Inductive Limits for Systems of Toeplitz Algebras

This article deals with inductive systems of Toeplitz algebras over arbitrary directed sets. For such a system the family of its connecting injective $*$-homomorphisms is defined by a set of natural numbers satisfying a factorization property. The motivation for the study of those inductive systems comes from our previous work on the inductive sequences of Toeplitz algebras defined by sequences of numbers and the limit automorphisms for the inductive limits of such sequences. We show that there exists an isomorphism in the category of unital $C^*$-algebras and unital $*$-homomorphisms between the inductive limit of an inductive system of Toeplitz algebras over a directed set defined by a set of natural numbers and a reduced semigroup $C^*$-algebra for a semigroup in the group of all rational numbers. The inductive systems of Toeplitz algebras over arbitrary partially ordered sets defined by sets of natural numbers are also studied.Comment: 12 page

Capture and recreation of higher order 3D sound fields via reciprocity

Presented at the 10th International Conference on Auditory Display (ICAD2004)We propose a unified and simple approach for capturing and recreating 3D sound fields by exploring the reciprocity principle that is satisfied between the two processes. Our approach makes the system easy to build, and practical. Using this approach, we can capture the 3D sound field by a spherical microphone array and recreate it using a spherical loudspeaker array, and ensure that the recreated sound field matches the recorded field up to a high order of spherical harmonics. A design example and simulation results are presented. For some regular or semi-regular microphone layouts, we design an efficient parallel implementation of the multi-directional spherical beamformer by using the rotational symmetries of the beampattern and of the spherical microphone array. This can be implemented in either software or hardware. A simple design example is presented to demonstrate the idea. It can be easily adapted for other regular or semi-regular layouts of microphones

Boundary Element Solution of Electromagnetic Fields for Non-Perfect Conductors at Low Frequencies and Thin Skin Depths

A novel boundary element formulation for solving problems involving eddy currents in the thin skin depth approximation is developed. It is assumed that the time-harmonic magnetic field outside the scatterers can be described using the quasistatic approximation. A two-term asymptotic expansion with respect to a small parameter characterizing the skin depth is derived for the magnetic and electric fields outside and inside the scatterer, which can be extended to higher order terms if needed. The introduction of a special surface operator (the inverse surface gradient) allows the reduction of the problem complexity. A method to compute this operator is developed. The obtained formulation operates only with scalar quantities and requires computation of surface operators that are usual for boundary element (method of moments) solutions to the Laplace equation. The formulation can be accelerated using the fast multipole method. The method is much faster than solving the vector Maxwell equations. The obtained solutions are compared with the Mie solution for scattering from a sphere and the error of the solution is studied. Computations for much more complex shapes of different topologies, including for magnetic and electric field cages used in testing are also performed and discussed

Modelling of strategic networks of interaction of enterprise structures

In paper developed idea of the concept of formation of a network of interaction of enterprise structure as a result of management of processes of strategic management is that the relations with direct contractors of enterprise structure become object of management. Organizational forms of interaction of the companies can be attributed to parameters of interaction of a network. © IDOSI Publications, 2013

Generalizing Binary Solubility Data for Low-Volatile Liquids in Supercritical Fluids

EXISTING GENERALIZATION METHODS The key parameters that govern the feasibility of the separation of a mixture by supercritical fluid extraction are the binary solubilities of the components of the mixture in the extractant over a wide range of state variables. Several approaches to predicting the binary solubilities of liquids in compressed gases are known (1) where y i and y j are the concentrations (mole fractions) of the components; B ii is the second virial coefficient, which accounts for the interaction between identical molecules; B ij is the second virial cross coefficient, which accounts for the interaction between different molecules; and v m and z m are the molar volume and the compressibility of the gas phase, respectively. Within the framework of the thermodynamic similarity method, B ij is computed by various relations of the form where P cr and v cr are, respectively, the critical pressure and the critical molar volume of the component; is the characteristic temperature; and ω ij is the characteristic acentricity factor. There is a comprehensive review [2] of methods for calculating the characteristic cross parameters of mixtures, including higher order virial coefficients. ω ij is usually defined as the arithmetic mean of the acentricity factors of the mixture components. It was suggested [1] to calculate the characteristic temperature with the use of the empirical binary intermolecular interaction parameter k ij : ). = A generalized formula for k ij has been derived [1] for the interaction of organic liquids with a compressed gaseous solvent. The formula gives k ij as a function of the number of carbon atoms in the molecule of the dissolved liquid: where n is the number of carbon atoms in the molecules of dissolved n -paraffins, ketones, alcohols, and aromatic hydrocarbons. The interactions of nonpolar molecules with one another and of nonpolar molecules with polar molecules have been considered. The generalized formula is empirical, and the discrepancy between the parameters k ij obtained by experimental data processing and the generalized curve considerably exceeds the experimental error. The binary solubilities of low-volatile substances, including solids, have been represented [3] as a function of the solvent density: where y is the binary solubility (mole fraction), P is the pressure in the system, P 0 is the standard pressure, ρ is the solvent density, and ρ 0 is the standard solvent density. The parameters A and B are interrelated b