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.     

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 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 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.     

Function of Al on the cycling behavior of the La–Mg–Ni–Co-type alloy electrodes

The cycling behavior of the _{La0.7Mg0.3Ni2.65-xCo0.75Mn0.1Alx}${\mathrm{La}}_{0.7}{\mathrm{Mg}}_{0.3}{\mathrm{Ni}}_{2.65-x}{\mathrm{Co}}_{0.75}{\mathrm{Mn}}_{0.1}{\mathrm{Al}}_x$(x=0,0.3)$(x=0,0.3)$ alloy electrodes was systematically investigated by XRD, SEM, EIS, XPS and AES measurements, and the function of Al in the La–Mg–Ni-based alloys and the reasons for the improvement of the cycling stability of the alloy electrode with Al were discussed. Results show that the cycling behavior of the _{La0.7Mg0.3Ni2.35Co0.75Mn0.1Al0.3}${\mathrm{La}}_{0.7}{\mathrm{Mg}}_{0.3}{\mathrm{Ni}}_{2.35}{\mathrm{Co}}_{0.75}{\mathrm{Mn}}_{0.1}{\mathrm{Al}}_{0.3}$ alloy electrode can be divided into three stages, i.e., the pulverization and Mg oxidation stage, the Mg oxidation and La and/or Al oxidation stage, and the La and Al oxidation and Al oxide film protection stage. The improvement of the cycling stability of the alloy electrode with Al can be ascribed to two factors. One is the decrease in the pulverization of the alloy particles during charge/discharge cycling due to the alloy with Al undergoes a smaller cell volume expansion and contraction. The other is the increase in the anti-oxidation/corrosion due to the formation of a dense Al oxide film during cycling, which is believed to be the most important reason for the improvement of the cycling stability of the La–Mg–Ni–Co–Mn–Al-type alloy electrodes.     

On the onset of thermal convection in rotating nanofluid layer saturating a Darcy–Brinkman porous medium

In this paper, the effect of rotation on the onset of thermal convection in a horizontal layer of nanofluid saturated by a Darcy–Brinkman porous medium is considered. A linear stability analysis based upon normal mode is used to find solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically and graphically. The effects of the concentration Rayleigh number, Taylor number, Lewis number, Darcy number and modified diffusivity ratio on the stability of the system are investigated. The sufficient conditions for the non-existence of overstability are also derived.     

Study on the characteristics of evaporation–atomization–combustion of biodiesel

A great deal of research is being carried out on renewable diesel fuels. The number of raw materials (especially waste, animal, and vegetable oils), production technologies, and additives of biodiesel is increasing. In our work, a evaporation–atomization–combustion system consisting of a biomass liquid fuel was designed to produce a laminar premixed flame for studying the combustion–emission characteristics of biodiesel. The combustion characteristics of biodiesel including flame height, flame front area, flame speed, and OH total signal intensity were studied by planar laser-induced fluorescence of OH (OH-PLIF). The emission characteristics of biodiesel (CO, CO₂, and NO) were studied with a flue gas analyzer. The experimental results showed that the flame height, flame front area, flame speed, and the OH total signal intensity changed with the equivalence ratio (Φ). The relationship between the OH radical intensity and the emission of CO/CO₂ was obtained from the OH-PLIF average signal intensity. The [CO]/[CO₂] ratio decreased with the OH-PLIF average signal intensity. Finally, we obtained the relationship between the OH-PLIF average signal intensity and the NO emissions.     

EXAFS investigation of the destabilization of the Mg–Ni–Ti (H) system

Ti doping destabilizes the Mg₂NiH₄ system, reducing the hydrogenation enthalpy from – 64 kJ/(mol H₂) to around – 40 kJ/(mol H₂). However, the equilibrium pressure is hardly affected, as also the entropy of reaction changes. To understand this thermodynamic behavior it is essential to understand the structure of the phases present in the Ti-doped Mg₂Ni system in metallic and hydrogenated state. We used Extended X-ray Absorption Fine Structure (EXAFS) to investigate the local coordination of Ni and Ti atoms in Mg–Ni–Ti thin films both in the as-prepared as well as in the hydrogenated state. In the as-prepared state two phases, Mg₂Ni and TiNi or TiNi₃, are formed, which transform in a single Ti-doped Mg₂NiH₄ phase in the hydrogenated state. These results are consistent with previous DFT calculations for this system.     

Search for Compromise Solution of the Multistage Axial Compressor's Stochastic Optimization Problem

INTRODUCTIONThecurrentmultistagehoalflowcompressorsde-signingandmodifyingprocessesarecloselyalliedwithalotofoptimizationproblemssolution.Thissituationisattributedtodesigner'snaturalaspirationforthe"best"designselectionfromasetoffeasibledesigns.Tillrecelltlythedesigner'sexperienceandintuitionplayedakeyroleinsearchforthe"best"design.Withthecurrefltlevelofcompressor'scomplexity,largenumberofdesign-pointparametersandgasdynamicperfectionisnecessarytouseanumericalop-timizationmethodtoaidthedesi…