Second-order conditions in C 1,1 constrained vector optimization

We consider the constrained vector optimization problem min _C f(x), g(x) ∈ ?K, where f:? ⁿ →? ^m and g:? ⁿ →? ^p are C ^1,1 functions, and C ? ^m and K ? ^p are closed convex cones with nonempty interiors. Two type of solutions are important for our considerations, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers). We formulate and prove in terms of the Dini directional derivative second-order necessary conditions for a point x ⁰ to be a w-minimizer and second-order sufficient conditions for x ⁰ to be an i-minimizer of order two. We discuss the reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanmäki, K?í?ek [21].     

Orbifolds and groupoids

We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper étale effective groupoid objects over the complex manifolds. Both on (Pre-Orb) and (Grp) there are natural equivalence relations on objects: (a natural extension of) equivalence of orbifold atlases on (Pre-Orb) and Morita equivalence in (Grp). We prove that F induces a bijection between the equivalence classes of its source and target.     

Local branching

The availability of effective exact or heuristic solution methods for general Mixed-Integer Programs (MIPs) is of paramount importance for practical applications. In the present paper we investigate the use of a generic MIP solver as a black-box ``tactical' tool to explore effectively suitable solution subspaces defined and controlled at a ``strategic' level by a simple external branching framework. The procedure is in the spirit of well-known local search metaheuristics, but the neighborhoods are obtained through the introduction in the MIP model of completely general linear inequalities called local branching cuts. The new solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the MIP solver at hand. It alternates high-level strategic branchings to define the solution neighborhoods, and low-level tactical branchings to explore them. The result is a completely general scheme aimed at favoring early updatings of the incumbent solution, hence producing high-quality solutions at early stages of the computation. The method is analyzed computationally on a large class of very difficult MIP problems by using the state-of-the-art commercial software ILOG-Cplex 7.0 as the black-box tactical MIP solver. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the new method exhibits consistently an improved heuristic performance: in 23 out of 29 cases, the MIP solver produced significantly better incumbent solutions when driven by the local branching paradigm. Mathematics Subject Classification (2000):90C06, 90C10, 90C11, 90C27, 90C59     

Personal income tax reforms: A genetic algorithm approach

Given a settled reduction in the present level of tax revenue, and by exploring a very large combinatorial space of tax structures, in this paper we employ a genetic algorithm in order to determine the ‘best’ structure of a real world personal income tax that allows for the maximisation of the redistributive effect of the tax, while preventing all taxpayers being worse off than with the present tax structure. We take Italy as a case study.     

The use of dynamical networks to detect the hierarchical organization of financial market sectors

Two kinds of filtered networks: minimum spanning trees (MSTs) and planar maximally filtered graphs (PMFGs) are constructed from dynamical correlations computed over a moving window. We study the evolution over time of both hierarchical and topological properties of these graphs in relation to market fluctuations. We verify that the dynamical PMFG preserves the same hierarchical structure as the dynamical MST, providing in addition a more significant and richer structure, a stronger robustness and dynamical stability. Central and peripheral stocks are differentiated by using a combination of different topological measures. We find stocks well connected and central; stocks well connected but peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. It results that the Financial sector plays a central role in the entire system. The robustness, stability and persistence of these findings are verified by changing the time window and by performing the computations on different time periods. We discuss these results and the economic meaning of this hierarchical positioning.     

Origin of magnetic interactions and their influence on the structural properties of Ni2MnGa and related compounds

In this work, we perform first-principles DFT calculations to investigate the interplay between magnetic and structural properties in Ni(2)MnGa. We demonstrate that the relative stability of austenite (cubic) and non-modulated martensite (tetragonal) phases depends critically on the magnetic interactions between Mn atoms. While standard approximate DFT functionals stabilize the latter phase, a more accurate treatment of electronic localization and magnetism, obtained with DFT+U, suppresses the non-modulated tetragonal structure for the stoichiometric compound, in better agreement with experiments. We show that the Anderson impurity model, with Mn atoms treated as magnetic impurities, can explain this observation and that the fine balance between super-exchange RKKY type interactions mediated by Ni d and Ga p orbitals determines the equilibrium structure of the crystal. The Anderson model is also demonstrated to capture the effect of the number of valence electrons per unit cell on the structural properties, often used as an empirical parameter to tune the behavior of Ni(2)MnGa based alloys. Finally, we show that off-stoichiometric compositions with excess Mn promote transitions to a non-modulated tetragonal structure, in agreement with experiments.     

CO(2) Fixation by Novel Copper(II) and Zinc(II) Macrocyclic Complexes. A Solution and Solid State Study

Solutions containing Zn(II) and Cu(II) complexes with [15]aneN(3)O(2) rapidly adsorb atmospheric CO(2) to give {[ZnL](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) (2) and {[CuL](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) (4) complexes. The crystal structures of both complexes have been solved (for 2, space group R3c, a, b = 22.300(5) ?, c = 17.980(8) ?, V = 7743(4) ?(3), Z = 6, R = 0.0666, R(w)(2) = 0.1719; for 4, space group R3c, a, b = 22.292(7) ?, c = 10.096(8) ?, V = 7788(5) ?(3), Z = 6, R = 0.0598, R(w)(2) = 0.1611), and the spectromagnetic behavior of 4 has been studied. In both compounds a carbonate anion triply bridges three metal cations. Each metal is coordinated by one oxygen of the carbonate, three nitrogens, and an oxygen of the macrocycle; the latter donor weakly interacts with the metals. Although the two compounds are isomorphous, they are not isostructural, because the coordination geometries of Zn(II) in 2 and Cu(II) in 4 are different. The mixed complex {[CuZn(2)L(3)](&mgr;(3)-CO(3))}.(ClO(4))(4) has been synthesized. X-ray analysis (space group R3c, a, b = 22.323(7) ?, c = 17.989(9) ?, V = 7763(5) ?(3), Z = 6, R = 0.0477, R(w)(2) = 0.1371) and EPR measurements are in accord with a &mgr;(3)-carbonate bridging one Cu(II) and two Zn(II) ions in {[CuZn(2)L(3)](&mgr;(3)-CO(3))}(4+). Both the Zn(II) and Cu(II) cations exhibit the same coordination sphere, almost equal to that found in the trinuclear Zn(II) complex 2. The systems Zn(II)/L and Cu(II)/Lhave been studied by means of potentiometric measurements in 0.15 mol dm(-)(1) NaCl and in 0.1 mol dm(-)(3) NaClO(4) aqueous solutions; the species present in solution and their stability constants have been determined. In both systems [ML](2+) species and hydroxo complexes [M(II)LOH](+) (M = Zn, Cu) are present in solution. In the case of Cu(II), a [CuL(OH)(2)] complex is also found. The process of CO(2) fixation is due to the presence of such hydroxo-species, which can act as nucleophiles toward CO(2). In order to test the nucleophilic ability of the Zn(II) complexes, the kinetics of the promoted hydrolysis of p-nitrophenyl acetate has been studied. The [ZnLOH](+) complex promotes such a reaction, where the Zn(II)-bound OH(-) acts as a nucleophile to the carbonyl carbon. The equilibrium constants for the addition of HCO(3)(-) and CO(3)(2)(-) to the [ZnL](2+) complex have been potentiometrically determined. Only [ML(HCO(3))](+) and [ML(CO(3))] species are found in aqueous solution. A mechanism for the formation of {[ML](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) is suggested.     

Single versus poly-crystalline layered oxide cathode materials for solid-state battery applications - a short review article

The recent developments in the application of single-crystalline (SC) cathode materials in solid-state batteries are discussed in this mini-review. The characteristics of SC and poly-crystalline (PC) cathode materials are explored, with emphasis on the kinetic and mechanical properties. The critical factors influencing their performance in liquid electrolyte and solid-state battery cells are investigated. Finally, the advantages and disadvantages of both morphologies are discussed and considerations to ensure a fair comparison between SC and PC cathodes in different systems are raised.     

q value and parent energy optimization using a low-voltage ionization approach increases resolution in linear ion trap mass spectrometry

In this work, the isolation step in the linear ion trap was performed using different “q values” conditions at a low collision-induced dissociation (CID) energy leading to the parent ion resolution improvements, reasonably due to better ion energy distribution. According to the results, we obtained a greater resolution and mass accuracy operating in both traditional electrospray and low voltage ionization near the q value = 0.778 and with a CID energy of 10%. This effect was evaluated with low-molecular-mass compounds (skatole and arginine). The proposed optimization yielded a superior instrument performance without adding technological complexity to mass spectrometry analyses.