K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

Studying genetic relationships among coconut varieties/populations using microsatellite markers

The extent of genetic diversity and the genetic relationships among 94 coconut varieties/populations (51 Talls and 43 Dwarfs) representing the entire geographic range of cultivation/distribution of the coconut was assessed using 12 pairs of coconut microsatellite primers. A high level of genetic diversity was observed in the collection with the mean gene diversity of 0.647+/-0.139, with that of the mean gene diversity of Talls 0.703+/-0.125 and 0.374+/-0.204 of Dwarfs. A phenetic tree based on DAD genetic distances clustered all the 94 varieties/ populations into two main groups, with one group composed of all the Talls from southeast Asia, the Pacific, west coast of Panama, and all Dwarfs and the other of all Talls from south Asia, Africa, and the Indian Ocean coast of Thailand. The allele distribution of Dwarfs highlighted a unique position of Dwarf palms from the Philippines exhibiting as much variation as that in the Tall group. The grouping of all Dwarfs representing the entire geographic distribution of the crop with Talls from southeast Asia and the Pacific and the allele distribution between the Tall and Dwarf suggest that the Dwarfs originated from the Tall forms and that too from the Talls of southeast Asia and the Pacific. Talls from Pacific Islands recorded the highest level of genetic diversity (0.6+/-0.26) with the highest number of alleles (51) among all the regions.

A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.

Distinguished algebraic semantics for t-norm based fuzzy logics:Methods and algebraic equivalencies

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ?-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics-namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.

Varieties of Economic Crisis, Varieties of Ideational Change: How and Why Macroeconomic Policy and Financial Regulation Differ

One of the principal tasks facing post-crash academic political economy is to analyse patterns of ideational change and the conditions that produce such change. What has been missing from the existing literature on ideational change at times of crises however, is a sense of how processes of persuasive struggle, and how the success of those ‘norm entrepreneurs’ arguing for ideational change is shaped by two contextual variables: the most immediate material symptoms and problems that a crisis displays (the variety of crisis); and the institutional character of the policy subsystem that agents have to operate within to affect change. Introducing these two variables into our accounts of persuasive struggle and ideational change enables us to deepen our understanding of the dynamics of ideational change at times of crisis. The article identifies that a quite rapid and radical intellectual change has been evident in the field of financial regulation in the form of an embrace of a macroprudential frame. In contrast in the field of macroeconomic policy - both monetary and fiscal policy, many pre-crash beliefs remain prominent, there is evidence of ideational stickiness and inertia, and despite some policy experimentation, overarching policy frameworks and their rationales have not been overhauled. The article applies Peter Hall’s framework of three orders of policy changes to help illuminate and explain the variation in patterns of change in the fields of financial regulation and macroeconomic policy since the financial crash of 2008. The different patterns of ideational change in macroeconomic policy and financial regulation in the post-crash period can be explained by timing and variety of crisis; sequencing of policy change; and institutional political differences between micro policy sub systems and macro policy systems.