Variable-priority queue and doughnut routing

This paper proposes a new data structure called a variable-priority queue. The queue supports, in addition to the ordinary queue operations, an operation MIN to find an item of minimum key and three operations to change keys of items. Any sequence of these m operations can be processed in O(m) time. Furthermore, as its application, this paper presents two efficient algorithms for network problems. The first finds multicommodity flows in cycles in linear time. The second, using the first, finds edge-disjoint paths connecting terminal pairs in a doughnut-shaped grid. The grid is bounded by two nested rectangles, and terminals are specified on the two rectangular boundaries outside the four corners. If there are k terminal pairs and all the terminals are ordered in clockwise order around rectangles, then the algorithm decides in O(k) time whether there are edge-disjoint paths connecting terminals in the grid, and actually finds edge-disjoint paths in O(k log k) time.     

Relation between Hall-magnetohydrodynamics and the kinetic Alfvén wave

Effects of a finite ion temperature on the Hall magnetohydrodynamics (MHD), which breaks down for a finite ion temperature, are clarified in terms of a rigorous three-field kinetic dispersion relation. The MHD mode equation becomes anisotropic with respect to the ion pressure because of the double adiabaticity in ion dynamics.     

Randomly displaced phase distribution design for computer-generated binary hologram with narrow recording spots

A random phase mask is often used for Fourier transform holography to improve its recording and reconstruction characteristics. However, a conventional random phase pattern has the disadvantage of expanding the recording spot, which is caused by the high-resolution phase modulation. Previously, we proposed a random phase pattern that makes the recording spot narrower than the conventional one with maintaining a moderate reconstruction quality. In the present study, we apply the proposed random phase pattern to computer-generated binary holograms and evaluate both the hologram distribution and reconstruction quality in terms of practical holographic memory systems. The results confirm the effectiveness of the random phase in the reconstruction for an elementary data pattern.     

Scattering from very rough metallic and dielectric surfaces: a theory based on the modified Kirchhoff approximation

This paper presents a theory of scattering from very rough metallic and dielectric surfaces using the first- and second-order Kirchhoff approximations (KA) modified with the angular and propagation shadowing. The shadowing functions limit the single and double scattered waves which are illuminated and not shadowed by the surface. The theoretical results are compared with the Monte Carlo simulations showing the range of validity of the theory. The theory is applicable to the range where the RMS height is close to a wavelength and the RMS slope is close to unity, and the second medium is lossy. The second-order scattering includes two waves travelling in opposite directions on the surface, giving a physical explanation of the enhanced backscattering.     

Semiconductor diamond heater in the Kawai multianvil apparatus: an innovation to generate the lower mantle geotherm

Semiconductor diamond is considered the best heater material to generate ultra-high temperatures in a Kawai cell. In two pioneering studies, a mixture of graphite and amorphous boron (or boron carbide, B₄C) was converted to semiconductor diamond in the diamond stability field and was confirmed to generate 2000°C and 3500°C, respectively. Following these works, we synthesized a homemade boron-doped graphite block with fine machinability. With this technical breakthrough, we developed a semiconductor diamond heater in a smaller Kawai-type cell assembly. Here, we report the procedure for making machinable boron-doped graphite, and the performance of the material as a heater in a Kawai cell at 15?GPa using tungsten carbide anvils and at ～50?GPa using sintered diamond anvils. Furthermore, we present a finite element simulation of the temperature distribution generated by a semiconductor diamond heater, which is much more homogeneous than that generated by a metal heater.     

Unipotent Algebraic Affine Supergroups and Nilpotent Lie Superalgebras

We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras, regarded as coalgebras, is also discussed. Presented by S. Montgomery Mathematics Subject Classification (2000) 16W30.     

A compact optical heterodyne interferometer by optical integration and its application

A compact high-resolution optical heterodyne interferometer combining a two-frequency light module and a minute optical system is described. The light module, which generates two independent frequencies of light, is fabricated by proton exchange method on LiNbO₃ substrate. We report an experiment evaluating measurement accuracy using a micro-displacement measurement system which incorporates this interferometer. Results of the experiment with a standard thickness sample show high thermal stability with maximum measurement error of 1.8 nm at a temperature from 19°C to 33°C. The system was used to measure the hysteresis of a piezoelectric element for displacements of several nm, thereby making it possible to analyze the system quantitatively in practice.     

The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011