The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.
In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with β=2 . Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.
The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.
In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with β=2 . Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.
Develop a comprehensive understanding of cardiac disease process Cardiovascular problems are on the rise in America. Care providers need to understand the overall clinical and statistical significance these life-changing events have to patients and families alike. Social Group Work with Cardiac Patients is a pragmatic guide that helps social workers and other psychosocial professionals develop and apply cardiac group work in a proactive and directed manner. This valuable text explores social group work with patients immediately recovering from a cardiac event—heart attack or failure, transplants, and implantable cardiac devices—as well the secondary effects of such events. Social Group Work with Cardiac Patients helps social work and healthcare professionals develop a comprehensive understanding of the psychosocial aspect of cardiac care. In addition to examining the correlation between cardiac disease and depression and anxiety, looking at the emotional aspects of heart disease, and providing an overview of social work group care, this unique text details the four core social groups—cognitive-behavioral, psychoeducational, skill development, and interpersonal. Both fundamental and state-of-the-art, this comprehensive approach serves to enhance practice skills for immediate and constructive implementation. Important topics discussed in Social Group Work with Cardiac Patients also include: understanding adherence to cardiac health and psychosocial variables suggestions for using basic social groups and their development adherence issues associated with care stress management management of anger among patients holistic affects of cardiac disease on patients and families compliance, follow-up, and follow through substance abuse human sexuality differences between support groups and social group work models group leadership and co-leadership skills and many more! Social Group Work with Cardiac Patients is an asset as a pragmatic, relevant guide for development and actuation of both general social groups and specialty group treatment. An accessible and practical stand-alone text, Social Group Work with Cardiac Patients is ideal for mental health and substance abuse social workers, counselors, cardiac nurse specialists, cardiac treatment staff, and students of social work.
This revised edition puts the most current information about gas-handling systems and facilities at your fingertips. The authors channeled their classroom and field experience into this volume, which features many new sections such as: * Heat recovery units * Kinetic inhibitors and anti-agglomerators * Trays and packing for distillation and absorption towers * Compressor valves * Foundation design considerations for reciprocating compressors * Pressure vessel issues and components * Nox reduction in engines and turbines * Safety management systems This book walks you through the equipment and processes used in gas-handling operations to help you design and manage a production facility. Production engineers will keep this volume on the desktop for the latest information on how to DESIGN, SPECIFY, and OPERATE gas-handling systems and facilities. The book allows engineers with little or background in production facility design to easily locate details about equipment, processes, and design parameters. With this volume, you will more completely comprehend the techniques of handling produced fluids from gas wells so your facility can be more efficient and productive. * Revised edition puts the most current information about gas-handling systems at your fingertips * Features brand new sections!
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