Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.     

Novel Stereoselective Phase Transfer Catalytic Synthesis and Some Applications of ( E )-2-Chlorovinylthioarenes and Hetarenes

A novel two-step method for the preparation of ( E )-2-chlorovinylthioarenes (or hetarenes) from thiols and 1,1,2-trichloroethane in the phase transfer catalytic systems solid K 2 CO 3 /solid KI/18-crown-6/xylene and solid KOH/18-crown-6/toluene has been developed. ( E )-2-chlorovinylthioarenes were isolated in yields up to 98%. Utilization of ( E )-2-chlorovinylthioarenes in the Heck and Stille reactions has been shown.     

Gray codes extending quadratic matchings

Is it true that every matching in the n-dimensional hypercube can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey–Savage problem is affirmative for every matching of size at most . The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube by edges of into a Hamilton cycle of . On the other hand, we show that for every there is a balanced matching in of size that cannot be extended in this way.     

Integrated Digital Image Correlation considering gray level and blur variations: Application to distortion measurements of IR camera

The acquisition of images with different modalities may involve different alterations with respect to an ideal model. Inhomogeneous brightness and contrast, blur due to non-ideal focusing, distortions are common. It is proposed herein to account for such effects for instance by registering a calibration target image with an actual optical image to measure lens distortions. An Integrated Digital Image Correlation (I-DIC) algorithm is proposed to account for the above artifacts and the algorithm is detailed. The resolution and uncertainty of the technique are first investigated on synthetic images, and then applied to the measurement of distortions for infrared (IR) images. The procedure is shown to reduce drastically the residual level assessing the validity of the image formation model, but more importantly allowing for a much improved registration of images.     

Asymptotically Constant Solutions of Functional Difference Systems

We consider the functional difference system ( A ) j x i ( n )= f i ( n ; X ), 1 h i h k , where X =( x 1 ,…, x k ) and f 1 (·; X ),…, f k (·; X ) are real-valued functionals of X , which may depend quite arbitrarily on values of X ( l ) for multiple values of l ] Z . We give sufficient conditions for ( A ) to have solutions that approach specified constant vectors as n M X . Some of the results guarantee only that the solutions are defined for n sufficiently large, while others are global. The proof of the main theorem is based on the Schauder-Tychonoff theorem. Applications to specific quasi-linear systems are included.     

On ω-limit Sets of Triangular Maps on the Unit Cube

We consider Sturm–Liouville eigenvalue problems of second order with arbitary seperated boundary conditions and perform a suitabl discretization of them. The obtained discrete Sturm–Liouville eigenvalue problems are examined and the asymptotic behavior of their eigenvalue as the norm of the partition tends to zero is investigated.     

The Different,but Interesting Behaviors of Benzyl Systems in the Willgerodt-Kindler Reaction under Solvent-Free Conditions

On the benzyl system, bearing various functional groups, have been carried out the Willgerodt-Kindler reaction to obtain thiobenzmorpholide ( 1 ). The reactions, under solvent-free conditions, were performed in both classical (reflux, room temperature) and nonclassical (microwave) conditions to attempt our elucidation of the reactions pathways. Unlike benzylamine and benzyl mercaptan, benzyl halides give poor result due to the type of amine. The experimental results suggest that the proposed reaction pathway involves the oxidation coupling of benzylic substrates, followed by a thiolation step and an attack of the amine on the thiolated product to give ( 1 ).     

Dynamics of the rotational degrees of freedom in an undercooled crystal of cyanoadamantane

Results of molecular dynamics are presented for a simple model of cyanoadamantane crystal. Rotator cubic phase was simulated over a wide range of temperatures. In this system, glass formation is not induced by quenched diluted disorder, but it occurs similarly to conventional glasses. Simulations have shown that the system evolves from free small-step rotational diffusion to jump like motion. The results obtained with this model are used to discuss the validity of the Mode Coupling Theory (MCT) predictions.