By L I Sedov London: Cleaver-Hume Press Ltd Pp xvi + 363 Price 105s This is really two separate books within the same pair of covers First of all Chapters 1-3, some 145 pages, are devoted to the discussion of similarity and dimensional, methods and their application to a variety of problems in mechanics and fluid mechanics

http://iopscience.iop.org/article/10.1088/0031-9112/11/6/008/pdf

Similarity and Dimensional Methods in Mechanics

This book is about the theoretical foundations of optimization algorithms, and also provides practical insights on how such methods should be implemented and applied. The goal of this text is not focused on in-depth details of state-of-the-art methods, but rather to provide a good foundation of the tried and trusted methods and how they can be used to solve real-world problems efficiently. The target audience for the text seems to be graduate students and engineers in industry as a good reference or self-study. However, it does not lend itself to easy adaption in a classroom setting due to the fact that only some chapters have problem sets and most chapters do not have a summary section. The book has four main parts each written by the one of the different authors. Two of the parts deal with standard unconstrained and constrained optimization techniques. The other two section deal with more complicated issues including solving problems that exhibit nonsmooth behavior and interior point methods. Solving optimization problems that have nonsmooth objectives or constraints is a formidable challenge because sensitivity information cannot be calculated using traditional approaches; the book provides a variety of ways to approach such problems. Interior point methods have been gaining popularity in the engineering optimization community for their efficiency and ability to maintain feasibility throughout the optimization process. There have been many textbooks written on the subject of numerical optimization. This book has the same flavor as many of these past books. A book with a very similar title by Nocedal and Wright [1] covered much of the same material, but it did not address nonsmooth problems. A classical book in the field by Flecther [2] considers nonsmooth problems but not interior point methods. Also, if one is more interested in comparing the performance of the various methods applied to engineering design problems, the book by Vanderplaats [3] may be more suitable. The appeal of this book is in the authors’ attention to detail and their advice on practical implementation issues. For many of the different optimization algorithms detailed flow charts are given. They also provide adequate examples to help the reader understand the methods better and explore possible pitfalls. There are, however, a few downsides of this book. The main one is that through translation of the book to English, it is evident that some of the finer points were lost and in some cases the text is hard to understand. The book could also have benefited from more figures; there are only 26. Finally, each of the dif

Numerical Optimization: Theoretical and Practical Aspects

￻￻ ￻ Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here on a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to ‘tip’ or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.

/pdf/tipping-points-in-open-systems-bifurcation-noise-induced-and-2qtvy441tg.pdf

Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

Given the square matrices $A, B, D, E$ and the matrix $C$ of conforming dimensions, we consider the linear matrix equation $A{\mathbf X} E+D{\mathbf X} B = C$ in the unknown matrix ${\mathbf X}$. Our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems, which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing.

/pdf/computational-methods-for-linear-matrix-equations-29c8rmvfvt.pdf

Computational Methods for Linear Matrix Equations

If a matrix or linear operator A is far from normal, its eigenvalues or, more generally, its spectrum may have little to do with its behavior as measured by quantities such as ||An|| or ||exp(tA)||. More may be learned by examining the sets in the complex plane known as the pseudospectra of A, defined by level curves of the norm of the resolvent, ||(zI - A)-1||. Five years ago, the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications. Since that time, analogous computations have been carried out for differential and integral operators. This paper, a companion to the earlier one, presents ten examples, each chosen to illustrate one or more mathematical or physical principles.

/pdf/pseudospectra-of-linear-operators-29doooi9kn.pdf

Pseudospectra of linear operators

We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second-order systems with fairly general operator coefficients and apply our bound to the perturbation of the damping term. The result is illustrated on a dissipative wave equation. As a consequence the exponential decay of some second-order systems is proved.

Bounds for Contractive Semigroups and Second-Order Systems

We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices which need not belong to either of these classes. Matrices of such structure arise in quantum models of possibly disordered systems with supersymmetry or graphene like symmetry. Some of the results immediately extend to infinite dimension.

/pdf/spectral-gap-estimates-for-some-block-matrices-2pmh7bssx3.pdf

Spectral gap estimates for some block matrices

In this paper we give an account of some recent results on the existence of wave operators for very general unperturbed operators and perturbations. In section 5 we give a completeness result under similar conditions for the case of dimension 1.

Scattering Theory for a General Class of Differential Operators

In this paper we consider the spectral concentration for a c1ass of J-selfadjoint operators which possess spectral decompositions like ordinary se1fadjoint operators. Let X be a Hilbert space with a scalar product (x, y) and the norm II x II = (x, X)1/2. Let T be a closed operator in X defined on 1) (T); by g (T), a (T), R ().,T), T*, R (T) we denote its resolvent set, spectrum, resolvent, adjoint and the range, respectively. If T is selfadjoint, E (t) denotes its spectral family (continuous from the right), while E (L1) denotes the speetral measure of a Borel set L1 from the real Irne.

/pdf/on-spectral-concentration-for-a-class-of-j-selfadjoint-83rrgha2o4.pdf

On spectral concentration for a class of j-selfadjoint operators

We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the generated semigroup is shown to be bounded by the upper real part of the numerical range of the underlying quadratic operator pencil.

Energy Decay of Damped Systems

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