2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Study of solid state reactions in Nb/Al multilayer thin films

Solid state reactions of sputter-deposited Nb/Al multilayer thin films, with periodicities in the range 10–333 nm, have been studied by differential scanning calorimetry. The first phase to form upon annealing the films in NbAl₃. Constant-heating-rate calorimetric measurements show the presence of two peaks for the formation of this phase, while isothermal scans reveal that the first peak is associated with a nucleation and growth type transformation. The formation of NbAl₃ is thus interpreted as a two-stage process of nucleation and growth to coalescence (first peak) followed by growth until the consumption of one or both reactants (second peak).We thank NSF for support through DMR-9308651, K. Coffey, S. Vivekanand and B. Gadicharla for assistance and TA Instruments for the donation of a 1600°C furnace.     

Reconstruction of the time dependence and signal parameters of far-field extended wideband sources: Part 2. Reconstruction of the directivity pattern of a moving source

The problem of measuring the radiation directivity pattern of a moving source in a horizontal plane is considered. It is shown experimentally that the angular dependence of radiation can be reconstructed at discrete frequencies in detecting an acoustic signal by a linear array positioned in the near field of the source followed by signal processing. The technique described in this work and its technical implementation can be used in developing and creating a measurement system for monitoring ship fields in the horizon plane.

     

Strong Homotopy Types,Nerves and Collapses

We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse. The advantage of using strong collapses is the existence and uniqueness of cores and their relationship with the nerves of the complexes. From this theory we derive new results for studying simplicial collapsibility with a different point of view. We analyze vertex-transitive simplicial G-actions and prove a particular case of the Evasiveness conjecture for simplicial complexes. Moreover, we reduce the general conjecture to the class of minimal complexes. We also strengthen a result of V. Welker on the barycentric subdivision of collapsible complexes. We obtain this and other results on collapsibility of polyhedra by means of the characterization of the different notions of collapses in terms of finite topological spaces.     

Automorphism groups of finite posets

For any finite group G, we construct a finite poset (or equivalently, a finite T₀-space) X, whose group of automorphisms is isomorphic to G. If the order of the group is n and it has r generators, X has n(r+2) points. This construction improves previous results by G. Birkhoff and M.C. Thornton. The relationship between automorphisms and homotopy types is also analyzed.     

Synthesis of pyrazol-quinazolinones and 2,3-dihydroquinazolin-4(1H)-ones using CoAl2O4 nanoparticles as heterogeneous catalyst

Journal of the Iranian Chemical Society - The preparation and characterization of cobalt aluminate (CoAl2O4) magnetic nanoparticles and its application as a catalyst for the synthesis of a novel...     

Fourier-Mellin expansion coefficients of scaled pupils

The experimental performance of beam smoothing by combined one-dimensional(1D) spectral dispersion and lens array(LA) technology is presented,as applied in the ninth beam of SG-II.Using 3ω spectral dispersion with a bandwidth of 270 GHz and a line dispersion that is 24.9 times the beam’s diffractionlimited width decreases the focal spot non-uniformity of 80% energy concentration from 46% to 17%.The multiple-beam interference properties of the LA are theoretically and experimentally validated by spatial power spectral density analysis.Peak-spectra suppression ratios of 20 and 10 dB are achieved in the dispersion and orthogonal directions,respectively.     

The effect of detector distance and beam width in acousto-optical beam deflection probing in air

We investigate the effect of detector distance and beam width in acousto-optic beam deflection probing in air. The study investigates pure refraction regime (beam width? acoustic wavelength). We find that in this regime the increase in beam width can significantly increase the detected signal up to 8 folds higher than previous detection geometries—while the detector distance has a less noticeable effect. Theoretical results are assessed through an experiment with a commercially available ultrasonic transducer. This investigation provides detailed theoretical approaches and quantitative experimental characterization that can be used for numerous applications requiring beam deflection probing in air.     

On a lower bound for the connectivity of the independence complex of a graph

Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false.