There has recently been considerable interest in an essentially quadratic method for computing n. The algorithm, first suggested by Salamin [6], is based upon an identity known to Gauss [-3, p. 377], [4]. This iteration has been used by two Japanese researchers, Y. Tamura and Y. Kanada, to compute 223 decimal digits of n in under 7 hours. They have now successfully computed 224 digits (more tha...

considering convergent product as an important manufacturing technology for digital products, we integrate functions and sub-functions using a comprehensive fuzzy mathematical optimization process. to form the convergent product, a web-based fuzzy network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is to be a link betwe...

Given a weakly convergent sequence of positive functions in W 1,p 0 (Ω), we prove the equivalence between its convergence in the sense of obstacles and the lower semicontinuity of the term by term duality product associated to (the p-Laplacian of) weakly convergent sequences of p-superharmonic functions of W 1,p 0 (Ω). This result implicitly gives new characterizations for both the convergence ...

Considering convergent product as an important manufacturing technology for digital products, we integrate functions and sub-functions using a comprehensive fuzzy mathematical optimization process. To form the convergent product, a web-based fuzzy network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is to be a link betwe...

Here, a collection of base functions and sub-functions configure the nodes of a web-based (digital)network representing functionalities. Each arc in the network is to be assigned as the link between two nodes. The aim is to find an optimal tree of functionalities in the network adding value to the product in the web environment. First, a purification process is performed in the product network ...

The natural product saudin was found to induce hypoglycemia in mice and, therefore, could be an appealing lead structure for the development of new agents to treat diabetes. A diastereoselective tandem Stille-oxa-electrocyclization reaction has been developed which provides access to the core structure of saudin in a rapid and convergent manner. This new reaction has been extended to the conver...

The fully functionalized macrocyclic core of the marine natural product iriomoteolide-1a has been successfully constructed in a convergent and enantioselective manner.

in this paper, we propose and analyze an efficient matrix methodbased on bell polynomials for numerically solving nonlinear fredholm- volterraintegral equations. for this aim, first we calculate operational matrix of integration and product based on bell polynomials. by using these matrices, nonlinearfredholm-volterra integral equations reduce to the system of nonlinear algebraicequations which...

a simple, efficient, and high yielding one-pot protocol has been developed for the synthesis of 4h-benzo[b]pyrans scaffolds installing a three-component tandem knoevenagel-cyclocondensation reaction of an aldehyde, malononitrile and dimedone using guanidinium chloride as polyfunctional organocatalyst under solvent-free conditions in high to excellent yields. various aromatic aldehydes were util...