Hyper Catastrophe on 4-Dimensional Canards

When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.

The role of AFAP1-AS1 in mitotic catastrophe and metastasis of triple-negative breast cancer cells by activating the PLK1 signaling pathway

Triple-negative breast cancer(TNBC)is characterized by fast growth,high metastasis,high invasion,and a lack of therapeutic targets.Mitosis and metastasis of TNBC cells are two important biological behaviors in TNBC malignant progression.It is well known that the long noncoding RNA AFAP1-AS1 plays a crucial role in various tumors,but whether AFAP1-AS1 is involved in the mitosis of TNBC cells remains unknown.In this study,we investigated the functional mechanism of AFAP1-AS1 in targeting Polo-like Kinase 1(PLK1)activation and participating in mitosis of TNBC cells.We detected the expression of AFAP1-AS1 in the TNBC patient cohort and primary cells by in situ hybridization(ISH),northern blot,fluorescent in situ hybridization(FISH)and cell nucleus/cytoplasm RNA fraction isolation.High AFAP1-AS1 expression was negatively correlated with overall survival(OS),disease-free survival(DFS),metastasis-free survival(MFS)and recurrence-free survival(RFS)in TNBC patients.We explored the function of AFAP1-AS1 by transwell,apoptosis,immunofluorescence(IF)and patient-derived xenograft(PDX)models in vitro and in vivo.We found that AFAP1-AS1 promoted TNBC primary cell survival by inhibiting mitotic catastrophe and increased TNBC primary cell growth,migration and invasion.Mechanistically,AFAP1-AS1 activated phosphorylation of the mitosis-associated kinase PLK1 protein.Elevated levels of AFAP1-AS1 in TNBC primary cells increased PLK1 pathway downstream gene expression,such as CDC25C,CDK1,BUB1 and TTK.More importantly,AFAP1-AS1 increased lung metastases in a mouse metastasis model.Taken together,AFAP1-AS1 functions as an oncogene that activates the PLK1 signaling pathway.AFAP1-AS1 could be used as a potential prognostic marker and therapeutic target for TNBC.

Mitotic Catastrophe的研究进展

细胞死亡是多细胞生物生命过程中重要的生理或病理现象,可分为坏死和程序性细胞死亡,而后者根据死亡细胞的形态学和发生机制的不同又可分为凋亡、自吞噬和mitotic catastrophe,其中mitotic catastrophe是近年来才被揭示报道,是指细胞在有丝分裂过程中死亡的现象,是一种发生在细胞有丝分裂期由于异常的细胞分裂而导致的细胞死亡,它常常伴随着细胞有丝分裂检查点的异常和基因或纺锤体结构的损伤而发生。现对mitotic catastrophe及相关的调控机制进行综述。

Risk Measure and Premium Distribution on Catastrophe Reinsurance

In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer＇s retention is accumu- lated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simu- lations in R environment.

Establishment and Application of Assessment Indicator System of Agricultural Catastrophe Vulnerability

To give play to the role of agricultural catastrophe risk fund in spreading agricultural catastrophe risk,we select natural conditions,economic conditions,social conditions,as the external vulnerability assessment indicators;select commodity rate of agricultural products,substitutability of agricultural products,the extent of agricultural products being related to the national economy and the people's livelihood,as the internal vulnerability assessment indicators.We assign weight to indicators using Analytic Hierarchy Process,and establish assessment indicator system of agricultural catastrophe vulnerability,to analyze the compensation for losses of different agricultural products arising from agricultural catastrophe in different regions.And we take the case of rice in Sichuan Province,to demonstrate the role this indicator system.

Assessment of Flood Catastrophe Risk for Grain Production at the Provincial Scale in China Based on the BMM Method

Flood catastrophe risk assessment is imperative for the steady development of agriculture under the context of global climate change,and meanwhile,it is an urgent scientific issue need to be solved in agricultural risk assessment discipline.This paper developed the methodology of flood catastrophe risk assessment,which can be shown as the standard process of crop loss calculation,Monte Carlo simulation,the generalized extreme value distribution（GEV） fitting,and risk evaluation.Data on crop loss were collected based on hectares covered by natural disasters,hectares affected by natural disasters,and hectares destroyed by natural disasters using the standard equation.Monte Carlo simulation based on appropriate distribution was used to expand sample size to overcome the insufficiency of crop loss data.Block maxima model（BMM） approach based on the extreme value theory was for modeling the generalized extreme value distribution（GEV） of flood catastrophe loss,and then flood catastrophe risk at the provincial scale in China was calculated.The Type III Extreme distribution（Weibull） has a weighted advantage of modeling flood catastrophe risk for grain production.The impact of flood catastrophe to grain production in China was significantly serious,and high or very high risk of flood catastrophe mainly concentrates on the central and eastern regions of China.Given the scenario of suffering once-in-a-century flood disaster,for majority of the major-producing provinces,the probability of 10% reduction of grain output is more than 90%.Especially,the probabilities of more than 15% decline in grain production reach up to 99.99,99.86,99.69,and 91.60% respectively in Anhui,Jilin,Liaoning,and Heilongjiang.Flood catastrophe assessment can provide multifaceted information about flood catastrophe risk that can help to guide management of flood catastrophe.

CUSP CATASTROPHE MODEL OF INSTABILITY OF PILLAR IN ASYMMETRIC MINING

A simplified mechanical model of pillar-hang wall was established in asymmetric mining and instability of the system was discussed by means of potential energy principle and cusp catastrophe theory. The necessary-sufficient condition and the jump value of displacement of pillar and the released energy expressions were derived, which established foundation for quantifying of the instability of system. The results show that instability of the system is related to load and its stiffness distribution. The critical load increases with the increasing relative stiffness, and the system is more stable. On the contrary, the instability of system is likely to occur, and the released energy is larger in instability process, and the harm is more tremendous accordingly. Furthermore, an example was calculated, and the estimated results are in good agreement with the practical experience, which provide basis for mining order and arranging stope.

DESCRIPTION AND PREDICTION OF CATASTROPHE OF VIBRATION STATE FOR FAULTY ROTORS

A sudden increase of vibration amplitude with no foreboding often results in an abrupt breakdown of a mechanical system.The catastrophe of vibration state of a faulty rotor is a typical nonlinear phenomenon,and very difficult to be described and predicted with linear vibration theory.On the basis of nonlinear vibration and catastrophe theory,fhe eatastrophe of the vibration amplitude of the faulty rotor is described;a way to predict its emergence is developed.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

GEOGRAPHIC ENVIRONMENT CHANGE AND FLOOD CATASTROPHE IN HUAIHE RIVER BASIN DURING LAST 2000 YEARS

ＧＥＯＧＲＡＰＨＩＣ ＥＮＶＩＲＯＮＭＥＮＴ ＣＨＡＮＧＥ ＡＮＤ ＦＬＯＯＤ ＣＡＴＡＳＴＲＯＰＨＥ ＩＮ ＨＵＡＩＨＥ ＲＩＶＥＲ ＢＡＳＩＮ ＤＵＲＩＮＧ ＬＡＳＴ ２０００ ＹＥＡＲＳＹａｎｇＤａｙｕａｎ（杨达源）（ＤｅｐａｒｔｍｅｎｔｏｆＧ...

PRICING CATASTROPHE OPTIONS WITH COUNTERPARTY CREDIT RISK IN A REDUCED FORM MODEL

In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.

Simulation of maize drought degree in Xi'an City based on cusp catastrophe model

Drought generally has significant impacts on crops.It is essential to quantitatively evaluate the relationship between crop production and drought degree to provide technical support for drought disaster prevention.In this study,a drought degree index that can reflect the changes in precipitation,evapotranspiration,and soil moisture was developed on the basis of crop yield reduction rate.Four drought scenarios were set up to simulate the effects of meteorological drought on drought degree of crops at different growth stages.A cusp catastrophe model was constructed to analyze the mutation characteristics of the drought degree of maize at different growth stages under different meteorological drought conditions.Xi'an City in China was selected as the study area,and summer maize was selected as the research crop.Precipitation and crop yield data from 1951 to 2010 were used as the fundamental data to investigate drought degree mutation of summer maize.The results show that,under the meteorological drought conditions at the emergence-jointing stage,drought degree may change abruptly,and soil moisture content at the sowingemergence,jointing-tasseling,and tasseling-mature stages should be kept higher than 39%.

Roll stability catastrophe mechanism of a flooded ship on regular sea waves

Based on a typical one-free-degree ship roll motion equation, the cusp catastrophe model is built including the bifurca- tion set equation, splitting factor ＇u＇ and regular factor ＇v＇, where both ＇u＇ and ＇v＇ are further expressed with typical flooded ship parameters. Then, the roll catastrophe mechanism is analyzed mainly by means of ＇u＇, under the given parameters of a typical trawler boat. The aim of this research is to reveal the mutagenic mechanism of the roll stability and provide a reference for improving ship roll stability.

The Study of Chamber Rockburst by the CUSP Model of Catastrophe Theory

By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .

Research on Instability Mechanism and Type of Ore Pillar Based on the Fold Catastrophe Theory

The stability of ore pillar in mine is essential for the safe and efficient mining.Based on the energy evolvement rule in ore pillar and roadway roof system,the roadway roof and ore pillar are treated as energy release body and energy dissipation body,respectively.Therefore,the double-block mechanical model is established with energy dissipation body and energy release body,and the energy mechanism of ore pillar instability is obtained,based on the fold catastrophe mathematical theory.The research result indicates that the dynamic instability of ore pillar is a physical instability problem caused by the strain softening property of ore mass,and the instability type of ore pillar is determined by the stiffness parameter of double-block mechanical system.When the systematical stiffness parameter is greater than or equal to 1,the equilibrium position of double-block mechanical system passes through shaft K-1 or the origin,from branch 1 of unstable equilibrium state to branch 2 of stable equilibrium state by smooth transition,and the ore pillar shows quasi-static fracture.When the systematical stiffness parameter is less than 1,the equilibrium position of double-block system mutates from branch 1 of unstable equilibrium state to branch 2 of stable equilibrium state by jumping transition,and the ore pillar shows dynamic instability.The research result could provide theoretical guidance for the prevention measures of ore pillar instability.

MECHANISM AND CATASTROPHE THEORY ANALYSIS OF CIRCULAR TUNNEL ROCKBURST

Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock＇s ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.

Fold catastrophe model of strike-slip fault earthquake

Using a differential form of the potential energy function and taking the effect of work applied by external force in far field into account, the mechanism of strike-slip fault earthquake is analyzed. The research indicates that each characteristic displayed with a fold catastrophe model in the catastrophe theory corresPonds to a specific primary characteristic of the strike-slip fault earthquake. The fold catastrophe can describe the positions of starting and end points of a fault failure and the distance of fault dislocation. These include the description of stability of the surrounding rock-fault system before and after the earthquake. Two different illustrations about elastic energy releasing amount of the surrounding rock with the fault failure are shown with the primary characteristics mutually demonstrated. The intensity of strike-slip fault earthquake is related to the surrounding rock press and the stiffness ratio of surrounding rock and fault. The larger the surrounding rock press, the smaller the stiffness ratio. The larger the included angle between the tangential stress axis and the causative fault surface, the stronger the earthquake.

Analysis of main shock of thrust fault earthquake by catastrophe theory

The relationship between work and energy increment of a thrust fault system with quasi-static deformation can be decomposed into two parts： volume strain energy and deviation stress energy. The relationship between work and energy increment of the deviation stress of a simplified thrust fault system is analyzed based on the catastrophe theory. The research indicates that the characteristics displayed by the fold catastrophe model can appropriately describe the condition of earthquake generation, the evolvement process of main shock of thrust fault earthquake, and some important aftershock proper- ties. The bigger the surrounding press of surrounding rock is, the bigger the maximum principal stress is, the smaller the incidences of the potential thrust fault surface are, and the smaller the ratio between the tangential stiffness of surrounding rock and the slope is, which is at the inflexion point on the softened zone of the fault shearing strength curve. Thus, when earthquake occurrs, the larger the elastic energy releasing amount of sur- rounding rock is, the bigger the earthquake magnitude is, the larger the half distance of fault dislocation is, and the larger the displacement amplitude of end face of surrounding rock is. Fracturing and expanding the fault rock body and releasing the volume strain energy of surrounding rock during the earthquake can enhance the foregoing effects to- gether.

Are chaos and catastrophe theories relevant to environmental sciences?

Data acquired in the area of Environmental Sciences are by their very nature often discontinuous and abrupt. As such, the mathematical theories of catastrophe and chaos may be of use in analyzing such scientific data and in formulating mathematical models.

CATASTROPHE FRACTURE OF THIN-WALL PRESSURE TUBES

Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture vas established, and a critical condition associated with the model is given.