Integral representation of Hermitian positive-matrix kernels of special structure

1989 ◽  
Vol 40 (5) ◽  
pp. 533-535
Author(s):  
M. V. Bekker
Keyword(s):  
Integral Representation ◽  
Special Structure ◽  
Positive Matrix ◽  
Matrix Kernels

A Perron-Frobenius-type Theorem for Positive Matrix Semigroups

Positivity ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 61-72
Author(s):  
L. Livshits ◽  
G. MacDonald ◽  
H. Radjavi
Keyword(s):  
Type Theorem ◽  
Positive Matrix ◽  
Matrix Semigroups

scholarly journals Geochemical Mapping, Risk Assessment, and Source Identification of Heavy Metals in Road Dust Using Positive Matrix Factorization (PMF)

Atmosphere ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 614
Author(s):  
Muhammad Faisal ◽  
Zening Wu ◽  
Huiliang Wang ◽  
Zafar Hussain ◽  
Chenyang Shen
Keyword(s):  
Heavy Metals ◽  
Risk Assessment ◽  
Matrix Factorization ◽  
Anthropogenic Activities ◽  
Contamination Factor ◽  
Road Dust ◽  
Positive Matrix Factorization ◽  
Prevention Measures ◽  
Positive Matrix ◽  
The City

Heavy metals in road dust pose a significant threat to human health. This study investigated the concentrations, patterns, and sources of eight hazardous heavy metals (Cr, Ni, Cu, Zn, As, Cd, Pb, and Hg) in the street dust of Zhengzhou city of PR China. Fifty-eight samples of road dust were analyzed based on three methods of risk assessment, i.e., Geo-Accumulation Index (Igeo), Potential Ecological Risk Assessment (RI), and Nemerow Synthetic Pollution Index (PIN). The results exhibited higher concentrations of Hg and Cd 14 and 7 times higher than their background values, respectively. Igeo showed the risks of contamination in a range of unpolluted (Cr, Ni) to strongly polluted (Hg and Cd) categories. RI came up with the contamination ranges from low (Cr, Ni, Cu, Zn, As, and Pb) to extreme (Cd and Hg) risk of contamination. The risk of contamination based on PIN was from safe (Cu, As, and Pb) to seriously high (Cd and Hg). The results yielded by PIN indicated the extreme risk of Cd and Hg in the city. Positive Matrix Factorization was used to identify the sources of contamination. Factor 1 (vehicular exhaust), Factor 2 (coal combustion), Factor 3 (metal industry), and Factor 4 (anthropogenic activities), respectively, contributed 14.63%, 35.34%, 36.14%, and 13.87% of total heavy metal pollution. Metal’s presence in the dust is a direct health risk for humans and warrants immediate and effective pollution control and prevention measures in the city.

Red phosphorus embedded in TiO2/C nanofibers to enhance the potassium-ion storage performance

Nanoscale ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 6635-6643
Author(s):  
Die Su ◽  
Jing Dai ◽  
Min Yang ◽  
Jiaxing Wen ◽  
Jianping Yang ◽  
...  
Keyword(s):  
Energy Storage ◽  
Electronic Conductivity ◽  
Potassium Ion ◽  
Special Structure ◽  
Red Phosphorus ◽  
Storage Performance ◽  
Ion Storage

TiO2-RP/CN was fabricated and found to possess a special structure and an excellent electronic conductivity, and the electrodes show outstanding energy storage in K half/full cells.

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

scholarly journals Noise-Reducing Fabric Electrode for ECG Measurement

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4305
Author(s):  
Takamasa Terada ◽  
Masahiro Toyoura ◽  
Takahide Sato ◽  
Xiaoyang Mao
Keyword(s):  
Special Structure ◽  
Electrode Impedance ◽  
Electrode Structure ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Chip Type ◽  
Low Pass ◽  
Filter Fabric

In this work, we propose a fabric electrode with a special structure that can play the role of a noise reduction filter. Fabric electrodes made of the conductive fabric have been used for long-term ECG measurements because of their flexibility and non-invasiveness; however, due to the large impedance between the skin and the fabric electrodes, noise is easily introduced into the ECG signal. In contrast to conventional work, in which chip-type passive elements are glued to the electrode to reduce noise, the proposed electrode can obtain a noise-reduced ECG by changing the structure of fabric. Specifically, the proposed electrode was folded multiple times to form a capacitor with a capacitance of about 3 nF. It is combined with the skin-electrode impedance to form a low-pass filter. In the experiment, we made a prototype of the electrodes and measured ECG at rest and during EMG-induced exercise. As a result, the SNR values at rest and during exercise were improved about 12.02 and 10.29 , respectively, compared with the fabric electrode without special structure. In conclusion, we have shown that changing the fabric electrode structure effectively removes noise in ECG measurement.

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