where hk = dim(A(∆)⊗AR) k. When the fan ∆ is rational, it corresponds to a toric variety X(∆) and the numbers hk are the even betti numbers of the cohomology of X(∆). In any case, they satisfy the Poincaré duality hk = hn−k. When the fan ∆ is complete but not necessarily simplicial, one can apply the same construction to the first barycentric subdivision B(∆) of ∆. We can label a 1-dimensional ...

We derive light-cone sum rules (LCSRs) for exclusive B-meson decays into light energetic hadrons from correlation functions within soft-collinear effective theory (SCET). In these sum rules the short-distance scale refers to “hard-collinear” interactions with virtualities of order ΛQCDmb. Hard scales (related to virtualities of order mb) are integrated out and enter via external coefficient fun...

Developable surfaces are of considerable importance to many industry applications, e.g. sheet metal forming processes. The objective of this paper is to provide algorithms on the approximation of developable surfaces with pieces of right circular cones. Special emphasis is devoted to practical choices of free parameters and to error estimation. Furthermore, a new algorithm for the approximation...

In this paper we study surfaces in Euclidean 3-space foliated by pieces of circles and that satisfy a Weingarten condition of type aH+bK = c, where a, b and c are constant and H and K denote the mean curvature and the Gauss curvature respectively. We prove that a such surface must be a surface of revolution, a Riemann minimal surface or a generalized cone.

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

We calculate the branching ratios of B → K1γ at next-to-leading order (NLO) of αs where K1 is the orbitally excited axial vector meson. The NLO decay amplitude is divided into the vertex correction and the hard spectator interaction part. The one is proportional to the weak form factor of B → K1 transition while the other is a convolution between light-cone distribution amplitudes and hard scat...

PURPOSE To describe the electrophysiological, histologic, and hereditary features of a naturally occurring rat model of cone function loss. METHODS Dark- and light-adapted electroretinograms (ERGs) were used to evaluate retinal function. The thickness and architecture of the retina were observed by light microscopy. The cone density was investigated by wholemount immunocytochemistry. The inhe...

Basic sphere geometric principles are used to analyze approximation schemes of developable surfaces with cone spline surfaces, i.e. G1surfaces composed of segments of right circular cones. These approximation schemes are geometrically equivalent to the approximation of spatial curves with G1-arc splines, where the arcs are circles in an isotropic metric. Methods for isotropic biarcs and isotrop...

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

Let M be a smooth, closed oriented 4−manifold. An orientation-compatible symplectic structure on M is a closed two form ω such that ω ∧ ω is nowhere vanishing and gives the orientation. Two such symplectic structures ω 1 and ω 2 on M are said to be deformation equivalent if there is an orientation-preserving diffeomorphism φ such that φ * ω 1 and ω 2 are connected by a path of symplectic forms....