The modernity of Dedekind’s anticipations contained in What are numbers and what are they good for?

Archive for History of Exact Sciences - We show that Dedekind, in his proof of the principle of definition by mathematical recursion, used implicitly both the concept of an inductive cone from an...     

The expansion of GPCR transactivation-dependent signalling to include serine/threonine kinase receptors represents a new cell signalling frontier

G protein-coupled receptor (GPCR) signalling is mediated through transactivation-independent signalling pathways or the transactivation of protein tyrosine kinase receptors and the recently reported activation of the serine/threonine kinase receptors, most notably the transforming growth factor-β receptor family. Since the original observation of GPCR transactivation of protein tyrosine kinase receptors, there has been considerable work on the mechanism of transactivation and several pathways are prominent. These pathways include the “triple membrane bypass” pathway and the generation of reactive oxygen species. The recent recognition of GPCR transactivation of serine/threonine kinase receptors enormously broadens the GPCR signalling paradigm. It may be predicted that the transactivation of serine/threonine kinase receptors would have mechanistic similarities with transactivation of tyrosine kinase pathways; however, initial studies suggest that these two transactivation pathways are mechanistically distinct. Important questions are the relative importance of tyrosine and serine/threonine transactivation pathways, the contribution of transactivation to overall GPCR signalling, mechanisms of transactivation and the range of cell types in which this phenomenon occurs. The ultimate significance of transactivation-dependent signalling remains to be defined but it appears to be prominent and if so will represent a new cell signalling frontier.     

New Develoopment of the Basic Theory of Extenics

In this paper,the new development of three basic theories of Extenics,incluing basic-element theory,extension set theory and extension logic theory ,has been introduced.And the new theoretical frame of Extenics has also been set forth.     

The Optimal Solution of the Model with Physical and Human Capital Adjustment Costs

We prove that the model with physical and human capital adjustment costs has optimal solution when the production function is increasing return and the structure of vetor fields of the model changes substantially when the prodution function from decreasing return turns to increasing return. And it is shown that the economy is improved when the coefficients of adjustment costs become small.