Finite tchebycheff transformations of generalized functions

By using Hilbert space techniques, the finite Tchebycheff transformations of the first and the second kind are defined on appropriate spaces of generalized functions. The inversion theorems are established and some operation transform formulas are obtained. These results are applied in solving certain distributional differential equations.     

Regioselective Hydration of Alkynes by Iron(III) Lewis/Brønsted Catalysis

The triflimide iron(III) salt [Fe(NTf₂)₃] promotes the direct hydration of terminal and internal alkynes with very good Markovnikov regioselectivities and high yields. The enhanced carbophilic Lewis acidity of the Fe^III cation mediated by the weakly‐coordinating triflimide anion is crucial for the catalytic activity. The iron(III) metal salt can be recycled in the form of the OPPh₃/[Fe(NTf₂)₃] system with similar activity and selectivity. However, spectroscopic and kinetic studies show that [Fe(NTf₂)₃] hydrolyzes under the reaction conditions and that catalytically less active Brønsted species are formed, which points to a Lewis/Brønsted co‐catalysis. This triflimide‐based catalytic system is regioselective for the hydration of internal aryl‐alkynes and opens the door to a new synthetic route to alkyl ketophenones. As a proof of concept, the synthesis of two antipsychotics Haloperidol and Melperone, with general butyrophenone‐like structure, is shown.     

Binding Study of the [Ru(NH3)5pz]2+ Complex to Bile Anion Aggregates through Kinetic Measurements

The electron transfer reaction between [Ru(NH₃)₅pz]²⁺ and [Co(C₂O₄)₃]^3? was studied in the presence of monomers and aggregates of bile salts (sodium deoxycholate, sodium taurodeoxycholate, and sodium glycocholate) at 298.2 ± 0.1 K. The results show a decreasing rate constant with the successive addition of bile salts. To rationalize the trends of the reaction rate on the [bile salts], two models were used. One of them takes into account the aggregation feature by considering a stepwise self‐association between monomers, whereas the other assumes the formation of a critical micellar concentration. Binding constants between [Ru(NH₃)₅pz]²⁺ species and deoxycholate or taurodeoxycholate aggregates were higher than that for glycocholate aggregates. These results are consistent with the way in which the monomers are added to form the bile anion aggregates.     

Strategies for spectrum slicing based on restarted Lanczos methods

In the context of symmetric-definite generalized eigenvalue problems, it is often required to compute all eigenvalues contained in a prescribed interval. For large-scale problems, the method of choice is the so-called spectrum slicing technique: a shift-and-invert Lanczos method combined with a dynamic shift selection that sweeps the interval in a smart way. This kind of strategies were proposed initially in the context of unrestarted Lanczos methods, back in the 1990’s. We propose variations that try to incorporate recent developments in the field of Krylov methods, including thick restarting in the Lanczos solver and a rational Krylov update when moving from one shift to the next. We discuss a parallel implementation in the SLEPc library and provide performance results.     

Economic lot scheduling with deliberated and controlled coproduction

This paper presents an algorithm to define the optimal parameters for deliberated and controlled coproduction in an economic lot scheduling problem setting (DCCELSP). Coproduction is said to be deliberated and controlled because it is possible to decide whether or not to coproduce when all the parameters associated with the process are known. The aim is to determine how to produce two products most economically where deliberated coproduction is an option. For this purpose, a procedure for defining optimal lot periods is introduced. Two models are proposed for this procedure and a numerical illustration is provided to gain insight into their dynamics. The cost advantages of coproduction were found to depend on the relationship between setup and holding costs, production rates, and demand for products. The more similar these system parameters are and the higher the machine usage ratio is, the more favourable coproduction is. Additionally, if coproduction is not deliberated appropriately, costs soar.     

Asymptotics of Higher Order Ospt-Functions for Overpartitions

In this paper we obtain asymptotic formulas for positive crank and rank moments for overpartitions. Moreover, we show that crank and rank moments are asymptotically equal while the difference is asymptotically positive. This indicates that there exist analogous higher ospt-functions for overpartitions, which we define.     

Cyclic coordinate descent in hydrothermal nonsmooth problems

In this paper we present an algorithm, inspired by the cyclic coordinate descent method, which allows the solution of hydrothermal optimization problems involving pumped-storage plants. The proof of the convergence of the succession generated by the algorithm was based on the use of an appropriate adaptation of Zangwill’s global theorem of convergence. Finally, the algorithm proposed is implemented using the Mathematica Package and is applied to an example to illustrate the results obtained.