Munich University of Applied Sciences

About: Munich University of Applied Sciences is a education organization based out in Munich, Germany. It is known for research contribution in the topics: Laser & Fiber Bragg grating. The organization has 3935 authors who have published 4819 publications receiving 71528 citations.

Singular value decomposition and least squares solutions

Abstract: Let A be a real m×n matrix with m≧n. It is well known (cf. [4]) that $$A = U\sum {V^T}$$ (1) where $${U^T}U = {V^T}V = V{V^T} = {I_n}{\text{ and }}\sum {\text{ = diag(}}{\sigma _{\text{1}}}{\text{,}} \ldots {\text{,}}{\sigma _n}{\text{)}}{\text{.}}$$ The matrix U consists of n orthonormalized eigenvectors associated with the n largest eigenvalues of AA T , and the matrix V consists of the orthonormalized eigenvectors of A T A. The diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values. We shall assume that $${\sigma _1} \geqq {\sigma _2} \geqq \cdots \geqq {\sigma _n} \geqq 0.$$ Thus if rank(A)=r, σ r+1 = σ r+2=⋯=σ n = 0. The decomposition (1) is called the singular value decomposition (SVD).

Smoothing by spline functions. II

Abstract: In this paper we generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence.

Mechanochemistry: the mechanical activation of covalent bonds.

Abstract: Regarding the activation of chemical reactions, today’s chemist is used to thinking in terms of thermochemistry, electrochemistry, and photochemistry, which is reflected in the organization and content of the standard physical chemistry textbooks. The fourth way of chemical activation, mechanochemistry, is usually less well-known. The purpose of the present review is to give a survey of the classical works in mechanochemistry and put the key mechanochemical phenomena into perspective with recent results from atomic force microscopy and quantum molecular dynamics simulations. A detailed historical account on the development of mechanochemistry, with an emphasis on the mechanochemistry of solids, was recently given by Boldyrev and Tkáčová.1 The first written document of a mechanochemical reaction is found in a book by Theophrastus of Ephesus (371-286 B.C.), a student of Aristotle, “De Lapidibus” or “On stones”. If native cinnabar is rubbed in a brass mortar with a brass pestle in the presence of vinegar, metallic mercury is obtained. The mechanochemical reduction probably follows the reaction:1-3 * To whom correspondence should be addressed. Telephone: ++49-89-289-13417. Fax: ++49-89-289-13416. E-mail: martin.beyer@ch.tum.de (M.K.B.); Telephone: ++49-89-12651417. Fax: ++49-89-1265-1480. E-mail: clausen-schaumann@ fhm.edu (H.C.-S.). † Technische Universität München. ‡ Institut für Strahlenschutz. § Current address: Munich University of Applied Sciences. HgS + Cu f Hg + CuS (1) Volume 105, Number 8