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We present here a new solution for the astronomical computation of the insolation quantities on Earth spanning from -250 Myr to 250 Myr. This solution has been improved with respect to La93 (Laskar et al. [CITE]) by using a direct integration of the gravitational equations for the orbital motion, and by improving the dissipative contributions, in particular in the evolution of the Earth–Moon System. The orbital solution has been used for the calibration of the Neogene period (Lourens et al. [CITE]), and is expected to be used for age calibrations of paleoclimatic data over 40 to 50 Myr, eventually over the full Palaeogene period (65 Myr) with caution. Beyond this time span, the chaotic evolution of the orbits prevents a precise determination of the Earth's motion. However, the most regular components of the orbital solution could still be used over a much longer time span, which is why we provide here the solution over 250 Myr. Over this time interval, the most striking feature of the obliquity solution, apart from a secular global increase due to tidal dissipation, is a strong decrease of about 0.38 degree in the next few millions of years, due to the crossing of the resonance (Laskar et al. [CITE]). For the calibration of the Mesozoic time scale (about 65 to 250 Myr), we propose to use the term of largest amplitude in the eccentricity, related to , with a fixed frequency of /yr, corresponding to a period of 405 000 yr. The uncertainty of this time scale over 100 Myr should be about , and over the full Mesozoic era.

Many industrial formulations such as detergents, paints, foodstuff and cosmetics contain both surfactants and polymers and their interaction govern many of the properties. This book is unique in that it discusses the solution chemistry of both surfactants and polymers and also the interactions between the two. The book, which is based on successful courses given by the authors since 1992, is a revised and extended version of the first edition that became a market success with six reprints since 1998. Surfactants and Polymers in Aqueous Solution is broad in scope, providing both theoretical insights and practical help for those active in the area. This book contains a thorough discussion of surfactant types and gives information of main routes of preparation. A chapter on novel surfactants has been included in the new edition. Physicochemical phenomena such as self-assembly in solution, adsorption, gel formation and foaming are discussed in detail. Particular attention is paid to the solution behaviour of surfactants and polymers containing polyoxyethylene chains. Surface active polymers are presented and their interaction with surfactants is a core topic of the book. Protein-surfactant interaction is also important and a new chapter deals with this issue. Microemulsions are treated in depth and several important application such as detergency and their use as media for chemical reactions are presented. Emulsions and the choice of emulsifier is discussed in some detail. The new edition also contains chapters on rheology and wetting. Surfactants and Polymers in Aqueous Solution is aimed at those dealing with surface chemistry research at universities and with surfactant formulation in industry.

Obtaining an electron-density map from X-ray diffraction data can be difficult and time-consuming even after the data have been collected, largely because MIR and MAD structure determinations currently require many subjective evaluations of the qualities of trial heavy-atom partial structures before a correct heavy-atom solution is obtained. A set of criteria for evaluating the quality of heavy-atom partial solutions in macromolecular crystallography have been developed. These have allowed the conversion of the crystal structure-solution process into an optimization problem and have allowed its automation. The SOLVE software has been used to solve MAD data sets with as many as 52 selenium sites in the asymmetric unit. The automated structure-solution process developed is a major step towards the fully automated structure-determination, model-building and refinement procedure which is needed for genomic scale structure determinations.

New software, OLEX2 , has been developed for the determination, visualization and analysis of molecular crystal structures. The software has a portable mouse-driven workflow-oriented and fully comprehensive graphical user interface for structure solution, refinement and report generation, as well as novel tools for structure analysis. OLEX2 seamlessly links all aspects of the structure solution, refinement and publication process and presents them in a single workflow-driven package, with the ultimate goal of producing an application which will be useful to both chemists and crystallographers.

Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

A statistical mechanical treatment of high polymer solutions has been carried out on the basis of an idealized model, originally proposed by Meyer, which is analogous to the one ordinarily assumed in the derivation of the ``ideal'' solution laws for molecules of equal size. There is obtained for the entropy of mixing of n solvent and N linear polymer molecules (originally disoriented), ΔS=−k[(n/β) ln v1+N ln v2] where v1 and v2 are volume fractions and β is the number of solvent molecules replaceable by a freely orienting segment of the polymer chain. This expression is similar in form to the classical expression for equal-sized molecules, mole fractions having been replaced by volume fractions. When the disparity between the sizes of the two components is great, this expression gives entropies differing widely from the classical values, which accounts for the large deviations of high polymer solutions from ``ideal'' behavior. The entropy of disorientation of a perfectly arranged linear polymer is found to be of the order of R cal. per chain segment. After introducing a suitable heat of mixing term, partial molal free energies are computed, and the calculations are compared with experimental data for all concentrations. Phase equilibria have been calculated in the region of partial miscibility. The theory predicts, in agreement with experiment, that the critical composition for partial miscibility lies at a low concentration of polymer. Low intrinsic viscosities of polymers dissolved in poor solvents are attributed to the tendency for the molecule to assume a more compact configuration in such an environment.

Abstract A simple analytic model is constructed to elucidate some basic features of the response of the tropical atmosphere to diabatic heating. In particular, there is considerable east‐west asymmetry which can be illustrated by solutions for heating concentrated in an area of finite extent. This is of more than academic interest because heating in practice tends to be concentrated in specific areas. For instance, a model with heating symmetric about the equator at Indonesian longitudes produces low‐level easterly flow over the Pacific through propagation of Kelvin waves into the region. It also produces low‐level westerly inflow over the Indian Ocean (but in a smaller region) because planetary waves propagate there. In the heating region itself the low‐level flow is away from the equator as required by the vorticity equation. The return flow toward the equator is farther west because of planetary wave propagation, and so cyclonic flow is obtained around lows which form on the western margins of the heating zone. Another model solution with the heating displaced north of the equator provides a flow similar to the monsoon circulation of July and a simple model solution can also be found for heating concentrated along an inter‐tropical convergence line.

Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closed-form solution to the least-squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 × 4 matrix. The elements of this matrix are combinations of sums of products of corresponding coordinates of the points.

Abstract Aqueous solutions of poly(N-isopropyl acrylamide) show a lower critical solution temperature. The thermodynamic properties of the system have been evaluated from the phase diagram and the heat absorbed during phase separation and the phenomenon is ascribed to be primarily due to an entropy effect. From viscosity, sedimentation, and light-scattering studies of solutions close to conditions of phase separation, it appears that aggregation due to formation of nonpolar and intermolecular hydrogen bonds is important. In addition, a weakening of the ordering effect of the water-amide hydrogen bonds as the temperature is raised contributes to the stability of the two-phase system.

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the Black-Scholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original Black-Scholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.

Macromolecular X-ray crystallography is routinely applied to understand biological processes at a molecular level. However, significant time and effort are still required to solve and complete many of these structures because of the need for manual interpretation of complex numerical data using many software packages and the repeated use of interactive three-dimensional graphics. PHENIX has been developed to provide a comprehensive system for macromolecular crystallographic structure solution with an emphasis on the automation of all procedures. This has relied on the development of algorithms that minimize or eliminate subjective input, the development of algorithms that automate procedures that are traditionally performed by hand and, finally, the development of a framework that allows a tight integration between the algorithms.

An expression for the viscosity of solutions and suspensions of finite concentration is derived by considering the effect of the addition of one solute-molecule to an existing solution, which is considered as a continuous medium.