Magnetochemistry is concerned with the study of magnetic properties in materials. It investigates the relationship between the magnetic properties of chemical compounds and their atomic and molecular structure. This rapidly growing field has a number of applications, and the measuring and interpreting of magnetic properties is often conducted by scientists who are not specialists in the field. Magnetochemistry requires complex mathematics and physics and so can be daunting for those who have not previously studied it in depth. Aimed at providing a single source of information on magnetochemistry, this book offers a comprehensive and contemporary review of the mathematical background and formula for predicting or fitting magnetic data, including a summary of the theory behind magnetochemistry to help understand the necessary calculations. Along with tables listing the key formula, there is also a model of the magnetic functions showing the effect of individual magnetic parameters. The clear structure and comprehensive coverage of all aspects of magnetochemistry will make this an essential book for advanced students and practitioners.
This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.
A reproduction of the Edexcel a-level mathematics formula booklet. Photographs have been added to the formula booklet to make it more pleasing to read, rather than just the plain formulae. All formulae in this booklet are available for free from Edexcel directly in a pdf format. M1 and M4 have no given formulae within the formula booklet. This book also contains statistical tables relevant to the S1 through S4 specifications. This is an economy black and white print of a book intended to be viewed in full colour, thus quality will not be of the same standard as that of other editions.