New Self-Adaptive Inertial-Like Proximal Point Methods for the Split Common Null Point Problem

Symmetry plays an important role in solving practical problems of applied science, especially in algorithm innovation. In this paper, we propose what we call the self-adaptive inertial-like proximal point algorithms for solving the split common null point problem, which use a new inertial structure to avoid the traditional convergence condition in general inertial methods and avoid computing the norm of the difference between xn and xn−1 before choosing the inertial parameter. In addition, the selection of the step-sizes in the inertial-like proximal point algorithms does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms. The proposed algorithms provide enlightenment for the further development of applied science in order to dig deep into symmetry under the background of technological innovation.

Spatially Separated Electron and Proton Beams in a Simulated Solar Coronal Jet

Magnetic reconnection is widely accepted to be a major contributor to nonthermal particle acceleration in the solar atmosphere. In this paper we investigate particle acceleration during the impulsive phase of a coronal jet, which involves bursty reconnection at a magnetic null point. A test-particle approach is employed, using electromagnetic fields from a magnetohydrodynamic simulation of such a jet. Protons and electrons are found to be accelerated nonthermally both downwards toward the domain’s lower boundary and the solar photosphere, and outwards along the axis of the coronal jet and into the heliosphere. A key finding is that a circular ribbon of particle deposition on the photosphere is predicted, with the protons and electrons concentrated in different parts of the ribbon. Furthermore, the outgoing protons and electrons form two spatially separated beams parallel to the axis of the jet, signatures that may be observable in in-situ observations of the heliosphere.

Plasma Flow Generation due to the Nonlinear Alfvén Wave Propagation around a 3D Magnetic Null Point

The behavior of current density accumulation around the sharp gradient of magnetic field structure or a 3D magnetic null point and with the presence of finite plasma pressure is investigated. It has to be stated that in this setup, the fan plane locates at the xy plane and the spine axis aligns along the z-axis. Current density generation in presence of the plasma pressure that acts as a barrier for developing current density is less well understood. The shock-capturing Godunov-type PLUTO code is used to solve the magnetohydrodynamic set of equations in the context of wave-plasma energy transfer. It is shown that propagation of Alfvén waves in the vicinity of a 3D magnetic null point leads to current density excitations along the spine axis and also around the magnetic null point. Besides, it is pointed out the x component of current density has oscillatory behavior while the y and z components do not show this property. It is plausible that it happens because the fan plane encompasses separating unique topological regions, while the spine axis does not have this characteristic and is just a line without separate topological regions. Besides, current density generation results in plasma flow. It is found that the y component of the current density defines the x component of the plasma flow behavior, and the x component of the current density prescribes the behavior of the y component of the plasma flow.

A STRONG CONVERGENCE AND NUMERICAL ILLUSTRATION FOR THE ITERATIVE METHODS TO SOLVE A SPLIT COMMON NULL POINT PROBLEM AND A VARIATIONAL INEQUALITY IN HILBERT SPACES

Trong bài báo này, chúng tôi giới thiệu hai thuật toán lặp để giải bài toán không điểm chung tách và bài toán bất đẳng thức biến phân đơn điệu trong không gian Hilbert. Các bài toán này có nhiều ứng dụng quan trọng trong những lĩnh vực như xử lý tín hiệu, xử lý ảnh, điều khiển tối ưu và nhiều lĩnh vực khác của toán học cũng như trong đời sống. Các phương pháp mà chúng tôi đề xuất dựa trên phương pháp lặp Halper n và phương pháp xấp xỉ mềm đã được áp dụng để giải các bài toán điểm bất động và bất đẳng thức biến phân. Sự hội tụ mạnh của thuật toán đã được chứng minh cùng với một số điều kiện nhất định đặt lên các dãy tham số. Cuối cùng chúng tôi đưa ra một ví dụ số giải bài toán tối ưu trong không gian hữu hạn chiều để minh họa cho sự hội tụ của thuật toán.

Spanning the isogeny class of a power of an elliptic curve

Let E E be an ordinary elliptic curve over a finite field and g g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E g E^g . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E 3 E^3 and of the Igusa modular form in dimension 4 4 . We illustrate our algorithms with examples of curves with many rational points over finite fields.