The bipolaron in the strong coupling limit

The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr\"{o}hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar-Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum $P$, provided $P$ is not too large.Comment: 31 page

An online handwritten music symbol recognition system

The original publication is available at www.springerlink.comArticleINTERNATIONAL JOURNAL ON DOCUMENT ANALYSIS AND RECOGNITION. 9(1): 49-58 (2007)journal articl

Scale Dependence of the Retarded van der Waals Potential

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit $\alpha \to 0$ together with the relative distance between the atoms increasing as $\alpha^{-\gamma} R$, $\gamma > 0$. In particular we determine explicitly the crossover function from the $R^{-6}$ van der Waals potential to the $R^{-7}$ retarded van der Waals potential, which takes place at scale $\alpha^{-2} R$.Comment: 19 page

Development of a dose distribution shifter to fit inside the collimator of a Boron Neutron Capture Therapy irradiation system to treat superficial tumours

The Kansai BNCT Medical Center has a cyclotron based epithermal neutron source for clinical Boron Neutron Capture Therapy. The system accelerates a proton to an energy of 30 MeV which strikes a beryllium target producing fast neutrons which are moderated down to epithermal neutrons for BNCT use. While clinical studies in the past have shown BNCT to be highly effective for malignant melanoma of the skin, to apply BNCT for superficial lesions using this system it is necessary to shift the thermal neutron distribution so that the maximum dose occurs near the surface. A dose distribution shifter was designed to fit inside the collimator to further moderate the neutrons to increase the surface dose and reduce the dose to the underlying normal tissue. Pure polyethylene was selected, and a Monte Carlo simulation was performed to determine the optimum thickness of the polyethylene slab. Compared with the original neutron beam, the shifter increased the thermal neutron flux at the skin by approximately 4 times. The measured and simulated central axis depth distribution and off axis distribution of the thermal neutron flux were found to be in good agreement. Compared with a 2 cm thick water equivalent bolus, a 26% increase in the thermal neutron flux at the surface was obtained, which would reduce the treatment time by approximately 29%. The DDS is a safe, simple and an effective tool for the treatment of superficial tumours for BNCT if an initially fast neutron beam requires moderation to maximise the thermal neutron flux at the tissue surface

Kramers degeneracy theorem in nonrelativistic QED

Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed total momentum is also investigated.Comment: LaTex, 11 page

Binding of Polarons and Atoms at Threshold

If the polaron coupling constant $\alpha$ is large enough, bipolarons or multi-polarons will form. When passing through the critical $\alpha_c$ from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explodes? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at $\alpha_c$. Similarly, we show that the same phenomenon occurs for atoms, e.g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schr\"odinger equation, and are very general. They use the fact that the Coulomb repulsion decays like $1/r$, while `uncertainty principle' localization energies decay more rapidly, as $1/r^2$.Comment: 19 page

A New Integer Linear Programming Formulation to the Inverse QSAR/QSPR for Acyclic Chemical Compounds Using Skeleton Trees

33rd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, IEA/AIE 2020, Kitakyushu, Japan, September 22-25, 2020.Computer-aided drug design is one of important application areas of intelligent systems. Recently a novel method has been proposed for inverse QSAR/QSPR using both artificial neural networks (ANN) and mixed integer linear programming (MILP), where inverse QSAR/QSPR is a major approach for drug design. This method consists of two phases: In the first phase, a feature function f is defined so that each chemical compound G is converted into a vector f(G) of several descriptors of G, and a prediction function ψ is constructed with an ANN so that ψ(f(G)) takes a value nearly equal to a given chemical property π for many chemical compounds G in a data set. In the second phase, given a target value y∗ of the chemical property π , a chemical structure G∗ is inferred in the following way. An MILP M is formulated so that M admits a feasible solution (x∗, y∗) if and only if there exist vectors x∗, y∗ and a chemical compound G∗ such that ψ(x∗)=y∗ and f(G∗)=x∗. The method has been implemented for inferring acyclic chemical compounds. In this paper, we propose a new MILP for inferring acyclic chemical compounds by introducing a novel concept, skeleton tree, and conducted computational experiments. The results suggest that the proposed method outperforms the existing method when the diameter of graphs is up to around 6 to 8. For an instance for inferring acyclic chemical compounds with 38 non-hydrogen atoms from C, O and S and diameter 6, our method was 5×104 times faster