Convex separable minimization problems with a linear constraint and bounded variables by Stefan M. Stefanov

“…A necessary and sufficient condition and a sufficient condition are proved for a feasible solution to be an optimal solution to these two problems, respectively. Iterative algorithms of polynomial complexity for solving such problems are suggested and convergence of these algorithms is proved. …”
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Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings by Watcharaporn Cholamjiak, Suthep Suantai

“…We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. …”
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Dual Approximate Solutions of the Unsteady Viscous Flow over a Shrinking Cylinder with Optimal Homotopy Asymptotic Method by Vasile Marinca, Remus-Daniel Ene

“…A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.…”
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Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation by Osama Moaaz, Ali Muhib, Saud Owyed, Emad E. Mahmoud, Aml Abdelnaser

“…Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.…”
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Numerical algorithms for one parabolic-elliptic problem by Raimondas Čiegis, Remigijus Čiegis

“…This scheme is used as a classical splitting scheme in the parabolic region of the problem definition and as a new iterative algorithm in the elliptic part of the problem. …”
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Analysis of a HBV Model with Diffusion and Time Delay by Noé Chan Chí, Eric ÁvilaVales, Gerardo García Almeida

“…If the basic reproductive number is greater than unity, by means of an iteration technique, sufficiently conditions are obtained for the global asymptotic stability of the infected steady state. …”
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OPTIMAL DESIGN OF CRANK BASED ON BOX-BEHNKEN METHOD by CHEN HongWu, TIAN Cheng, PENG CongCong

“…Using BBD to optimize the structure and finish 49 iterations. Solid Works can’t fully fit the data. Design the BBD by DOE software Design-Expert and input the simulation data. …”
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A New Hybrid Algorithm for Solving a System of Generalized Mixed Equilibrium Problems, Solving a Family of Quasi-𝜙-Asymptotically Nonexpansive Mappings, and Obtaining Common Fixed... by J. F. Tan, S. S. Chang

“…The main purpose of this paper is to introduce a new hybrid iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, set of common fixed points of a family of quasi-𝜙-asymptotically nonexpansive mappings, and null spaces of finite family of 𝛾-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. …”
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Extended integer tent maps and dynamic hash function by LIU Jian-dong

“…Based on the analysis of uniform distribution property of the extended integer tent maps,a novel dynamic hash function with the output length of 160bit was constructed.In addition,the MD structure was improved so that the capacity of collision resistance of the middle iteration process of the hash function was enhanced without extending intermediate states.Preliminary security testing indicates that,this hash function has a high degree of security,and it can be realized easily with great rapidity.The algorithm of hash function is an ideal subsititution for traditional hash function.…”
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Asymptotic Properties of a Hepatitis B Virus Infection Model with Time Delay by Xiaohong Tian, Rui Xu

“…If the basic reproduction ratio is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the virus-infected equilibrium. …”
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Projected Adaptive Cubic Regularization Algorithm with Derivative-Free Filter Technique for Box Constrained Optimization by Lingyun He, Peng Wang, Detong Zhu

“…The affine scaling interior-point cubic model is based on the quadratic probabilistic interpolation approach on the objective function. The new iterations are obtained by the solutions of the projected adaptive cubic regularization algorithm with filter technique. …”
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INVESTIGATION OF HYDRAULIC OPERATIONAL REGIMES OF CIRCULATING SYSTEM AT THERMAL POWER PLANT OF VOLZHSKY AUTOMOTIVE WORKS USING COMPUTER MODEL by V. V. Dikop, A. V. Bukhtiarov, A. G. Kovalenko, V. V. Kotov, V. A. Kudinov

“…The models simulates hydraulic processes by means of an iterated solution of a set of algebraic non-linear equations that is formed while using a graph theory The circulating system is considered as a unit in the model. …”
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Controversies and future directions of endoscope in breast surgery by CAO Xuchen

“…Endoscope will become a new iterative tool in the field of breast surgery and is expected to provide a safer and minimally invasive way to serve more patients.…”
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Differential fault analysis on the SMS4 cipher by inducing faults to the key schedule by LI Wei, GU Da-wu

“…On the basis of the byte-oriented fault model and the differential analysis,a differential fault analysis on the SMS4 cipher by inducing faults in its key schedule was proposed.Mathematical analysis and simulating experiment show that the attack could recover its 128-bit secret key by introducing only eight faulty ciphertexts.Simultaneously,a method of distinguishing effective faults was presented to increase the efficiency of fault injection and decrease the num-ber of faulty ciphertexts.Thus,experiment results are beneficial to the analysis of other iterated block ciphers.…”
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An Efficient Variational Method for Image Restoration by Jun Liu, Ting-Zhu Huang, Xiao-Guang Lv, Si Wang

“…To solve this problem, we employ the split Bregman iteration method and the Chambolle’s algorithm. The convergence property of the algorithm is established. …”
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Rational-type fixed-point theorems in b-metric spaces and their application to economic growth and market equilibrium by Khaled Aldwoah, Syed Khayyam Shah, Alaa Mustafa, Mohammed A. Almalahi, Mohammed Hassan, Amer Alsulami

“…Utilizing the idea of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), novel fixed-point results are demonstrated via the iteration technique. Illustrative examples are presented to reinforce the authenticity and validity of the established results. …”
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Adaptive algorithm to compensate varying group_delay by YANG Zhi-xing, DENG Yong-jun, PAN Chang-yong, SONG Jian

“…A simple and effective adaptive algorithm was proposed to compensate varying group delay in data transmission employing baseband signal processing.Based on the structure of an all-digital parallel receiver（APRX）,the algorithm util-ized the gradient descent（GD）algorithm to iteratively minimize the cost function of constant modulus algorithm（CMA）,and updates the coefficients of group delay compensator.Simulation results show that the group delay can be effectively and adaptively compensated by the proposed algorithm,where the closed eye-diagram is opened successfully.…”
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Rapid Convergence for Telegraph Systems with Periodic Boundary Conditions by Peiguang Wang, Xiang Liu

“…We develop nonlinear iterates of order n-1 which will be different with n being even or odd. …”
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Modified Homotopy Perturbation Method for Solving Fractional Differential Equations by A. A. Hemeda

“…The obtained results reveal that this method is very effective and simple, accelerates the rapid convergence of the series solution, and reduces the size of work to only one iteration.…”
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Exploring multimodality, literacy and learning with young adult fiction by Melissa Schieble

“…A sociocultural approach to literacy instruction emphasizes meaning making as an iterative process between text and a reader's lived social, cultural and linguistic experiences. …”
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