Heat capacity of a five-coordinated iron(III) complex with spin S = 32, bromobis(N,N-diethyldithiocarbamato)iron(III), between 0.4 and 300 K

Heat capacity measurements have been made for six kinds of specimens prepared by different methods. Among them, Sample A exhibited a A-type ferromagnetic pahse transition at 1.347 K and a Schottky-type anomaly due to the zero-field splitting around 9K. The total entropy and enthalpy were (11.05 ± 0.04) J K^?1mol^?1 and (97.0 ± 0.4) J mol^?1, respectively. Sample B exhibited a Sehottky-type anomaly around 0.4 K due to the ferro-magnetic dimeric coupling with $\text{J}{}_{\mathrm{D}}\text{k}\text{= + 0.30}\text{K}$ as well as the Schottky-type anomaly at 9K. The total magnetic entropy and enthalpy were (11.45 ± 0.03) JK^?1 mol^?1 and (93.8 ± 0.8) J mol^?1, respectively. The remaining samples are simple mixtures of the λ-type modification and the dimeric modification. Irrespective of the magnetic behavior at low temperatures, all the samples showed a non-magnetic first-order phase transition around 270 K. The heat capacity and entropy of this phase transition have been accounted for in terms of the Frenkel theory of heterophase fluctuation. Construction of an adiabatic-type calorimeter workable between 1.5 and 393 K has been also presented.     

Computing simple circuits from a set of line segments

We address the problem of connecting line segments to form the boundary of a simple polygon—a simple circuit. However, not every set of segments can be so connected. We present anO(n logn)-time algorithm to determine whether a set of segments, constrained so that each segment has at least one endpoint on the boundary of the convex hull of the segments, admits a simple circuit. Furthermore, this technique can also be used to compute a simple circuit of minimum perimeter, or a simple circuit that bounds the minimum area, with no increase in computational complexity.     

On the dimension to represent a graph by a unit distance graph

It is proved that if a graphG has maximum degreed, then its vertices can be represented by distinct unit vectors inR ^2d so that two vectors are orthogonal if and only if the corresponding vertices are adjacent. As a corollary it follows that if a graph has maximum degreed, then it is isomorphic to a unit distance graph inR ^2d.     

Nuclearity of a nonnegative definite integral kernel on a separable metric space

The aim of this paper is to characterize the nuclearity of an integral operator, defined by a continuous non-negative definite square integrable kernel on a separable metric space, in terms of the integrability of the trace of the kernel function. Nuclearity here plays a role forU-statistics.     

Broadband waveguide intersections with low cross talk in photonic crystal circuits

We propose a new mechanism for constructing waveguide intersections with broad bandwidth and low cross talk in photonic crystal (PC) circuits. The intersections are created by combination of coupled-cavity wave-guides (CCWs) with conventional line-defect waveguides. This mechanism utilizes the strong dependence of the defect coupling on the field pattern in the defects and the alignment of the defects (i.e., the coupling angle) in CCWs. By properly designing the defect mode, we demonstrate through numerical simulation the establishment of such a waveguide intersection in one of the most useful PCs, which is based on a two-dimensional triangular lattice of air holes made in a dielectric material. The transmission of a 500-fs pulse at ~1.3 microm is simulated by use of the finite-difference time-domain method, showing negligible distortion and low cross talk.     

The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.     

Energy loss of 1000 keV electrons in thin silicon crystals as measured by high voltage electron microscopy

Abstract

Energy loss spectra of 1000 keV electrons transmitted by [111]-: riented thin silicon crystals were observed by an energy analyzer attached to the HVEM. The crystals were set to the systematic 220 Bragg reflection. Measurements were made for crystal thickness ranging from 1000 to 10,000 Å, which were determined by observations of pendellösung fringes.

Results were analyzed with Landau's transport equation, giving the : onclusion that the loss probability, which is the reciprocal of the mean free path, is 0.52 ± 0.02 × 10^?3 A^?1 for plasmon excitation and 1.50 ± 0.02 × 10^?3 A^?1 for L-electron excitation.     

Resistivity control of sputtered amorphous-silicon by ion-implantation

The resistivity of a hydrogenated sputtered amorphous-silicon is controlled by using room temperature implantation of P⁺. It is found that the defects produced by implantation can be minimized by annealing at 300°C in an H₂ atmosphere, and also found that there is a threshold implanted dose, beyond which the resistivity begins to be controlled by changing the dose.