AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.

Citation and bibliographic coupling between authors in the field of social network analysis

Purpose:We analyzed the structure of a community of authors working in the field of social network analysis(SNA)based on citation indicators:direct citation and bibliographic coupling metrics.We observed patterns at the micro,meso,and macro levels of analysis.Design/methodology/approach:We used bibliometric network analysis,including the“temporal quantities”approach proposed to study temporal networks.Using a two-mode network linking publications with authors and a one-mode network of citations between the works,we constructed and analyzed the networks of citation and bibliographic coupling among authors.We used an iterated saturation data collection approach.Findings:At the macro-level,we observed the global structural features of citations between authors,showing that 80%of authors have not more than 15 citations from other works.At the meso-level,we extracted the groups of authors citing each other and similar to each other according to their citation patterns.We have seen a division of authors in SNA into groups of social scientists and physicists,as well as into other groups of authors from different disciplines.We found some examples of brokerage between different groups that maintained the common identity of the field.At the micro-level,we extracted authors with extremely high values of received citations,who can be considered as the most prominent authors in the field.We examined the temporal properties of the most popular authors.Research limitations:The main challenge in this approach is the resolution of the author’s name(synonyms and homonyms).We faced the author disambiguation,or“multiple personalities”(Harzing,2015)problem.To remain consistent and comparable with our previously published articles,we used the same SNA data collected up to 2018.The analysis and conclusions on the activity,productivity,and visibility of the authors are relative only to the field of SNA.Practical implications:The proposed approach can be utilized for similar objectives and identifying key structures and characteristics in other disciplines.This may potentially inspire the application of network approaches in other research areas,creating more authors collaborating in the field of SNA.Originality/value:We identified and applied an innovative approach and methods to study the structure of scientific communities,which allowed us to get the findings going beyond those obtained with other methods.We used a new approach to temporal network analysis,which is an important addition to the analysis as it provides detailed information on different measures for the authors and pairs of authors over time.

Numerical Simulation and Parallel Computing of Acoustic Wave Equation in Isotropic-Heterogeneous Media

In this paper,we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media.The stability analysis of the scheme using the von Neumann stability method has been studied.We conducted a study on modeling the propagation of acoustic waves in a heterogeneous medium and performed numerical simulations in various heterogeneous media at different time steps.Developed parallel code using Compute Unified Device Architecture(CUDA)technology and tested on domains of various sizes.Performance analysis showed that our parallel approach showed significant speedup compared to sequential code on the Central Processing Unit(CPU).The proposed parallel visualization simulator can be an important tool for numerous wave control systems in engineering practice.

QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.

Numerical Simulation of Thermocapillary Convection with Evaporation Induced by Boundary Heating

The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.In particular,the cases of local heating from below and distributed thermal load from the lateral walls are considered.The simulation is carried out within the frame of a two-sided evaporative convection model based on the Boussinesq approximation.A benzine–air system is considered as reference system.The variation in time of the contact angle is described for both heating modes.Under lateral heating,near-wall boundary layers emerge together with strong convection,whereas the local thermal load from the lower wall results in the formation of multicellular motion in the entire volume of the fluids and the appearance of transition regimes followed by a steady-state mode.The results of the present study can aid the design of equipment for thermal coating or drying and the development of methods for the formation of patterns with required structure and morphology.

New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties

In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving.

Stability Study of Low Voltage Electrical Distribution Network: Audit and Improvement of DJEGBE Mini Solar Photovoltaic Power Plant in the Commune of OUESSE (Benin)

The supply of quality energy is a major concern for distribution network managers. This is the case for the company ASEMI, whose subscribers on the DJEGBE mini-power station network are faced with problems of current instability, voltage drops, and repetitive outages. This work is part of the search for the stability of the electrical distribution network by focusing on the audit of the DJEGBE mini photovoltaic solar power plant electrical network in the commune of OUESSE (Benin). This aims to highlight malfunctions on the low-voltage network to propose solutions for improving current stability among subscribers. Irregularities were noted, notably the overloading of certain lines of the PV network, implying poor distribution of loads by phase, which is the main cause of voltage drops;repetitive outages linked to overvoltage caused by lightning and overcurrent due to overload;faulty meters, absence of earth connection at subscribers. Peaks in consumption were obtained at night, which shows that consumption is greater in the evening. We examined the existing situation and processed the data collected, then simulated the energy consumption profiles with the network analyzer “LANGLOIS 6830” and “Excel”. The power factor value recorded is an average of 1, and the minimum value is 0.85. The daily output is 131.08 kWh, for a daily demand of 120 kWh and the average daily consumption is 109.92 kWh, or 83.86% of the energy produced per day. These results showed that the dysfunctions are linked to the distribution and the use of produced energy. Finally, we proposed possible solutions for improving the electrical distribution network. Thus, measures without investment and those requiring investment have been proposed.

Fluctuating Asymmetry of Elopes lacerta (Valenciennes, 1847) Otoliths in the Western African Waters

The importance of this study lies in the in-depth exploration of the ecological diversity of otoliths in Elopes lacerta, based on the analysis of data from 260 individuals collected from various sites, including the Porto Novo lagoon, the Cotonou lagoon, Lake Nokou, and the Atlantic coast in southern Benin. The results highlight significant variations in otolith morphology, establishing relevant links with the biological parameters of the fish at each site. Exploration of the asymmetry between the right and left sides reveals notable distinctions between these two aspects. Analysis of otolith shape thus emerges as a valuable tool for discriminating between stocks and providing a better understanding of ecological variations. The local diversity observed highlights the crucial importance of implementing adaptive management strategies to ensure effective conservation of the species and its habitat.

Analysis of Otolith Shape as a Tool for Discriminating Stocks of Cassava Croaker (Pseudotolithus senegalensis) in Beninese Waters

This study examined the right and left otoliths of 174 individuals of Pseudotolithus senegalensis from the Porto-Novo lagoon, Lake Nokoué and the Atlantic coast. The results show a significant variation in the population according to geographic location. Mixed-effects linear analysis showed no significant variation by site, side or sex (p > 0.05). Analysis of otolith shape using ANOVA showed significant differences for length, width and area (p 0.05). Canonical discriminant analysis revealed significant differences between sites (p < 0.05). Finally, shape analyses showed significant differences between sites (p = 0.0001) and between right and left sides (p = 0.007), but no difference by sex (p = 0.395). The study of otolith morphology is therefore proving to be a valuable tool for differentiating stocks and understanding ecological variations.

Convergence of a Generalized Riemann Problem Scheme for the Burgers Equation

In this paper,we study the convergence of a second-order finite volume approximation of the scalar conservation law.This scheme is based on the generalized Riemann problem(GRP)solver.We first investigate the stability of the GRP scheme and find that it might be entropy-unstable when the shock wave is generated.By adding an artificial viscosity,we propose a new stabilized GRP scheme.Under the assumption that numerical solutions are uniformly bounded,we prove the consistency and convergence of this new GRP method.

Hyperbolic Conservation Laws,Integral Balance Laws and Regularity of Fluxes

Hyperbolic conservation laws arise in the context of continuum physics,and are mathematically presented in differential form and understood in the distributional(weak)sense.The formal application of the Gauss-Green theorem results in integral balance laws,in which the concept of flux plays a central role.This paper addresses the spacetime viewpoint of the flux regularity,providing a rigorous treatment of integral balance laws.The established Lipschitz regularity of fluxes(over time intervals)leads to a consistent flux approximation.Thus,fully discrete finite volume schemes of high order may be consistently justified with reference to the spacetime integral balance laws.

Analysis of the COVID-19, Outbreak in Brazil Using Topological Weighted Centroid: An Intelligent Geographic Information System Approach

This study used Topological Weighted Centroid (TWC) to analyze the Coronavirus outbreak in Brazil. This analysis only uses latitude and longitude in formation of the capitals with the confirmed cases on May 24, 2020 to illustrate the usefulness of TWC though any date could have been used. There are three types of TWC analyses, each type having five associated algorithms that produce fifteen maps, TWC-Original, TWC-Frequency and TWC-Windowing. We focus on TWC-Original to illustrate our approach. The TWC method without using the transportation information predicts the network for COVID-19 outbreak that matches very well with the main radial transportation routes network in Brazil.

Contribution of Satellite Observations in the Optical and Microphysical Characterization of Aerosols in Burkina Faso, West Africa

In this work, we proceed to an optical and microphysical analysis of the observations reversed by the MODIS, SeaWiFS, MISR and OMI sensors with the aim of proposing the best-adapted airborne sensor for better monitoring of aerosols in Burkina Faso. To this end, a comparison of AOD between satellite observations and in situ measurements at the Ouagadougou site reveals an underestimation of AERONET AOD except for OMI which overestimates them. Also, an inter-comparison done based on the linear regression line representation shows the correlation between the aerosol models incorporated in the airborne sensor inversion algorithms and the aerosol population probed. This can be seen through the correlation coefficients R which are 0.84, 0.64, 0.55 and 0.054 for MODIS, SeaWiFS, MISR and OMI respectively. Furthermore, an optical analysis of aerosols in Burkina Faso by the MODIS sensor from 2001 to 2016 indicates a large spatial and temporal variability of particles strongly dominated by desert dust. This is corroborated by the annual and seasonal cycles of the AOD at 550 nm and the Angström coefficient measured in the spectral range between 412 nm and 470 nm. A zoom on a few sites chosen according to the three climatic zones confirms the majority presence of mineral aerosols in Burkina Faso, whose maxima are observed in spring and summer.

Strong Consistency of the Spline-Estimation of Probabilities Density in Uniform Metric

In the present paper as estimation of an unknown probability density of the spline-estimation is constructed, necessity and sufficiency conditions of strong consistency of the spline-estimation are given.

UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Weighted approximation of functions with singularities by Bernstein operators

As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.

EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS

The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions.

Heisenberg Group and Energy-Momentum Conservative Law in de-Sitter Spaces—— In Memory of the 100th Anniversary of Einstein＇s Special Relativity and the 70th Anniversary of Dirac＇s de-Sitter Spaces

In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.

ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE

A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.

A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

Suppose f is a spirallike function of type β and order α on the unit disk D.Let Ωn,p1,p2,…,pn={z=（z2,z2,…,zn）′∈C^n：∑j=1^n｜zj）^Pj〈1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers.In this paper,we will prove that Φn,β2,γ2,…βn,γn（f）（z）=（f（z1）, preserves spirallikeness of type β and order α on Ωn,p1,p2,…,Pn.