Analytical Linear Inequality Systems and Optimization

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.     

Existence and uniqueness of v-asymptotic expansions and Colombeau's generalized numbers

We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of the v-asymptotic expansion of an integral with a large parameter. As another application (with significance in the non-linear theory of generalized functions) we show that every Colombeau's generalized number has a v-asymptotic expansion. A similar result follows for Colombeau's generalized functions, in particular, for all Schwartz distributions.     

Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

Motzkin predecomposable sets

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.     

Polarization reflection holographic gratings in azobenzene-containing gelatine films

We have written polarization reflection holograms in an azobenzene-containing material. Two waves with circular polarization were used to record the gratings; the light resulting from their overlap induces chirality in the samples. The holographic reflection of the polarization gratings has the properties of Bragg reflection in cholesteric liquid crystals.     

Photoinduced dichroism in lightsensitive suspension layers of As2S3 dispersed in gelatin

The absorption edge shift and the spectra of the dichroism in suspension layers of As₂S₃ dispersed in gelatin induced by a linearly polarized laser light are measured. The results are compared to the photoinduced changes in evaporated As₂S₃ layers.     

Are current-induced forces conservative?

The expression for the force on an ion in the presence of current can be derived from first principles without any assumption about its conservative character. However, energy functionals have been constructed that indicate that this force can be written as the derivative of a potential. On the other hand, there exist specific arguments that strongly suggest the contrary. We propose physical mechanisms that invalidate such arguments and demonstrate their existence with first-principles calculations. While our results do not constitute a formal resolution to the fundamental question of whether current-induced forces are conservative, they represent a substantial step forward in this direction.     

A functional model for polynomially posinormal operators

In this paper we introduce a class of operators naturally extending the classes of hyponormal and posinormal operators. For this class we construct a generating family of eigendistributions, unitary invariants and a functional model.     

Current-induced embrittlement of atomic wires

Recent experiments suggest that gold single-atom contacts and atomic chains break at applied voltages of 1 to 2 V. In order to understand why current flow affects these defect-free conductors, we have calculated the current-induced forces on atoms in a Au chain between two Au electrodes. These forces are not by themselves sufficient to rupture the chain. However, the current reduces the work to break the chain, which results in a dramatic increase in the probability of thermally activated spontaneous fracture of the chain. This current-induced embrittlement poses a fundamental limit to the current-carrying capacity of atomic wires.     

Influence of pH of the BSA solutions on velocity of the rising bubbles and stability of the thin liquid films and foams

Influence of pH of the BSA solutions on velocity of the rising bubbles, stability of foams, and properties of single foam and wetting films was studied. It was found that the solution pH affected significantly the BSA surface activity and properties of the protein adsorption layer under dynamic and static conditions. At pH close to the isoelectric point (pH_IEP=4.8) the BSA showed the highest surface activity. The equilibrium microscopic foam films of thicknesses of 64–80 nm, depending on the BSA concentration, were obtained at pH=5.8. Under dynamic conditions the bubble rising velocity was reduced in a highest degree and the foam formed were most stable at the solutions pH-5.8 and 4.8. Lowering the bubble velocity shows that the BSA adsorption layer was formed, which retarded fluidity of the bubble surface. When the solution pH was significantly lower (pH=3.9) or much higher (pH=10) than the pH_IEP then the BSA practically had no influence on the bubble velocity and the foam stability was drastically reduced. Moreover, the pH variations affected also the time of the three-phase contact (TPC) formation on mica surface covered by the BSA adsorption layers. These pH dependent changes in the BSA surface activity indicate that the BSA linear conformers, existing at pH far away from the pH_IEP, have much higher affinity to aqueous phase resulting from higher net electrical charge present over the extended BSA molecule conformers.