MathSciDoc: An Archive for Mathematician ∫

We give a classification of birational transformations on smooth projective surfaces which have a Zariski-dense set of noncritical periodic points. In particular, we show that if the first dynamical degree is greater than one, the union of all noncritical periodic orbits is Zariski-dense.

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We reduced the unsolved problem of Evans triangles to the problem of nding rational points on a class of elliptic curves, the twisted Edwards curves En. We proved that the set of all Evans triangles with a given ratio is isomorphic to a quotient group of En(Q). After this, using Sage, we can solve the Evans problem for an amount of cases within the capacity of computer. Even without the help of a computer, we can still obtain a large class of new Evans triangles, and nd an eective way to test if the rank of an Edwards curve is positive or not.

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.

Quotient sets have attracted the attention of mathe- maticians in the past three decades. The set of quotients of primes is dense in the positive real numbers and the set of all quotients of Gauss- ian primes is also dense in the complex plane. Sittinger has proved that the set of quotients of primes in an imaginary quadratic ring is dense in the complex plane and the set of quotients of primes in a real quadratic number ring is dense in R: An interesting open question is introduced by Sittinger: Is the set of quotients of Hurwitz primes dense in the quaternions? In this paper, we answer the question and prove that the set of all quotients of Hurwitz primes is dense in the quaternions.

Sign language bridges the communication between the deaf-mute and the rest of the world. With the development of computer technology, the research on sign language recognition is prospering. Currently, there are two kinds of research methods. One is based on machine vision, the other is based on wearable input devices. Comparing with machine vision, wearable devices have the advantage of being able to get real-time information of the bend of the fingers and the movement of the hand. The essay applies recent technology in the field of voice recognition, and aims at finding out the best algorithm for medium vocabulary continuous sign language recognition. By building a hybrid Deep Neural Network-Hidden Markov Model, and designing and making a low-cost digital glove, the essay successfully compares the features between Dynamic Time Warping (DTW), Gaussian Mixture Model-Hidden Markov Model (GMM-HMM) and Deep Neural Network-Hidden Markov Model (DNN-HMM) as of solving the problem of sign language recognition. Tests show that in terms of calculating the observation probability, DNN has a much better performance than HMM, especially when syntax is not provided, meaning that DNN better suits the developing trend of sign language recognition. Real-time recognition is achieved on the intelligent terminal with an accuracy of over 97%, using the trained model and a decoding program.

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The development of modern technology is closely related to the use of metals, whose demand has been shifting from common industrial metals to a variety of minor metals, such as cobalt or indium. The industrial importance and limited geological availability of some minor metals have led to them being considered more “critical.” In this research, we develop a novel approach to investigate metal criticality. Instead of quantifying the supply risk of critical metals with static indicators, as used in conventional criticality measures, we propose a dynamic method by looking at the stock trend of the major critical metal producers, who would, in turn, influence the future supply. This allows us to utilize high-frequency time series data in creating machine learning models that predict the stock prices using metal-related features. Specifically, we use regularized linear regression, logistic regression, support vector machine and gradient boosted trees as base models. An ensemble of them is then used for the final prediction, with methods including majority vote, logistic regression stacking, and gradient boosted trees stacking. Based on a misclassification error of 34% in the validation set, we further develop a stock trading strategy, which leads to a back-tested return of 313%, or an excess return of 147%. More importantly, a set of significant features selected by our models leads to insightful suggestions that certain unseeming features, such as markets of other metal cycles and currency exchange rates, may play important roles in influencing the supply of critical metals.

This paper studies a special class of population-size-dependent branching processes, in which the offspring distribution is supercritical when the population size does not exceed a given threshold 𝐾𝐾, and is subcritical or critical when the population size exceeds 𝐾𝐾. Up to now, the author has found no paper concerning continuous time threshold processes, and study of the discrete case is also limited to the extinction time 𝑇𝑇 and 𝔼𝔼𝑇𝑇. In this paper, both of the two cases were studied more thoroughly: for the discrete case, a limit theorem of the process has been proved; for the continuous case, the existence of Markovian threshold processes has been proved, and an equivalent condition for the process to extinct almost surely was also given. This paper also further generalized discrete time threshold processes by giving a random delay to the threshold’s influence of offspring distribution. The properties of these delayed threshold processes were studied, and a limit theorem was obtained.

Structural variations in genome could be more critical than SNP (Single-Nucleotide Polymorphism) in causing tumor cells, immune system diseases and fatness. It is necessary and important to detect structural variations with next generation sequencing data by means of efficient and accurate algorithms. This paper introduced a new algorithm using k-mers (short fragments of genome), string algorithms and graph algorithms, which combines similarity check, variation detection with sequence assembly. Our results showed that our method has high accuracy and it is more reliable than methods using reference and more efficient than popular algorithms.