Multidimensional analogues of the geometrics⇌t duality

Duality between Multidimensional Convolutional Codes and Systems

Multidimensional convolutional codes arise as a generalization of “classical” onedimensional codes. We will introduce m-dimensional convolutional codes of length n as submodules of Dn where D is the polynomial ring in m variables over a finite field. Besides their coding theoretic significance, they can also be regarded as the annihilating modules of systems of partial difference equations, the...

Esscher Transform and the Duality Principle for Multidimensional Semimartingales

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. ...

Preparation of the Phencyclidine Analogues (Part II)

Using a-tetralone, as starting material, a series of phencyclidine analogues were synthesized. This ketone was reacted separately with ethylmagnesium bromide, P-methoxyphenylmagnesium bromide and P-methylphenylmagnesium bromide. The resultant alcohols were treated with a suspension of NaN3 and CCl3COOH in CHCl3. The azides were subsequently...

Extensions of Classical Multidimensional Scaling: Variable Alternation and Nonconvex Duality∗

Classical multidimensional scaling constructs a configuration of points that minimizes a certain measure of discrepancy between the configuration’s interpoint distance matrix and a fixed dissimilarity matrix. Recent extensions have replaced the fixed dissimilarity matrix with a closed and convex set of dissimilarity matrices. These extensions lead to optimization problems with two sets of decis...

Trace, residue currents and multidimensional residues, duality and division