We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial and explicitly calculable S-matrix for scattering from the boundary. Unlike all other exactly solvable conformal field theories, it is non-rational (i.e. has ...

This note proposes to modify the definition of quasiconvexity of a function f Úìm˜n r Ï ñ Ú ̈ ñ T −ðÙð( on the spaceìm˜n of m ˜ n matrices in such a way that (i) the polyconvexity implies quasiconvexity without any additional measurability or continuity assumption on f and (ii) the pointwise supremum of any family of quasiconvex functions is a quasiconvex function. Property (ii) allows one to de...

In 2008, E. Ekici [13] introduced a new class of generalized open sets in a topological space called e-open sets. M. Ozkoc and G Aslim [26], in their recent paper (Bull. Korean Math. Soc. 47 (2010), No. 5, pp. 10251036), initiated two strong forms of e-open sets for the study of stronglyθ-e-continuous functions. J. Dontchev [8] introduced the notion of contra continuous functions. In this paper...

This paper considers how the concept of data provenance, developed in e-Science, can be applied to e-Social Science, specifically Evidence Based Policy Assessment. It considers what Evidence Based Policy Assessment is and what types of information can be used in such research. Quantitative and qualitative data and analytical/ interpretative approaches are outlined and the implications of these ...

This paper establishes the Manin conjecture for a certain non-split singular del Pezzo surface of degree four X ⊂ P4. In fact, if U ⊂ X is the open subset formed by deleting the lines from X, and H is the usual projective height function on P4(Q), then the height zeta function P x∈U(Q) H(x) −s is analytically continued to the half-plane 17/20.

6. Suppose X is a metric space, let BX be the σ-algebra generated by the open sets of X, we call BX the Borel σ-algebra and its elements Borel sets. 7. A countable intersection of open sets is called a Gδ set ; a countable union of closed sets is called an Fσ set . 8. We call a collection of subsets of X an elementary family if (i) ∅ ∈ E ; (ii) if E,F ∈ E , then E ∩ F ∈ E ; and (iii) if E ∈ E ,...

This paper contains a proof of the Manin conjecture for the singular del Pezzo surface X : x0x1 − x2 = x0x4 − x1x2 + x3 = 0, of degree four. In fact, if U ⊂ X is the open subset formed by deleting the unique line from X, and H is the usual height function on P(Q), then the height zeta function P x∈U(Q) H(x) −s is analytically continued to the half-plane 9/10. Mathematics Subject Classif...

Objective of this article is to provide a brief view on current state of free and open source E-Learning 2.0 software, and discuss about future in the context of free and open source software oriented E-Learning solutions. E-Learning 2.0 is a term, which is used to define E-Learning solutions combining the usage of Web 2.0 technologies, and the related E-Learning aspects, which are widely emplo...

abstract. suppose g is an nvertex and medge simple graph with edge set e(g). an integervalued function f: e(g) → z is called a flow. tutte was introduced the flow polynomial f(g, λ) as a polynomial in an indeterminate λ with integer coefficients by f(g,λ) in this paper the flow polynomial of some dendrimers are computed.