Preliminary Identification of a Prime Number Other Than 2 and 3, the Origin of Twin Prime Numbers, the Structure of the Chain of Prime Numbers and the Set of Prime Numbers Less Than a Given Integer

The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it Esp. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted Enp. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted Ep. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.

REGULARIZATION APPROACH FOR FAST INTEGER AMBIGUITY RESOLUTION OF MEDIUM-LONG BASELINE GPS NETWORK RTK

An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be improved by the regularized matrix. The relative floating ambiguity can be computed only by using the data of several epochs. Combined with the LAMBDA method, the new approach can correctly and quickly fix the integer ambiguity and the success rate is 100% in experiments. Through using measured data sets from four mediumlong baselines, the new method can obtain exact ambiguities only by the Ll-frequency data of three epochs. Compared with the existing methods, the improved method can solve the ambiguities of the medium-long baseline GPS network RTK only using L1-frequency GPS data.

A Modified Algorithm for Nonliear Integer Programming

Based on the analysis to the random sear ch algorithm of LUUS, a modified random directed integer search algorithm (MRDI SA) is given for first time. And a practical example is given to show that the adva ntage of this kind of algorithm is the reliability can’t be infuenced by the ini tial value X (0) and the start search domain R (0) . Besides, i t can be applied to solve the higher dimensional constrained nonlinear integer p rogramming problem.

基于Java BigInteger类的大整数运算应用

在许多应用场合都需要高精度的计算,这些计算问题超出了一般程序语言所能表示的最大范围,如精确到100位小数的黄金分割系数计算;在密码问题中的大素数问题;求解梅森素数问题等,都涉及大整数运算。应用Java提供的BigInteger类,可以较好地解决这些问题。研究了应用Java的BigInteger类计算高精度黄金分割系数、100位以上大素数计算、300位以内梅森素数计算问题,给出了Java程序。

Method of integer overflow detection to avoid buffer overflow

A simplified integer overflow detection method based on path relaxation is described for avoiding buffer overflow triggered by integer overflow. When the integer overflow refers to the size of the buffer allocated dynamically, this kind of integer overflow is most likely to trigger buffer overflow. Based on this discovery, through lightly static program analysis, the solution traces the key variables referring to the size of a buffer allocated dynamically and it maintains the upper bound and lower bound of these variables. After the constraint information of these traced variables is inserted into the original program, this method tests the program with test cases through path relaxation, which means that it not only reports the errors revealed by the current runtime value of traced variables contained in the test case, but it also examines the errors possibly occurring under the same execution path with all the possible values of the traced variables. The effectiveness of this method is demonstrated in a case study. Compared with the traditional buffer overflow detection methods, this method reduces the burden of detection and improves efficiency.

Solution for integer linear bilevel programming problems using orthogonal genetic algorithm

An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.

Hybrid particle swarm optimization with chaotic search for solving integer and mixed integer programming problems

A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.

The Integer Parts of a Nonlinear Form with Integer Variables and Mixed Powers 2 and 4

The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x12＋ λ2x22＋ λ3x34 are prime infinitely often for natural numbers x1, x2, x3.

Scheduling Step-Deteriorating Jobs on Parallel Machines by Mixed Integer Programming

Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.

An Exact Virtual Network Embedding Algorithm Based on Integer Linear Programming for Virtual Network Request with Location Constraint

Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in network virtualization. VNE is NP-hard and former VNE algorithms are mostly heuristic in the literature.VNE exact algorithms have been developed in recent years. However, the constraints of exact VNE are only node capacity and link bandwidth.Based on these, this paper presents an exact VNE algorithm, ILP-LC, which is based on Integer Linear Programming(ILP), for embedding virtual network request with location constraints. This novel algorithm is aiming at mapping virtual network request(VNR) successfully as many as possible and consuming less substrate resources.The topology of each VNR is randomly generated by Waxman model. Simulation results show that the proposed ILP-LC algorithm outperforms the typical heuristic algorithms in terms of the VNR acceptance ratio, at least 15%.

General Exact Penalty Functions in Integer Programming

In this paper, the general exact penalty functions in integer programming were studied. The conditions which ensure the exact penalty property for the general penalty function with one penalty parameter were given and a general penalty function with two parameters was proposed.

Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems

This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.

A secure image steganography algorithm based on least significant bit and integer wavelet transform

The rapid development of data communication in modern era demands secure exchange of information. Steganography is an established method for hiding secret data from an unauthorized access into a cover object in such a way that it is invisible to human eyes. The cover object can be image, text, audio,or video. This paper proposes a secure steganography algorithm that hides a bitstream of the secret text into the least significant bits（LSBs） of the approximation coefficients of the integer wavelet transform（IWT） of grayscale images as well as each component of color images to form stego-images. The embedding and extracting phases of the proposed steganography algorithms are performed using the MATLAB software. Invisibility, payload capacity, and security in terms of peak signal to noise ratio（PSNR） and robustness are the key challenges to steganography. The statistical distortion between the cover images and the stego-images is measured by using the mean square error（MSE） and the PSNR, while the degree of closeness between them is evaluated using the normalized cross correlation（NCC）. The experimental results show that, the proposed algorithms can hide the secret text with a large payload capacity with a high level of security and a higher invisibility. Furthermore, the proposed technique is computationally efficient and better results for both PSNR and NCC are achieved compared with the previous algorithms.

Extraordinary transmission and reflection in PT-symmetric two-segment-connected triangular optical waveguide networks with perfect and broken integer waveguide length ratios

By adjusting the waveguide length ratio, we study the extraordinary characteristics of electromagnetic waves propagating in one-dimensional(1D) parity-time-symmetric(PT-symmetric) two-segment-connected triangular optical waveguide networks with perfect and broken integer waveguide length ratios respectively. It is found that the number and the corresponding frequencies of the extremum spontaneous PT-symmetric breaking points are dependent on the waveguide length ratio. Near the extremum breaking points, ultrastrong extraordinary transmissions are created and the maximal can arrive at, respectively, 2.4079 × 10^14 and 4.3555 × 10^13 in both kinds of networks. However, bidirectional invisibility can only be produced by the networks with broken integer waveguide length ratio, whose mechanism is explained in detail from the perspective of photonic band structure. The findings of this work can be useful optical characteristic control in the fabrication of PT-symmetric optical waveguide networks, which possesses great potential in designing optical amplifiers,optical energy saver devices, and special optical filters.

Ground State Energy Calculations of Isoelectronic Series of He in Double-Zeta Approximation Using Coulomb Potential with Noninteger Indices

Using formulae for one- and two-electron integrals of Coulomb interaction potential fk （r） = r^-k with non-integer indices k established by one of the authors with the help of complete orthonormal sets of ψ^α-exponential-type orbitals （α = 1, 0,-1,-2,…）, we perform the calculations for isoelectronic series of the He atom containing nuclear charges from 2 to 10, where k = 1 - μ （-1 〈 μ 〈 0）. For this purpose we have used the double-zeta approximation, the configuration interaction and coupled-cluster methods employing the integer-n Slater-type orbitals as basis sets. It is demonstrated that the results of calculations obtained are better than the numerical Hartree-Fock values.

Optimal set integer programming algorithm for multiple maneuvering targets tracking in clutter

The aim of this paper is to solve the problems of multitarget tracking in clutter. Firstly, the data association of measurement-to-target is formulated as an integer programming problem. Through using the linear programming （LP） based branchand-bound method and adjusting the constraint conditions, an optimal set integer programming （OSIP） algorithm is then proposed for tracking multiple non-maneuvering targets in clutter. For the case of maneuvering targets, this paper introduces the OSIP algorithm into the filtering step of the interacting multiple model （IMM） algorithm resulting in the IMM based on OSIP algorithm. Extensive Monte Carlo simulations show that the presented algorithms can obtain superior estimations even in the case of high density noises.

A new all-zero 4×4 block determination rule for integer transform and quantization in AVS-M encoder

A new all-zero block determination rule was used to reduce the complexity of the AVS-M encoder. It reuses the sum of absolute difference of 4x4 block obtained from motion estimation or intra prediction as parameters so that the determination threshold need to be computed only once when quantization parameter (QP) is invariable for given video sequence. This method avoids a lot of computation for transform, quantization, inverse transform, inverse quantization and block reconstruction. Simulation results showed that it can save about 20%～50% computation without any video quality degradation.

Seismic data compression based on integer wavelet transform

Due to the particularity of the seismic data, they must be treated by lossless compression algorithm in some cases. In the paper, based on the integer wavelet transform, the lossless compression algorithm is studied. Comparing with the traditional algorithm, it can better improve the compression rate. CDF (2, n) biorthogonal wavelet family can lead to better compression ratio than other CDF family, SWE and CRF, which is owe to its capability in can- celing data redundancies and focusing data characteristics. CDF (2, n) family is suitable as the wavelet function of the lossless compression seismic data.

An Explicit Integer Programming Model of the Minimal Spanning Tree Problem for Digraphs with Asymmetric Weights

As far as the minimal spanning tree problem for the digraph with asymmetric weightsis concerned, an explicit integer programming model is proposed, which could be solved successfullyusing the integer programming packages such as LINDO, and furthermore this model is extendedinto the stochastic version, that is, the minimal spanning tree problem for the digraph with theweights is not constant but random variables. Several algorithms are also developed to solve themodels. Finally, a numerical demonstration is given.

Short-Term Scheduling of Combined Cycle Units Using Mixed Integer Linear Programming Solution

Combined cycle plants (CCs) are broadly used all over the world. The inclusion of CCs into the optimal resource scheduling causes difficulties because they can be operated in different operating configuration modes based on the number of combustion and steam turbines. In this paper a model CCs based on a mixed integer linear programming approach to be included into an optimal short term resource optimization problem is presented. The proposed method allows modeling of CCs in different modes of operation taking into account the non convex operating costs for the different combined cycle mode of operation.