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The Research about Invariants of Ordinary Differential Equations
Readers acquainted with the differential calculus and the concept of a polynomial can effortlessly acquire an excellent perspective about invariants for differential equations by using a system of computer algebra to interact with the examples in Chapters 16 and 17. During the years 1879--1889, there were differential equations for which mathematicians found particular combinations of the coefficients that possessed an invariant character under unrestricted transformations. In fact, specific examples of basic relative invariants as the most interesting kind were discovered by E. Laguerre in 1879, G.-H. Halphen in 1880-1884, A. R. Forsyth in 1888, and P. Appell in 1989. However, there was lit...
Group-Pattern Matrices
This mathematical monograph uses the concept of a group-pattern throughout to conveniently characterize various matrices of unusual historical interest. While a reader should be able to add and multiply matrices in a suitable context, a prior knowledge about groups is not needed. Numerous multiplication tables for sets of n objects are presented in Chapter 1. When the formal definition of a group appears in Chapter 2, it has been well motivated. A group-pattern for a group G that has n elements is provided by the n x n interior of any multiplication table for G in which the identity element of G occupies each of the n principal diagonal positions. An n x n group-pattern matrix results when e...
Enhancing the Postdoctoral Experience for Scientists and Engineers
The concept of postdoctoral training came to science and engineering about a century ago. Since the 1960s, the performance of research in the United States has increasingly relied on these recent PhDs who work on a full-time, but on a temporary basis, to gain additional research experience in preparation for a professional research career. Such experiences are increasingly seen as central to careers in research, but for many, the postdoctoral experience falls short of expectations. Some postdocs indicate that they have not received the recognition, standing or compensation that is commensurate with their experience and skills. Is this the case? If so, how can the postdoctoral experience be enhanced for the over 40,000 individuals who hold these positions at university, government, and industry laboratories? This new book offers its assessment of the postdoctoral experience and provides principles, action points, and recommendations for enhancing that experience.
Radially Symmetric Patterns of Reaction-Diffusion Systems
Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.
Invariants of Boundary Link Cobordism
An $n$-dimensional $\mu$-component boundary link is a codimension $2$ embedding of spheres $L=\sqcup_{\mu}S DEGREESn \subset S DEGREES{n+2}$ such that there exist $\mu$ disjoint oriented embedded $(n+1)$-manifolds which span the components of $L$. This title proceeds to compute the isomorphism class of $C_{
Chromatin and Chromosomal Protein Research II
Chromatin and Chromosomal Protein Research II
The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra
In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.
Torus Fibrations, Gerbes, and Duality
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O} DEGREES{\times}$ gerbe over a genus one fibration which is a twisted form
