Multiple Period Repair Kit Problem with Capacity Considerations

The repair kit problem seeks an optimal stock of parts for a repair kit for purposes of remote repairs. This problem has often been studied when restocking is possible between each order, or when the number of orders is known between each restocking. This research evaluates a model for the repair kit stocking problem for which there is multiple-period demand with a known time interval between each restocking, but an unknown number of on-site repair visits is required during the restocking period. Most previous work focuses on minimum cost subject to some minimum service level;in the case where the value of technician time and customer service is relatively large, the space constraint of the kit and volume of parts comes into play. This work contributes to the literature by testing the robustness of a heuristic originally proposed by [1] in a field study. We conduct numerical experiments to evaluate the heuristic over a wide range of parameterizations. Our results indicate that the heuristic performs close to optimum, and its performance improves as the problem size grows.

MULTIPLE SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH PERIODIC NONLINEARITY AND STRONG RESONANCE

I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V is periodic in x1 with the period T>0, （V. 3） V→O, Vx→O as |x2|→∞, uniformly in （t, x1）.

The Zhaxikang Vein-type Pb-Zn-Ag-Sb Deposit in Himalayan Orogen, Tibet： Product by Overprinting and Remobilization Processes during Post-collisional Period

The Zhaxikang Pb-Zn-Ag-Sb deposit, the largest polymetallic deposit known in the Himalayan Orogen of southern Tibet, is characterized by vein-type mineralization that hosts multiple mineral assemblages and complicated metal associations. The deposit consists of at least six steeply dipping vein- type orebodies that are hosted by Early Jurassic black carbonaceous slates and are controlled by a Cenozoic N-S-striking normal fault system. This deposit records multiple stages of mineralization that include an early period （A） of massive coarse-grained galena-sphalerite deposition and a later period （B） of Sb-bearing vein-type mineralization. Period A is only associated with galena-sphalerite mineralization, whereas period B can be subdivided into ferrous rhodochrosite-sphalerite-pyrite, quartz -sulfosalt-sphalerite, calcite-pyrite, quartz-stibnite, and quartz-only stages of mineralization. The formation of brecciated galena and sphalerite ores during period A implies reworking of pre-existing Pb -Zn sulfides by Cenozoic tectonic deformation, whereas period B mineralization records extensive open- space filling during ore formation. Fluid inclusion microthermometric data indicate that both periods A and B were associated with low-medium temperature （187-267℃） and low salinity （4.00-10.18% wt. NaCl equivalent） ore-forming fluids, although variations in the physical-chemical nature of the period B fluids suggest that this phase of mineralization was characterized by variable water/rock ratios. Microprobe analyses indicate that Fe concentrations in sphalerite decrease from period A to period B, and can be divided into three groups with FeS concentrations of 8.999-9.577, 7.125-9.109, 5.438-1.460 mol.%. The concentrations of Zn, Sb, Pb, and Ag within orebodies in the study area are normally distributed in both lateral and vertical directions, and Pb, Sb, and/or Ag concentrations are positive correlation within the central part of these orebodies, but negatively correlate in the margins. Sulfide S isotope compositions are highly variable （4‰-13‰）, varying from 4‰ to 11‰ in period A and 10‰ to 1‰ in period B. The Pb isotope within these samples is highly radiogenic and defines linear trends in 206pb/204pb vs. 207pb/204pb and 206pb/204pb vs. 208pb/204pb diagrams, respectively. The S and Pb isotopic characteristics indicate that the period B orebodies formed by mixing of Pb-Zn sulfides and regional Sb- bearing fluids. These features are indicative of overprinting and remobilization of pre-existing Pb-Zn sulfides by Sb-bearing ore-forming fluids during a post-collisional period of the Himalayan Orogeny. The presence of similar ore types in the north Rhenish Massif that formed after the Variscan Orogeny suggests that Zhaxikang-style mineralization may be present in other orogenic belts, suggesting that this deposit may guide Pb-Zn exploration in these areas.

Extended tanh-function Method for Solving Traveling Wave Solutions of Nonlinear Kundu Equation

In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO A SECOND-ORDER NONLINEAR DIFFERENCE SYSTEM

In this paper, by the critical point theory, a sufficient condition for the existence of multiple periodic solutions to a nonlinear second order difference system is obtained. An illustrative example is given. Our results improve and generalize some known ones.

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO LOTKA-VOLTERRA NETWORK-LIKE FOOD-CHAIN SYSTEM WITH DELAYS AND IMPULSES ON TIME SCALES

In this paper, we have studied a general kind of n-species Lotka-Volterra network- like food-chain system with delays and impulses on time scales. Applying Mawhin＇s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient criteria have been established to guarantee the existence of at least 2n periodic solutions to this model. One example is given to illustrate the effectiveness of our results.

3D image reconstruction with controllable spatial filtering based on correlation of multiple periodic functions in computational integral imaging

We propose a novel method of slice image reconstruction with controllable spatial filtering by using the correlation of periodic delta-function arrays （PDFAs） with elemental images in computational integral imaging. The multiple PDFAs, whose spatial periods correspond to object＇s depths with the elemental image array （EIA）, can generate a set of spatially filtered EIAs for multiple object depths compared with the conventional method for the depth of a single object. We analyze a controllable spatial filtering effect by the proposed method. To show the feasibility of the proposed method, we carry out preliminary experiments for multiple objects and present the results.

MULTIPLE PERIODIC SOLUTIONS TO A MICHAELIS-MENTEN-TYPE PREDATOR-PREY SYSTEM WITH DELAY AND HARVESTING

In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin’s coincidence degree theory.

EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION

In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.

MULTIPLE PERIODICITY TO A CLASS OF DELAYED STATE-DEPENDENT PREDATOR-PREY SYSTEM

The existence of the multiple positive periodic solutions to a delayed statedependent predator-prey system with non-monotonic functional response is considered. Using the continuation theorem based on Mawhin＇s coincidence degree, some more generalized results are obtained.

Multiple directional enhanced light source through a periodic metal grating structure

In recent years, semiconductor quantum dots （QDs） have been widely used as photon sources in quantum optics due to their special properties, such as high quantum effi- ciency, narrow and tunable emission spectrum, easy manipulation, and so on. The spontaneous emission of QDs also depends on the surrounding environment.

Phase group synchronization between any signals and its physical characteristics

The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resolution,equivalent phase comparison frequency and so on.Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail.Using the basic principle and the variation law of group phase difference,the frequency stability better than 10-14/s can be easily obtained in the time&frequency measurement and control domain,and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization,and locked precision with 10-13/s can be reached based on phase group synchronization.The phase group synchronization can provide technical support to frequency linking among radio frequency,microwave and light frequency.