scholarly journals A Study of the Second-Kind Multivariate Pseudo-Chebyshev Functions of Fractional Degree

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 978 ◽  
Author(s):  
Paolo Emilio Ricci ◽  
Rekha Srivastava
Keyword(s):  
Wide Class ◽  
Complex Matrices ◽  
R Matrix ◽  
Principal Value ◽  
Fixed Matrix ◽  
Chebyshev Functions

Here, in this paper, the second-kind multivariate pseudo-Chebyshev functions of fractional degree are introduced by using the Dunford–Taylor integral. As an application, the problem of finding matrix roots for a wide class of non-singular complex matrices has been considered. The principal value of the fixed matrix root is determined. In general, by changing the determinations of the numerical roots involved, we could find n r roots for the n-th root of an r × r matrix. The exceptional cases for which there are infinitely many roots, or no roots at all, are obviously excluded.

Pseudo-Lucas Functions of Fractional Degree and Applications

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 51
Author(s):  
Clemente Cesarano ◽  
Pierpaolo Natalini ◽  
Paolo Emilio Ricci
Keyword(s):  
Orthogonal Polynomial ◽  
Chebyshev Polynomials ◽  
Recent Article ◽  
Sum Rules ◽  
Jacobi Matrix ◽  
Fractional Powers ◽  
R Matrix ◽  
Representation Formulas ◽  
Chebyshev Functions

In a recent article, the first and second kinds of multivariate Chebyshev polynomials of fractional degree, and the relevant integral repesentations, have been studied. In this article, we introduce the first and second kinds of pseudo-Lucas functions of fractional degree, and we show possible applications of these new functions. For the first kind, we compute the fractional Newton sum rules of any orthogonal polynomial set starting from the entries of the Jacobi matrix. For the second kind, the representation formulas for the fractional powers of a r×r matrix, already introduced by using the pseudo-Chebyshev functions, are extended to the Lucas case.

THE ROLE OF POLYETHYLENIMINE IN ENHANCING PERFORMANCE OF GLUTAMATE BIOSENSORS

2018 ◽  
Vol 8 (3) ◽  
pp. 36-41
Author(s):  
Diep Do Thi Hong ◽  
Duong Le Phuoc ◽  
Hoai Nguyen Thi ◽  
Serra Pier Andrea ◽  
Rocchitta Gaia
Keyword(s):  
First Generation ◽  
Good Reproducibility ◽  
Complex Matrices ◽  
Long Term Stability ◽  
In Vitro Characterization ◽  
Glutamate Oxidase

Background: The first biosensor was constructed more than fifty years ago. It was composed of the biorecognition element and transducer. The first-generation enzyme biosensors play important role in monitoring neurotransmitter and determine small quantities of substances in complex matrices of the samples Glutamate is important biochemicals involved in energetic metabolism and neurotransmission. Therefore, biosensors requires the development a new approach exhibiting high sensibility, good reproducibility and longterm stability. The first-generation enzyme biosensors play important role in monitoring neurotransmitter and determine small quantities of substances in complex matrices of the samples. The aims of this work: To find out which concentration of polyethylenimine (PEI) exhibiting the most high sensibility, good reproducibility and long-term stability. Methods: We designed and developed glutamate biosensor using different concentration of PEI ranging from 0% to 5% at Day 1 and Day 8. Results: After Glutamate biosensors in-vitro characterization, several PEI concentrations, ranging from 0.5% to 1% seem to be the best in terms of VMAX, the KM; while PEI content ranging from 0.5% to 1% resulted stable, PEI 1% displayed an excellent stability. Conclusions: In the result, PEI 1% perfomed high sensibility, good stability and blocking interference. Furthermore, we expect to develop and characterize an implantable biosensor capable of detecting glutamate, glucose in vivo. Key words: Glutamate biosensors, PEi (Polyethylenimine) enhances glutamate oxidase, glutamate oxidase biosensors

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