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The subject of counting positive lattice points in n-dimensional simplexes has interested mathematicians for decades due to its applications in singularity theory and number the- ory. Enumerating the lattice points in a right-angled simplex is equivalent to determining the geometric genus of a singularity of a weighted homogeneous complex polynomial. It is also a method to shed insight into large gaps in the sequence of prime numbers. Seeking to contribute to these applications, this research project proves the Yau Geometric Con- jecture in six dimensions, a sharp upper bound for the number of positive lattice points in a six-dimensional tetrahedron. The main method of proof is summing existing sharp upper bounds for the number of points in 5-dimensional simplexes over the cross sections of the six- dimensional simplex. This research project paves the way for the proof of a fully general sharp upper bound for the number of lattice points in a simplex. It also moves the mathematical community one step closer towards proving the Yau Geometric and Yau Number-Theoretic Conjectures in full generality.

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No abstract uploaded!

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.

Matrix factorization methods are widely used for extracting latent factors for low rank matrix completion and rating prediction problems arising in recommender systems of on-line retailers. Most of the exist- ing models are based on L2 delity (quadratic functions of factorization error). In this work, a coordinate descent (CD) method is developed for matrix factorization under L1 delity so that the related minimization is done one variable at a time and the factorization error is sparsely distributed. In low rank random matrix completion and rating predic- tion of MovieLens 100k datasets, the CDL1 method shows remarkable stability and accuracy under gross corruption of training (observation) data while the L2 delity based methods rapidly deteriorate. A closed form analytical solution is found for the one-dimensional L1-delity sub- problem, and is used as a building block of CDL1 algorithm whose con- vergence is analyzed. A connection with robust principal component analysis is drawn.

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No abstract uploaded!

This work focuses on the problem of high quality style transfer for Chinese characters, converting Chinese printed with standard typograph into those in calligraphic style. Traditional approaches include employing derivative network structures of CNN, RNN, and GAN, yet generation results are not satisfactory enough. In this paper, we proposed an integrated system of pix2pix structure, auxiliary classifier, and WGAN. Trials were run to evaluate the performance of traditional CNN and GAN. Cross-comparative sets of experiments among GAN, AC-GAN, and our proposed AC-WGAN have been conducted to test the capabilities of our proposed model. Inference and interpolation tests are conducted as well. Our proposed model outperformed existing style transfer system in generation’s delicacy, similarity, and efficiency. Incorporated with WGAN, the model also demonstrated a strong ability in providing a truthful training indicator with its loss. Study also suggested that AC and pix2pix adaption hold huge significance in accelerating the training process. Research validates the viability of fulfilling Chinese character transformation with style transfer. With handwriting recognition network, fast, high-quality Chinese character style transfer forms the basis for instantaneous conversion between printed and written work. Optimization on algorithm may be another direction for further exploration.

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No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

Two noted drawbacks can be found in nowadays’ power adapting technological scheme: the first is found in both of AC & DC adapters which is that the connection between power supply and appliance is only electrical connection. Such a connection can almost do nothing against such accidents as electric shock, illegal electricity-using, and accidents resulted from overcurrent, overvoltage, overheat and/or the like; the second is mainly found in DC power adapters, which is that one power adapter can only supply power with specified electrical parameters. It means that one adapter can only power its designated electrical appliance, which will inevitably lures two issues: one is that once the electrical appliance become out of work, its power adapter would also have to be abandoned, even if it is still in good conditions, such an outcome will result in waste of resources and environmental pollution, in addition to inconvenience for users who would have to take various kinds of adapters with them during their work and life. To solve the drawbacks above, here puts forward an adapting scheme in which electricity adapters and appliances will first conduct “communication and negotiation” prior to power delivery. The noted features of this scheme are as followings: the first, it is the first set of protocols designed for power adaptation by which all power delivery will not be conducted only with a simple electrical connection marked as “Contact and Power”, but one marked as “Agree and Power” in which power delivery will not happen unless an “agreement” by and between the power supply and the appliance has been concluded in advance. Such an electrical adapting scheme will certainly ensure that all electrical parameters may stay within the coverage specified in the course of electrical adaptation and this would thus avoid almost all safety issues resulted from electric shock, illegal electricity-using, overcurrent, overvoltage, overheat and so on; and the second, it is first time achieving the goal of which one adapter is able to provide electricity for various kinds of appliances within the designated range automatically , i.e. the power supply will be able to provide electricity with right parameters for appliances according to their requests. Such two features above will make a way for solving issues of waste of resources, environmental pollution and inconvenience of carrying different kinds of adapters. This scheme thus designed a protocol which has taken much effort to develop Topology, Connection Methods, Data Structures and the like and thus built up a set of standards related to communications necessarily by and between power adapter and appliance. Further, here also developed a physical device which implemented UPP, the “UPP Power Adapter”. According to the experiments and tests, the device reached all engineering goals designed: it can supply correct electricity and provide parameter-specified safety protection according to the requests of appliances automatically within its specified range It can be seen that UPP will soon head adapters marked as great variety and low-compatibility nowadays to unity following with more and more application of UPP in adapters just as USB had ever done on uniting computer peripherals. It will undoubtedly not only make peoples’ work and life more convenient and comfortable, but also positively contribute much to reducing pollution, protecting environment and saving resources.

In this paper, the differential equations for copolymerization of multiple monomers are derived based on the steady-status assumption of Alfrey-Goldfinger and Valvassori-Sartori respectively, and a numerical method is implemented in C++ language. The differential equations of copolymer composition with wide application presented in this paper provide a theoretical guidance for industrial production and academic research of multiple free radical copolymerization.

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A physical method is developed to analyze the Riemann zeta function and the L-function. First, a physical model of an elastic bar fixed at both ends and subjected to symmetric axial loads with respect to the mid-span is constructed. The axial force of the bar at the left end is calculated with two methods: the equilibrium of forces and the principle of minimum potential energy. With the help of the orthogonality of {sinix} (i 1, 2, 3, ) , the Parseval identity and the Bessel inequality of the physical model are obtained. Further, it is proven that, in all the possible displacements which satisfy the boundary conditions, the real one minimizes the total potential energy of the bar. With the equivalence of the two methods, an identity of a type of infinite series is derived. Based on the identity, L(1) , L(3) , a recurrence formula of L(2k 1) (k  3) ,  (2) ,  (4) , and a relationship between  (2k) (k  2) and L(2i 1) (i  1, 2, ..., k) are then deduced with power axial load functions. The upper and lower bounds for the Riemann zeta function  (2k -1) and the L-function L(2k) are given. The numerical results show that the upper and lower bounds are in excellent agreement with the accurate value. Finally, two improvement methods are proposed for estimating the circumference ratio. The numerical results show that the two methods can estimate the circumference ratio with high accuracy and that the L -function is more efficient than the Riemann zeta function in estimating the circumference ratio.

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No abstract uploaded!

▲With the rapid development of bicycle-sharing system since 2016, illegal parking has become one of the most significant social issues. While the existing management methods cannot meet the demand, object detection technology provides a possibility. The Video Surveillance System can be utilized as a rich source of information. However, there is technical challenge to handle complex scenarios. Faster R-CNN, chosen because of its excellent overall performance, cannot specify the proposals of shared bikes especially in distant view. Processing the consecutive images in videos is neither necessary nor efficient. The original results are limited by interference of moving bikes and blocking effects. ▲ In this paper, I introduce a Faster R-CNN over Attention (FoA) that combines the from-coarse-to-fine visual mechanism with deep neural networks. FoA realizes fine-grained detection of shared bikes in complex circumstances. It consists of an Attention Region Extraction (ARE) and an optimized Faster R-CNN. In ARE, I introduce the concept of Attention Region and define it as video background, then apply Gaussian Mixture Model. ARE processes the surveillance video into discrete regions, allowing concentration on certain areas and efficiency in detection. In Faster R-CNN, I put forward an anchor box optimization in regards of the remarkable region-based characteristic in R-CNN. The optimization applies k-means to refine the anchor boxes and generate more appropriate region proposals. ▲ I construct a categorized shared bike data set of 4,291 images and 12,697 labeled objects for FoA training and testing. FoA performs excellently with the detection and recognition ratios of 94.19% and 92.73% respectively. The optimization is proved to make a difference. ▲ The paper not only provides a new direction for solving illegal parking issue and managing bicycle-sharing system, but also generalizes FoA into a new detection framework of Attention Region Extraction plus Region-Based Convolutional Neural Network, which can be applied to certain object detection in various scenes. The mechanism that combines ARE and R-CNN organically allows the towards-real-time detection to possess both practicality and universality. FoA is one of its robust implements.

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The linear congruence equations are the ancient and significant research contents. Most discussions of the linear congruence equations focus on the special cases, for example, there is a linear congruent theorem for solving the congruent linear equation in one unknown and the Chinese remainder theorem for solving the simultaneous congruent linear equations in one unknown, which are involved to find a special solution using the properties of the integer number, and some papers discuss the equation in unknowns. But all the results are not convenient and efficient to solve the equations and not adapt to solving the general system of congruent linear equations in n unknowns. There is no uniform, convenient and efficient technique and theory for the general system of congruent linear equations, like the theory of linear equations over real numbers. The inspiration arose from the elimination of variables when solving the linear equations over real numbers, Generalized the elementary transformations of matrix over real numbers to the integer numbers modulo m, the paper discussed the properties of the modular matrix under the elementary transformations and a similar equivalent transforming theorem for matrix modulom theorem was obtained that any matrix modulo m can be transformed into a canonical diagonal form by means of a finite number of elementary row and column operations. furthermore, by means of the equivalent transforming theorem, the solution criterion theorem and structure theorem were proposed for the general congruent linear equations based on the modular matrix transformations, which extended the theories of the congruent linear equations, and finally, the detailed steps of the uniform method were given for solving the general system of congruent linear equations based on the elementary transformations of matrix modulo m, it can be easily written out the solutions of the system immediately as determining solutions of the system conveniently by elementary matrix transformations. Analysis and discussions indicate that the results are most valuable in science and the proposed technique for solving the system is convenient, efficient and adaptable.

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