Abstract:
Quantum mechanics, one of the important theories of modern physics, is fairly esoteric and abstract. Based on the characteristics of the quantum mechanics course, the article studies the modernization of quantum mechan-ics teaching in four aspects: the modernization of the teaching idea, Computer-Aided Instruc-tion, the development of Information technology software and the establishment of three-di-mensional digital curriculum teaching resource library.

Abstract:
In this paper, we compute the non-detection probability of a randomly moving target by a stationary or moving searcher in a square search region. We find that when the searcher is stationary, the decay rate of the non-detection probability achieves the maximum value when the searcher is fixed at the center of the square search region; when both the searcher and the target diffuse with significant diffusion coefficients, the decay rate of the non-detection probability only depends on the sum of the diffusion coefficients of the target and searcher. When the searcher moves along prescribed deterministic tracks, our study shows that the fastest decay of the non-detection probability is achieved when the searcher scans horizontally and vertically.

Abstract:
Solar collectors can provide clean, renewable, and domestic energy. The tilt angle and horizontal direction of solar collectors significantly affect its efficiency. There are many good methods to search the optimum tilt angle and horizontal direction to realize the maximum total radiation on the solar collector within a particular day or a specific period. However, it is hard to realize it when solar collectors are placed under obstacle’s shadows; especially when some obstacles, such as trees, have irregular shapes. This paper presents algorithms to achieve the best tilt angle and horizontal direction for solar collector’s performance under the free-form surfaces 3D obstacle’s shadow. The solution process is composed of 4 steps. First, it creates a 3D scene, in which a unique color is given to the solar collector. Second, it employs orthographic projection from the point of view to get an image of the scene. Third, the number of pixels is used to represent the efficiency of the solar collector by counting the pixels of the unique color. Fourth, the efficiency of solar collector in each direction in a period of time is calculated with many images to further select the best direction.

Abstract:
We consider the problem of searching for a target that moves between a hiding area and an operating area over multiple fixed routes. The search is carried out with one or more cookie-cutter sensors, which can detect the target instantly once the target comes within the detection radius of the sensor. In the hiding area, the target is shielded from being detected. The residence times of the target, respectively, in the hiding area and in the operating area, are exponentially distributed. These dwell times are mathematically described by Markov transition rates. The decision of which route the target will take on each travel to and back from the operating area is governed by a probability distribution. We study the mathematical formulation of this search problem and analytically solve for the mean time to detection. Based on the mean time to capture, we evaluate the performance of placing the searcher(s) to monitor various travel route(s) or to scan the operating area. The optimal search design is the one that minimizes the mean time to detection. We find that in many situations the optimal search design is not the one suggested by the straightforward intuition. Our analytical results can provide operational guidances to homeland security, military, and law enforcement applications.

Abstract:
Nowadays, path planning has become an important field of research focus. Considering that the ant colony algorithm has numerous advantages such as the distributed computing and the characteristics of heuristic search, how to combine the algorithm with two-dimension path planning effectively is much important. In this paper, an improved ant colony algorithm is used in resolving this path planning problem, which can improve convergence rate by using this improved algorithm. MAKLINK graph is adopted to establish the two-dimensional space model at first, after that the Dijkstra algorithm is selected as the initial planning algorithm to get an initial path, immediately following, optimizing the select parameters relating on the ant colony algorithm and its improved algorithm. After making the initial parameter, the authors plan out an optimal path from start to finish in a known environment through ant colony algorithm and its improved algorithm. Finally, Matlab is applied as software tool for coding and simulation validation. Numerical experiments show that the improved algorithm can play a more appropriate path planning than the origin algorithm in the completely observable.

We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the non-detection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher’s detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.

Abstract:
We study the problem of detecting a target that moves between a hiding area and an operating area over multiple fixed routes. The research is carried out with one or more cookie-cutter sensors with stochastic intermission, which turn on and off stochastically governed by an on-rate and an off-rate. A cookie-cutter sensor, when it is on, can detect the target instantly once the target comes within the detection radius of the sensor. In the hiding area, the target is shielded from being detected. The residence times of the target, respectively, in the hiding area and in the operating area, are exponentially distributed and are governed by rates of transitions between the two areas. On each travel between the two areas and in each travel direction, the target selects a route randomly according to a probability distribution. Previously, we analyzed the simple case where the sensors have no intermission (i.e., they stay on all the time). In the current study, the sensors are stochastically intermittent and are synchronized (i.e., they turn on or off simultaneously). This happens when all sensors are affected by the same environmental factors. We derive asymptotic expansions for the mean time to detection when the on-rate and off-rate of the sensors are large in comparison with the rates of the target traveling between the two areas. Based on the mean time to detection, we evaluate the performance of placing the sensor(s) to monitor various travel route(s) or to scan the operating area.

Abstract:
We study the problem of a diffusing particle confined in a large
sphere in the n-dimensional space being absorbed into a small sphere at the
center. We first non-dimensionalize the problem using the radius of large
confining sphere as the spatial scale and the square of the spatial scale
divided by the diffusion coefficient as the time scale. The non-dimensional
normalized absorption rate is the product of the physical absorption rate and
the time scale. We derive asymptotic expansions for the normalized absorption
rate using the inverse iteration method. The small parameter in the asymptotic
expansions is the ratio of the small sphere radius to the large sphere radius.
In particular, we observe that, to the leading order, the normalized absorption
rate is proportional to the (n － 2)-th power of the small parameter for .

Innovation is the precondition for the sustainable development of corporation, and the purpose of “reform of the supply front” which the government puts forward at present is to improve the innovation capacity of corporation. In this paper, in order to provide reference for improving innovation capacity and seek the factor of improving the innovation capacity, an evaluation index system of corporation’s innovation capacity is established after analyzing the input, profit, steady finance and governance capacity of the corporations which are listed on the Growth Enterprises Market by comparing the score of each corporation’s innovation capacity.

Abstract:
although china's national people's congress announced its decision to ratify the who's framework convention on tobacco control (fctc) on sunday, august 28, 2005, fundamental challenges to tobacco control still exist. a survey at the "no smoking day" on may 31, 2004 in china showed that over 73% of respondents do not think that human society will be able to get rid of the consumption of tobacco products. although the prevalence of smoking declined 1.2% from 1996 to 2002, the absolute number of smokers increased by 30 million during this period. it is estimated that smoking prevalence will decline 10% in the next 25 years. however, due to the population increase, the total number of tobacco consumers will be about the same as today, which is 320 million. as long as the tobacco industry continues to be significant in overall economic development, and as long as the government continues to play a significant role in tobacco production, the debate between tobacco production and tobacco control will continue. although china has already made significant efforts with regard to tobacco control, it is still in the beginning of its "long march" towards improving the population's health status by reducing tobacco consumption in china.