Towards a classification of global integral constructions and functorial liftings using the small representations method

This is a survey article in which we discuss some recent approach toward the classification of global factorizable integrals, and constructions of Langlands functorial lifting using small representations. To do that we use the language of unipotent orbits and their relation to Fourier coefficients. We also introduce the dimension equation, and set our goal to classify all global integrals of a certain form which satisfies this equation.     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

Scheduling electric power production at a wind farm

We present a model for scheduling power generation at a wind farm, and introduce a particle swarm optimization algorithm with a small world network structure to solve the model. The solution generated by the algorithm defines the operational status of wind turbines for a scheduling horizon selected by a decision maker. Different operational scenarios are constructed based on time series data of electricity price, grid demand, and wind speed. The computational results provide insights into management of a wind farm.     

Effect of surface character of filler particles on rheology of heat-set whey protein emulsion gels

Small-deformation and large-deformation rheological properties of heat-set whey protein emulsion gels containing active and inactive filler particles have been investigated using a controlled stress rheometer. The results suggest that the contributions to the gel network are quite different for pure protein gels and emulsion gels having similar storage moduli. An emulsion gel containing inactive filler has a larger phase angle due to the energy dissipation at the ‘slippery’ droplet surface under the influence of the applied shear stress. The large-deformation rheology of the heat-set protein gel has behaviour intermediate between that for an entropic biopolymer gel and that for a particle gel. Emulsion gels containing active or inactive fillers behave more like typical particle gel systems.     

Gas damping force noise on a macroscopic test body in an infinite gas reservoir

We analyze here the force noise associated with the mechanical damping of a test body surrounded by a large volume of rarefied gas, considering the statistics of momentum exchange in inelastic molecular collisions. In addition to calculating the force noise on a cube, sphere, and cylinder, we discuss the limits in applying this analysis to experimental configurations in which the test body is surrounded by an enclosure that is only slightly larger than the test body itself.     

Existence results for a degenerated nonlinear elliptic partial differential equation

The aim of this paper is to establish the existence of weak solutions to a steady state two-dimensional irrotational compressible flow around a thin profile. This flow is described by the small disturbance equations. If the speed of sound exceeds the fluid one, the governing equations remain elliptic. But when the fluid speed is beyond the sound one, the flow becomes locally hyperbolic and shock waves arise. For a modified elliptic model, using convexity arguments, we prove the existence of a solution which is the solution to the first model when the flow remains subsonic.     

Scheduling periodic customer visits for a traveling salesperson

The problem considered in this paper deals with determining daily routes for a traveling salesperson who provides customers in Upper Austria with product range information of a large, global food wholesaler. Each customer has to be visited at least once a year, with some customers requiring up to one visit per month. Further, some customers may not be visited each day of the week. Our decision support system uses a commercial GIS software to extract customer data for input into the optimization procedure and to visualize the results obtained by the algorithm. The optimization approach is based on the variable neighborhood search algorithm which assigns customers to days and determines routes for the salesperson for each day with the primary objective to minimize the total travel time of the salesperson. Another objective studied is to minimize the number of days needed by the salesperson to visit all customers in a given month. Further we analyze the effects of changes in the business environment like increases in the amount or flexibility of the salesperson’s working time and variations in the possible days for customer visits. Finally, we enrich the objective function by considering periodicity requirements for customer visits. Specifically, we penalize irregular schedules, where the time between two successive customer visits varies.     

涉及小函数的亚纯函数

是否可以将第二基本定理的一般形式中常数替换为小函数,这一直是人们试图解决的重大问题.该文研究了涉及小函数的第二基本定理的推广问题, 并利用主要结果得到了几个惟一性定理, 改进了张庆德, Toda N和姚卫红等人的有关定理.     

A Functional LIL for <Emphasis Type="Italic">d</Emphasis>-Dimensional Stable Processes; Invariance for Lévy- and Other Weakly Convergent Processes

We establish a functional LIL for the maximal process M(t) :=sup _0≤s≤t ‖X(s)‖ of an ℝ ^d -valued α-stable Lévy process X, provided X(1) has density bounded away from zero over some neighborhood of the origin. We also provide a broad invariance result governing a class independent-increment processes related to the domain of attraction of X(1). This breadth is particularly notable for two types of processes captured: First, it not only describes any partial sum process built from iid summands in the domain of normal attraction of X(1), but also addresses those with arbitrary iid summands in the full domain of attraction (here we give a technical condition necessary and sufficient for the partial sum process to share the exact LIL we prove for X). Second, it reveals that any Lévy process L such that L(1) satisfies the technical condition just mentioned will also share the LIL of X. Supported in part by NSF Grant DMS 02-05034.     

Xanthines as a scaffold for molecular diversity

Summary Xanthines represent a new, versatile scaffold for combinatorial chemistry. A five-step solid-phase synthesis of xanthine derivatives is described which includes alkylations, a nucleophilic displacement reaction at a heterocycle and a ring closure reaction by condensation of a nitroso function with an activated methylene group. The selected reaction sequence allows the production of a highly diverse small-molecule combinatorial compound library.