Jozef Valuch, Ondrej Hamuľák., and Obsahuje bibliografické odkazy
A new species of Acanthochondria Oakley, 1927 (Copepoda, Poecilostomatoida, Chondracanthidae), parasitic on Serranus auriga (Cuvier) from the Argentinean coastal zone, is described and illustrated. The new species differs from its congeners by the relative length of the neck and the protopod of leg 2. This is the second record of this genus for the South-eastern Atlantic and the first one from a serranid host.
The following acanthocolpid species are reported from New Caledonia. Acaenodera nautili sp. n. from Conger cinereus Rüppel differs from other Acaenodera species in details of the body-spination, the sucker-ratio and the bipartite seminal vesicle; Stephanostomum murielae sp. n. from Carangoides hedlandensis (Whitley) differs from most species of Stephanostomum in the average of 36 circum-oral spines, the circum-oral spine rows with a ventral hiatus and the anterior extent of the vitellarium being >10% of the hindbody length from ventral sucker. The species is distinguished from the three other species with these characters in a detailed review. The other species reported are: Stephanostomum aaravi Bray et Cribb, 2003 from Lethrinus miniatus and L. rubrioperculatus; Stephanostomum ditrematis (Yamaguti, 1939) from Gnathanodon speciosus; Stephanostomum japonocasum Durio et Manter, 1969 from Cephalopholis urodeta, Epinephelus areolatus, E. chlorostigma, E. maculatus, E. retouti, Lethrinus miniatus and Variola louti; Stephanostomum uku Yamaguti, 1970 and Pleorchis uku Yamaguti, 1970 from Aprion virescens.