Planar graphs without specific cycles are 2-degenerate

A graph G is k-degenerate if each subgraph of G has a vertex of degree at most k. It is known that every simple planar graph with girth 6, or equivalently without 3-, 4-, and 5-cycles, is 2-degenerate. In this work, we investigate for which k every planar graph without 4-, 6-, … , and 2k-cycles is 2-degenerate. We determine that k is 5 and the result is tight since the truncated dodecahedral graph is a 3-regular planar graph without 4-, 6-, and 8-cycles. As a related result, we also show that every planar graph without 4-, 6-, 9-, and 10-cycles is 2-degenerate.     

Limit cycle bifurcations of planar piecewise differential systems with three zones

This paper considers the limit cycle bifurcation problem of planar piecewise differential systems with three zones. Some computation formulas studied the problem of limit cycle bifurcations are provided by introducing multiple parameters. As an application to the obtained method, the number of limit cycles of a piecewise linear system with three zones studied in Lima et al. (2017) is discussed and some more limit cycles are found.     

The planar discontinuous piecewise linear refracting systems have at most one limit cycle

In this paper we investigate the limit cycles of planar piecewise linear differential systems with two zones separated by a straight line. It is well known that when these systems are continuous they can exhibit at most one limit cycle, while when they are discontinuous the question about maximum number of limit cycles that they can exhibit is still open. For these last systems there are examples exhibiting three limit cycles.The aim of this paper is to study the number of limit cycles for a special kind of planar discontinuous piecewise linear differential systems with two zones separated by a straight line which are known as refracting systems. First we obtain the existence and uniqueness of limit cycles for refracting systems of focus-node type. Second we prove that refracting systems of focus–focus type have at most one limit cycle, thus we give a positive answer to a conjecture on the uniqueness of limit cycle stated by Freire, Ponce and Torres in Freire et al. (2013). These two results complete the proof that any refracting system has at most one limit cycle.     

Hopf Bifurcation Analysis for a Delayed Business Cycle Model-The Equivalence of Multiple Time Scales Versus Center Manifold Reduction Methods

In this paper, we study the Hopf bifurcation of a model with a second order term, which is the business cycle model with delay. Multiple time scales method, which is mainly used by the engineering researchers, and center manifold reduction method, which is mainly used by researchers from mathematical society, are used to derive the two types of normal forms near the Hopf critical point. A comparison between the two methods shows that the two normal forms are equivalent. Scholars can derive the normal form by choosing appropriate methods according to their actual demands. Moreover, bifurcation analysis and numerical simulations are given to verify the analytical predictions.     

Design of the pulse duty cycle of the pseudolite signal in local area augmentation systems

The short-pulse TDMA signal is an excellent solution to the near-far problem in the pseudolite augmentation systems,and the pulse duty cycle is an important element in the solution.This paper aims at designing the duty cycle of the pseudolite pulse signals with a theoretical method.At first,the scope of the duty cycle is derived theoretically with the object of ensuring the reception of both the pseudolite signals and the satellite signals,and the expression for the theoretical upper limit is given.Then bas...     

A risk forecasting process for nanostructured materials, and nanomanufacturing

Nanomaterials exhibit novel properties that enable new applications ranging from molecular electronics to energy production. Proactive consideration of the potential impacts on human health and the environment resulting from nanomaterial production and use requires methods for forecasting risk associated with of these novel materials. However, the potential variety of nanomaterials is virtually infinite and a case-by-case analysis of the risks these materials may pose is not possible. The challenge of forecasting risk for a broad number of materials is further complicated by large degrees of uncertainty concerning production amounts, the characteristics and uses of these materials, exposure pathways, and a scarcity of data concerning the relationship between nanomaterial characteristics and their effects on organisms and ecosystems. A traditional risk assessment on nanomaterials is therefore not possible at this time. In its place, an evolving process is needed for analyzing the risks associated with emerging nanomaterials-related industries.In this communication, we propose that such a process should include the following six key features: (1) the ability to generate forecasts and associated levels of uncertainty for questions of immediate concern; (2) a consideration of all pertinent sources of nanomaterials; (3) an inclusive consideration of the impacts of activities stemming from nanomaterial use and production that extends beyond the boundaries of toxicology and include full life cycle impacts; (4) the ability to adapt and update risk forecasts as new information becomes available; (5) feedback to improve information gathering; and (6) feedback to improve nanomaterial design. Feature #6 implies that the potential risks of nanomaterials must ultimately be determined as a function of fundamental, quantifiable properties of nanomaterials, so that when these properties are observed in a new material, they can be recognized as indicators of risk. Thus, the required risk assessment process for nanomaterials addresses needs that span from urgent, short-term questions dealing with nanomaterials currently in commerce, to longer-term issues that will require basic research and advances in theory. In the following sections we outline issues surrounding each of these six features and discuss.     

中国企业生命表矛盾现象的数学解释与启示

以企业生命周期理论为依据,对比分析中国企业生命表与中国人寿保险业经验生命表(1990-1993)(男女混合),提出中国企业生命表的矛盾现象,并对此现象做出了数学解释,得出这一矛盾现象是由于中国企业低龄的高死亡率造成的,并依此提出相应的几点启示.     

FIVE LIMIT CYCLES TO A CLASS OF SYSTEMS IN R~3

In this paper, a bridge between near-homogeneous and homogeneous vector fields in R 3 is found. By the relationship between homogeneous vector fields and the induced tangent vector fields of two-dimensional manifold S 2 , we prove the existence of at least 5 isolated closed orbits for a class of n + 1 (n ≥ 2) systems in R 3 , which are located on the five invariant closed cones of the system.     

基于谱分析的波罗的海干散货运价指数周期研究

对于航运市场周期波动规律的研究有利于航运市场经营者更好地把握市场运行态势,规避市场风险。本文主要以波罗的海干散货运价指数(BFI/BDI)为研究对象,运用谱分析的方法分别研究了运价指数每日数据和月度数据的周期特征,结论是1985年-1999年BFI具有两年、一年、半年的周期成分;1999年-2009年BDI具有三年、一年、半年的周期成分。     

最小度不小于3的图的圈长问题

Bondy和Vince曾证明最小度不小于3的图包含两个长度相差为1或者2的圈,这个结果回答了ErdSs提出的问题．Haggkvist和scott证明了除肠外,所有的3-正则图都包含两个长度相差2的圈．通过不同的方法,我们得到了下面的结论：除了每个端块都是硒的图外,所有最小度不小于3的图都包含两个长度相差2的圈．