Aims: It was aimed to investigate postoperative conformal radiotherapy planning that provides the best target volume and the least dose for critical organs in cancers of stomach. Methods: This study was conducted on the CT simulation images of thirty patients diagnosed with gastric cancer. Target volumes and the organs at risk were contoured. AP-PA reciprocal parallel field conventional plan an...

It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Löwner evolutions. Based on the existence of a logarithmic null vector in an indecomposable highest-weight module of the Virasoro algebra, the representation theory of the logarithmic conformal field theory is related to entities conserved in mean under t...

A shear-free ray congruence on Minkowski space is a 3-parameter family of null geodesics along which Lie transport of a complementary 2dimensional spacelike subspace (called the screen space) is conformal. Such congruences are defined by complex analytic surfaces in the associated twistor space CP 3 and are the basis of the construction of massless fields. On a more general space-time, it is un...

We apply ideas from conformal field theory to study symplectic four-manifolds, by using modular functors to “linearise” Lefschetz fibrations. In Chern-Simons theory this leads to the study of parabolic vector bundles of conformal blocks. Motivated by the Hard Lefschetz theorem, we show the bundles of SU(2) conformal blocks associated to Kähler surfaces are Brill-Noether special, although the as...

Abstract. In this paper, we have studied a conformal transformation between two almost Hermitian manifolds and shown that the associated Nijenhuis tensor is conformally invariant under this transformation. We have also discussed the properties of contravariant almost analytic vector field, covariant almost analytic vector field and some other properties in almost Hermitian manifold under this t...

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the conformal Ricci flow equations because of the role that conformal geometry plays in constraining the scalar curvature and because these equations are the vector field sum of a conformal flow equation and a...

A class of two dimensional conformal field theories is known to correspond to three dimensional Chern-Simons theory. Here we claim that there is an analogous class of four dimensional field theories corresponding to five dimensional Chern-Simons theory. The four dimensional theories give a coupling between a scalar field and an external divergenceless vector field and they may have some applica...

The main difficulty in the nonrelativistic case is that one can only use a smaller group of commuting vector fields. In particular, since one cannot use the generators of the hyperbolic rotations, due to the different wave speeds, the earlier approach of Klainerman [9] breaks down. This is because the invariant Sobolev inequality that plays a key role in [9] does not hold if one uses a smaller ...

We continue our study of the semi-classical (large central charge) expansion of the toroidal one-point conformal block in the context of the 2d/4d correspondence. We demonstrate that the Seiberg-Witten curve and ( 1-deformed) differential emerge naturally in conformal field theory when computing the block via null vector decoupling equations. This framework permits us to derive 1-deformations o...

Conformal fields are a recently discovered class of representations of the algebra of vector fields in N dimensions. Invariant first-order differential operators (exterior derivatives) for conformal fields are constructed. 1 1. Introduction In order to describe physical quantities, a coordinate system has to be introduced, but physics itself should not depend on how this is done. Therefore any ...