Optimum packing density and crystal structure of tin-doped indium oxide thin films for high-temperature annealing processes

The influence of high-temperature annealing on the electrical properties and microstructure of tin-doped indium oxide (ITO) thin films was investigated as a function of oxygen gas flow ratio to argon gas during the sputtering deposition. The ITO thin films were annealed at 500 °C in air after the deposition. It was found that the ITO thin films, which were deposited in relatively low oxygen gas flow ratio, exhibited high Hall mobility and low-resistivity after the annealing. Furthermore, the X-ray reflectivity and diffraction measurement revealed that the ITO thin film with low-resistivity after annealing exhibited high packing density, smooth surface and low crystallization degree. It can be considered that the carrier electron scattering was suppressed with increasing in the packing density of the ITO thin film; as a result, the Hall mobility and resistivity were improved.     

Effects of crystalline grain size and packing ratio of self-forming core/shell nanoparticles on magnetic properties at up to GHz bands

Self-forming core/shell nanoparticles of magnetic metal/oxide with crystalline grain size of less than 40 nm were synthesized. The nanoparticles were highly concentrated in an insulating matrix to fabricate a nanocomposite, whose magnetic properties were investigated. The crystalline grain size of the nanoparticles strongly influenced the magnetic anisotropy field, magnetic coercivity, relative permeability, and loss factor (tan δ=μ″/μ′) at high frequency. The packing ratio of the magnetic metallic phase in the nanocomposite also influenced those properties. High permeability with low tan δ of less than 1.5% at up to 1 GHz was obtained in the case of the nanoparticles with crystalline grain size of around 15 nm with large packing ratio of the nanoparticles.     

Computing stable loads for pallets

This paper describes an Integer Programming model for generating stable loading patterns for the Pallet Loading Problem under several stability criteria. The results obtained during evaluation show great improvement in the number of stable patterns in comparison with results reported earlier. Moreover, most of the solved cases also ensure optimality in terms of utilization of a pallet.     

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。     

SOME GEOMETRIC PROPERTIES OF BROWNIAN MOTION ON SIERPINSKI GASKET

Let {X(t),t≥0} be Brownian motion on Sierpinski gasket,The Hausdorff and packing dimensions of the image of a ompact set are studied,The uniform Hausdorff and packing dimensions of the inverse image are also discussed.     

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 tree search method for the container loading problem with shipment priority

This paper addresses a special kind of container loading problem with shipment priority. We present a tree search method, which is based on a greedy heuristic. In the greedy heuristic, blocks made up of identical items with the same orientation are selected for packing into a container. Five evaluation functions are proposed for block selection, and the different blocks selected by each evaluation function constitute the branches of the search tree. A method of space splitting and merging is also embedded in the algorithm to facilitate efficient use of the container space. In addition, the proposed algorithm covers an important constraint called shipment priority to solve practical problems. The validity of the proposed algorithm is examined by comparing the present results with those of published algorithms using the same data.     

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.