CUT ELIMINATION IN HYPERSEQUENT CALCULUS FOR SOME LOGICS OF LINEAR TIME

This is a sequel article to [10] where a hypersequent calculus (HC) for some temporal logics of linear frames including Kt4.3 and its extensions for dense and serial flow of time was investigated in detail. A distinctive feature of this approach is that hypersequents are noncommutative, i.e., they are finite lists of sequents in contrast to other hypersequent approaches using sets or multisets. Such a system in [10] was proved to be cut-free HC formalization of respective logics by means of semantical argument. In this article we present an equivalent variant of this calculus for which a constructive syntactical proof of cut elimination is provided.

Mathematics of a Sudo-Kurve

We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.

Generalized Hausdorff capacities and their applications

Let {\mathfrak{P}({\mathbb{R}^{n}})} be the power set of {\mathbb{R}^{n}} and let {\varphi:\mathfrak{P}({\mathbb{R}^{n}})\rightarrow[0,\infty]} be a set function. In this paper, the authors introduce a class of generalized Hausdorff capacities {H_{\varphi}} with respect to φ. Some basic properties of {H_{\varphi}} including the strong subadditivity are obtained. An equivalent variant of {H_{\varphi}} defined via dyadic cubes is also introduced and proved to be Choquet capacity. The authors then prove the boundedness of some maximal operators, such as the Hardy–Littlewood maximal operator, on Lebesgue spaces with respect to {H_{\varphi}}. As an application, the predual spaces of weighted Morrey spaces are described via these capacities.

A novel, resistance-linked ovine PrP variant and its equivalent mouse variant modulate the in vitro cell-free conversion of rPrP to PrPres

Prion diseases are associated with the conversion of the normal cellular prion protein, PrPc, to the abnormal, disease-associated form, PrPSc. This conversion can be mimicked in vitro by using a cell-free conversion assay. It has recently been shown that this assay can be modified to use bacterial recombinant PrP as substrate and mimic the in vivo transmission characteristics of rodent scrapie. Here, it is demonstrated that the assay replicates the ovine polymorphism barriers of scrapie transmission. In addition, the recently identified ovine PrP variant ARL168Q, which is associated with resistance of sheep to experimental BSE, modulates the cell-free conversion of ovine recombinant PrP to PrPres by three different types of PrPSc, reducing conversion efficiencies to levels similar to those of the ovine resistance-associated ARR variant. Also, the equivalent variant in mice (L164) is resistant to conversion by 87V scrapie. Together, these results suggest a significant role for this position and/or amino acid in conversion.

A simple proof for optimality of (s, S) policies in infinite-horizon inventory systems

The classical proofs for the existence of a stationary (s, S) inventory policy that minimizes the total discounted or average cost over an infinite horizon are lengthy because they depend heavily on the optimality results for corresponding finite-horizon models. This note presents a simpler alternative. Since optimal stationary (s, S) policies are relatively simple to characterize, it is easy to construct a solution to the optimality equation which is satisfied by an (s, S) policy or an equivalent variant thereof. For the discounted model, the proof characterizes an (s, S) policy that is optimal for all initial inventory positions. This policy can be generated by a simple existing algorithm. For the average-cost model, the optimality proof is completed with some additional arguments, which are simple but novel, to overcome the normal difficulties encountered in models with unbounded one-step expected costs.

A simple proof for optimality of (s, S) policies in infinite-horizon inventory systems

The classical proofs for the existence of a stationary (s, S) inventory policy that minimizes the total discounted or average cost over an infinite horizon are lengthy because they depend heavily on the optimality results for corresponding finite-horizon models. This note presents a simpler alternative. Since optimal stationary (s, S) policies are relatively simple to characterize, it is easy to construct a solution to the optimality equation which is satisfied by an (s, S) policy or an equivalent variant thereof. For the discounted model, the proof characterizes an (s, S) policy that is optimal for all initial inventory positions. This policy can be generated by a simple existing algorithm. For the average-cost model, the optimality proof is completed with some additional arguments, which are simple but novel, to overcome the normal difficulties encountered in models with unbounded one-step expected costs.