Development of the method of production of the ultrafine macrohomogeneous composite powder

ABSTRACT

A method of ultrafine macro-homogeneous composite powder – B₄C–ZrO₂ production using a planetary mill was developed. From the macro-homogeneous composite high-density ceramics, B₄C–ZrB₂ was produced by the method of reactive sintering (in situ) at 2000°C under the pressure of 41–42?MPa. The effect of ZrO₂ grain size and of its distribution in the matrix on the consolidation parameters, and the microstructure of the obtained ceramics was studied.     

Axiomatic characterization of linear differential systems (and operators)

In his IEEE Trans. Aut. Contr. paper in 1991, Willems posed the following question: given a set of smooth trajectories, when does there exist a linear constant coefficient differential operator whose kernel is precisely the given set? We show that the properties that are necessary and sufficient for a set of smooth trajectories to admit a “kernel” representation are: linearity, time-invariance, jet-closedness and jet-determinedness. (It is interesting to note that the properties of jet-closedness and jet-determinedness were introduced by Willems himself in his Automatica paper in 1986.)     

Radiation from a Line Source Placed in Two-dimensional Photonic Crystals

A novel formulation of radiation from a localized line source placed in two-dimensional photonic crystals consisting of layered periodic arrays of parallel circular cylinders is presented. The method employs the spectral domain approach. The spectral response of the photonic crystals to the line source excitation is calculated using the lattice sums, the T-matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The far-zone radiated field is obtained using the conventional asymptotic method to the spectral response. The radiation patterns of the localized line source sandwiched by two photonic crystals are numerically studied.     

State representations of ARMA-models

A state representation of an arbitrary ARMA-model is computed explicitly. It is shown then that every ARMA-model is homotopy equivalent to its state representation, and that two state models are homotopy equivalent if and only if they are similar.     

Linear systems,and ARMA- and Fliess models

Linear (dynamical) systems are central objects of study (in linear system theory), and ARMA- and Fliess models are two very important classes of models that are used to represent them. This article is concerned with the question of what is a relation between them (in case of higher dimensions). It is shown that the category of linear systems, the ‘weak’ category of ARMA-models and the category of Fliess models are equivalent to each other.     

Fractional representations of linear systems

A fractional representation of an arbitrary linear system is obtained that can be viewed as a generalization of a classical fractional representation of a transfer function. Conversely, a state-space model, not necessarily observable or controllable, can be assigned to any such fractional model. It is then shown that the categories of state-space and fractional representations of a linear system are equivalent.     

EFFECT OF PERIODIC DEFECTS ON ELECTROMAGENTIC SCATTERING BY THE TWO-DIMENSIONAL PHOTONIC CRYSTALS

Electromagnetic scattering from two-dimensional photonic crystals with two-dimensionally periodic defects is analyzed using a model of multilayered periodic arrays of parallel circular cylinders. The reflectance of the photonic crystals of finite thickness, which are free-standing or embedded in a dielectric slab, is obtained in terms of the lattice-sums, the T-matrix of a circular cylinder, and the generalized reflection matrix for a layered system. Numerical examples demonstrate that the refection and transmission bands of the crystals are reformed by introducing the periodic defects and their band natures are very sensitive to the polarization of excitation and the relative position of the defect element within a unit cell.     

The PBH test for multidimensional LTID systems

In this article, the classical Popov–Belevitch–Hautus controllability test is generalized to higher dimensions.     

Convolutional Codes and Coherent Sheaves

We present a sheaf-theoretic setting for convolutional codes in that coherent sheaves (over a projective line) play the same role as finite-dimensional linear spaces in the theory of block codes. Using coherent sheaves (and their cohomologies), we give natural straightforward proofs of the main results on the structural properties of convolutional codes. Received: May 7, 1999; revised version: August 11, 2000