Journal of Mathematics Research
ISSN / EISSN : 1916-9795 / 1916-9809
Published by: Canadian Center of Science and Education (10.5539)
Total articles ≅ 936
Latest articles in this journal
Published: 25 August 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n5p5
Equation of motion of a free particle in a space of constant curvature applies to many fields, such as the fixed reduction of the second member of the Burgers classes, the study of fusion of pellets, equations of Yang-Baxter, the concept of univalent functions as well as spheres of gaseous stability to mention but a few. In this study, the authors want to examine the linearization of the said equation using both point and non-point transformation methods. As captured in the title, the methods under examination here are the differential forms (DF) and the generalized Sundman transformations (GST), which are point and non-point transformation methods respectively. The comparative analysis of the solutions obtained via the two linearizability methods is also taken into account.
Published: 24 August 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n5p1
In this paper, we get a lower bound of the smallest singular value of an arbitrarily matrix A by the trace of H(A) and the Euclidean norm of H(A), where H(A) is Hermitian part of A, numerical examples show the e ectiveness of our results.
Published: 29 July 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n4p85
Let M be a smooth manifold and let D(M) be the module of first order differential operators on M. In this work, we give a link between Jacobi manifolds and Contact manifolds. We also generalize the notion of contactomorphism on M and thus, we characterize the Contact diffeomorphisms.
Published: 27 July 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n4p81
Let U be a nonempty set of R-modules and V be a submodule of ⊕_ʌU_λ, U_λ∈U for all λ∈Λ. A U_V generated module is a generalization of U-generated module by using the concept of V-coexact sequence. We say that an R-module N is generated by U_V if there is an epimorphism from V to N. In this paper, we introduce the definition of rank of U_V-generated modules. Furthermore, we investigate some properties of rank of UV-generated modules.
Published: 26 July 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n4p77
Inspired by the results that functions preserve orthogonality of full matrices, upper triangular matrices, and symmetric matrices. We finish the work by finding special orthogonal matrices which satisfy the conditions of preserving orthogonality functions. We give a characterization of functions preserving orthogonality of Hermitian matrices.
Published: 12 July 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n4p30
The freezing-thawing processes in soils are important components of terrestrial hydrology, which significantly influence energy and water exchanges between land surface and sub-surface. Long-term changes in frost and thaw depths are also an important indicator of climate change. A water-heat coupled movements model is established with frozen soil in this paper, which treats the freezing/thawing front as a moving interface governed by some Stefan problems with two free boundaries. The numerical simulation is conducted by using the modified finite difference method. The model is validated to compare its predictions with GEWEX Asian Monsoon Experiment(GAME)-Tibet observations at D66 site in Tibetan Plateau. The results show that the simulated soil temperature, soil water content and frost/thaw depth are in excellent agreement with the measured values. Finally, optimal error estimation for L^∞ norm is derived on the model problem by using coordinate transformation method. The numerical simulation system is established on the basis of rigorous mathematics and mechanics, which successfully solved the important and difficult problems of environmental science.
Published: 12 July 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n4p50
In this article, we analyze the real meteorological data recorded by Wenzhou Meteorological Bureau from 1951 to 1997. The data has not been used elsewhere and is available at Meteorological Station Wenzhou (ID: CHM00058659) at https://geographic.org/global_weather/china. We perform the time series volatility analysis including ARMA, ARIMA, ARCH-LM, PARCH, SARMA and Morlet wavelet analysis and use the Mann-Kendall (M-K) test to analyze both the trend and mutation defined by statistics sequence. In addition, a Morete wavelet time-frequency model is established to show that both the precipitation and temperature have a very important 12-month cycle and the precipitation is also very unstable. We then employ the STL, coif1 decompositions and NAR model to capture both the volatility and Heteroscedasticity in the data. In addition, the performance of the fitted model has been proven to be satisfactory on actual climate data with the small Mean Square Error (MSE), Root-Mean-Squarred Error (RMSE), and coefficient of determination. Finally, monthly average temperature is added as an exogenous (covariate) variable and a nonlinear autoregressive exogenous model is employed to improve the performance of the model. Our results show that the performance of NARX model is more accurate and stable with better mean square error.
Published: 24 June 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n4p19
We use the implicit Bogning function (iB-function) to proceed to a kind of inventory of the possible solutions of the modified nonlinear partial differential equation which characterizes the modified power line of Noguchi. Firstly, we make an inventory of the forms of solutions through a field of possible solutions, then we identify the most probable forms that we set out to look for. The iB-function is used because it summarizes within it several types of different functions depending on the choice of its characteristics and it is easy to handle in the case of strongly nonlinear partial differential equations. In other words, we use the notion of probability to locate, through the characteristic indices of iB-functions, the forms of solitary and traveling wave solutions likely to propagate in the modified Noguchi power line.
Published: 22 June 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n4p1
In this paper, a class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied. First, an existence-uniqueness result for the solution of general SDEsGp based on Poisson processes with т-periodic stochastic intensity of time t has been given, for some т> 0. Then, using the properties of periodic Markov processes, sufficient conditions for the existence and uniqueness of a periodic solution of the considered equations are obtained. We will then apply the obtained results to the propagation of malaria in a periodic environment.
Published: 30 May 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n3p65
Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 13, No. 3, 2021.