We study suitable weak solutions to the fractional incompressible Navier-Stokes equations. We give some regularity criterion for suitable weak solutions and estimates for Hausdorff dimension of singular set.

The coset construction studies the commutant of a vertex operator subalgebra in a vertex operator algebra. A Schur-Weyl duality associated to the subalgebra and the commutant is obtained.

As utility companies use various mechanisms of Demand Side Management (DSM) to regulate and modify consumer demand for energy, manufacturing plants also look for ways to improve the quality/cost ratio by saving energy cost. Several approaches are available for a plant to save energy, one of which is to reschedule the operation hours of electrical devices and take advantage of incentives and favorable pricing offered by utilities. This paper attempts to develop a load optimization model for plants to minimize the cost incurred by energy consumption. Many practical factors are considered in the model, such as electrical device clustering, night schedule extra labor charge, devices with fixed operation schedules, etc. A discussion of solutions to the optimization model is presented. An online tool for energy assessment and load optimization is also briefly introduced.

I review a recent remarkable discovery made by Gamayun, Iorgov, Lisovyy. They found that the Painleve tau functions have Fourier expansions in terms of four point Virasoro conformal blocks. As a result, since Virasoro conformal blocks correspond to the Nekrasov partition functions of a certain class of 4d supersymmetric gauge theories, the Painleve tau functions has explicit series expansions.

When be an array of rowwise extended negatively dependent subgausian random variables we study the strong law of large numbers of weighted sums under some appropriate conditions, whereis an array of constants. Finally, we give some corollaries.

学术报告日本筑波大学数学系佐垣大辅 (Sagaki Daisuke) 教授将在2014年12月22日至26日在同济大学数学系致远楼107教室作关于《路径模型引论 (Introduction to path models)》的系列讲座, 每次二小时左右, 热烈欢迎你们及你们的研究生参加, 具体日程安排如下:12月22，23，25，26日 (星期一，二，四，五) 下午14:00-16:3012月24日(星期三) 上午9:30-12:00欢迎各位参

First, I'd like to explain Littelmann's path models. Let be a symmetrizable Kac-Moody algebra (such as, etc.). In the papers "A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras (1994)" and "Paths and root operators in representation theory (1995)", Littelmann introduced Lakshmibai-Seshadri (LS) paths of shape λ (where λ is an integral weight for), and gave the set of them a crystal structure in terms of his root operators; Kashiwara and Joseph proved independently that if λ is dominant, then the crystal of LS paths of shape λ is isomorphic to the crystal basis of the integrable highest weight module of highest weight λ. Using Littelmann's path model (consisting of LS paths), we can describe

The difference between quantum sl_n and quantum gl_n is just an extra generator in the zero part. However, that in the affine case is huge. We have developed a new approach to study the structure and representations of quantum affine gl_n. In the series of talks, I will discuss the entire theory including a new realisation, the Lusztig form and the representation theory of affine q-Schur algebras