Rotational Activity around an Obstacle in 2D Cardiac Tissue in Presence of Cellular Heterogeneity

Waves of electrical excitation rotating around an obstacle is one of the important mechanisms of dangerous cardiac arrhythmias occurring in the heart damaged by a post-infarction scar. Such a scar is also surrounded by the region of heterogeneity called a gray zone. In this paper, we perform the first comprehensive numerical study of various regimes of wave rotation around an obstacle surrounded by a gray zone. We use the TP06 cellular ionic model for human cardiomyocytes and study how the period and the pattern of wave rotation depend on the radius of a circular obstacle and the width of a circular gray zone. Our main conclusions are the following. The wave rotation regimes can be subdivided into three main classes: (1) functional rotation, (2) scar rotation and the newly found (3) gray zone rotation regimes. In the scar rotation regime, the wave rotates around the obstacle, while in the gray zone regime, the wave rotates around the gray zone. As a result, the period of rotation is determined by the perimeter of the scar, or gray zone perimeter correspondingly. The transition from the scar to the gray rotation regimes can be determined from the minimal period principle, formulated in this paper. We have also observed additional regimes associated with two types of dynamical instabilities which may affect or not affect the period of rotation. The results of this study can help to identify the factors determining the period of arrhythmias in post-infarction patients.

Periodic Solutions with Prescribed Minimal Period for 2 n th-Order Nonlinear Discrete Systems

In this paper, by using the critical point theory, some new results of the existence of at least two nontrivial periodic solutions with prescribed minimal period to a class of 2 n th-order nonlinear discrete system are obtained. The main approach used in our paper is variational technique and the linking theorem. The problem is to solve the existence of periodic solutions with prescribed minimal period of 2 n th-order discrete systems.

Periodic solutions with prescribed minimal period for second order even Hamiltonian systems

<p style='text-indent:20px;'>In this paper, we develop a new method to study Rabinowitz's conjecture on the existence of periodic solutions with prescribed minimal period for second order even Hamiltonian system without any convexity assumptions. Specifically, we first study the associated homogenous Dirichlet boundary value problems for the discretization of the Hamiltonian system with given step length and obtain a sequence of nonnegative solutions corresponding to different step lengths by using discrete variational methods. Then, using the sequence of nonnegative solutions, we construct a sequence of continuous functions which can be shown to be precompact. Finally, by utilizing the limit function of convergent subsequence and the symmetry of the potential, we will obtain the desired periodic solution. In particular, we prove Rabinowitz's conjecture in the case when the potential satisfies a certain symmetric assumption. Moreover, our main result greatly improves the related results in the literature in the case where <inline-formula><tex-math id="M1">\begin{document}$ N = 1 $\end{document}</tex-math></inline-formula>.</p>

Periodic solutions with prescribed minimal period to Hamiltonian systems

In this article, we study the existence of periodic solutions to second order Hamiltonian systems. Our goal is twofold. When the nonlinear term satisfies a strictly monotone condition, we show that, for any $T>0$ T > 0 , there exists a T-periodic solution with minimal period T. When the nonlinear term satisfies a non-decreasing condition, using a perturbation technique, we prove a similar result. In the latter case, the periodic solution corresponds to a critical point which minimizes the variational functional on the Nehari manifold which is not homeomorphic to the unit sphere.

Moving Average Convergence-Divergence (MACD) Trading Rule: An Application in Nepalese Stock Market "NEPSE"

There are two types of analysis done for a stock market. One is fundamental analysis, where an investor looks at an intrinsic value of the stock, and another is technical analysis, where investors determine the future trend of the market looking at the current pattern or trend of the market. This paper is focused on one of the technical analysis tools, i.e., Moving Average Convergence-Divergence. It is a tool based on the three exponential moving average (9-12-26 EMA Rule). The MACD analysis, with the help of a single line, was helpful to find out the exact bullish and the bearish trend of the Nepse. A signal line is a benchmark to determine the stock market moving either to a bullish or bearish trend. It can help an investor, where the market is going in a direction. A market convergence, divergence, and crossover were better identified with the help of the MACD histogram. The paper found that the Nepse return was stable for a very minimal period from 1998-99 to 2019-20. The shift from the bullish to bearish or vice-verse were seen easily identified with the help of a MACD histogram. Finally, a better-combined knowledge of moving average and candlestick chart analysis will help an investor, to put a clear picture of a market trend with the help of MACD analysis.

Existence of periodic solutions with minimal period for fourth-order discrete systems via variational methods

By using critical point theory, some new existence results of at least one periodic solution with minimal period pM for fourth-order nonlinear difference equations are obtained. Our approach used in this paper is a variational method.

Tropical cycles

The Lyness equation (1) \begin{equation}{X_{n + 1}} = \frac{{{X_n} + a}}{{{X_{n - 1}}}},\,(a,{x_1},{x_2} > 0)\end{equation} was introduced in 1947 by Lyness [1] and it, and related equations, have long been studied; see [1, 2, 3, 4, 5, 6, 7] and references therein. Perhaps surprisingly, all solutions of (1) are bounded (i.e. for all x1, x2, the set {xn} is bounded) - we will show that below. Furhter, there often exist periodic solutions (i.e. xn = xn+N for all n in which case we say that (xn) has period N). See [8] for a discussion of which periods are possible for a given α. We note that a sequence of period, say, 5 also has periods 10, 15, 20, …. so we use the term minimal period for the smallest positive N such that xn = xn+N for all n.