In this paper we are concerned with the properties of positivity, uncertainty principle and continuity in Lp spaces of a generalized spectrogram. In particular we study the connections of a generalized spectrogram, as a subclass of the Cohen class, with the Rihaczek and the Wigner representations. We also consider the behavior of the generalized spectrogram with respect to the positivity and th...

IN SITU BIODEGRADABLE INTERBODY FUSION CAGE DESIGN BY THE INTEGRATED GLOBAL AND LOCAL TOPOLOGY OPTIMIZATION AN EXAMPLE ON DESIGNING YUCATAN MINIPIG LUMBAR INTERBODY FUSION CAGE FOR LARGE ANIMAL STUDY Hee Suk Kang1,3, Scott J. Hollister2,1,3, Frank LaMarca3,2, Chia-Ying Lin3,2 1Mechanical Engineering, University of Michigan, Ann Arbor, MI; 2Biomedical Engineering, University of Michigan, Ann Arb...

We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel-algebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The...

We propose a new concept of generalized di erentiation of setvalued maps that captures rst order information. This concept encompasses the standard notions of Fréchet di erentiability, strict di erentiability, calmness and Lipschitz continuity in single-valued maps, and the Aubin property and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen the relationship between th...

It is well-known that a Hausdorff space is exponentiable if and only if it is locally compact, and that in this case the exponential topology is the compact-open topology. It is less well-known that among arbitrary topological spaces, the exponentiable spaces are precisely the core-compact spaces. The available approaches to the general characterization are based on either category theory or co...

Given a topological space X and a complete lattice L, we study the space of L-predicates F L (X) = X ! L op ] op , continuous maps from X to L op in its Scott-topology. It yields a functor F L () from TOP-L, a full subcategory of TOP subsuming continuous domains, to SUP, the category of complete sup-lattices and maps preserving suprema. Elements of F 2 (X) are continuous predicates (= closed se...

Scott discovered his domain-theoretic models of the λ-calculus, isomorphic to their function space, in 1969. A natural completeness problem then arises: whether any two terms equal in all Scott models are convertible. There is also an analogous consistency problem: whether every equation between two terms, consistent with the λ-calculus, has a Scott model. We consider such questions for wider s...

In 2002, Császár [1] introduced the notions of generalized topology and generalized continuity. In 2008, Császár [3] defined an enlargement and construct the generalized topology induced by an enlargement; introduced the concept of (κ, λ)-continuity and (κμ, λμ)continuity on enlargements. In 2008, Császár [4] defined and studied the notions of product of generalized topologies. In 2010, S. Mara...

In 1973 William Lawvere published a paper (reprinted as (Lawvere 2002)) where he explained that partial orders and metric spaces are examples of categories enriched in a closed category. Indeed, preorders are categories enriched over the two-element Boolean algebra 2, while (generalized) metric spaces are categories enriched over ([0,∞],+). Lawvere’s idea has been extremely influential in the f...