In this paper an original algorithm for tlie choice of a relevaiit
belief formula is presented. Belief forinulas are treated as external representations of internal States of cognition directed at an ontologically existing atom object. This algorithrn is based on the idea of intentional semantics and uses soft methods based on the theory of consensus and choice.
For any d≥11 we construct graphs of degree d, diameter 2, and order 825d2+O(d), obtained as lifts of dipoles with voltages in cyclic groups. For Cayley Abelian graphs of diameter two a slightly better result of 925d2+O(d) has been known \cite{MSS} but it applies only to special values of degrees d depending on prime powers.
In this paper we use cohomology of Lie algebras to study the variety of laws associated with filiform Lie algebras of a given dimension. As the main result, we describe a constructive way to find a small set of polynomials which define this variety. It allows to improve previous results related with the cardinal of this set. We have also computed explicitly these polynomials in the case of dimensions 11 and 12.
In this paper a problem of consumption and investment is presented as a model of a discounted Markov decision process with discrete-time. In this problem, it is assumed that the wealth is affected by a production function. This assumption gives the investor a chance to increase his wealth before the investment. For the solution of the problem there is established a suitable version of the Euler Equation (EE) which characterizes its optimal policy completely, that is, there are provided conditions which guarantee that a policy is optimal for the problem if and only if it satisfies the EE. The problem is exemplified in two particular cases: for a logarithmic utility and for a Cobb-Douglas utility. In both cases explicit formulas for the optimal policy and the optimal value function are supplied.
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.
For lower-semicontinuous and convex stochastic processes Zn and nonnegative random variables ϵn we investigate the pertaining random sets A(Zn,ϵn) of all ϵn-approximating minimizers of Zn. It is shown that, if the finite dimensional distributions of the Zn converge to some Z and if the ϵn converge in probability to some constant c, then the A(Zn,ϵn) converge in distribution to A(Z,c) in the hyperspace of Vietoris. As a simple corollary we obtain an extension of several argmin-theorems in the literature. In particular, in contrast to these argmin-theorems we do not require that the limit process has a unique minimizing point. In the non-unique case the limit-distribution is replaced by a Choquet-capacity.
Any given increasing [0,1]2→[0,1] function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.
The chromosome complements of thirteen species of the planthopper family Dictyopharidae are described and illustrated. For each species, the structure of testes and, on occasion, ovaries is additionally outlined in terms of the number of seminal follicles and ovarioles. The data presented cover the tribes Nersiini, Scoloptini and Dictyopharini of the subfamily Dictyopharinae and the tribes Ranissini, Almanini, and Orgeriini of the Orgeriinae. The data on the tribes Nersiini and Orgeriini are provided for the first time. Males of Hyalodictyon taurinum and Trimedia cf. viridata (Nersiini) have 2n = 26 + X; Scolops viridis, S. sulcipes, and S. abnormis (Scoloptini) 2n = 36 + X; Callodictya krueperi (Dictyopharini) 2n = 26 + X; Ranissus edirneus and Schizorgerius scytha (Ranissini) 2n = 26 + X. Males of Almana longipes and Bursinia cf. genei (Almanini) have 2n = 26 + X and 2n = 24 + XY, respectively. The latter chromosome complement was not recorded previously for the tribe Almanini. Males of Orgerius ventosus and Deserta cf. bipunctata (Orgeriini) have 2n = 26 + X. The testes of males of A. longipes and B. cf. genei each have 4 seminal follicles, which is characteristic of the tribe Almanini. Males of all other species have 6 follicles per testis. When the ovaries of a species were also studied, the number of ovarioles was coincident with that of seminal follicles. For comparison, Capocles podlipaevi (2n = 24 + X and 6 follicles per testis in males) from the Fulgoridae, the sister family to Dictyopharidae, was also studied. We supplemented all the data obtained with our earlier observations on Dictyopharidae. The chromosomal complement of 2n = 28 + X or that of 2n = 26 + X and 6 follicles per testis are suggested to be the ancestral condition among Dictyopharidae, from which taxa with various chromosome numbers and testes each with 4 follicles have differentiated.