The Connectedness of Some Varieties and the Deligne—Simpson Problem

The Deligne—Simpson problem (DSP) (respectively, the weak DSP) is formulated as follows: give necessary and sufficient conditions for the choice of the conjugacy classes C_j GL(n, ) or c_j gl(n, ) so that there exist irreducible (respectively, with trivial centralizer) (p + 1)-tuples of matrices M_j C_j or A_j c_j satisfying the equality M₁ ... M_p+1 = I or A₁ + ... + A_p+1 = 0. The matrices M_j and A_j are interpreted as monodromy operators of regular linear systems and as matrices-residua of Fuchsian ones on the Riemann sphere. For ((p + 1))-tuples of conjugacy classes one of which is with distinct eigenvalues we prove that the variety {(M₁, ..., M_p+1) | M_j C_j, M₁ ... M_p+1 = I} or {(A₁, ..., A_p+1) | A_j c_j, A₁ + ... + A_p+1 = 0| is connected if the DSP is positively solved for the given conjugacy classes and give necessary and sufficient conditions for the positive solvability of the weak DSP.2000 Mathematics Subject Classification. 15A30, 15A24, 20G05.     

The Deligne–Simpson Problem and the Connectedness of some Varieties

The Deligne–Simpson problem is formulated as follows: give necessary and sufficient conditions for the choice of the conjugacy classes or so that there exist irreducible (p+1)-tuples of matrices M _j ∈ C _j or A _j ∈ c _j satisfying the equality M ₁ ⋯ M _p+1 = I or A ₁ + ⋯ + A _p+1 = 0. The matrices M _j and A _j are interpreted as monodromy operators of regular linear systems and as matrices-residues of Fuchsian ones on the Riemann sphere. We prove that in the so-called simple case the subset or of the variety or consisting of all irreducible (p+1)-tuples (if nonempty) is connected. “Simple” means that the greatest common divisor of all quantities of Jordan blocks of a given size, of a given matrix M _j or A _j , and with a given eigenvalue is 1. To the memory of my mother     

On the Riemann–Hilbert Problem in Dimension 4

We consider the problem of existence of a Fuchsian system with a prescribed 4-dimensional monodromy. We give a classification of all cases of negative solution of this problem in terms of reducibility pattern of the representation, its local structure (which is described by a modification of Jordan form), and restrictions on asymptotics of solutions to Fuchsian systems in lower dimensions. We also show that realization of a reducible 4-dimensional representation by a Fucshian system, if it exists, can be chosen in a block upper-triangular form (though not necessarily with the same reducibility pattern). At the end of the paper, we present new counterexamples to the Riemann–Hilbert problem in dimension 4.     

On Two Types of Representations of the Braid Group Associated with the Knizhnik–Zamolodchikov Equation of the B nType

A generalization of the Kohno theorem on the restricted Riemann–Hilbert problem for the KZ equation of the B_n type is given. The representation of the the braid group of the B_n type in the algebra of symmetrical chord diagrams is constructed and its connection with the B_n type quasi-bialgebra structure and with the monodromy of the generalized KZ equation of the B_n type is discussed.     

On the C^r-Closing Lemma and the Koebe–Morse Coding of Geodesics on Surfaces

We consider the -closing lemma for vector fields with finitely many singularities on an orientable closed surface M of genus g2. Given a nontrivially recurrent trajectory, there is the corresponding geodesic having the same asymptotic directions (both negative and positive). Using the Koebe–Morse coding for the corresponding geodesic, we introduce the notion of p-expansions in the form of two sequences of nonnegative integers. The main result is the following. Suppose a vector field , r, has a nontrivially recurrent trajectory l through a point m; then there exists arbitrarily close to X (in the -topology) having a periodic trajectory through m provided that the Koebe–Morse coding of the corresponding geodesic g(l) has p-expansions of unrestricted type.     

Some Qualitative Results in the Linear Theory of Micropolar Solid–Solid Mixtures

This paper deals with the linear theory of micropolar solid–solid mixtures. First, some existence, uniqueness and continuous dependence results are derived. Then, the propagation of plane waves is studied. There are possible four types of waves: longitudinal displacement waves, longitudinal microrotation waves, transverse displacement waves and transverse microrotation waves. A detailed analysis is presented for the longitudinal displacement waves and the longitudinal microrotation waves.     

On the preparation of amorphous Mg–Ni alloys by mechanical alloying

This paper deals with the preparation of the amorphous Mg–Ni alloys. By mechanical alloying (MA) the amorphous Mg–Ni alloys with different compositions have been prepared of pure elemental magnesium and nickel powder. The as-milled powder was characterized by X-ray diffraction analysis and transition electron microscope (TEM) observation. The results showed that the 30 < Ni < 70 at.% composition could be amorphized with a milling time strongly dependent on the starting chemical compositions. The investigation on the early stage of MA showed that the different compositions amorphized by two different paths. On the magnesium rich side of 30–70 at.% Ni, the as-milled powders first formed the intermetallic compound Mg₂Ni, which subsequently destabilized into the amorphous phase. For the nickel rich side, the amorphous was obtained directly from the mechanical blend of magnesium and nickel powder by the suppression of the formation of thermodynamic equilibrium phase MgNi₂. © 1999 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved.     

On the long-term cyclic stability of near-eutectic Mg–Mg2Ni alloys

In this investigation, we report the cyclic performance, microstructure and thermal properties of near eutectic Mg–Ni alloys with different Ni contents (4.4, 11.3 and 16.3 at%). The starting cast ingots are mechanically chipped to flakes of about 400 μm, all displaying composite structures characterized by a typical eutectic microstructure with rather coarse features (1–5 μm). The flakes are cycled 1000 times at 330 °C under 30/1 bar H₂ for the absorption/desorption processes. The hydrogen storage capacity is maintained throughout the cycling: 5.09, 4.46 and 3.49 wt% H₂ for Ni16.3, Ni11.3 and Ni4.4 (at%), respectively. No significant microstructural change is observed, indicating the excellent stability of the alloys at elevated temperatures. Nevertheless, a marked porosity, and spheroidal Mg₂Ni clusters can be noted after cycling, however their exact contribution to reaction kinetics has yet to be fully elucidated. An attempt is made to estimate the dehydrogenation activation energy of Ni16.3, and the calculated value seems comparable to that obtained for an early cycling stage (10 cycles). In the light of the superior stability under cyclic service and the low decomposition temperature, the Mg–Mg₂Ni system is shown to possess an excellent potential for long-term hydrogen and heat storage applications.     

On the Two-Temperature Green–Naghdi Thermoelasticity Theories

The constitutive laws for two-temperature Green–Naghdi theories are given. It is proved that the two-temperature thermoelasticity theory admits dissipation of energy and the theory of elasticity without energy dissipation is valid only when the two-temperatures coincide. The uniqueness and reciprocal theorems are proved for a linear anisotropic and inhomogeneous thermoelastic centro-symmetric solid in the frame of two-temperature Green–Naghdi theories. The convolutional variational principle is established for the two-temperature Green–Naghdi theory of type III. A continuous dependence result is given for an isotropic solid.     

Some properties of the pressure—entropy diagram

Some explanations are given upon properties of the pressure-entropy diagram for liquid and steam and for ideal gases.The representation on this graph not only of classical thermodynamic cycles, but also of reheat and regenerative modern cycles, shows that it may be considered as a useful complement of Mollier diagrams.     

On the spectrum of α-rigid maps

We show that there exists an α-rigid transformation with α ≤ 1/2 whose spectrum has a Lebesgue component. This answers the question stated by Klemes and Reinhold in [30]. Moreover, we introduce a new criterion to identify a large class of α-rigid transformations with singular spectrum.     

Constructive Solutions to the Riemann–Hilbert Problem and Middle Convolution

In this paper, we present a general scheme to generate constructive solutions to the Riemann–Hilbert problem via middle convolution and illustrate this approach for a Fuchsian system with four singular points.     

On the income–nuclear energy–CO2 emissions nexus revisited

This paper seeks to contribute to the debate over the income–nuclear enery–CO₂ emissions nexus by taking specific account of the possible endogeneity of income, which has been largely ignored by early studies. A multivariate cointegrated vector autoregression (CVAR) is applied to top six nuclear generating countries. We find that nuclear energy tends to reduce CO₂ emission for all countries. It is also found that income has a beneficial effect on the environment only in some countries. Finally, we find that CO₂ emissions and income are indeed determined simultaneously, while nuclear energy acts exogenously, indicating that nuclear energy is the driving variable, which significantly influences the long-run movements of CO₂ emissions and income, but is not affected by CO₂ emissions and income in the model.     

On an acoustics–thermal–fluid coupling model for the prediction of temperature elevation in liver tumor

The present study is aimed at predicting liver tumor temperature during a high-intensity focused ultrasound (HIFU) thermal ablation using the proposed acoustics–thermal–fluid coupling model. The linear Westervelt equation is adopted for modeling the incident finite-amplitude wave propagation. The nonlinear hemodynamic equations are also taken into account in the simulation domain that contains a hepatic tissue domain, where homogenization dominates perfusion, and a vascular domain, where blood convective cooling may be essential in determining the success of HIFU. Energy equation for thermal conduction involves two heat sinks to account for tissue perfusion and forced convection-induced cooling. The effect of acoustic streaming is also included in the development of the current HIFU simulation study. Convective cooling in large blood vessel and acoustic streaming were shown to change the temperature near blood vessel. It was shown that acoustic streaming effect can affect the blood flow distribution in hepatic arterial branches and leads to the mass flux redistribution.     

On the Courant–Friedrichs–Lewy criterion of rotating grids in 2D vertical-axis wind turbine analysis

The Courant–Friedrichs–Lewy (CFL) criterion for the stability of numerical schemes is herein investigated at the conservative interface that divides rotating grids embedded within fixed grids. This issue is of specific interest to correctly assess the power coefficient and the energy production of vertical-axis wind turbines (VAWTs).The CFL number is here manipulated in a convenient form to tackle rotating grids; this manipulation discloses the dependence of the CFL number from the angular location of rotating grid elements and also from the tip speed ratio of the rotating grid. An upper bound of the CFL number that does not depend on the angular location of the rotating grid element is derived. The angular marching step has dramatic effects on the accuracy of results and strongly affects the calculation of the most important integral property (the power coefficient); however, local quantities are affected to a lesser extent and this fact is misleading. Large errors are generated if the angular marching step is too coarse or, in other words, if the CFL criterion is violated. Angular marching steps as small as only 1° do not warrant accurate results, particularly for very small tip speed ratios and fine spatial discretizations. It is found in this study that rotating grids call for a more restrictive (lower) bound (e.g., CFL number less than 0.15) as compared with the literature criterion. This restriction prompts severe limitations to obtain trustable results from numerical simulations of VAWTs.     

On the growth of Li2CO3 dendrites in nickel–cadmium industrial batteries

A large amount of Li₂CO₃ dendrites has been detected on positive electrodes in Ni–Cd industrial pocket plate batteries, intended to work in stationary applications, after 3 years in float charge. The lattice parameters were refined to a=8.353(1) Å, b=4.974(1) Å, c=6.194(1) Å and β=114.6(1)° [monoclinic], which is in complete agreement with structural data reported in the literature. Oxidation of graphite present in the positive active material is enhanced at elevated temperatures, and at high anodic potentials. This results in an extremely high carbonate concentration in the active material, as well as in the electrolyte. The high carbonate content, in combination with the relatively high lithium concentration present in both electrolyte and positive electrode, is very likely to be the reason for the formation of the Li₂CO₃ dendrites. As this process continues, agglomerates of the dendrites in combination with attached β-Cd(OH)₂ and graphite may generate short circuits between the positive and the negative electrodes.     

Picard–Fuchs Equations and Gauss–Manin Systems with a View Towards the Riemann–Hilbert Problem

We study Abelian integrals associated with a tame polynomial function and their Picard–Fuchs equations using the theory of algebraic Gauss–Manin systems. Especially, we look for a basis of the Petrov module, in which the Picard–Fuchs equations become as simple as possible. As an application, we discuss the related Riemann–Hilbert problem and prove that it has a positive answer under some conditions. In this case, we compute the Jordan normal form of the residue matrices of the corresponding Fuchsian system in terms of local data. 2000 Mathematics Subject Classification. 32S40, 34C20.     

On the dynamic detonation parameters in acetylene–oxygen mixtures with varying amount of argon dilution

In this investigation, the dynamic detonation parameters for stoichiometric acetylene–oxygen mixtures diluted with varying amount of argon are measured and analyzed. The experimental results show that the critical tube diameter and the critical energy for direct initiation of spherical detonations increase with the increase of argon dilution. The scaling behavior between the critical tube diameter d_c and the detonation cell size λ as well as the critical direct initiation energy E_c is systematically studied with the effect of argon dilution. The present results again validate that the relation d_c = 13λ holds for 0–30% argon diluted mixtures and breaks down when argon dilution increases up to 40%. It is found that the explosion length scaling of R_o ∼ 26λ becomes also invalid when the mixture contains approximately this same amount of argon dilution or more. This critical argon dilution is indeed close to that found from experiments in porous-walled tubes by Radulescu and Lee (2002) which exhibit a distinct transition in the failure mechanism. Cell size analysis in literature also indicates that the cellular detonation front starts to become more regular (or stable) when the argon dilution reaches more than 40–50%. Regardless of the degree of argon dilution or mixture sensitivity, the phenomenological model developed from the surface energy concept by Lee, which provides a relation that links the critical tube diameter and the critical energy remains valid. The present experimental results also follow qualitatively the observation from chemical kinetic and detonation instability analyses.