scholarly journals On Consecutive Perfect Powers with Elementary Methods

Author(s):  
Paolo Leonetti
Keyword(s):  
Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 318
Author(s):  
Jiafan Zhang ◽  
Yuanyuan Meng

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.


Author(s):  
Fei Wu ◽  
Ashley Phelps ◽  
Michael Hodges ◽  
Yiqiong Zhang ◽  
Xiaofen D. Keating ◽  
...  

Purpose: To review past research on teaching methods courses with preservice physical education teachers and preservice elementary classroom teachers. Method: This study was guided by the 2017 National Standards for Initial Physical Education Teacher Education. A thorough literature search was conducted using online databases, and a total of 28 articles were selected for review. Results: About two thirds of the reviewed studies were related to elementary methods courses, and 10.7% of the studies were quantitative. Perceptions and confidence in teaching physical education were the focus of studies for preservice elementary classroom teachers, while pedagogical knowledge development and restructuring was the primary emphasis for preservice physical education teachers via elementary methods course. Research on the secondary methods course yielded no salient themes. Conclusions: Research on the topic has been incongruent with the national standards. More experimental and quantitative studies are needed in the future.


Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 303 ◽  
Author(s):  
Zhao Jianhong ◽  
Chen Zhuoyu

The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.


Author(s):  
Francesco Rea ◽  
Francesco Amoroso ◽  
Rosario Pecora ◽  
Maria Chiara Noviello ◽  
Maurizio Arena

In the framework of Clean Sky 2 Airgreen 2 (REG-IADP) European research project, a novel multifunctional morphing flap technology was investigated to improve the aerodynamic performances of the next Turboprop regional aircraft (90 passengers) along its flight mission. The proposed true-scale device (5 meters span with a mean chord of 0.6 meters) is conceived to replace and enhance conventional Fowler flap with new functionalities. Three different functions were enabled: overall airfoil camber morphing up to +30° (mode 1), +10°/−10° (upwards/downwards) deflections of the flap tip segment (mode 2), flap tip “segmented” twist of ±5° along the outer flap span (mode 3). Morphing mode 1 is supposed to be activated during take-off and landing only to enhance aircraft high-lift performances and steeper initial climb and descent. Thanks to this function, more airfoil shapes are available at each flap setting and therefore a dramatic simplification of the flap deployment system may be implemented. Morphing modes 2 and 3 are enabled in cruise and off-design flight conditions to improve wing aerodynamic efficiency. The novel structural concept of the three-modal morphing Fowler flap (3MMF) was designed according to the challenges posed by real wing installation issues. The proposed concept consists of a multi-box arrangement activated by segmented ribs with embedded inner mechanisms to realize the transition from the baseline configuration to different target aero-shapes while withstanding the aerodynamic loads. Lightweight and compact actuating leverages driven by electromechanical motors were properly synthesized to comply with stringent requirements for real aircraft implementation: minimum actuating torque, minimum number of motors, reduced weight, and available design space. The methodology for the kinematic design of the inner mechanisms is based on a building block approach where the instant center analysis tool is used to preliminary select the locations of the hinges’ leverages. The final geometry of the inner mechanisms is optimized to maximize the mechanical advantage as well as to provide the kinematic performances required by the three different morphing modes. The load-path was evaluated, and the cross-sectional size of leverages was subsequently optimized. Finally, actuating torques predicted by instant center analysis were compared to the calculated values from finite element analysis. The structural sizing process of the multi-box arrangement was carried out considering elementary methods, and results were compared with finite element simulations.


The aim of this paper is to integrate Emmons & Brainerd’s equations analytically for arbitrary values of the Prandtl number and the Mach number, using the powerful asymptotic method of integration developed by the author in a previous paper (Meksyn 1948), dealing with the boundary layer in an incompressible fluid. It is shown here that in the first approximations the asymptotic integration gives ample accuracy and that it can be determined by simple and elementary methods. The results of this comparatively rapid calculation are in very satisfactory agreement with the results of the lengthy numerical calculations made by Emmons & Brainerd for certain specific values of Prandtl number and Mach number.


2019 ◽  
Vol 32 (02) ◽  
pp. 2030001 ◽  
Author(s):  
J. Avron ◽  
O. Kenneth

This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of [Formula: see text] qubits, the dimension is exponentially large in [Formula: see text]. The space of states can be visualized, to some extent, by its simple cross sections: Regular simplexes, balls and hyper-octahedra. a When the dimension gets large, there is a precise sense in which the space of states resembles, almost in every direction, a ball. The ball turns out to be a ball of rather low purity states. We also address some of the corresponding, but harder, geometric properties of separable and entangled states and entanglement witnesses. “All convex bodies behave a bit like Euclidean balls.” Keith Ball


1976 ◽  
Vol 13 (02) ◽  
pp. 392-399
Author(s):  
N. L. Johnson ◽  
Samuel Kotz

A generalized occupancy distribution obtained by Uppuluri and Carpenter (1971) is derived by elementary methods, and extended to a multivariate situation.


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