‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

A particularly simple and flexible mathematical framework for the study of probability theory classical, quantum and otherwise is the notion of a test space, i.e., a collection of (possibly overlapping) discrete sample spaces (as developed in the 1970s and 80s by D. J. Foulis, C. H. Randall and others). “Quantum logics” arise quite naturally as invariants of test spaces; however, the latter are...

We construct localization cofiber sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of spectral categories. Using a “global” construction of the THH and TC of a scheme in terms of the perfect complexes in a spectrally enriched version of the category of unbounded complexes, the sequences specialize to localization cofiber sequences associated to the in...

We provide a new construction of the topological cyclic homology TC(C) of any spectrally-enriched ∞-category C, which affords a precise algebro-geometric interpretation of the cyclotomic trace map K(X) → TC(X) from algebraic K-theory to topological cyclic homology for any scheme X. This construction rests on a new identification of the cyclotomic structure on THH(C), which we find to be a conse...

objective: despite the huge efforts, chronic kidney disease (ckd) remains as an unsolved problem in medicine. many studies have shown a central role for transforming growth factor beta-1 (tgfβ-1) and its downstream signaling cascades in the pathogenesis of ckd. in this study, we have reanalyzed a microarray dataset to recognize critical signaling pathways controlled by tgfβ-1. materials and met...

Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.

For a quantaloid Q, considered as a bicategory, Walters introduced categories enriched in Q. Here we extend the study of monad-quantale-enriched categories of the past fifteen years by introducing monad-quantaloid-enriched categories. We do so by making lax distributive laws of a monad T over the discrete presheaf monad of the small quantaloid Q the primary data of the theory, rather than the l...

Bound states at sharp corners have been widely viewed as the hallmark of two-dimensional second-order topological insulators and superconductors. In this paper, we show that existence sublattice degrees freedom can enrich tunability bound on boundary hence lift constraint their locations. We take Kane-Mele model with honeycomb-lattice structure to illustrate underlying physics. With introductio...