As recently recognized, distillation columns, operating with reflux and boilup as independent inputs, may have multiple steady-state solutions, even in the ideal binary case. Two fundamentally different sources may cause the multiplicity, and in both cases some operating points are found to be unstable. This article provides evidence for the instability and discusses the effect of operating con...

This paper reviews the rational addiction (RA) model of Becker and Murphy (1988) (BM) to demonstrate how its conclusions are based on assumptions about model parameters. The BM analysis emphasises the existence of an unstable steady state but the presumption of instability imposes strong restrictions on model parameters and is unlikely. Moreover, with two steady states (one stable, one unstable...

Eddying flow in the ocean develops as a result of baroclinic instability, and the environment in which the flow develops is vertically and horizontally inhomogeneous. A theory that takes into account the vertical inhomogeneities and predicts the magnitude and structure of the eddy potential vorticity flux for strongly baroclinically unstable mean shears is reviewed and extended to include the f...

The existing methods improved for the unstable objectives with dead time include Smith predictor, PID, IMC and others. There is little issue to deal with stabilization control of high order and unstable system with dead time. We employ the method of twice optimization control (TOC) for the unstable system with dead time. The factor e expands as a linear expression at first step. The controlled ...

This research examines the moderating roles of self-esteem level and self-esteem instability in the relationship between perceived unfair treatment and depressive mood. Based on the assumption that unfairness is a threat to one's social standing and self-esteem, the authors proposed that individuals with highly fragile self-esteem (i.e., the combination of unstable and high self-esteem) react m...

It is known that unit root test statistics may not have the usual asymptotic properties when the variance of innovations is unstable. In particular, persistent changes in volatility can cause the size of unit root tests to differ from the nominal level. In this paper we propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification...

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.  

Recognition of injuries to the cervical spine is of critical importance. Such injuries may be difficult to recognize in patients who have an altered level of consciousness or other significant injuries. We present the case of an alert ambulatory patient with no complaint of neck pain, no tenderness of the neck on physical examination, and , o history of trauma who, while being evaluated for fev...

The authors examined the notion that individuals with unstable high self-esteem possess implicit self-doubt. They adopted the framework of the biopsychosocial model of challenge and threat and assessed spontaneous cardiovascular reactions in the face of success versus failure performance feedback. Study 1 revealed predicted interactions between feedback condition, self-esteem level, and self-es...

Coronary angioplasty was performed in 53 patients in whom unstable angina had reoccurred after 48 hr and within 30 days after sustained myocardial infarction. Single-vessel disease was present in 64% of the patients and multivessel disease in 36%. The preceding myocardial infarction had been small to moderate in size in the majority of the patients. The left ventricular ejection fraction was mo...