The minimal excludant and Schmidt's partition theorem

In this work, we study Schmidt's partition theorem in a combinatorial manner, and find a strong refinement which connects the minimal excludant of ordinary partitions to the length of Schmidt's partitions. As a byproduct, we obtain a bivariate form of an identity recorded in Ramanujan's lost notebook.     

HOW REYE'S CONFIGURATION HELPS IN PROVING THE BELL–KOCHEN–SPECKER THEOREM: A CURIOUS GEOMETRICAL TALE

It is shown that the 24 quantum states or rays used by Peres (J. Phys. A 24, 174-8 (1991)) to give a proof of the Bell–Kochen–Specker (BKS) theorem have a close connection with Reye's configuration, a system of twelve points and sixteen lines known to projective geometers for over a century. The interest of this observation stems from the fact that it provides a ready explanation for many of the regularities exhibited by the Peres rays and also permits a systematic construction of all possible non-coloring proofs of the BKS theorem based on these rays. An elementary exposition of the connection between the Peres rays and Reye's configuration is given, following which its applications to the BKS theorem are discussed.     

Optical multiresolution analysis with spatial localization

Multiresolution analysis is very useful for characterization of textures, segmentation tasks, and feature enhancement. The development of optical methods to perform such procedures is highly promissory for real-time applications. Usually, the optical implementations of multiresolution analysis consist in the decomposition of the input scene in different frequency bands, obtaining various filtered versions of the scene. However, under certain circumstances it could be useful to provide just one version of the scene where the different filters are applied in different regions. This procedure could be specially interesting for biological and medical applications in situations when the approximate localization of the scale information is known a priori. In this paper we present a fully optical method to perform multiresolution analysis with spatial localization. By means of the proposed technique, the multi-scale analysis is performed at once in a unique image. The experimental set-up consist of a double-pass convergent optical processor. The first stage of the device allows the multiple band decomposition, while the second stage confines the information of each band to different regions of the object and recombines it to achieve the desired operation. Numerical simulations and experimental results, which prove the very good performance of the method, are presented.     

Optical technique for classification, recognition and identification of obscured objects

The capability to classify, recognize and to identify objects from spatially low resolution images has high significance in security related applications especially in a case that recognition of camouflaged object is required.In this paper we present a novel approach in which the scenery containing obscured objects which we wish to classify, recognize or identify is illuminated by spatially coherent beam (e.g. laser) and therefore secondary speckles pattern is reflected from the objects. By special image processing algorithm developed for this research and which is basically based upon temporal tracking of the random speckle pattern one may extract the temporal signature of the object. And right after, to use it for its classification (e.g. its separation from the other objects in the scenery), its recognition and identification even in a case that the imager provides poor spatial resolution that by itself does not allow doing the specified detection related operations.     

Generalization of the Hellmann-Feynman theorem

The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.     

Aspects of multistation quantum information broadcasting

We study quantum information transmission over multiparty quantum channel. In particular, we show an equivalence of different capacity notions and provide a multiletter characterization of a capacity region for a general quantum channel with k senders and m receivers. We point out natural generalizations to the case of two-way classical communication capacity.     

Numerical resolution of the modified Langevin equation using a differential expression: Application to the Jiles magnetostriction law of approach

The Langevin equation is classically used to model the anhysteretic magnetization curve. A modified version of this equation has been introduced by Jiles to take into account the effects of magnetostriction on the anhysteretic magnetization behavior when a ferromagnetic material undergoes mechanical stresses. The numerical resolution of the modified Langevin equation is usually performed with a root-finding algorithm. In this paper, a differential form of the modified Langevin equation is proposed, allowing a faster numerical resolution.     

Vacuum Radiation,Entropy, and Molecular Chaos

Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t ^1/2, and the fractional changes in momentum and energy are proportional to t ^−1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change in momentum of a particle in a gas is very small. However, at the end of the mean free path each particle undergoes an interaction that magnifies the preceding change, and the net result is that the momentum distribution of the particles in a gas is randomized in a few collision times. In this way the random action of vacuum radiation and its subsequent magnification by molecular interaction produces entropy increase. This process justifies the assumption of molecular chaos used in the Boltzmann transport equation.     

Theoretical study of new acceptor and donor molecules based on polycyclic aromatic hydrocarbons

Functionalized polycyclic aromatic hydrocarbons (PAHs) are an interesting class of molecules in which the electronic state of the graphene-like hydrocarbon part is tuned by the functional group. Searching for new types of donor and acceptor molecules, a set of new PAHs has recently been investigated experimentally using ultraviolet photoelectron spectroscopy (UPS). In this work, the electronic structure of the PAHs is studied theoretically with the help of B3LYP hybrid density functionals. Using the ΔSCF method, electron binding energies have been determined which affirm, specify and complement the UPS data. Symmetry properties of molecular orbitals are analyzed for a categorization and an estimate of the related signal strength. While σ-like orbitals are difficult to detect in UPS spectra of condensed film, calculation provides a detailed insight into the hidden parts of the electronic structure of donor and acceptor molecules. In addition, a diffuse basis set (6-311++G**) was used to calculate electron affinity and LUMO eigenvalues. The calculated electron affinity (EA) provides a classification of the donor/acceptor properties of the studied molecules. Coronene-hexaone shows a high EA, comparable to TCNQ, which is a well-known classical acceptor. Calculated HOMO-LUMO gaps using the related eigenvalues have a good agreement with the experimental lowest excitation energies. TD-DFT also accurately predicts the measured optical gap.     

John Bell and the Identical Twins

I present a biographical profile of John S. Bell based upon extensive interviews I had with him. I present Bell‘s views on the quantum theory along with a simple explanation of his identity. Jeremy Bernstein is Professor Emeritus of Physics at the Stevens Institute of Technology and a former staff writer for The New Yorker.