scholarly journals Method of Binary Analytic Programming to Look for Optimal Mathematical Expression

2017 ◽  
Vol 103 ◽  
pp. 597-604 ◽  
Author(s):  
A.I. Diveev ◽  
N.B. Konyrbaev ◽  
E.A. Sofronova
Keyword(s):  
Mathematical Expression ◽  
Analytic Programming

Sense the pen: Classification of online handwritten sequences (text, mathematical expression, plot/graph)

2021 ◽  
Vol 172 ◽  
pp. 114588
Author(s):  
Junaid Younas ◽  
Muhammad Imran Malik ◽  
Sheraz Ahmed ◽  
Faisal Shafait ◽  
Paul Lukowicz
Keyword(s):  
Mathematical Expression

scholarly journals Correction for the Partial Volume Effects (PVE) in Nuclear Medicine Imaging: A Post-Reconstruction Analytic Method

2021 ◽  
Vol 11 (14) ◽  
pp. 6460
Author(s):  
Fabio Di Martino ◽  
Patrizio Barca ◽  
Eleonora Bortoli ◽  
Alessia Giuliano ◽  
Duccio Volterrani
Keyword(s):  
Nuclear Medicine ◽  
Imaging System ◽  
Tomographic Reconstruction ◽  
Mathematical Expression ◽  
Reconstruction Algorithm ◽  
Volume Effect ◽  
Nuclear Medicine Imaging ◽  
Theoretical Derivation ◽  
Reconstruction Process ◽  
Partial Volume

Quantitative analyses in nuclear medicine are increasingly used, both for diagnostic and therapeutic purposes. The Partial Volume Effect (PVE) is the most important factor of loss of quantification in Nuclear Medicine, especially for evaluation in Region of Interest (ROI) smaller than the Full Width at Half Maximum (FWHM) of the PSF. The aim of this work is to present a new approach for the correction of PVE, using a post-reconstruction process starting from a mathematical expression, which only requires the knowledge of the FWHM of the final PSF of the imaging system used. After the presentation of the theoretical derivation, the experimental evaluation of this method is performed using a PET/CT hybrid system and acquiring the IEC NEMA phantom with six spherical “hot” ROIs (with diameters of 10, 13, 17, 22, 28, and 37 mm) and a homogeneous “colder” background. In order to evaluate the recovery of quantitative data, the effect of statistical noise (different acquisition times), tomographic reconstruction algorithm with and without time-of-flight (TOF) and different signal-to-background activity concentration ratio (3:1 and 10:1) was studied. The application of the corrective method allows recovering the loss of quantification due to PVE for all sizes of spheres acquired, with a final accuracy less than 17%, for lesion dimensions larger than two FWHM and for acquisition times equal to or greater than two minutes.

scholarly journals Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 678 ◽  
Author(s):  
Yixuan Song ◽  
Fang Yuan ◽  
Yuxia Li
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Random Sequence ◽  
Mathematical Expression ◽  
Digital Signal ◽  
Approximate Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Key Space ◽  
Sequence Generator

In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

scholarly journals The WL_PCR: A Planning for Ground-to-Pole Transition of Wheeled-Legged Pole-Climbing Robots

Robotics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 96
Author(s):  
Yankai Wang ◽  
Qiaoling Du ◽  
Tianhe Zhang ◽  
Chengze Xue
Keyword(s):  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Process ◽  
Mathematical Expression ◽  
Truss Structure ◽  
Centre Of Mass ◽  
Climbing Robots ◽  
Wheeled Vehicle ◽  
Motion Modes

Hybrid mobile robots with two motion modes of a wheeled vehicle and truss structure with the ability to climb poles have significant flexibility. The motion planning of this kind of robot on a pole has been widely studied, but few studies have focused on the transition of the robot from the ground to the pole. In this study, a locomotion strategy of wheeled-legged pole-climbing robots (the WL_PCR) is proposed to solve the problem of ground-to-pole transition. By analyzing the force of static and dynamic process in the ground-to-pole transition, the condition of torque provided by the gripper and moving joint is proposed. The mathematical expression of Centre of Mass (CoM) of the wheeled-legged pole-climbing robots is utilized, and the conditions for the robot to smoothly transition from the ground to the vertical pole are proposed. Finally, the feasibility of this method is proved by the simulation and experimentation of a locomotion strategy on wheeled-legged pole-climbing robots.

scholarly journals The Influence of Filler Size and Crosslinking Degree of Polymers on Mullins Effect in Filled NR/BR Composites

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2284
Author(s):  
Miaomiao Qian ◽  
Bo Zou ◽  
Zhixiao Chen ◽  
Weimin Huang ◽  
Xiaofeng Wang ◽  
...  
Keyword(s):  
Particle Size ◽  
Strain Energy ◽  
Mathematical Expression ◽  
Rubber Matrix ◽  
Mullins Effect ◽  
Butadiene Rubber ◽  
Crosslinking Degree ◽  
Test Range ◽  
Two Factors ◽  
The Matrix

Two factors, the crosslinking degree of the matrix (ν) and the size of the filler (Sz), have significant impact on the Mullins effect of filled elastomers. Herein, the result. of the two factors on Mullins effect is systematically investigated by adjusting the crosslinking degree of the matrix via adding maleic anhydride into a rubber matrix and controlling the particle size of the filler via ball milling. The dissipation ratios (the ratio of energy dissipation to input strain energy) of different filled natural rubber/butadiene rubber (NR/BR) elastomer composites are evaluated as a function of the maximum strain in cyclic loading (εm). The dissipation ratios show a linear relationship with the increase of εm within the test range, and they depend on the composite composition (ν and Sz). With the increase of ν, the dissipation ratios decrease with similar slope, and this is compared with the dissipation ratios increase which more steeply with the increase in Sz. This is further confirmed through a simulation that composites with larger particle size show a higher strain energy density when the strain level increases from 25% to 35%. The characteristic dependence of the dissipation ratios on ν and Sz is expected to reflect the Mullins effect with mathematical expression to improve engineering performance or prevent failure of rubber products.

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