‎in this paper we study the existence of fixed points for mappings defined on complete metric spaces‎, ‎satisfying a general contractive inequality depending on two additional mappings‎.

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...

A new algorithm, SPMF, for finding the complete chain of solutions of the product selection model is presented in this report. λ-directed simple residual path is identified to the only kind of residual path necessary for the new algorithm. By augmenting the right amount of flows along λ-directed simple residual paths, the new algorithm is monotone convergent. (Note: This work was first presente...

Two enantioselective total syntheses of the nortriterpenoid natural product rubriflordilactone A are described, which use palladium- or cobalt-catalyzed cyclizations to form the CDE rings, and converge on a late-stage synthetic intermediate. These key processes are set up through the convergent coupling of a common diyne component with appropriate AB-ring aldehydes, a strategy that sets the sta...

The total synthesis of the antifungal macrolide antibiotic roxaticin has been accomplished. The synthesis relies principally on aldol and directed reduction steps to construct the extended 1,3-polyol array present in the natural product. Three principal nonpolyene containing fragments were assembled and then coupled using Julia olefination and methyl ketone aldol addition reactions. A series of...

The convergent total synthesis of polycarcin V, a gilvocarcin-type natural product that shows significant cytotoxicity with selectivity for nonsmall-cell lung cancer, breast cancer, and melanoma cells, has been achieved in 13 steps from 7, 8, and 22; the sequence features a stereoselective α-C-glycosylation reaction for the union of protected carbohydrate 7 and naphthol 8. The association const...

A mild and general protocol for the Pd(0)-catalyzed heteroannulation of o-bromoanilines and alkynes is described. Application of a Pd(0)/P((t)Bu)3 catalyst system enables the efficient coupling of o-bromoanilines at 60 °C, mitigating deleterious side reactions and enabling access to a broad range of useful unnatural tryptophans. The utility of this new protocol is demonstrated in the highly con...

A convergent synthesis of the C31-C52 bis-tetrahydropyran core of the natural product amphidinol 3 is reported. A common intermediate was synthesized from d-tartaric acid utilizing an asymmetric glycolate alkylation/ring-closing metathesis sequence to construct the THP rings. Differential elaboration of the common intermediate allowed the synthesis of two distinct coupling partners which were j...

We consider nonsingular saddle-point matrices whose leading block is maximally rank deficient, and show that the inverse in this case has unique mathematical properties. We then develop a class of indefinite block preconditioners that rely on approximating the null space of the leading block. The preconditioned matrix is a product of two indefinite matrices, but under certain conditions the con...