We describe the convergent synthesis of three prototypical examples a new class analogues complex, cytotoxic marine macrolide (−)-zampanolide that incorporate an embedded N-substituted morpholine moiety in place natural tetrahydropyran ring. The final construction macrolactone core was based on high-yielding intramolecular HWE olefination, while hemiaminal-linked side chain elaborated through s...

The aim of this paper is to introduce and study a new concept ofstrong double $(A)_ {Delta}$-convergent sequence offuzzy numbers with respect to an Orlicz function and also someproperties of the resulting sequence spaces of fuzzy   numbers areexamined. In addition, we define the double$(A,Delta)$-statistical convergence of fuzzy  numbers andestablish some connections between the spaces of stron...

Throughout molecular evolution, organisms create assorted chemicals in response to varying ecological niches. Catalytic landscapes underlie metabolic evolution, wherein mutational steps alter the biosynthetic properties of enzymes. Here we report the first systematic quantitative characterization of the catalytic landscape underlying the evolution of sesquiterpene chemical diversity. On the bas...

Expanding and forwarding are two graphic parameters related to the connectivity and the capacity of the network—the undirected graph with a given routing. Many large networks are composed from some existing smaller networks by using, in terms of graph theory, Cartesian product. The expanding and forwarding parameters of such large networks are associated strongly with that of the corresponding ...

If J is a set and Xj are topological spaces for each j ∈ J , let X = ∏ j∈J Xj and let πj : X → Xj be the projection maps. A basis for the product topology on X are those sets of the form ⋂ j∈J0 π −1 j (Uj), where J0 is a finite subset of J and Uj is an open subset of Xj , j ∈ J0. Equivalently, the product topology is the initial topology for the projection maps πj : X → Xj , j ∈ J , i.e. the co...

We study the ergodicity of backward product of stochastic and doubly stochastic matrices by introducing the concept of absolute infinite flow property. We show that this property is necessary for ergodicity of any chain of stochastic matrices, by defining and exploring the properties of a rotational transformation for a stochastic chain. Then, we establish that the absolute infinite flow proper...

Herein we describe in full our investigations leading to the first total syntheses of ent-dioxepandehydrothyrsiferol and armatol A. Discovery of a bromonium-initiated epoxide-opening cascade enabled novel tactics for constructing key fragments found in both natural products and have led us to revise the proposed biogeneses. Other common features found in the routes include convergent fragment c...

Gene expression can be modulated in two opposite directions, towards higher or lower amounts of product. How do diametric changes in gene dosage influence neurological development and function? Recent studies of transgenic and knockout mouse models, genomic copy-number variants, imprinted-gene expression alterations, and sex-chromosome aneuploidies are revealing examples of 'mirror-extreme' bra...