Comparison of Green Functions and Harmonic Measures for Parabolic Operators

In this paper, we prove two-sided pointwise estimates for the Green function of a parabolic operator with singular first order term on a C^1,1-cylindrical domain . Basing on these estimates, we establish the equivalence of the parabolic measure, the adjoint parabolic measure and the surface measure on the lateral boundary of . These results are first studied by some authors for certain elliptic and less general parabolic operators. Mathematics Subject Classifications (2000) 31B25, 35B05, 35K10, 58J35.     

Finding the efficiency score and RTS characteristic of DMUs by means of identifying the efficient frontier in DEA

Data envelopment analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as decision-making units (DMUs), where the presence of multiple inputs and outputs makes comparisons difficult. The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, a method for identifying the efficient frontier is introduced. Then, the efficiency score and returns to scale (RTS) characteristic of DMUs will be produced by means of the equation of efficient frontier.     

Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution

This paper discusses full fuzzy linear programming (FFLP) problems of which all parameters and variable are triangular fuzzy numbers. We use the concept of the symmetric triangular fuzzy number and introduce an approach to defuzzify a general fuzzy quantity. For such a problem, first, the fuzzy triangular number is approximated to its nearest symmetric triangular number, with the assumption that all decision variables are symmetric triangular. An optimal solution to the above-mentioned problem is a symmetric fuzzy solution. Every FLP models turned into two crisp complex linear problems; first a problem is designed in which the center objective value will be calculated and since the center of a fuzzy number is preferred to (its) margin. With a special ranking on fuzzy numbers, the FFLP transform to multi objective linear programming (MOLP) where all variables and parameters are crisp.     

Predictive control of periodic-review production inventory systems with deteriorating items

In this paper a predictive control strategy is applied to a periodic-review dynamic inventory system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach is the use of future information of the inventory target level and the desired production rate, which are available, along the fixed horizon. The deterioration coefficient may be known or unknown and both cases are considered. In the case where it is unknown, the self-tuning predictive control is applied. The proposed control algorithms are illustrated by simulations.     

On the Symmetric H q -Semiclassical Polynomial Sequences of Even Class. Some Examples from the Class Two

In the present work, we deal with the quadratic decomposition of symmetric H _q -semiclassical polynomial sequences of even class. Some examples from class two are settled. We give an integral and discrete measure representations for each of considered symmetric forms.     

On a numerical technique for finding multiple zeros and its dynamic

An optimal method is developed for approximating the multiple zeros of a nonlinear function, when the multiplicity is known. Analysis of convergence for the proposed technique is studied to reveal the fourth-order convergence. We further investigate the dynamics of such multiple zero finders by using basins of attraction and their corresponding fractals in the complex plane. A fourth-order method will also be presented, when the multiplicity m is not known. Numerical comparisons will be made to support the underlying theory of this paper.     

Steady state analysis of an M/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.     

New Analytical Method using Coupled Enzymes for Determination of Polyunsaturated Fatty Acid Content in Olive Oil

A new, simple, and original method is described for specific measurement of polyunsaturated fatty acid content in olive oil. This analytical system uses coupled enzymes, lipase and lipoxygenase. The system consists of lipase-catalyzed hydrolysis of triacylglycerol and subsequent lipoxygenation of liberated polyunsaturated fatty acids. The hydroperoxy-fatty acids formed were easily monitored by spectrophotometry at 234 nm. After being optimized, the method was validated in terms of linearity, precision sensitivity, and recovery. Linear calibration graph was obtained in the range 50–500 µg mL^?1, with a correlation coefficient higher than 0.921 and a detection limit (S/N?=?3) of 15 µg mL^?1. The precision of the method (relative standard deviation) for within and between days is better than 7% and 12%, respectively. The proposed method was successfully applied to the estimation of polyunsaturated fatty acids level in olive oil samples and results obtained were in excellent agreement with those obtained by the classical official method. The proposed method is accurate, simple, cheap, and can be satisfactorily used for routine analysis of edible oils.     

Transformations de N-acylaziridines catalysées par des supports à base de silice et d’alumine : une élucidation mécanistique

The silica gel, neutral alumina and acid activated clays transform the N-acyl-2,2-dimethylaziridines 1 into a mixture of N-methallylamides 2, oxazolines 3 and amidoalcohols 4. The reaction of N-benzoyl-2,2-dimethylaziridine with benzylcyanid anion leads to a mixture of amidopyrroline 5 and iminopyrrolidine 6. The product 5 was converted into its tautomer 6 by chromatogaphy on silica gel. Ionic mechanisms were then proposed to explain the formation of products 2–6 resulting from the regioselective ring opening on the more substituted C2 carbon side.     

Electron affinities of biscyclopentadienyl and phospholyl uranium(IV) borohydride complexes: Experimental and DFT studies

Electron affinities (EAs) of a series of biscyclopentadienyl and phospholyl uranium(IV) complexes L₂U(BH₄)₂ [L₂ = Cp₂, (tmp)₂, (tBuCp)₂, (Cp*)(tmp) and Cp*₂] related to the U(III)/U(IV) redox system were calculated using relativistic Density Functional Theory (DFT) based methods coupled with the Conductor-like Screening Model for Real Solvents (COSMO-RS) approach. Electrochemical measurements of half-wave potentials in solution (tetrahydrofuran THF) were carried out for all these compounds under the same rigorous conditions. A good correlation (r² = 0.99) is obtained between the calculated EA values, at the ZORA/BP86/TZ2P level, and the half-wave reduction potentials measured by electrochemistry. The investigations bring to light the importance of spin-orbit coupling and solvent effect and the use of a large basis set in order to achieve such a good agreement between theory and experiment. The study confirms the instability of the Cp₂U(BH₄)₂ complex during the reduction process. The influence of the substituted aromatic ligand L₂, namely their electron donating ability, on EA was studied. The role of involved orbitals (singled occupied molecular orbital –SOMO– of anionic species or lowest unoccupied molecular orbital –LUMO– of neutral species) in the redox process was revealed.