Synthesis of 4-substituted glutarimides by free radical addition of iodoacetamide to α,β-unsaturated esters

Free radical addition of either methyl bromoacetate or iodoacetamide to an α,β,-unsaturated ester gave the 4-substituted glutarate or glutarimide respectively, whereas the radical cyclisation of N-bromoacetyl crotonamide gave the 2-substituted succinimide.     

Finslersche Zahlen

Ohne Zusammenfassung     

An algorithm for solving Fredholm integro-differential equations

The aim of this paper is to present an efficient numerical procedure for solving linear second order Fredholm integro-differential equations. The scheme is based on B-spline collocation and cubature formulas. The analysis is accompanied by numerical examples. The results demonstrate reliability and efficiency of the proposed algorithm.      

Diophantische Gleichungen und die universelle Eigenschaft Finslerscher Zahlen

Ohne Zusammenfassung     

The algebraic and geometric classification of associative algebras of dimension five

The scheme Alg₅ of associative, unitary algebra structures on k⁵, k an algebraically closed field with char (k)2 is investigated. We establish the list of GL₅-orbits on Alg₅ under the action of structural transport. The numberalg₅ of irreducible components of Alg₅ is 10; a list of generic structures is included. We exhibit upper and lower bounds for the asymptotic behaviour of the numberalg_n.     

Visualizing the Relationship between Two Time Series by Hierarchical Smoothing Models

Abstract

Let x(t_i), y(t_i) be two time series such that y(t_i) = μ(t_i, x) + ε_i, where μ is a smooth function and ε_i is a zero mean stationary process. Which model may be assumed for μ depends on the subject specific context. This article was motivated by questions raised in the context of musical performance theory. The general problem is to understand the relationship between the symbolic structure of a music score and its performance. Musical structure typically consists of a hierarchy of global and local structures. This motivates the definition of hierarchical smoothing models (or HISMOOTH models) that are characterized by a hierarchy of bandwidths b ₁ > b ₂ > … > b_M and a vector of coefficients β ∈ R^M. The expected value μ(t_i x) = E[y(t_i)‖x] is equal to a weighted sum of smoothed versions of x. The “errors” ε_i are modeled by a Gaussian process that may exhibit long memory. More generally, we may observe a collection of time series y_r (r = 1, …, N) that are related to a common time series x by y_r(t_i) = μ _r(t_i, x) + ε_{r, i} where ε _r are independent error processes. For repeated time series, HISMOOTH models lead to a visual and formal classification into clusters that can be interpreted in terms of the relationship to x. An analysis of tempo curves from 28 performances of Schumann's “Träumerei” op. 15/7 illustrates the method. In particular, similarities and differences of “melodic styles” can be identified.