Rational solutions of the graphsack problem

A graphsack problem is a certain binary linear optimization problem with applications in optimal network design. From there a rational graphsack problem is derived by allowing the variables to vary continuously between 0 and 1. In this paper we deal with rational graphsack problems. First we develop the concept of compressed solutions and the concept of augmenting cuts. Making use of these concepts a very simple optimality criterion is derived. Finally an efficient algorithm solving rational graphsack problems is given which is polynomially bounded in time and which is closely related to the simplex algorithm.     

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $\left|g^{\prime }\left(z\right)\right|\le \left|h^{\prime }\left(z\right)\right|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.     

A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms

The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”. R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion of Science.     

低氧低分压环境下泡塑吸附原子吸收光谱法测定矿石中的金

在青海低氧低分压环境下,试样用王水分解,在王水介质中用多孔聚氨酯泡沫振荡吸附富集,然后用硫脲加热解脱,再直接用火焰原子吸收分光光度计测定。通过对泡塑的吸附振荡,解脱时间,硫脲浓度等条件的探讨,确定了最佳分析条件,解决了低氧低分压环境下常量A u的测定。     

A globally convergent method for computing multiple vortices in a supersymmetric field theory

Computation of the solutions to the gauge field equations is known of great importance for the simulation of various particle physics systems. In this work, we establish a globally convergent iterative method for computing the multiple vortex solutions arising in a self-dual system of non-Abelian gauge field equations derived in a supersymmetric theory model. Using this method, we present a few numerical examples which demonstrate the effectiveness of the method and, at the same time, provide a concrete realization of the soliton-like behavior of the vortexlines concentrated around centers of vortices, which is believed to be essential for linear confinement in QCD.     

Representation of Bounded Convex Sets By Rational Convex Hull Of Its Gamma-Extreme Points

H. Minkowski proved C= convext C whenever C is a compact convex subset of a finite-dimensional linear space. If C is bounded but not closed, this representation does not hold anymore. In this case, we introduce the set of so-called γ-extreme points extγC of C and show C = convext γ C = raco extγ C, where raco M denotes the rational convex hull of M.     

The limit of the partial sums process of spatial least squares residuals

We establish a functional central limit theorem for a sequence of least squares residuals of spatial data from a linear regression model. Under mild assumptions on the model we explicitly determine the limit process in the case where the assumed linear model is true. Moreover, in the case where the assumed linear model is not true we explicitly establish the limit process for the localized true regression function under mild conditions. These results can be used to develop non-parametric model checks for linear regression. Our proofs generalize ideas of a univariate geometrical approach due to Bischoff [W. Bischoff, The structure of residual partial sums limit processes of linear regression models, Theory Stoch. Process. 8 (24) (2002) 23–28] which is different to that proposed by MacNeill and Jandhyala [I.B. MacNeill, V.K. Jandhyala, Change-point methods for spatial data, in: G.P. Patil, et al. (Eds.), Multivariate Environmental Statistics. Papers Presented at the 7th International Conference on Multivariate Analysis held at Pennsylvania State University, University Park, PA, USA, May 5–9 1992, in: Ser. Stat. Probab., vol. 6, North-Holland, Amsterdam, 1993, pp. 289–306 (in English)]. Moreover, Xie and MacNeill [L. Xie, I.B. MacNeill, Spatial residual processes and boundary detection, South African Statist. J. 40 (1) (2006) 33–53] established the limit process of set indexed partial sums of regression residuals. In our framework we get that result as an immediate consequence of a result of Alexander and Pyke [K.S. Alexander, R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance, Ann. Probab. 14 (1986) 582–597]. The reason for that is that by our geometrical approach we recognize the structure of the limit process: it is a projection of the Brownian sheet onto a certain subspace of the reproducing kernel Hilbert space of the Brownian sheet. Several examples are discussed.     

On analytic functions related with generalized Robertson functions

Analytic functions f are called Robertson functions for which zf^′ is α-spiral-like. This concept is generalized by several authors and a class real, of analytic functions is introduced and studied. It is noted that the functions in are of bounded boundary rotation and consists of Robertson functions.In this paper, we use the class to define a new class of analytic functions which unifies a number of classes previously studied such as the class of close-to-convex functions of higher order. Some interesting properties of this class, including coefficient problems, inclusion results and a sufficient condition for univalency are studied.     

PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS

We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.     

Naive audience and communication bias

We introduce the possibility that the receiver naively believes the sender’s message in a game of information transmission with partially aligned objectives. We characterize an equilibrium in which the communication language is inflated, the action taken is biased, and the information transmitted is more precise than in the benchmark fully-strategic model. We provide comparative statics results with respect to the amount of asymmetric information, the proportion of naive receivers, and the size of the sender’s bias. As the state space grows unbounded, the equilibrium converges to the fully-revealing equilibrium that results in the limit case with unbounded state space.