On the tvGARCH(1,1) model: Existence, CLT, and tail index

We study the properties of the tvGARCH(1, 1) model (1.8) with logistic coefficients. We obtain conditions for the existence of an L ^p -bounded solution (p ⩾ 0) of Eq. (1.8). For p ⩾ 4, we prove an exponential decay of the lagged correlation function and the central limit theorem for partial sums of the squared tvGARCH(1, 1) process under similar conditions as in the stationary case. In the second part of the paper, we study the (weak) tail index of the tvGARCH(1, 1) model.     

Characterization of incipient cavitation in axial valve by hydrophone and visualization

As the effects of cavitation in valves are devastating, the choice of the correct valve for a given operating range is crucial. For this, the valve characteristic is needed, whereby one side of the operating range depends on the determination of the incipient cavitation.In this paper, the visualization method for incipient cavitation detection is presented. For the purpose of comparison, pressure oscillations inside the pipeline were simultaneously measured with a hydrophone. The effect of operating pressure was studied for two different openings of the valve.For each operating point of incipient cavitation, corresponding points were measured for developed cavitation and no-cavitation state, based on a constant-portion change of volumetric flow rate with regard to the incipient cavitation volumetric flow rate. The visualization and hydrophone signals were compared.The visualization method proved efficiency over hydrophone measurements because it is more sensitive to cavitation and the signal is independent of the operating pressure. The main drawback is the preparation of the observation window.     

Ascending and descending regions of a discrete Morse function

We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse–Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of our algorithm compared to similar existing results is that it works, at least theoretically, in any dimension. Practically, there are dimensional restrictions due to the size of cellular complexes of higher dimensions, though. We prove that the algorithm is correct in the sense that it always produces a decomposition into descending and ascending regions of the critical cells in a finite number of steps, and that, after a finite number of subdivisions, all the regions are topological disks. The efficiency of the algorithm is discussed and its performance on several examples is demonstrated.     

On automorphisms of Banach algebras

We prove an extension of the Jacobson density theorem for Banach algebras with automorphisms, and discuss its applications. In particular, automorphisms a \alpha of Banach algebras such that the map a- 1 \alpha - 1 is spectrally bounded are characterized.     

Hardness and Elastic Modulus Profiles of Hybrid Coatings

Instrumented-indentation testing (IIT) provided with a continuous stiffness measurement (CSM) technique was employed to measure hardness and elastic modulus profiles of thin organic/inorganic hybrid coatings on glass surfaces. Hybrids were synthesized by the hydrolytic condensation of (3-methacryloxypropyl) trimethoxysilane (MPMS) or vinyltrimethoxysilane (VMS), with 5–30 wt% tetraethoxysilane (TEOS), in the presence of formic acid. Coatings of 600–800 nm on glass substrates were obtained by dip-coating solutions of these hybrids with benzoyl peroxide (BPO) addition, and curing in an oven following a thermal cycle up to 120C. Both hardness and elastic modulus showed a maximum value close to the surface, followed by a plateau and a significant increase at higher penetrations. Hybrids based on MPMS and 20–30 wt% TEOS exhibited a good combination of intrinsic values of hardness (0.50 GPa) and brittle index (0.06–0.07), that makes them suitable for coatings of plastic substrates.     

Kinematic Model for Determination of Human Arm Reachable Workspace

In physiotherapy, a standard method to determine the movability and functionality of the human arm is to measure the ranges of motion in joints in sagittal, horizontal and frontal plane. It is clear, however, that these angles can hardly interpret the characteristics of the arm. The main idea in the article is to combine these angles with an adequate kinematic model in order to compute and graphically represent the reachable workspace of the arm, which then serves as an advanced criterion for a more objective evaluation. In this article, we report an improved kinematic model of the human arm which is appropriate for computing and visualizing the human arm reachable workspace. Optical measurements were performed to define the structure and parameters of the model and to develop the mathematical relations between the joint angles. The kinematic model was implemented in a computer programme which is now being introduced in practice and can be used in rehabilitation, ergonomics and sports.     

A Note on the Shortness Coefficient and the Hamiltonicity of 4-Connected Line Graphs

Thomassen proposed a well-known conjecture: every 4-connected line graph is hamiltonian. In this note, we show that Thomassens conjecture is equivalent to the statement that the shortness coefficient of the class of all 4-connected line graphs is one and the statement that the shortness coefficient of the class of all 4-connected claw-free graphs is one respectively.Research partially supported by the fund of the basic research of Beijing Institute of Technology, by the fund of Natural Science of Jiangxi Province and by grant No. LN00A056 of the Czech Ministry of Education     

A solvent recirculation trapping device for supercritical fluid extraction of polyaromatic hydrocarbons

A new device has been developed for the trapping of volatile pollutants in trapping solvents. The device allows solvent recirculation and cryogenic trapping of evaporated volatiles to minimize the stripping effect and any losses of volatile analytes. Due to solvent recirculation, the trapping solvent column height remains constant during the extraction without any need for replenishment. Also mass transfer conditions are favorable due to the flattened shape of bubbles of CO2 and the longer extraction time. The bubbles have higher interfacial area and they have to pass a three times longer distance in the solvent column. The device produces more concentrated extracts, reduces solvent consumption, and reduces or eliminates its evaporation to the environment. The cryotrapping part reduces losses of volatile analytes and the stripping effect. It also enables single-phase extraction into much smaller solvent volumes. Due to constant and favorable extraction conditions, the precision of the method was also greatly improved (RSDs decreased from 2.2 to 0.8%). As proved by a set of rapid spiked-sample extractions of highly volatile compounds at very high flow rates, the relative standard deviation of the experiments performed in the new device is 3.5 times lower.     

Functional Identities on Upper Triangular Matrix Algebras

Let , be the algebra of upper triangular r×r matrices over field aF. We describe multilinear maps , where n≤r, such that [f(A,...,A), A]=0 for all , provided that |F| >n + 1. As an application of the results obtained, we describe linear automorphisms θ of such that [θ(A²), θ(A)]=0 for all . Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15, 2000.