Double-slit Interference and Temporal Topos

The electron double-slit interference is re-examined from the point of view of temporal topos. Temporal topos (or t-topos) is an abstract algebraic (categorical) method using the theory of sheaves. A brief introduction to t-topos is given. When the structural foundation for describing particles is based on t-topos, the particle-wave duality of electron is a natural consequence. A presheaf associated with the electron represents both particle-like and wave-like properties depending upon whether an object in the site (t-site) is specified (particle-like) or not (wave-like). It is shown that the localization of the electron at one of the slits is equivalent to choosing a particular object in the t-site and that the electron behaves as a wave when it passes through a double-slit because there are more than one object in the t-site. Also, the single-slit diffraction is interpreted as a result of the possibility of many different ways of factoring a morphism between two objects.     

Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces

The existence of strong solutions of Cauchy problem for the following evolution equation du(t)/dt+∂?¹(u(t))-∂?²(u(t))∋f(t) is considered in a real reflexive Banach space V, where ∂?¹ and ∂?² are subdifferential operators from V into its dual V^*. The study for this type of problems has been done by several authors in the Hilbert space setting.The scope of our study is extended to the V-V^* setting. The main tool employed here is a certain approximation argument in a Hilbert space and for this purpose we need to assume that there exists a Hilbert space H such that V⊂H≡H^*⊂V^* with densely defined continuous injections.The applicability of our abstract framework will be exemplified in discussing the existence of solutions for the nonlinear heat equation: where Ω is a bounded domain in R^N. In particular, the existence of local (in time) weak solution is shown under the subcritical growth condition q<p^* (Sobolev's critical exponent) for all initial data This fact has been conjectured but left as an open problem through many years.     

Synthesis of antimicrobial agents. IV. synthesis of 1-hydroxypiperazine dihydrochloride and its applications to pyridone carboxylic acid antibacterial agents

1-Hydroxypiperazine dihydrochloride 7 was prepared and it was applied to the syntheses of new pyridone carboxylic acid antibacterial agents (PCA-antibacterial agents). 1-Cyclopropyl-6,8-difluoro-1,4-dihydro-7-(4-hydroxypiperazin-1-yl)-4-oxoquinoline-3-carboxylic acid 13 showed the most potent antibacterial activity.     

Models of an abelian variety with complex multiplication over small fields

A few existence theorems are proved for the models of an abelian variety of CM-type with a given zeta function over a field which does not necessarily contain the reflex field.     

Development of FEL and SASE in the far-infrared region at ISIR, Osaka University

Free electron laser (FEL) and self-amplified spontaneous emission (SASE) are being developed in the far-infrared region using the L-band electron linac at the Institute of Scientific and Industrial Research (ISIR), Osaka University. The L-band linac was recently remodeled extensively not only for higher operational stability and reproducibility but also for high power operation of FEL. After commissioning of the linac, we first began SASE experiment with a newly-developed strong-focusing wiggler. Recently we began FEL experiment and obtained lasing with the high peak power at 70 μm again after a long break.     

Local existence of solutions to some degenerate parabolic equation associated with the p-Laplacian

The existence of local (in time) solutions of the initial-boundary value problem for the following degenerate parabolic equation: ut(x,t)−Δpu(x,t)−|u|^q−2u(x,t)=f(x,t), (x,t)∈Ω×(0,T), where 2?p<q<+∞, Ω is a bounded domain in RN, is given and Δp denotes the so-called p-Laplacian defined by Δpu:=∇⋅(|∇u|^p−2∇u), with initial data u₀∈Lr(Ω) is proved under r>N(q−p)/p without imposing any smallness on u₀ and f. To this end, the above problem is reduced into the Cauchy problem for an evolution equation governed by the difference of two subdifferential operators in a reflexive Banach space, and the theory of subdifferential operators and potential well method are employed to establish energy estimates. Particularly, Lr-estimates of solutions play a crucial role to construct a time-local solution and reveal the dependence of the time interval [0,T₀] in which the problem admits a solution. More precisely, T₀ depends only on Lr|u₀| and f.     

Weighted energy-dissipation functionals for doubly nonlinear evolution

This paper is concerned with the Weighted Energy-Dissipation (WED) functional approach to doubly nonlinear evolutionary problems. This approach consists in minimizing (WED) functionals defined over entire trajectories. We present the features of the WED variational formalism and analyze the related Euler-Lagrange problems. Moreover, we check that minimizers of the WED functionals converge to the corresponding limiting doubly nonlinear evolution. Finally, we present a discussion on the functional convergence of sequences of WED functionals and present some application of the abstract theory to nonlinear PDEs.     

Thrombocytogenesis by megakaryocyte; Interpretation by protoplatelet hypothesis

Serial transmission electron microscopy of human megakaryocytes (MKs) revealed their polyploidization and gradual maturation through consecutive transition in characteristics of various organelles and others. At the beginning of differentiation, MK with ploidy 32N, e.g., has 16 centrosomes in the cell center surrounded by 32N nucleus. Each bundle of microtubules (MTs) emanated from the respective centrosome supports and organizes 16 equally volumed cytoplasmic compartments which together compose one single 32N MK. During the differentiation, single centriole separated from the centriole pair, i.e., centrosome, migrates to the most periphery of the cell through MT bundle, corresponding to a half of the interphase array originated from one centrosome, supporting one "putative cytoplasmic compartment" (PCC). Platelet demarcation membrane (DM) is constructed on the boundary surface between neighbouring PCCs. Matured PCC, composing of a tandem array of platelet territories covered by a sheet of DM is designated as protoplatelet. Eventually, the rupture of MK results in release of platelets from protoplatelets. (Communicated by Tadamitsu Kishimoto, M.J.A.).     

Controllable preparation, network structures and properties of unusual metal-organic frameworks constructed from 4,4'-(hexafluoroisopropylidene)diphthalic acid and 4,4'-bipyridyl

Three novel 3D metal-organic frameworks of [Ni(2)(hfpdpt)(bpy)(2)(H(2)O)(2)](H(2)O)(8) (1), [Ni(3)(Hhfpdpt)(2)(bpy)(4)](H(2)O)(2) (2), and [Mn(2)(hfpdpt)(H(2)O)(2)] (3) have been synthesized by the hydrothermal reaction of Ni(II) or Mn(II) nitrate, 4,4'-(hexafluoroisopropylidene)diphthalic acid (H(4)hfpdpt), and 4,4'-bipyridyl (bpy). Complex 1 self-assembles into a 3D framework with unconventional 4-connected network topology, while 2 and 3 exhibit two kinds of unusual (4,8)-connected topological networks. Notably, in 1 and 2, the bpy coligand participates in the construction of their 3D frameworks, and the pH value also plays an important role to tune their space arrangements, while in 3, the bpy coligand is not involved in the final crystalline lattice. Furthermore, a detailed investigation on their magnetic and adsorptive properties is carried out.