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991.
Let S={x1,…,xn} be a set of n distinct positive integers. For x,y∈S and y<x, we say the y is a greatest-type divisor of x in S if y∣x and it can be deduced that z=y from y∣z,z∣x,z<x and z∈S. For x∈S, let GS(x) denote the set of all greatest-type divisors of x in S. For any arithmetic function f, let (f(xi,xj)) denote the n×n matrix having f evaluated at the greatest common divisor (xi,xj) of xi and xj as its i,j-entry and let (f[xi,xj]) denote the n×n matrix having f evaluated at the least common multiple [xi,xj] of xi and xj as its i,j-entry. In this paper, we assume that S is a gcd-closed set and . We show that if f is a multiplicative function such that (f∗μ)(d)∈Z whenever and f(a)|f(b) whenever a|b and a,b∈S and (f(xi,xj)) is nonsingular, then the matrix (f(xi,xj)) divides the matrix (f[xi,xj]) in the ring Mn(Z) of n×n matrices over the integers. As a consequence, we show that (f(xi,xj)) divides (f[xi,xj]) in the ring Mn(Z) if (f∗μ)(d)∈Z whenever and f is a completely multiplicative function such that (f(xi,xj)) is nonsingular. This confirms a conjecture of Hong raised in 2004. 相似文献
992.
This paper considers the semi-resumable model of single machine scheduling with a non-availability period. The machine is
not available for processing during a given time interval. A job cannot be completed before the non-availability period will
have to partially restart after the machine has become available again. For the problem with objective of minimizing makespan,
the tight worst-case ratio of algorithm LPT is given, and an FPTAS is also proposed. For the problem with objective of minimizing total weighted completion time, an
approximation algorithm with worst-case ratio smaller than 2 is presented. Two special cases of the latter problem are also
considered, and improved algorithms are given. 相似文献
993.
Numerical Algorithms - The purpose of this paper is to study and analyze two different kinds of extragradient-viscosity-type iterative methods for finding a common element of the set of solutions... 相似文献
994.
Dionne Cross Francis Verily Tan Celeste Nicholas 《School science and mathematics》2019,119(7):382-395
In this paper, we examined students’ engagement in an implementation of a Workplace Simulation Project (WSP). The WSP was designed to actively engage students in learning disciplinary content by inviting engineers from industry to have a physical presence within the school building to collaborate with teachers and students to complete projects which simulate the tasks authentic to their work. We focus on the first year implementation of the program that partnered a high school in the rural Midwest with an engineering unit of a government organization. Using a multiple methods study design, we analyzed disciplinary and interdisciplinary pre and posts test along with students’ interviews to determine learning gains as well as students’ interpretations of creative and critical thinking as experienced in the project and their knowledge of the engineering design process. Effect sizes showed that students in the WSP group had notable gains over the control group participants. Additionally, students’ knowledge of core elements of the design process were identified in inductive analyses of the interviews. Findings from this study will provide usable knowledge about effective ways to support systems and design thinking and ways to support expert‐novice collaboration to ensure success. 相似文献
995.
Quang A. Dang Manh T. Hoang Deccy Y. Trejos Jose C. Valverde 《Mathematical Methods in the Applied Sciences》2019,42(18):7517-7527
In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations. 相似文献
996.
997.
Meccanica - A method for designing the key parameters of rotational centrifugal pendulum vibration absorbers is proposed herein. The vibration equations of the pendulum and rotor were established... 相似文献
998.
Tan Sandra S. Y. Varvitsiotis Antonios Tan Vincent Y. F. 《Journal of Optimization Theory and Applications》2021,190(1):56-81
Journal of Optimization Theory and Applications - We introduce a new framework for unifying and systematizing the performance analysis of first-order black-box optimization algorithms for... 相似文献
999.
Numerical Algorithms - In this paper, we consider a fully third-order nonlinear boundary value problem that is of great interest of many researchers. First, we establish the existence and... 相似文献
1000.
Xixi Wang Jiankai Shan Wei Liu Jing Li Hongwei Tan Xichen Li Guangju Chen 《Molecules (Basel, Switzerland)》2021,26(13)
In this work, we have investigated the binding conformations of the substrate in the active site of 5-HIU hydrolase kpHIUH and its catalytic hydrolysis mechanism. Docking calculations revealed that the substrate adopts a conformation in the active site with its molecular plane laying parallel to the binding interface of the protein dimer of kpHIUH, in which His7 and His92 are located adjacent to the hydrolysis site C6 and have hydrogen bond interactions with the lytic water. Based on this binding conformation, density functional theory calculations indicated that the optimal catalytic mechanism consists of two stages: (1) the lytic water molecule is deprotonated by His92 and carries out nucleophilic attack on C6=O of 5-HIU, resulting in an oxyanion intermediate; (2) by accepting a proton transferred from His92, C6–N5 bond is cleaved to completes the catalytic cycle. The roles of His7, His92, Ser108 and Arg49 in the catalytic reaction were revealed and discussed in detail. 相似文献