Partial frames provide a rich context in which to do pointfree structured and unstructured topology. A small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. These axioms are sufficiently general to include as examples bounded distributive...

We carry out a relativistic calculation of the cross sections of electron-O and -C quasi-elastic scattering and quasi-free ∆ production and compare with the (e, e) data systematically in the wide energy range of 0.5 – 1.5 GeV. Using the same formalism, we examine the νμ quasi-elastic scattering from O. The model incorporating the nuclear correlation effects agrees better with the electron-nucle...

Spline quasi-interpolants with best approximation orders and small norms are useful in several applications. In this paper, we construct the so-called near-best discrete and integral quasi-interpolants based on H-splines, i.e., B-splines with regular hexagonal supports on the uniform three-directional mesh of the plane. These quasi-interpolants are obtained so as to be exact on some space of po...

In a recent result, Khot and Saket [FOCS 2014] proved the quasi-NP-hardness of coloring a 2-colorable 12-uniform hypergraph with 2(logn) Ω(1) colors. This result was proved using a novel outer PCP verifier which had a strong soundness guarantee. We reduce the arity in their result by modifying their 12-query inner verifier to an 8-query inner verifier based on the hypergraph coloring hardness r...

As a rule, an energy method is widely adopted for b-spline curve smoothing, but this method has the disadvantages such as massive calculation, computation complexity and low efficiency. Compared with the energy method, multi-resolution smoothing approaches nicely overcome these obstacles. Presently, some researches have been conducted on multi-resolution smoothing, but these efforts mainly aime...

In a recent result, Khot and Saket [FOCS 2014] proved the quasi-NP-hardness of coloring a 2-colorable 12-uniform hypergraphwith 2 Ω(1) colors. This result was proved using a novel outer PCP verifier which had a strong soundness guarantee. In this note, we show that we can reduce the arity of their result by modifying their 12-query inner verifier to an 8-query inner verifier based on the hyperg...