For cardinals κ, λ,μ we let bκ,λ,μ be the smallest size of a subset B of λμ unbounded in the sense of ≤κ ; that is, such that there is no function f ∈ λμ such that {α < λ : g(α) > f (α)} has size less than κ for all g ∈ B. Similarly for dκ,λ,μ, the general dominating number, which is the smallest size of a subset B of λμ such that for every g ∈ λμ there is an f ∈ B such that the above set has s...

Research thrusts in silicon photonics are developing control operations using higher order waveguide modes for next generation high-bandwidth communication systems. In this context, devices allowing optical processing of multiple waveguide modes can reduce architecture complexity and enable flexible on-chip networks. We propose and demonstrate a hybrid resonator dually resonant at the 1st and 2...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

Quasi-nearness biframes provide an asymmetric setting for the study of nearness; in [1] a completion (called a quasi-completion) was constructed for such structures and in [2] completeness was characterized in terms of the convergence of regular Cauchy bifilters. In this talk, questions of functoriality for this quasi-completion are considered and one sees that having enough regular Cauchy bifi...

Higher order generalizations of Lie algebras have equivalently been conceived as Lie n-algebras, as L∞-algebras, or, dually, as quasi-free differential graded commutative algebras. Here we discuss morphisms and higher morphisms of Lie n-algebras, the construction of inner derivation Lie (n+1)-algebras, and the existence of short exact sequences of Lie (2n + 1)-algebras for every transgressive L...

In this paper, a new scheme employing the time-recursive approach to compute the discrete cosine transform (DCT) and discrete sine transform (DST) is presented. Using such approach, parallel lattice structure that can dually generate the DCT and DST simultaneously is developed. The resulting architecture is regular, module, and without global communication and can be applied to any transform si...

Let X be a topological abelian group and H subgroup of X. We find conditions under which local quasi-convexity both X/H results in the same property for This is true instance if precompact, or metrizable dually embedded also either discrete bounded torsion. give some general principles point out errors we have found existing literature on this problem.

In this work we prove that the set of points at infinity S8 :“ ClRPm pSqXH8 of a semialgebraic set S Ă R that is the image of a polynomial map f : R Ñ R is connected. This result is no longer true in general if f is a regular map. However, it still works for a large family of regular maps that we call quasi-polynomial maps.