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861.
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
862.
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
863.
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
864.
865.
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
866.
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
867.
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
868.
Light incident onto an anisotropic crystal is divided into the ordinary and the extraordinary waves which vibrate in two perpendicular directions. Because of the tensor property of the dielectric constant, the direction of the electric displacement is not parallel to the vector of the incident electric field. An optical torque is induced by incidence of the linearly polarized light and propagating through the crystal. The optical torque tends to rotate the directions of eigenvibration which results in self-modulation of the ordinary and the extraordinary waves, and causes an energy splitting of the left (l)-, and the right (r)-handed circularly polarized waves in the crystal. The l- and the r-photons are correlated through the optical torque, which are found to be in an entanglement state. 相似文献
869.
ABSTRACT A new catalytic kinetic fluorescent quenching method for the determination of trace gold(III) was investigated. The method was based on the catalytic effect of gold on oxidation of 3-(3′-methylphenyl)-5- (2′-arsenoxylphenylazo) rhodanine by hydrogen peroxide in potassium hydrogen phthalate–hydrochloric acid (pH = 3.4). Under the optimum conditions, the great decrease of fluorescence intensity has a linear relationship against the concentration of gold in the range of 0 to 12.0 µg·L?1 with a detection limit of 6.0 × 10?10g·L?1. The coexistent metal ions can be separated, and gold can be enriched by TBP resin of solid-phase extraction, which greatly improves the selectivity and sensitivity of the system. The method can be used to determine trace amounts of gold in ore samples successfully with satisfactory results. 相似文献
870.
BaWO4-II has been synthesized at 5 GPa and 610°C. Its high pressure behavior was studied by in situ synchrotron X-ray diffraction measurements at room temperature up to 17 GPa. BaWO4-II retains its monoclinic structure. Bulk and axial moduli determined by fitting a third-order Birch–Murnaghan equation of state to lattice parameters are: K 0=86.2±1.9 GPa, K 0(a)=56.0±0.9 GPa, K 0(b)=85.3±2.4 GPa, and K 0(c)=146.1±3.2 GPa with a fixed K′=4. Analysis of axial compressible modulus shows that the a-axis is 2.61 times more compressible than the c-axis and 1.71 times more compressible than the b-axis. The beta angle decreases smoothly between room pressure and 17 GPa from 93.78° to 90.90°. 相似文献