${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is an ideal three-dimensional topological insulator in which the chemical potential can be brought into bulk band gap with antimony doping. Here, we utilize ultrafast time-resolved transient reflectivity to characterize photoexcited carrier decay ${\mathrm{Bi}}_{2\ensuremath{-}x}{\mathrm{Sb}}_{x}{\mathrm{Se}}_{3}$ nanoplatelets. We report a substantial slowi...

After the introduction of fuzzy sets by Zadeh [20] in 1965, several researchers have been working on the generalization of the fuzzification. In 1986, Atanassov [2] introduced the notion of intuitionistic fuzzy sets. For more details on the intuitionistic fuzzy sets, we refer to [2-4]. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true [18]. Kim and Jun [7, 8] int...

${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is an ideal three-dimensional topological insulator in which the chemical potential can be brought into bulk band gap with antimony doping. Here, we utilize ultrafast time-resolved transient reflectivity to characterize photoexcited carrier decay ${\mathrm{Bi}}_{2\ensuremath{-}x}{\mathrm{Sb}}_{x}{\mathrm{Se}}_{3}$ nanoplatelets. We report a substantial slowi...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

We discuss invariants of Cohen-Macaulay local rings that admit a canonical module $\omega$. Attached to each such ring R, when $\omega$ is an ideal, there are integers--the type the reduction number $\omega$--that provide valuable metrics express deviation R from being Gorenstein ring. In arXiv:1701.05592 and arXiv:1711.09480 we enlarged this list with degree bi-canonical degree. work extend wh...

Let In be the (big) diagonal ideal of (C). Haiman proved that the q, t-Catalan number is the Hilbert series of the graded vector space Mn = ⊕ d1,d2 (Mn)d1,d2 spanned by a minimal set of generators for In. We give simple upper bounds on dim (Mn)d1,d2 in terms of partition numbers, and find all bi-degrees (d1, d2) such that dim (Mn)d1,d2 achieve the upper bounds. For such bi-degrees, we also find...

Burn injuries have been reported to be an important cause of morbidity and mortality and they are still considered as unmet clinical need. Although there is a myriad of effective stem cells that have been suggested for skin regeneration, there is no one ideal scaffold. The aim of this study was to develop a three-dimensional (3D) bi-layer scaffold made of biological decellularized human amnioti...

Let A be a Hopf algebra and Γ be a bicovariant first order differential calculus over A. It is known that there are three possibilities to construct a differential Hopf algebra Γ = Γ/J that contains Γ as its first order part. Corresponding to the three choices of the ideal J , we distinguish the ‘universal’ exterior algebra, the ‘second antisymmetrizer’ exterior algebra, and Woronowicz’ externa...