Four wave nonlinear optical mixing as real time holography

The phenomenon of four-wave optical mixing is an exact analog of the sequential operations of holographic recording and reconstruction. It should thus be possible to realize, in real time, holographic experiments and devices using such mixing.     

Percolation,fractals, and anomalous diffusion

Both the infinite cluster and its backbone are self-similar at the percolation threshold,p _c . This self-similarity also holds at concentrationsp nearp _c , for length scalesL which are smaller than the percolation connectedness length,. ForL<, the number of bonds on the infinite cluster scales asL ^D , where the fractal dimensionalityD is equal to(d-/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed.     

K-Theory for Triangulated Categories 3 1/2 (B): A Detailed Proof of the Theorem of Homological Functors Dedicated to Daniel Quillen and to the Memory of Robert Thomason

This article is a sequel to K-theory for triangulated categories 3 1/2 (A). In this article, we complete the proof of the main theorem of the previous article.     

A note on the equal division kernel and the α‐power model

The equal division kernel and the α‐power solution are two recently proposed theories of coalition formation in n‐person characteristic function games with sidepayments. A closed form solution for payoff disbursement is derived from the α‐power model for n‐person games with only 1, n‐1, and n‐person permissible coalitions and no weak players. It is shown that for this class of games, which are frequently employed to experimentally test theories of coalition formation, the equal division kernel is a special case of the α‐power model with α = 1/2.     

Optimal enlistment age: A cost–benefit analysis and some simulations

Enlistment at the earliest viable age maximizes the country’s wartime army size and thereby the country’s attack-deterrence capacity. Injuries and death generate a loss of quantity and quality of life that reduces the benefit from early-age enlistment. The benefit from any age of recruitment is also affected by the rise and decline of the individual’s military performance and civilian productivity and by the changes in the individual’s adjustment costs over his lifecycle. The simulations of an optimization model incorporating these cost and benefit elements suggest that if the intensity of the rise and decline of the individual’s military performance is sufficiently larger than the intensity of the rise and decline of his civilian productivity, there exists an interior optimal enlistment age that is greater than the commonly practiced 18. In such a case, most of the simulation results are closely scattered around 21 despite large parameter changes.     

Towards a fully conjugated, double-stranded cycle: a mass spectrometric and theoretical study.

The two compounds, 1 and 5, are investigated by means of collision-induced dissociation experiments by using ion cyclotron resonance mass spectrometry and other mass spectrometric techniques as to their ability to act as precursors for the fully unsaturated double-stranded target compound 2. These experiments are complemented by flask-type pyrolyses of 5, the products of which are analyzed by mass spectrometry. For 1, no conditions were found under which the expected molecular ion of 2 at m/z 932 appeared, however, for its derivative 5 this was possible. This interesting finding is not in contradiction with the chemical structure of the long sought for compound 2 but calculations suggest that this compound may have isomerized into one where the conjugation is interrupted by hydrogen shift from the solubilizing alkyl chains into the cycle's perimeter. The key driving force for such an isomerization would be the considerable relief of strain energy.     

K-Theory for Triangulated Categories 3 $\frac{3}{4}$\frac{3}{4}: A Direct Proof of the Theorem of the Heart

Let be a triangulated category, and assume it admits at least one model. In this article, we define a K-theory for . The main theorem is that, given any bounded i-structure on , the K-theory of the heart agrees with the K-theory of . An immediate consequence tells us that, if two Abelian categories occur as hearts of a triangulated category for two different t-structures, then their K-theories must be isomorphic.The proof was also sketched in previous articles in this series. The virtue of this article is in the careful detail in which it is written down.     

On residue complexes,dualizing sheaves and local cohomology modules

According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of -modules, theresidue complex . These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes, and , which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms.