吴海兵：7天的简捷文化

和吴海兵的采访地点,他希望能约在地铁口附近的咖啡馆。比约定的时间迟到了一会,他一个劲地道歉：“没想到北京的地铁换乘要走这么远。”他背着双肩包,一个人来北京出差,你很难把这个风尘仆仆,出行时喜欢坐地铁的男人,和纽交所上市公司CFO的身份联系起来。     

Incremental Gradient Algorithms with Stepsizes Bounded Away from Zero

We consider the class of incremental gradient methods for minimizing a sum of continuously differentiable functions. An important novel feature of our analysis is that the stepsizes are kept bounded away from zero. We derive the first convergence results of any kind for this computationally important case. In particular, we show that a certain -approximate solution can be obtained and establish the linear dependence of on the stepsize limit. Incremental gradient methods are particularly well-suited for large neural network training problems where obtaining an approximate solution is typically sufficient and is often preferable to computing an exact solution. Thus, in the context of neural networks, the approach presented here is related to the principle of tolerant training. Our results justify numerous stepsize rules that were derived on the basis of extensive numerical experimentation but for which no theoretical analysis was previously available. In addition, convergence to (exact) stationary points is established when the gradient satisfies a certain growth property.     

Universal Covers of Geometries of Far Away Type

The geometries studied in this paper are obtained from buildings of spherical type by removing all chambers at non-maximal distance from a given element or flag. I consider a number of special cases of the above construction chosen among those which most frequently appear in the literature, proving that the resulting geometry is always simply connected but for three cases of small rank defined over GF(2) and GF(4). I also compute the universal cover in those exceptional cases.     

Rong coupling method in a scalar (3)-symmetric theory

Theoretical and Mathematical Physics -     

Professor Alexander Ženíšek Passed Away

Applications of Mathematics -     

Density of Smooth Functions in Anisotropic Weighted Sobolev Spaces with Weights that are Locally Bounded and Locally Bounded Away from Zero

Mathematical Notes - The density of smooth functions in weighted Sobolev spaces that are anisotropic with respect to the order of the derivatives and the weight functions is established.     

On the Asymptotics of the Sojourn Probability of a Poisson Process between Two Nonlinear Boundaries That Move Away from One Another

We obtain the complete asymptotic decomposition of the sojourn probability of a homogeneous Poisson process inside a domain with curvilinear boundaries. The coefficients of this decomposition are determined by the solutions of parabolic problems with one and two boundaries.     

Artinian Serial Modules over Commutative (or,Left Noetherian) Rings are at Most One Step Away from Being Noetherian

We introduce and study the concept of dual perfect dimension which is a Krull-like dimension extension of the concept of acc on finitely generated submodules. We observe some basic facts for modules with this dimension, which are similar to the basic properties of modules with Noetherian dimension. For Artinian serial modules, we show that these two dimensions coincide. Consequently, we prove that the Noetherian dimension of non-Noetherian Artinian serial modules over the rings of the title is 1.