On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Si3N4 single-crystal nanowires grown from silicon micro- and nanoparticles near the threshold of passive oxidation

A simple and most promising oxide-assisted catalyst-free method is used to prepare silicon nitride nanowires that give rise to high yield in a short time. After a brief analysis of the state of the art, we reveal the crucial role played by the oxygen partial pressure: when oxygen partial pressure is slightly below the threshold of passive oxidation, a high yield inhibiting the formation of any silica layer covering the nanowires occurs and thanks to the synthesis temperature one can control nanowire dimensions

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

A note on the Lorenz-maximal allocations in the imputation set

In this note we introduce the Lorenz stable set and provide an axiomatic characterization in terms of constrained egalitarianism and projection consistency. On the domain of all coalitional games, we find that this solution connects the weak constrained egalitarian solution (Dutta and Ray, 1989) with their strong counterpart (Dutta and Ray, 1991)

Solution equilibria of cytosine- and guanine-rich sequences near the promoter region of the n-myc gene that contain stable hairpins within lateral loops

Cytosine-and guanine-rich regions of DNA are capable of forming complex structures named i-motifs and G-quadruplexes, respectively. In the present study the solution equilibria at nearly physiological conditions of a 34 -bases long cytosine-rich sequence and its complementary guanin e-rich strand corresponding to the first intron of the n-mycgene were studied. Both sequences , not yet studied, contain a 12 - base tract capable of forming stable hairpins inside the i-motif and G-quadruplex structures, respectively ...

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

A new look at the Heston characteristic function

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factorization of the moment generating function as product of Bessel type factors, and an approximating sequence to the law of log-spot is deduced.

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory, fourth-order Møller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+ 1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values

Oxidation of silicon: further tests for the interfacial silicon emission model

The classical description of Si oxidation given by Deal and Grove has well-known limitations for thin oxides (below 200 Ã). Among the large number of alternative models published so far, the interfacial emission model has shown the greatest ability to fit the experimental oxidation curves. It relies on the assumption that during oxidation Si interstitials are emitted to the oxide to release strain and that the accumulation of these interstitials near the interface reduces the reaction rate there. The resulting set of differential equations makes it possible to model diverse oxidation experiments. In this paper, we have compared its predictions with two sets of experiments: (1) the pressure dependence for subatmospheric oxygen pressure and (2) the enhancement of the oxidation rate after annealing in inert atmosphere. The result is not satisfactory and raises serious doubts about the model’s correctness

Changes in chromosomal polymorphism and global warming: The case of Drosophila subobscura from Apatin (Serbia)

Abstract In this study, chromosomal inversion polymorphism data for a natural population of Drosophila subobscura from a swampy region near the town of Apatin (Serbia) were compared with data for the same population collected approximately 15 years earlier. The pattern of chromosomal inversion polymorphism changed over time. There were significant increases in the frequency of characteristic southern latitude ("warm" adapted) chromosomal arrangements and significant decreases in the frequency of characteristic northern latitude ("cold" adapted) chromosomal arrangements in the O and U chromosomes. The chromosomal arrangements O3+4 and O3+4+22 (derived from the O3+4 arrangement)showed significant increases in 2008 and 2009 with regard to the 1994 sample. There was also a significant increase (~50%) in the U1+2 arrangement, while U1+8+2 (a typical southern arrangement) was detected for the first time. Since the Apatin swampy population ofD. subobscura has existed for a long time in a stable habitat with high humidity that has not been changed by man our results indicate that natural selection has produced chromosomal changes in response to the increase in temperature that has occurred in the Balkan Peninsula of central southeastern European. Key words: chromosomal inversions, Drosophila subobscura, global warming, karyotypes.

Prediction of crude protein and classification of the growth stage of wheat plant samples from NIR spectra

Near-infrared spectroscopy (NIRS) was used to analyse the crude protein content of dried and milled samples of wheat and to discriminate samples according to their stage of growth. A calibration set of 72 samples from three growth stages of wheat (tillering, heading and harvest) and a validation set of 28 samples was collected for this purpose. Principal components analysis (PCA) of the calibration set discriminated groups of samples according to the growth stage of the wheat. Based on these differences, a classification procedure (SIMCA) showed a very accurate classification of the validation set samples : all of them were successfully classified in each group using this procedure when both the residual and the leverage were used in the classification criteria. Looking only at the residuals all the samples were also correctly classified except one of tillering stage that was assigned to both tillering and heading stages. Finally, the determination of the crude protein content of these samples was considered in two ways: building up a global model for all the growth stages, and building up local models for each stage, separately. The best prediction results for crude protein were obtained using a global model for samples in the two first growth stages (tillering and heading), and using a local model for the harvest stage samples.

The measurement of ice velocity, mass balance and thinning-rate on Johnsons Glacier, Livingston Island, South Shetland Islands, Antarctica

A network of twenty stakes was set up on Johnsons Glacier in order to determine its dynamics. During the austral summers from 1994-95 to 1997-98, we estimated surface velocities, mass balances and ice thickness variations. Horizontal velocity increased dow nstream from 1 m a- 1 near the ice divides to 40 m a- 1 near the ice terminus. The accumulation zone showed low accumulation rates (maximum of 0,6 m a- 1 (ice)), whereas in the lower part of the glacier, ablation rates were 4,3 m a- 1 (ice). Over the 3-year study period, both in the accumulation and ablation zones, we detected a reduction in the ice surface level ranging from 2 to 10 m from the annual ve rt ical velocities and ice-thinning data, the mass balance was obtained and compared with the mass balance field values, resulting in similar estimates. Flux values were calculated using cross-section data and horizontal velocities, and compared with the results obtained by means of mass balance and ice thinning data using the continuity equation. The two methods gave similar results.

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

The binding energies of deformed even-even nuclei have been analyzed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner-Kirkwood ̄h expansion up to fourth order, instead of the usual Strutinsky averaging scheme, to compute the shell corrections in a deformed Woods-Saxon potential including the spin-orbit contribution. For a large set of 561 even-even nuclei with Z 8 and N 8, we find an rms deviation from the experiment of 610 keV in binding energies, comparable to the one found for the same set of nuclei using the finite range droplet model of Moller and Nix (656 keV). As applications of our model, we explore its predictive power near the proton and neutron drip lines as well as in the superheavy mass region. Next, we systematically explore the fourth-order Wigner-Kirkwood corrections to the smooth part of the energy. It is found that the ratio of the fourth-order to the second-order corrections behaves in a very regular manner as a function of the asymmetry parameter I=(N−Z)/A. This allows us to absorb the fourth-order corrections into the second-order contributions to the binding energy, which enables us us to simplify and speed up the calculation of deformed nuclei.