Schrödinger Operators with Random Sparse Potentials. Existence of Wave Operators

We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date.     

Organization of nanoscale objects via polymer demixing

We present an extremely versatile method for the lateral organization of nano-scale objects (NOs) based on the phenomenon of polymer demixing. NOs are suspended in a solution of two immiscible polymers, which is used to form a thin polymer film by spin coating. During spin coating the two polymers separate to give a microphase structure, whose length scale depends on the experimental conditions. The NOs spontaneously partition into one or other of the polymer phases resulting in their lateral organization. In this work, the organization of CdSe nanoparticles and fluorescent organic dyes was studied by fluorescence microscopy. The NOs were organized in the polymer film in stochastic patterns or in ordered designs on substrates pre-patterned by soft-lithography techniques. Single-particle measurements, using confocal microscopy, showed that at low concentrations there was little aggregation of the particles.     

The use of synchrotron X-ray scattering coupled with in situ mechanical testing for studying deformation and structural change in isotactic polypropylene

The mechanical behaviour of semi-crystalline polymers is greatly influenced by the properties of the crystalline and the amorphous phases. As a result this topic has been the subject of extensive research. However, to date, a comprehensive relationship between the structure and mechanical properties for semi-crystalline polymers has yet to be established. This present study concerns the commissioning of a novel method for in situ data collection during the deformation of polymers. This involves the combination of three different techniques into a single experiment, namely tensile testing, synchrotron radiation wide angle X-ray scattering, and optical microscopy. For this current investigation, three isotactic polypropylene samples have been studied, produced using different thermal treatments. This enables the influence of thermal treatment on the mechanical properties and crystallographic structure to be assessed. The results indicate that tensile properties are influenced by thermal treatment via the relative fraction of -phase material in the sample. As the temperature increases at which thermal treatment takes place, iPP ductility decreases due to the greater rigidity of the increasing -phase content. Differences in crystal strain between the different iPP crystal phases are also observed although the reasons for such differences remain unclear.     

The Impact of the Phenyl Spacer on the Electronic Structure and Spectra of Porphyrin Dimers

Quantum-chemical investigation of the electronic structure and properties of the excited states of porphyrin dimers, in which monomeric subunits are linked by the phenyl spacer, is performed by semiempirical methods. The molecular orbitals of the monomeric subunits are shown to interact with each other via molecular orbitals of the phenyl ring. Comparison of the experimental absorption data and quantum-chemical calculations of electronic absorption spectra for different conformations of Zn-tetraphenylporphyrin dimer is performed and the main conformation of the dimer in a solution at 295 K, in which the planes of tetrapyrrole macrocycles are located at an angle of about 60°, is substantiated.     

α-Particle Loss from Cylindrical Magnetized DT Plasma

-particles from fusion reactions in a DT magnetized plasma are confined inside the plasma not only by magnetic fields but also by induced electric fields which are due to the different mobilities of -particles and electrons. Criteria are derived for the -confinement in a cylindrical plasma, inertially confined by a heavy liner. It is observed that the suprathermal population in the DT plasma will influence the overall dynamics.     

The Order Parameter and Phase Transformations in Compounds with Ionic Stoichiometry

The paper considers instability of a symmetric linear ion chain against a spontaneous distortion that orders ions of opposite charge without a multiple change in the spacing. Transverse deformation in dense chains is observed. The dipolar interaction responsible for 3D ordering of similar structures of Cu—O chains in yttrium perovskites has been assessed. The superclose ion packing in Cu—O chains is explained by the existence of an oriented hole orbital in the electronic structure of bivalent copper. The possible role of this orbital as an additional degree of freedom leading to thermodynamic singularities at intermediate temperatures below the tetra–ortho transition temperature has been investigated.     

New MnO–Nb(Ta)2O5 Phases Produced at High Pressures and Temperatures

Phase formation at high pressures and temperatures were studied in the MnO–Nb(Ta)₂O₅ system. New rhombohedral modifications of Mn₄Nb₂O₉ and Mn₄Ta₂O₉, two new modifications of MnTa₂O₆, and two modifications of Mn₂Ta₂O₇ were obtained. They were structurally identified.     

A Biokinetic Model to Describe Consequences of Inhibition/Stimulation in <Emphasis Type="Italic">DNA</Emphasis>-Proofreading and -Repair,Part 4

Summary. In previous papers a strongly simplified physical-mathematical (biokinetic) model has been presented, which dealt with the factors influencing the timely development of DNA mismatches dependent cells (malignant cells) in their kinetic competition to the development of normal somatic cells (i.e. cells with correct genetic information). The kinetic results have been studied by comparing them with experimental results reported in the literature upon inhibiting the organisms own enzymatic DNA-proofreading and repair machinery. In spite of the fact that the model uses fully the chances of kinetics, which allows to describe even rather complicated systems with many regulation circuits and feed back loops in a rather simple, summarizing way, it has been demonstrated that the model does not only well describe the experimentally found significant increases of mutants in cases when the DNA repair system has been inhibited, but it can also reflect cancer-development and the efficacy of classical cancer therapies like surgery or chemotherapy as well.In applying the predictions of the model as to the opposite of an inhibition of the DNA repair system, i.e., in testing the results, if the organisms own repair systems were stimulated, the model shows that there could be a chance for a new, adjuvant cancer-therapy if this concept was combined with biochemical facts and clinical findings which are reported in the literature.In continuation of this concept, the predictions of the model have been compared with findings upon cancer-therapies by apoptosis-triggerers like tamoxifen. Further, according to the fact that there exists literature by which it is demonstrated by clinical facts that it is not necessary to use living cells (e.g. from umbilical cords blood or bone-marrow) to achieve surprising therapeutic successes in cancer therapy, but also cell-free human-placenta-extracts (HPEs) can be similarily effective, it has been tried in a first preliminary analytical effort to characterize effector-substances contained therein.Received January 27, 2003; accepted (revised) March 25, 2003 Published online August 18, 2003     

A Complete Solution to a Conjecture on the β-Polynomials of Graphs

In 1990, Gutman and Mizoguchi conjectured that all roots of the -polynomial (G,C,x) of a graph G are real. Since then, there has been some literature intending to solve this conjecture. However, in all existing literature, only classes of graphs were found to show that the conjecture is true; for example, monocyclic graphs, bicyclic graphs, graphs such that no two circuits share a common edge, graphs without 3-matchings, etc, supporting the conjecture in some sense. Yet, no complete solution has been given. In this paper, we show that the conjecture is true for all graphs, and therefore completely solve this conjecture.     

Evidence of Ternary Inclusion Complexes Formation Using Factorial Design and Determination of Their Formation Constant

Evidence of the interaction among the [PbAc]⁺ and[PbEDTA]^-2 with the -cyclodextrin (-CD)is shown, using a 2⁴ factorial design. The factors used werethe [Pb(II)], [-CD], [Ac^-] and [EDTA] concentrationsat pH = 6.2. The statistical results indicate that the changes inchemical response for these species are associated to theinteraction among these factors. Spectrophotometric andelectrochemical studies were undertaken to assess the interactions.The equilibrium constants for inclusion complexes were determinedFor -CD-[PbAc]⁺ and -CD-[PbEDTA]^-2.