This article studied the speed of addition and multiplication of natural number in different scale systems, the times of addition and multiplication in different scale systems have been compared quantificationally through a function model presented. The conclusion is that binary system is the best for addition, binary system and ternary system are better than other scale systems for multiplication, and they each has a suitable range.

In this paper, we study the decomposition of sets of consecutive integers, i.e., how to express the set {0, 1, . . . ,mn−1} as the Minkovski sum of two sets, one with m terms and the other with n terms. First, we translate the problem into the language of polynomials. Then we use the properties of cyclotomic polynomials to determine the structure of all the solutions. Then, we deduce formulas for the number of such expressions. Finally, we give an algorithm to calculate the number of such expressions and analyze its computational complexity.

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.

Forums have been one of the most important internet services since the 21st century. However, Forum users have to receive information in a passive way currently. The topics in forums are ordered by last update time (last reply time), thus the information that a user is interested in may be overwhelmed by a large number of other information. Users always have to scan many pages to find a minority of information they need. In this paper, based on the analysis of users' needs, I have designed a personalized forum topic ranking system. This personalized ranking system first calculates all the factors that will influence the user’s decision-making as to whether or not to view a topic by using his/her browsing history. Then the system predicts the click probability for each topic according to all the influence factors using a learned maximum entropy model. Finally, forum topics can be ranked by the predicted click probability, so as to make users find their favorite information easier. As shown by the experiments, the precision of the personalized ranking system is about 60% to 75%, which improves the traditional method (ordered by last update time) by 50% to 85%. In addition, with the normalization of the indicator functions of the maximum entropy model and the selection of the iterative endpoint, the training time can be lowered to an average of 0.01 seconds for each user. It indicates that such a model is able to meet the requirements of practical applications.

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