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Bioengineering of the Skin
  • Language: en
  • Pages: 400

Bioengineering of the Skin

  • Type: Book
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  • Published: 1996-12-03
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  • Publisher: CRC Press

Through continuous research and development of modern instrumentation, it is now possible to visualize minute structures of the skin surface not visible to the human eye. Bioengineering of the Skin: Skin Surface Imaging and Analysis, written by an internationally based group of scientists, addresses engineering techniques for visualizing and analyzing skin surface images and profiles. This skin bioengineering reference offers comprehensive information about the technology of instruments in this field and the art of applying them in experimental studies. It explains what the instruments measure and why and when they should be used in skin research and product testing.

Radially Symmetric Patterns of Reaction-Diffusion Systems
  • Language: en
  • Pages: 102

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
  • Language: en
  • Pages: 128

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_{

Allergic to Life
  • Language: en
  • Pages: 186

Allergic to Life

This easy-to-read title provides a comprehensive discussion of the major changes in daily life that have led to states of increased bodily inflammation. Indeed, today there is an epidemic of allergic and autoimmune disease in the first and developing world. While outdoor climate change is now considered common knowledge, the impact of longer work hours, artificial lighting, increased food shelf life, and changes to the microbiome all have made a large impact in increasing allergies worldwide. An allergy, best defined as a “damaging response from the Immune system due to a substance in the environment,” starts with warning signals, or generalized "symptoms," that are caused by something i...

High Dimensional Probability
  • Language: en
  • Pages: 336

High Dimensional Probability

  • Type: Book
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  • Published: 2012-12-06
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  • Publisher: Birkhäuser

What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.

Linear Algebra
  • Language: en
  • Pages: 318

Linear Algebra

This textbook invites readers to dive into the mathematical ideas of linear algebra. Offering a gradual yet rigorous introduction, the author illuminates the structure, order, symmetry, and beauty of the topic. Opportunities to explore, master, and extend the theory abound, with generous exercise sets embodying the Hungarian tradition of active problem-solving. Determinants, matrices, and systems of linear equations begin the book. This unique ordering offers insights from determinants early on, while also admitting re-ordering if desired. Chapters on vector spaces, linear maps, and eigenvalues and eigenvectors follow. Bilinear functions and Euclidean spaces build on the foundations laid in ...

Probability in Banach Spaces, 9
  • Language: en
  • Pages: 422

Probability in Banach Spaces, 9

The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop erties that the processes share. The reward of research like this is that occasionally one can gain deep insight, ev...

Elliptic Partial Differential Operators and Symplectic Algebra
  • Language: en
  • Pages: 130

Elliptic Partial Differential Operators and Symplectic Algebra

This investigation introduces a new description and classification for the set of all self-adjoint operators (not just those defined by differential boundary conditions) which are generated by a linear elliptic partial differential expression $A(\mathbf{x}, D)=\sum_{0\, \leq\, \left s\right \, \leq\,2m}a_{s} (\mathbf{x})D DEGREES{s}\;\text{for all}\;\mathbf{x}\in\Omega$ in a region $\Omega$, with compact closure $\overline{\Omega}$ and $C DEGREES{\infty }$-smooth boundary $\partial\Omega$, in Euclidean space $\mathbb{E} DEGREES{r}$ $(r\geq2).$ The order $2m\geq2$ and the spatial dimensio

Some Generalized Kac-Moody Algebras with Known Root Multiplicities
  • Language: en
  • Pages: 137

Some Generalized Kac-Moody Algebras with Known Root Multiplicities

Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.

Exponentially Small Splitting of Invariant Manifolds of Parabolic Points
  • Language: en
  • Pages: 102