Let A =< A,≤A> and B =< B,≤B> be lattices such that A ∩ B is a filter in A and an ideal in B, and the orderings ≤A and ≤B coincide on A ∩ B. Then ≤A ∪ ≤B ∪ (≤A ◦ ≤B), is a lattice ordering on A ∪ B and the resulting lattice, called a sum of A and B, is denoted by A ⊕ B. The sum operation was introduced by Wroński [5], and its special case with A∩B = {1A} = {0B} by Troelstra [4]. In particular, ...

Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior terms Heyting-valued structures. In this paper, we first provide a systematic treatment sheaves from the viewpoint categorical logic. then prove form {\L}o\'s's theorem for also characterization which holds with respect any maximal filter.

semi-supervised multi-view data Xiaohong Chen, Songcan Chen, Hui Xue , Xudong Zhou 1 Department of Mathematics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China 2 Department of Computer Science and Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China 3 State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210093...

This paper introduces filter structures for interpolation and decimation by a factor of two. The structures are derived by using the frequency-response masking approach, in which the overall filter makes use of a periodic model filter, its complementary filter, and two masking filters. The periodic model filters are obtained by replacing each delay element in a model filter with M delay element...

In this paper, we study the degenerate principal series of a split, simply-connected, simple p-adic group type $E_7$. We determine points reducibility and maximal semi-simple subrepresentation at each point.