Synthesis of (2,2,2-trifluoroethyl) substituted pyridazin-3(2H)-ones and 1,5-dihydropyrrol-2-ones from α,β-unsaturated γ-lactones and hydrazines

This paper presents the transformation of α,β-unsaturated γ-lactones into 2,2,2-trifluoroethyl substituted pyridazin-3(2H)-ones and 1,5-dihydropyrrol-2-ones starting from various hydrazines. The influence of the γ-lactone substitution (sulfanyl versus sulfonyl moiety) and the nature of the hydrazines (unsubstituted, alkyl- or aryl-substituted) on the outcome of the reaction were studied. All new heterocycles were characterized using 1D NMR, IR, MS and their data was compared with those of two reported X-ray diffraction structures. The two possible competitive pathways leading to pyridazin-3(2H)-ones and/or 1,5-dihydropyrrol-2-ones are discussed. Abinitio DFT calculations were also performed in order to rationalize several experimental results.     

Influence of liquid layers on energy absorption during particle impact

The influence of the thickness of a covering liquid layer and its viscosity as well as the impact velocity on energy loss during the normal impact on a flat steel wall of spherical granules with a liquid layer was studied. Free-fall experiments were performed to obtain the restitution coefficient of elastic-plastic γ- Al2O3 granules by impact on the liquid layer, using aqueous solutions of hydroxypropyl methylcellulose with different concentrations for variation of viscosity （1-300 mPa s）, In the presence of a liquid layer, increase of liquid viscosity decreases the restitution coefficient and the minimum thickness of the liquid layer at which the granule sticks to the wall. The measured restitution coefficients were compared with experiments performed without liquid layer. In contrast to the dry restitution coefficient, due to viscous losses at lower impact velocity, higher energy dissipation was obtained, A rational explanation for the effects obtained was given by results of numerically solved force and energy balances for a granule impact on a liquid layer on the wall. The model takes into account forces acting on the granule including viscous, surface tension, capillary, contact, drag, buoyancy and gravitational forces. Good agreement between simulations and experiments has been achieved.     

Entropy as an Objective Function of Optimization Multimodal Transportations

This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real time in an optimal way with an unacceptable increase in the risk at one of its next stages and predict the redistribution of the load of transport nodes. The aim of this study is to develop a mathematical model for the optimal choice of an alternative route, the best for one or more objective functions in real time. In addition, it is proposed to use this mathematical model to estimate the dynamic change in turnover through intermediate transport nodes, forecasting their loading over time under different conditions that also include long-term risks which are significant in magnitude. To substantiate the feasibility of the proposed mathematical model, the analysis and forecast of cargo turnover through the seaports of Ukraine are presented, taking into account and analysing the existing risks.     

The First Observation of 4f-Luminescence in New Heteronuclear Lanthanide–Germanium Complexes

New lanthanide–germanium complexes with diethylenetriaminepentaacetic acid (DTPA) have been synthesized and were characterized by means of elemental analysis, IR-, UV-absorption and luminescent spectroscopy. The 4f-luminescence of heteronuclear Ln(Ge-DTPA)2 (Ln=Sm, Eu, Tb, Dy) complexes in aqueous solutions was investigated for the first time.     

A parameter choice strategy for the inversion of multiple observations

In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate strategies are required to choose a set of ‘good’ parameters. In this study, we present a fairly general method for choosing such a set of parameters, provided that discrete direct, but maybe noisy, measurements of the underlying quantity are included in the observation data, and the inner product of the reconstruction space can be accurately estimated by the inner product of the discretization space. Then the proposed parameter choice method gives an accuracy that only by an absolute constant multiplier differs from the noise level and the accuracy of the best approximant in the reconstruction and in the discretization spaces.     

Computational study of the US stock market evolution: a rank correlation-based network model

This paper presents a computational study of global characteristics of the US stock market using a network-based model referred to as the market graph. The market graph reflects similarity patterns between stock return fluctuations via linking pairs of stocks that exhibit “coordinated” behavior over a specified period of time. We utilized Spearman rank correlation as a measure of similarity between stocks and considered the evolution of the market graph over the recent decade between 2001–2011. The observed market graph characteristics reveal interesting trends in the stock market over time, as well as allow one to use this model to identify cohesive clusters of stocks in the market.     

Approximation of Fractional Brownian Motion by Martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.     

A network-based data mining approach to portfolio selection via weighted clique relaxations

We introduce a new network-based data mining approach to selecting diversified portfolios by modeling the stock market as a network and utilizing combinatorial optimization techniques to find maximum-weight s-plexes in the obtained networks. The considered approach is based on the weighted market graph model, which is used for identifying clusters of stocks according to a correlation-based criterion. The proposed techniques provide a new framework for selecting profitable diversified portfolios, which is verified by computational experiments on historical data over the past decade. In addition, the proposed approach can be used as a complementary tool for narrowing down a set of “candidate” stocks for a diversified portfolio, which can potentially be analyzed using other known portfolio selection techniques.     

Checking solvability of systems of interval linear equations and inequalities via mixed integer programming

This paper deals with the problems of checking strong solvability and feasibility of linear interval equations, checking weak solvability of linear interval equations and inequalities, and finding control solutions of linear interval equations. These problems are known to be NP$\mathit{NP}$-hard. We use some recently developed characterizations in combination with classical arguments to show that these problems can be equivalently stated as optimization tasks and provide the corresponding linear mixed 0–1 programming formulations.     

Homotopy Types of Stabilizers and Orbits of Morse Functions on Surfaces

Let M be a smooth compact surface, orientable or not, with boundary or without it, P either the real line ℝ ¹ or the circle S ¹, and D(M) the group of diffeomorphisms of M acting on C^∞(M, P) by the rule h⋅ f = f ∘ h ⁻¹ for h ∊ D(M) and f ∊ C^∞ (M,P). Let f: M → P be an arbitrary Morse mapping, Σ _f the set of critical points of f, D(M,Σ _f ) the subgroup of D(M) preserving Σ _f , and S(f), S (f,Σ _f ), O(f), and O(f,Σ _f ) the stabilizers and the orbits of f with respect to D(M) and D(M,Σ _f ). In fact S(f) = S(f,Σ _f ).In this paper we calculate the homotopy types of S(f), O(f) and O(f,Σ _f ). It is proved that except for few cases the connected components of S(f) and O(f,Σ _f ) are contractible, π _k O(f) = π _k M for k ≥ 3, π₂ O(f) = 0, and π₁ O(f) is an extension of π₁ D(M) ⊕ Z ^k (for some k ≥ 0) with a (finite) subgroup of the group of automorphisms of the Kronrod-Reeb graph of f.We also generalize the methods of F. Sergeraert to give conditions for a finite codimension orbit of a tame smooth action of a tame Lie group on a tame Fréchet manifold to be a tame Fréchet manifold itself. In particular, we obtain that O(f) and O(f, Σ _f ) are tame Fréchet manifolds. Communicated by Peter Michor Vienna Mathematics Subject Classifications (2000): 37C05, 57S05, 57R45.