A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

An electron microscopic study of nickel sulfide inclusions in toughened glass

It has been known since the early sixties that nickel sulfide inclusions cause spontaneous fracture of toughened (thermally tempered) glass, but despite the considerable amount of work done on this problem in the last four decades, failures still occur in the field with regularity. In this study we have classified (by viewing through a 60x optical microscope) inclusions into two groups, which are classic and atypical nickel sulfides. The classics look like the nickel sulfide inclusions found at the initiation-of-fracture of windows that have broken spontaneously. We have compared the structure and composition of the atypical inclusions with the structure and composition of the classics. All of the classic and atypical nickel sulfide inclusions studied in this work were found to have a composition in the range of Ni52S48 to Ni48S52. Inclusions on the nickel rich side of stoichiometric NiS were found to be two-phase assemblies, and inclusions on the sulphur rich side of NiS were single phase. It had been proposed that the atypicals were passive, and of a different composition to the classics. However, we found that the difference between passive and dangerous nickel sulfide inclusions was not a difference in composition but rather a difference in the type of material in the internal pore space. The passive's had carbon char in their internal pore space, whereas the pore space of dangerous inclusions contained Na2O. The presence of Na2O and carbon char with the inclusions indicates that the formation of the inclusions results from a reaction of a nickel-rich phase with sodium sulphate and carbon. (C) 2001 Kluwer Academic Publishers.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Beneficial effects of air inclusions on the performance of ethylene vinyl acetate (EVA) mouthguard material

Objective: To investigate the impact characteristics of an ethylene vinyl acetate (EVA) mouthguard material with regulated air inclusions, which included various air cell volumes and wall thickness between air cells. In particular, the aim was to identify the magnitude and direction of forces within the impacts. Method: EVA mouthguard material, A mm thick and with and without air inclusions, was impacted with a constant force impact pendulum with an energy of 4.4 J and a velocity of 3 m/s. Transmitted forces through the EVA material were measured using an accelerometer, which also allowed the determination of force direction and magnitude within the impacts. Results: Statistically significant reductions in the transmitted forces were observed with all the air inclusion materials when compared with EVA without air inclusions. Maximum transmitted force through one air inclusion material was reduced by 32%. Force rebound was eliminated in one material, and reduced second force impulses were observed in all the air inclusion materials. Conclusion: The regulated air inclusions improved the impact characteristics of the EVA mouthguard material, the material most commonly used in mouthguards world wide.

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

Towards an understanding of the age and origin of mesothermal gold mineralisation in the Etheridge Goldfield, Georgetown region, north Queensland

Small mesothermal vein quam-gold-base-metal sulfide deposits from which some 20 t of Au-Ag bullion have been extracted, are the most common gold deposits in the Georgetown region of north Queensland-several hundred were mined or prospected between 1870 and 1950. These deposits are mostly hosted by Proterozoic granitic and metamorphic rocks and are similar to the much larger Charters Towers deposits such as Day Dawn and Brilliant, and in some respects to the Motherlode deposits of California. The largest deposit in the region-Kidston (> 138 t of Au and Ag since 1985)- is substantially different. It is hosted by sheeted quartz veins and cavities in brecciated Silurian granite and Proterozoic metamorphics above nested high-level Carboniferous intrusives associated with a nearby cauldron subsidence structure. This paper provides new information (K-Ar and Rb-Sr isotopic ages, preliminary oxygen isotope and fluid-inclusion data) from some of the mesothermal deposits and compares it with the Kidston deposit. All six dated mesothermal deposits have Siluro-Devonian (about 425 to 400 Ma) ages. All nine of such deposits analysed have delta(18)O quartz values in the range 8.4 to 15.7 parts per thousand, Fluid-inclusion data indicate homogenisation temperatures in the range 230-350 degrees C. This information, and a re-interpretation of the spatial relationships of the deposits with various elements of the updated regional geology, is used to develop a preliminary metallogenic model of the mesothermal Etheridge Goldfield. The model indicates how the majority of deposits may have formed from hydrothermal systems initiated during the emplacement of granitic batholiths that were possibly, but not clearly, associated with Early Palaeozoic subduction, and that these fluid systems were dominated by substantially modified meteoric and/or magmatic fluids. The large Kidston deposit and a few small relatives are of Carboniferous age and formed more directly from magmatic systems much closer to the surface.

Corruption and auctions

We investigate how corruption affects the outcome of a first-price auction (bidding behavior, efficiency and the seller's expected revenue). The auctioneer approaches the winner to offer the possibility of a reduction in his bid in exchange for a bribe. The bribe can be a percentage of the difference between the winning and the second-highest bid or a fixed amount. We show that there exists a symmetric bidding strategy equilibrium that is monotone, i.e., higher valuation buyers bid higher. Corruption does not affect efficiency but both the auctioneer's expected bribe and the seller's expected revenue depend on the format of the bribe payments. We also find the optimal bribe scheme.

A systemic parvo-like virus in the freshwater crayfish Cherax destructor

Systemic Cowdry Type A inclusions (CAs) were observed in a moribund Cherax destructor collected at an aquaculture farm in South Australia. Inclusions were most common in the gills and were associated with multifocal necrosis of the main gill axis and lamellae. The hepatopancreas was necrotic; however, only one CA was observed in the interstitial tissues. CAs were associated with necrosis in the abdominal and gut musculature. CAs were also observed in the spongy connective tissues and the epicardium. Empty capsids (17.5 +/- 0.5 nm) and microfilaments were most commonly observed within these inclusions by transmission electron microscopy. Complete icosahedral viral particles (20.8 +/- 1.2 nm) were difficult to distinguish within the viroplasm, but were visualised better in aggregates between the viroplasm and the inner nuclear membrane. The nucleolus was closely associated with the developing viroplasm, and was hypertrophied and segregated into its fibrillar and granular components. The virus was named Cherax destructor systemic parvo-like virus (CdSPV) on the basis of its histopathology, cytopathology and morphology. CdSPV is the first systemic virus described in a freshwater crayfish.