In physically-based image synthesis, the path space of light transport paths is usually explored by stochastic sampling. The two main families of algorithms are Monte Carlo/quasi-Monte Carlo sampling and Markov chain Monte Carlo. While the former is known for good uniform discovery of important regions, the latter facilitates efficient exploration of local effects. We introduce a hybrid samplin...

In general relativity, quasi-local energy-momentum expressions have been constructed from various formulae. However, Newtonian theory of gravity gives a well known and an unique quasi-local mass expression (surface integration). Since geometrical formulation of Newtonian gravity has been established in the covariant Newtonian space-time, it provides a covariant approximation from relativistic t...

In this paper, we give a detailed proof to result of Gabber (unpublished) on the lifting problem quasi-excellent rings, extending previous work Nishimura-Nishimura. As corollary, establish that an ideal-adic completion excellent (resp. quasi-excellent) ring is quasi-excellent).

The construction of the fusion ring of a quasi-rational CFT based on sl(3) k at generic level k ∈ Q is reviewed. It is a commutative ring generated by formal characters, elements in the group ring Z[ ˜ W ] of the extended affine Weyl group˜W of sl(3) k. Some partial results towards the sl(4) k generalisation of this character ring are presented.

We study the effects of nonmagnetic impurities in a spin Bose-metal SBM phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges D. N. Sheng et al., arXiv:0902.4210 . This phase is a quasi-one-dimensional quasi-1D descendant of a two-dimensional 2D spin liquid with spinon Fermi sea and the present study aims at interpolating between the 1D and 2D cases. Different types ...

We investigate functors between abelian categories having a left adjoint and a right adjoint that are similar (these functors are called quasi-Frobenius functors). We introduce the notion of a quasi-Frobenius bimodule and give a characterization of these bimodules in terms of quasi-Frobenius functors. Some applications to corings and graded rings are presented. In particular, the concept of qua...

module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

A spacetime is a four-manifold with a pseudo-metric of signature (+,+,+,−). A hypersurface or a 2-surface in a spacetime is spacelike if the induced metric is positive definite. A quasi-local energy-momentum vector is a vector in R associated to a spacelike 2-surface which depends on its first and second fundamental forms and the connection to its normal bundle in the spacetime. The time compon...