A semi-oriented radial measure for measuring the efficiency of decision making units with negative data,using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data.     

A synthetic entry to furo[2,3-b]pyridin-4(1H)-ones and related furoquinolinones via iodocyclization

[reaction: see text] N-Methyl-4-alkoxy-3-alkynylpyridin-2(1H)-ones readily undergo iodine-promoted 5-endo-heteroannulation under mild conditions to 3-iodofuropyridinium triiodide salts in moderate to good yields. The latter may be dealkylated in situ upon exposure to an iodide anion to provide the corresponding 3-iodofuro[2,3-b]pyridin-4(1H)-ones. The same strategy applies to the formation of furo[2,3-b]quinolin-4(9H)-ones.     

Quantum-Like Tunnelling and Levels of Arbitrage

We apply methods of wave mechanics to financial modelling. We proceed by assigning a financial interpretation to wave numbers. This paper makes a plea for the use of the concept of ‘tunnelling’ (in the mathematical formalism of quantum mechanics) in the modelling of financial arbitrage. Financial arbitrage is a delicate concept to model in social science (i.e. in this case economics and finance) as its presence affects the precision of benchmark financial asset prices. In this paper, we attempt to show how ‘tunnelling’ can be used to positive effect in the modelling of arbitrage in a financial asset pricing context.     

Intermediate range order in supercooled water

ABSTRACT

The temperature dependence of the heights of the first and second x-ray diffraction peaks in supercooled water measured down to 244?K are found to display very different behaviours. While the first peak intensity remains essentially constant, the second peak increases strongly with decreasing temperature. In real space this is concomitant with the reduction of the number of non-bonded interstitial molecules between the first and second shells. It is found that although the first O-O shell in supercooled water is unchanged upon supercooling, the variations in intermediate range order are mainly associated with the growth of a predominantly tetrahedral network that is distinctly different from ice-Ih. Moreover, in this temperature regime we find a direct correlation between the height of the second diffraction peak and the intensity changes in the 2nd, 3rd, 4th and 5th peaks in the oxygen-oxygen pair distribution function.     

Tensor products of unipotent characters of general linear groups over finite fields

Given unipotent characters U ₁, . . . , U _k of GL _n $ \left( {{{\mathbb{F}}_q}} \right) $ , we prove that $ \left\langle {{U_1} \otimes \cdots \cdots \otimes {U_k},1} \right\rangle $ is a polynomial in q with non-negative integer coefficients. We study the degree of this polynomial and give a necessary and sufficient condition in terms of the representation theory of symmetric groups and root systems for this polynomial to be non-zero.     

Complex structured singular value analysis using fixed-structure dynamic D-scales

Models of systems are always inexact. Hence, to better predict the performance of a system it is necessary to take into account uncertainty in a nominal model of a system. The structured singular value was developed to nonconservatively analyze robust stability and performance for systems with multiple-block uncertainty. In practice, optimization techniques are used to compute an upper bound on the structured singular value. For dynamic uncertainty with bounded magnitude and arbitrary phase (i.e., "complex uncertainty"), the standard approach to computing an upper bound involves finding diagonal scaling matrices D(jω) that minimize σ_max (D(jω)G(jω)D^-1(jω)) over a (theoretically) infinite number of frequencies. The order of the corresponding stable, minimum phase, rational function D(s) (if it exists) is hence arbitrary, which can lead to very high order controllers when D(s) is used for controller synthesis. This paper develops a fixed-structure approach to computing an upper bound for the complex structured singular value. In particular, by relying on results from mixed-norm H₂/H_∞ analysisD(s) is a priori constrained to be a rational matrix function of a chosen order and a new approach to computing an upper bound on the structured singular value is developed. The results are illustrated using two examples which clearly demonstrate the suboptimality of standard curve fitting. The proposed approach can be extended to mixed uncertainty and structured singular value controller synthesis without D — K type iteration.     

Parabolic Schemes for Quasi-Linear Parabolic and Hyperbolic PDEs via Stochastic Calculus

We consider two quasi-linear initial-value Cauchy problems on ? ^d : a parabolic system and an hyperbolic one. They both have a first order non-linearity of the form φ(t, x, u)·?u, a forcing term h(t, x, u) and an initial condition u ₀ ∈ L ^∞(? ^d ) ∩ C ^∞(? ^d ), where φ (resp. h) is smooth and locally (resp. globally) Lipschitz in u uniformly in (t, x). We prove the existence of a unique global strong solution for the parabolic system. We show the existence of a unique local strong solution for the hyperbolic one and we give a lower bound regarding its blow up time. In both cases, we do not use weak solution theory but a direct construction based on parabolic schemes studied via a stochastic approach and a regularity result for sequences of parabolic operators. The result on the hyperbolic problem is performed by means of a non-classical vanishing viscosity method.     

Elastic energy of a straight dislocation and contribution from core tractions

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach–Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than those gliding in {112} planes.     

Electro-chemical manifestation of nanoplasmonics in fractal media

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.