Generalizations of p-valent functions via the hadamard product by Anil K. Soni

“…The author studies, among other things, the classes of p-valent functions R(α+p−1) where p is a positive integer and α is any integer with α+p>0. The author shows in particular that R(α+p)⊂R(α+p−1) and also obtains the radius of R(α+p) for the class R(α+p−1).…”
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Accelerating cryptographic computation with parallel computing mechanisms in Android platform by Ning FANG, Weibing CAO, Donghe NI, Guandong DI

“…Aiming to accelerate cryptographic computation in Android platform,parallel computing method is adopted.Utilizing RenderScript framework in Android platform,big integer multiplication operation is implemented in parallel,which provides efficient and fast basic operations for cryptographic schemes such as elliptic curve.Storage structure and computing logic are designed and implemented for parallel computation of big integer multiplication.Integers are decomposed and handled as matrix elements,so that all additive and multiplicative operations can be performed simultaneously,which provides accelerated intermediate result for multiplication operations.Experiment results show that,compared to the original Java library for big integers in the Android platform,the proposed method has distinctive advantage in execution time.…”
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On the Multiplicity of a Proportionally Modular Numerical Semigroup by Ze Gu

“…A proportionally modular numerical semigroup is the set Sa,b,c of nonnegative integer solutions to a Diophantine inequality of the form ax mod b≤cx, where a,b, and c are positive integers. …”
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Research on GPS geometry-based observational stochastic error model by Taoyun ZHOU, Baowang LIAN, Dongdong YANG, Yi ZHANG, Chenglin CAI

“…Aiming at the problem of not enough influencing factors were considered in traditional methods,a much more realistic stochastic model was built.In which error corrections were introduced into the geometry-based function model,an improved least squares variance component estimation (LS-VCE) algorithm with space-for-time was used to solve the model,two sets of real GPS data were collected to evaluate the performance of the model,and with which the carrier phase integer ambiguity was solved.The experimental results show that the proposed methods are superior to the traditional methods in terms of model accuracy,model solution complexity and integer ambiguity resolution.…”
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Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image by Yi-Fei Pu, Ji-Liu Zhou, Patrick Siarry, Ni Zhang, Yi-Guang Liu

“…The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. …”
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Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints by Dinesh B. Seenivasan, Alberto Olivares, Ernesto Staffetti

“…Multiple phases increase model complexity, and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. …”
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The Diophantine Equation 8x+py=z2 by Lan Qi, Xiaoxue Li

“…Using certain results of exponential Diophantine equations, we prove that (i) if p≡±3(mod  8), then the equation 8x+py=z2 has no positive integer solutions (x,y,z); (ii) if p≡7(mod  8), then the equation has only the solutions (p,x,y,z)=(2q-1,(1/3)(q+2),2,2q+1), where q is an odd prime with q≡1(mod  3); (iii) if p≡1(mod  8) and p≠17, then the equation has at most two positive integer solutions (x,y,z).…”
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Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems by Junhai Luo, Heng Liu

“…In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. …”
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Multiplierless discrete Fourier transform based on moments by LIU Zhen-bing, LIU Jian-guo, WANG Guo-you

“…A novel algorithm to perform Discrete Fourier Transform（DFT） multiplierlessly was proposed.First, by modular mapping and truncating Taylor series expansion, the DFT was expressed in the form of the product of the constants and discrete moments.Second, by performing appropriate bit operations and shift operations in binary system, the product could be transformed to some additions of integers.The proposed algorithm only involved integer additions and shifts because the discrete moments could be computed only by integer additions.The systolic VLSI was designed to perform the new algorithm, followed by complexity analysis.Compared with the state-of-the-art systolic structure, the proposed design was multiplierless and easier to implement with less hardware and time.The approach was also applicable to other discrete transforms.…”
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Cooperative spectrum sensing scheduling scheme based on discrete particle swarm optimization algorithm by Xing ZHANG, Ye WANG, Yi YANG, Qin-yu ZHANG

“…The statistical characteristics of the network state changes were analyzed by using the CTMC model.Considering the difference of each secondary user’s sensing ability,two integer programming problems on cooperative sensing scheduling scheme were established from two aspects:the primary users and the secondary users respectively.A discrete particle swarm optimization algorithm was proposed to solve the integer programming problems,and compared with the traditional random scheduling scheme and greedy scheduling scheme based on SNR.The simulation results show that the cooperative sensing scheduling scheme based on discrete particle swarm optimization algorithm is superior to random scheduling scheme and greedy scheduling scheme based on the SNR,which gets a higher spectrum sensing accuracy.…”
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Short Paper - The Binary Linearization Complexity of Pseudo-Boolean Functions by Walter, Matthias

“…Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. …”
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The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation by Fatih Yılmaz, Durmuş Bozkurt

“…Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. …”
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STABILITY ANALYSIS AND REPAIR OF STIFFENED COMPOSITE WALL SLAB WITH A DELAMINATONG AT THE STRINGER INTERFACE by ZHAO Jie, LU Hua, WANG MingChun

“…Full-scale static test of structures with Delaminatong has indicated that the integer load-carrying capability is determined by the stability of the wall slab. …”
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Structure of weakly periodic rings with potent extended commutators by Adil Yaqub

“…A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property that, for each x in R, there exists an integer n(x)>1 such that xn(x)=x is necessarily commutative. …”
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An Interesting Property of a Class of Circulant Graphs by Seyed Morteza Mirafzal, Ali Zafari

“…Suppose that Π=Cay(Zn,Ω) and Λ=Cay(Zn,Ψm) are two Cayley graphs on the cyclic additive group Zn, where n is an even integer, m=n/2+1, Ω=t∈Zn∣t  is  odd, and Ψm=Ω∪{n/2} are the inverse-closed subsets of Zn-0. …”
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An Identity in Commutative Rings with Unity with Applications to Various Sums of Powers by Miomir Andjić, Romeo Meštrović

“…We prove that for each positive integer k there holds ∑i=02k-1(-1)i2k-1i22k-1-iniS2k-1-i(A)=0. …”
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Simple power analysis attack against cryptosystems based on Montgomery algorithm by Gang GAN, Min WANG, Zhi-bo DU, Zhen WU

“…In particular, a SPA attack against RSA cryptosystem was showed based on large integer modular exponentiation. The results show that the attack algorithm is correct and effective.…”
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Study on distributed and dynamic resource management for delay-sensitive sensor network by Wei LIU, Jun LIU

“…The delay-aware dynamic resource management problem was investigated in sensor network,with a focus on resource allocation among the sensors and power control along the time.By taking account of average delay requirements and power constraints,the considered problem was formulated into a stochastic optimization problem.Inspired by Lyapunov optimization theory,the intractable stochastic optimization problem was transformed into a tractable deterministic optimization problem,which was a mixed-integer resource management problem.By exploiting the specific problem structure,the mixed-integer resource management problem was equivalently transformed into a single variable problem,and the cooperative distributed method was present to effectively solve it with guaranteed global optimality.Finally,a dynamic resource management algorithm was proposed to solve the original stochastic optimization problem.Simulation results show the performance of the proposed dynamic algorithm and reveal that there exists a fundamental tradeoff between delay requirements and power consumption.…”
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Computational Comparison of Exact Solution Methods for 0-1 Quadratic Programs: Recommendations for Practitioners by Richard J. Forrester, Noah Hunt-Isaak

“…This paper is concerned with binary quadratic programs (BQPs), which are among the most well-studied classes of nonlinear integer optimization problems because of their wide variety of applications. …”
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On Hilbert polynomial of certain determinantal ideals by Shrinivas G. Udpikar

“…The said Hilbert polynomial is completely determined by certain integer valued functions FD(m,p,a). In this paper we prove some important properties of these integer valued functions.…”
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