Computational techniques derived from digital signal processing are playing a significant role in the security and digital copyrights of audio, video, and visual arts. In light of the quantum computing, the corresponding algorithms are becoming a new research direction in today’s high-technology world. The nature of quantum computer guarantees the security of quantum data, so a safe and effective quantum watermarking algorithm is in demand. Quantum watermarking is the technique that embeds the invisible quantum signal into quantum multimedia data for copyright protection. This research presents a quantum watermarking algorithm in discrete M-band wavelet domain. Different from most traditional algorithms, we propose a new algorithm which applies quantum watermarking in M-band wavelet domain. Assured by the Heisenberg uncertainty principle and quantum no-cloning theorem, the security of quantum watermark can reach a very high-level standard. In other words, this watermarking algorithm can defeat nearly all attackers, no matter using classical computer or quantum computer.

The aim of this study is to figure out the optimization of survival probability of the generals in the card game "Legends of the Three Kingdoms". First, based on combinatorics and probability theory, the PASCAL program was performed to analyze the probabilities of success when several popular generals perform their special skills in the game. The results are as follows: Second, seven typical generals, including Zhou Tai, Zhang Jiao, Zhen Ji, Lu Xun, Ma Chao, Xiahou Dun, and Guo Jia, were chosen, and their abilities including attacking and defense were arbitrarily quantified according to a model constructed in the present study. The scores are as follows: Card-drawing Changing Attacking Defense Blood-selling Zhen Ji 5.62 Zhou Tai 1.04 Ma Chao 1.68 Xiahou Dun 1.19 Guo Jia 3.36 Lu Xun 3.55 Zhang Jiao 2.55 The abilities of different generals were sorted, and by comparison with the statistical record online, the reliability of the model was proved. Thus, the irrationality of the game is identified in this study, and we recommend the game designer to modify the abilities of some generals and to obtain an optimized value according to the output of the model, by which the game would be more popular.

Cartographical projection is mathematical cartography. Map projection is the mathematical model of geoid. Gauss-Kruger projection is unable to realize seamless splicing between adjoining sheet maps. While Mercator projection, especially web Mercator projection, is able to realize seamless splicing but has larger measurement error. How to combine with the advantage of the two projections, apply the method of map projection transformation and realize accurate measurement under the framework of a global map, is the purpose of thisarticle. In order to demonstrate that the problem of measurement could be solved by map projection transformation, we studied the mathematical principle of Gauss - Kruger Projection and the Mercator Projection and designed the algorithm model based on characteristics of both projections. And established simulated data in ArcMap, calculated the error of the three indicators-the area, the length and the angle- under areas in different latitude(0°-4°、30°-34°、60°-64°)and longitude (120°-126°)range which validated the algorithm model. The conclusion suggests that it is feasible that using web Mercator Projection is capable to achieve a global map expression. Meanwhile, calculations of area, distance and angle using map projection transformation principle are feasible as well in Gauss - Kruger Projection. This algorithm combines the advantage of the two different kinds of projection, is able to satisfy uses' high demand and covers the shortage of measurement function of online map services in China. It has certain practical value.

Dijkstra and Bellman-ford are the two basic methods to solve Single-source shortest paths problem，and SPFA is the optimized version of Bellman-ford. However, since the algorithm time complexity is 0 (kn), SPFA’s time efficiency has some instabilities. This paper will compare the time efficiency between Dijkstra optimized with heap and three kinds of SPFA in different density graphs. Meanwhile, random data is created to test optimized Dijkstra and 3 types of SPFA. Finally, according to the calculation result of two methods’ time efficiency, some suggestion is given for their application under different situation.

The problem we study in this paper originated from a simple high school math competition (AMC 12) question on a geometric probability model: “A frog makes 3 jumps, each exactly 1 meter long. The directions of the jumps are chosen independently at random. What is the probability that the frog’s final position is no more than 1 meter from its starting position?” [1] From here, we changed the number of jumps the frog made, the length of each jump and the dimensions of the space. Using recursion, we obtained the recursive formula of the probability of a frog landing x meters within its original spot after jumping m 1-meter jumps in an N -dimension space by integrating the probability distribution of the former step. We also suggested a concept “the intensity of the probability field” to describe the relative probability of each spot and gave an expression of the intensity of each spot of a 2-dimensional space when the frog makes m jumps.