Rapprochement of artificial intelligence and dynamics

It is proposed that continuous time is in effect discretized in the brain by dynamic pattern recognition mechanisms in neurons. Time discretization is required to support formal computations in continuous time systems consisting of a large number of components. The ability to perform formal computations is necessary if the system is to execute high level algorithms of the type used in present day artificial intelligence. The weakness of such algorithms is that they work efficiently only when the forms of patterns and objects presented to them are highly constrained. The dynamic mechanisms which discretize the brain's time line also serve to code patterns into constrained forms suitable for high level processing.     

On Truncated Matricial Stieltjes Type Moment Problems

We study two slightly different versions of truncated generalized matricial moment problems of Stieltjes type. A central topic is the construction and investigation of distinguished solutions of both moment problems under consideration. These solutions turn out to be nonnegative Hermitian Borel measures on the real axis which are concentrated on a finite number of points. Our approach is mainly algebraic. It is based on the use of particular matrix polynomials constructed from a nonnegative Hermitian block Hankel matrix.     

Special-valued subgroups of lattice-ordered groups

We prove that the intersection of all maximal special-valued subgroups of a lattice-ordered group is the special-valued quasi-torsion radical of a lattice-ordered group , which extends our earlier result that the intersection of all maximal finite-valued subgroups of a lattice-ordered group is the finite-valued torsion radical of . We also show that the class of almost finite-valued lattice-ordered groups is a quasi-torsion class, and the quasi-torsion radical of a group is equal to the intersection of the group with the lateral completion of the finite-valued torsion radical of the group.

     

Finite Group Schemes over Bases with Low Ramification

Let A be a complete characteristic (0,p) discrete valuation ring with absolute ramification degree e and a perfect residue field. We are interested in studying the category FF _A' of finite flat commutative group schemes over A withp-power order. When e= 1, Fontaine formulated the purely linear algebra notion of a finite Honda system over A and constructed an anti-equivalence of categories betweenineFF _A'> and the category of finite Honda systems over A when p> 2. We generalize this theory to the case e – 1.     

STOPPING RULES AND THE CONTROL OF STOCK POLLUTANTS

A stock pollutant is defined as a residual waste that might accumulate over time. This paper examines some of the important distinctions between degradable and nondegradable stock pollutants and between nondegradable stock pollutants with known versus uncertain environmental cost. The latter case is examined using the more recent literature on stochastic control with Brownian motion. The presence of irreversibility and uncertainty is known to lead to more conservative investment rules and places a value on the preservation of options. In the case of a nondegradable stock pollutant with Brownian environmental cost, options are preserved by stopping accumulation at a lower level than in the corresponding certainty-equivalent problem. The model presented in this paper permits the derivation of closed-form stopping rules. For a simple numerical problem, the optimal nondegradable stock with Brownian environmental cost was 20 to 45 percent lower than the optimal level with known environmental cost. The empirical study of an actual nondegradable stock pollutant will require time series data on private and social cost in order to estimate drift and variance parameters which will influence the actual extent to which the optimal stock is less than the certainty-equivalent stock.     

Synthesen von Dibenzo[b,e][1,4]dioxin-2,3-chinonen,einschliesslich der Ecklonochinone A und B sowie der Isoecklonochinone A und B

Syntheses of Dibenzo[b,e][1,4]dioxin-2,3-quinones Including the Ecklonoquinones A and B and the Isoecklonoquinones A and B Oxidation of monomesyloxy-substituted pyrocatechols with MnO₂ in toluene using phase-transfer conditions leads in high yield to monomesyloxy-substituted dibenzo[b,e][1,4]dioxin-2,3-quinones with loss of one mesyloxy group. In this way, ecklonoquinone A ( 2 ), ecklonoquinone B ( 3 ), isoecklonoquinone A ( 43 ), and isoecklonoquinone B ( 44 ) were prepared. Their structures are based on X-ray analyses of ecklonoquinone-A leucoacetate ( 45 ) and the mesyloxy-substituted quinone 20 . The reddish-violet dibenzodioxin-diquinone 49 was prepared from an intermediate of the iso-series. The parent compound 1 has been synthesized in yields better than 50% from pyrocatechol and methyl 2,5-dioxo-2,5-dihydrobenzoate as oxidant and 2-methoxypyridin as catalyst. To rationalize the specific effect on the dimerisation step of the mesyloxy group, the intermediacy of 1,4-quinone monoacetals is proposed. This also applies to a proposed biogenetic scheme.