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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus…
Bakry Musa, Jiancheng Liu
In this paper, we investigate the space of L p p -harmonic 1-forms on a complete noncompact orientable δ -stable hypersurface M m that is immersed in space form with nonnegative BiRic curvature. We prove the nonexistence of L p p -harmonic 1-forms on M m . Mo…
Ze Zhu, Wanzhou Ye, Haijun Kuang
We proposed a generalized adaptive learning rate (GALR) PCA algorithm, which could be guaranteed that the algorithm’s convergence process would not be affected by the selection of the initial value. Using the deterministic discrete time (DDT) method, we gave…
Zuojun Hu
The 3 X + 1 problem (Collatz conjecture) has been proposed for many years, however no major breakthrough has been made so far. As we know, the Crandall conjecture is a well-known generalization of the 3 X + 1 problem. It is worth noting that, both conjectures…
Kung Kuen Tse
The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point P on the graph such that the tangent at P is parallel to the secant through the two endpoints. The mean value theorem for definite integ…
Maria E. X. Guimarães
The main purpose of this paper is to show that the Poincaré q -polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q -series elliptic genera can be expres…
Zigli David Delali, Obeng-Denteh William, Brew Lewis, Ansah Richard Kwame
The aim of this study is to establish that, the equivalent class which is made up of homotopic loops is a group with respect to in the general interval [ m , n ] . The study proved from homotopical point of view that is associative, has an identity and invers…
Shuilian Xie
Tensor complementarity problem (TCP) is a special kind of nonlinear complementarity problem (NCP). In this paper, we introduce a new class of structure tensor and give some examples. By transforming the TCP to the system of nonsmooth equations, we develop a s…
Qi Zhang
In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the ini…
Chuanmiao Chen, 1 1
This paper proves Riemann conjecture (RH), i.e ., that all the zeros in critical region of Riemann ξ -function lie on symmetric line σ =1/2 . Its proof is based on two important properties: the symmetry and alternative oscillation for ξ = u + iv . Denote . Ri…
Guoguang Lin, Lujiao Yang
In this paper, we studied the long-time properties of solutions of generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for the nonlinear source term g ( u ) and Kirchhoff stress term M ( s ) in the equatio…
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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
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