In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...

The aim of this paper is sketch a theory of divisibility and factorisation in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely topologised topological monoids. In particular, we define the topological factorisation monoid, a generalisation of the factorisation monoid for algebraic monoids, and...

A multiple-market framework is developed to measure the size and distribution of research benefits. The model considers an upstream raw product market and a downstream finished product market and allows for imperfect competition in the intermediary food-processing sector. A central conceptual result is derived: an increase in raw product output is a sufficient condition for costreducing innovat...

A sequence {vj} is said to be Cauchy if for each > 0, there exists a natural number N such that ‖vj−vk‖ < for all j, k ≥ N . Every convergent sequence is Cauchy, but there are many examples of normed linear spaces V for which there exists non-convergent Cauchy sequences. One such example is the set of rational numbers Q. The sequence (1.4, 1.41, 1.414, . . . ) converges to √ 2 which is not a ra...

We argue that energy minimization can explain the pattern of cell movements in the morphogenetic process known as convergent extension provided that the cell-cell adhesive energy has a certain type of anisotropy, which we describe. This single simple property suffices to cause the cell elongation, cell alignment, and lengthening of a cellular array that characterize convergent extension. We sho...

During development, vertebrate embryos undergo dramatic changes in shape. The lengthening and narrowing of a field of cells, termed convergent extension, contributes to a variety of morphogenetic processes. Focusing on frogs and fish, we review the different cellular mechanisms and the well-conserved signaling pathways that underlie this process.

A new and convergent synthesis of ascididemin is presented. Using an anionic cascade ring closure as the key step, this natural product is obtained in 45% overall yield in just 6 steps starting from 2'-fluoroacetophenone. This new approach was extended to the synthesis of a new isomer of ascididemin.

Stereoselective convergent synthesis of the C15-C36 segment of goniodomin A, an actin-targeting marine polyether macrolide natural product, has been achieved. The present synthesis features palladium(0)-catalyzed, copper(I)-mediated Liebeskind-Srogl cross-coupling as the fragment assembly process.

The tetracyclic core of the integrastatin natural products has been prepared in a convergent and rapid manner. Our strategy relies upon a palladium(II)-catalyzed oxidative cyclization to form the central [3.3.1]-dioxabicycle of the natural product core. Overall, the core has been completed in only 4 linear steps from known compounds.