Weierstrass型函数图象的分形维数

考虑函数f(x)=sum from i=1 to ∞(?)~(-1)φ((?) θ_n)和w(x)=sum from n=1 to ∞(?)φ_(?)((?)x θ_(?)),式中0<α<(?)是任意实数,在一定条件下,估计了函数f图象的Hausdorff维数的下界,并求得了w函数图象的Box维数和Packing维数。     

Sets in Abelian groups with distinct sums of pairs

A subset S={s₁,…,sk} of an Abelian group G is called an St-set of size k if all sums of t different elements in S are distinct. Let s(G) denote the cardinality of the largest S₂-set in G. Let v(k) denote the order of the smallest Abelian group for which s(G)?k. In this article, bounds for s(G) are developed and v(k) is determined for k?15 by computing s(G) for Abelian groups of order up to 183 using exhaustive backtrack search with isomorph rejection.     

Self-similar sets with optimal coverings and packings

We prove that if a self-similar set E in Rn with Hausdorff dimension s satisfies the strong separation condition, then the maximal values of the Hs-density on the class of arbitrary subsets of Rn and on the class of Euclidean balls are attained, and the inverses of these values give the exact values of the Hausdorff and spherical Hausdorff measure of E. We also show that a ball of minimal density exists, and the inverse density of this ball gives the exact packing measure of E. Lastly, we show that these elements of optimal densities allow us to construct an optimal almost covering of E by arbitrary subsets of Rn, an optimal almost covering of E by balls and an optimal packing of E.     

New upper bounds for online strip packing

In this paper, we consider the online strip packing problem, in which a list of online rectangles has to be packed without overlap or rotation into one or more strips of width 1 and infinite height so as to minimize the required height of the packing. By analyzing a two-phase shelf algorithm, we derive a new upper bound 6.4786 on the competitive ratio for online one strip packing. This result improves the best known upper bound of 6.6623. We also extend this algorithm to online multiple strips packing and present some numeric upper bounds on their competitive ratios which are better than the previous bounds.     

A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids

The problem of packing ellipsoids in the three-dimensional space is considered in the present work. The proposed approach combines heuristic techniques with the resolution of recently introduced nonlinear programming models in order to construct solutions with a large number of ellipsoids. The introduced approach is able to pack identical and non-identical ellipsoids within a variety of containers. Moreover, it allows the inclusion of additional positioning constraints. This fact makes the proposed approach suitable for constructing large-scale solutions with specific positioning constraints in which density may not be the main issue. Numerical experiments illustrate that the introduced approach delivers good quality solutions with a computational cost that scales linearly with the number of ellipsoids; and solutions with more than a million ellipsoids are exhibited.     

Synthesis of Poly（p-phenyleneethynylene）s with Crosslinkable End or Side Groups and Its Solid State Structure and Optical Properties Before and after Crosslinking

Two crosslinkable poly(p-phenyleneethynylene)s(PPEs): poly[2,5-di(2'-ethyl-hexyloxy)-1,4-phenylenee-thynylene] with end-capped vinyl(PPE1) and poly[2,5-di(allyloxy)-1,4-phenyleneethynylene-2,5-di(2'-ethyl-hexyloxy)-1,4-phenyleneethynylene](PPE2) were synthesized. Via the thermal addition reactions of vinyl end groups of PPE1 and allyloxy side groups of PPE2, crosslinked polymers C-PPE1 and C-PPE2 were obtained, respectively. The two polymers were characterized by wide-angle X-ray diffraction(WXRD), ultravio...     

Optimization of multiweighing packing proceedings

In this paper we study the variability reduction gain that results from the use of multiweighing proceedings in packing processes with the objective of sales at constant nominal weights. According to this, we have proposed a packing algorithm that includes the formation of units with variable number of pieces and we have obtained the value of the percentage variability reduction index. Collaborator in the Catalan Institute of Tecnology (ICT).     

Polymethylhydrosiloxane surface deactivation of silica particles for packed capillary column supercritical fluid chromatography

Summary Spherical porous silica particles (10 μm diameter, 300 ? and 80 ? pores), spherical nonporous silica particles (10 μm diameter), and irregular porous silica particles (≈ 10 μm diameter, 80 ? pores) were deactivated with polymethylhydrosiloxane (PS). The surface activities of the deactivated silica particles were investigated using various polar compounds under supercritical fluid chromatography (SFC) conditions (neat CO₂), and compared with a commercial C₁₈-bonded phase. The small pore (80 ?) silica particles could be more completely deactivated than larger pore (300 ?) and nonporous silica particles. The success of the PS deactivation method is ascribed to the excellent match between the reactive groups on the polymer backbone and the silica surface, and the formation of a highly crosslinked polymeric layer over the surface. Physical processes, such as adsorption and desorption of the deactivation reagent on the surface and diffusion from the surface, were found to have important effects on the deactivation. Using capillary columns packed with PS deactivated silica particles, typical polar organic compounds, including hydroxyl-containing compounds, carbonyl-containing compounds, free amines, and free carboxylic acids, were separated by SFC and compared with results from a commercial C₁₈-bonded phase. While the results clearly show that the PS deactivated particles were more inert than the C₁₈-bonded phase, better deactivation methods are still needed for separation of free acids and alkylamines.     

THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS

Suppose {Xn} is a random walk in time-random environment with state space Zd,|Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index a. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.