AES and ELS study of titanium oxidation in high vacuum

In the present work, results of the interaction of O₂ with polycrystalline titanium using AES, and ELS techniques, are presented. Changes in the shapes of Ti(LMV) and Ti(LMM) transitions and in the Ti(LM)O(V)/Ti(LMV) and Ti(LMV) Ti(LMM) amplitude ratios as well as a shift of the 34 eV loss peak [Ti(3p level], are studied as function of the oxygen exposure.At O₂ pressures equal or less than 10^–6 Pa and exposure up to 2000 L(O₂) (weak oxidation), the Ti(LM)O(V)/Ti(LMV) and Ti(LMV)/Ti(LMM) ratios show three clearly distinct regions: (i) up to 20L there is a chemisorbed phase with the Ti(LMV)/Ti(LMM) ratio remaining constant and a fast linear increase in the Ti(LM)O(V)/Ti(LMM) ratio. (ii) At exposures higher than 20L the oxidation begins being characterized by a linear variation of the Ti(LM)O(V)/Ti(LMV) and Ti(LMV)/Ti(LMV) ratios, with positive and negative slopes, respectively. (iii) At 125L there is a change in both slopes but no stable value is achieved, despite the O(KLL)/Ti(LMM) ratio remains constant. Hence, it can be concluded that TiO is the final oxide obtained after that treatment, from features like the shape of the transitions and a maximum shift of 3eV of the Ti(3p) level, complemented with ESD experiments.On the other hand, experiments at pressures higher than 10^–4Pa with or without the surfaces at 900K (strong oxidation) indicate that the most likely final oxide is TiO₂.Work presented to the IXIVC-VICSS. Madrid (1983)     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Screw dislocation in spherical particle

The elastic fields generated by a straight-line screw dislocation axially arranged in a spherical particle have been calculated and analyzed. Some features of the distribution of elastic fields in this case and in the case of a screw dislocation lying along the axis of a cylindrical whisker are similar. The elastic energies per unit dislocation length differ slightly in the two cases. This corroborates the validity of application of some of the results obtained for screw dislocations in elastic cylinders to the study of properties of screw dislocations in equiaxed particles.Authors are very indebted to dr. A. B. Lebedev for his kind support.     

Algorithms for multi-extremal mathematical programming problems employing the set of joint space-filling curves

Some powerful algorithms for multi-extremal non-convex-constrained optimization problems are based on reducing these multi-dimensional problems to those of one dimension by applying Peano-type space-filling curves mapping a unit interval on the real axis onto a multi-dimensional hypercube. Here is presented and substantiated a new scheme simultaneously employing several joint Peano-type scannings which conducts the property of nearness of points in many dimensions to a property of nearness of pre-images of these points in one dimension significantly better than in the case of a scheme with a single space-filling curve. Sufficient conditions of global convergence for the new scheme are investigated.This paper was presented at the II. IIASA Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Discriminant versus rough sets approach to vague data analysis

This paper presents a comparative study of the use of two different methods of data analysis on a common set of data. The first is a method based on rough sets theory and the second is the location model method from the field of discriminant analysis. To investigate the comparative performance of these methods, a set of real medical data has been used. The data considered are of both discrete and continuous character. During the comparison, particular attention is paid to data reduction and to the derivation of decision rules and classification functions from the reduced set.     

On non-measurability of in its second dual

We show that with the weak topology is not an intersection of Borel sets in its Cech-Stone extension (and hence in any compactification). Assuming (CH), this implies that has no continuous injection onto a Borel set in a compact space, or onto a Lindelöf space. Under (CH), this answers a question of Arhangel'ski.

     

On Borel Sets in Function Spaces with the Weak Topology

It is proved that the duality map ,:(, weak)x(()*, weak*)R isnot Borel. More generally, the evaluation e:(C)(K),x KR, e(f,x) = f(x), is not Borel for any function space C(K) on a compactF-space. It is also shown that a non-coincidence of norm-Boreland weak-Borel sets in a function space does not imply thatthe duality map is non-Borel.     

Dynamic Global Constraints in Backtracking Based Environments

Global constraints provide strong filtering algorithms to reduce the search space when solving large combinatorial problems. In this paper we propose to make the global constraints dynamic, i.e., to allow extending the set of constrained variables during search. We describe a generic dynamisation technique for an arbitrary monotonic global constraint and we compare it with the semantic-based dynamisation for the alldifferent constraint. At the end we sketch a dynamisation technique for non-monotonic global constraints. A comparison with existing methods to model dynamic problems is given as well.     

The Inverse Scattering Method and Systems of Equations qxy = F(q,qy)

Consider equations of the form where q is in general a complex vector and the function F depends nontrivially both on q and on q_y. We show that a family S of such equations can be investigated by the inverse scattering method. If an equation (*) belongs to S, the function F depends linearly on q and algebraically on q_y. We show that the family S contains a subfamily in which each equation can be obtained from the two dimensional Toda lattice equations by a Bäcklund transformation.