An exact method with variable fixing for solving the generalized assignment problem

We propose a simple exact algorithm for solving the generalized assignment problem. Our contribution is twofold: we reformulate the optimization problem into a sequence of decision problems, and we apply variable-fixing rules to solve these effectively. The decision problems are solved by a simple depth-first lagrangian branch-and-bound method, improved by our variable-fixing rules to prune the search tree. These rules rely on lagrangian reduced costs which we compute using an existing but little-known dynamic programming algorithm.     

Combined Routeing and Scheduling for the Transportation of Containerized Cargo

A tractor-trailer problem, with full load, from the class of combined routeing and scheduling problems is described. Distinctive features of the problem are: movements must be carried out within certain time windows; subsets of movements are linked in the sense that they must be executed in a certain order; and different priorities are attached to different movements. A new bidirectional sequential constructive heuristic is developed for the solution of this problem. The method constructs routes and schedules for the available tractor fleet. The algorithm attempts to minimize the total time for all the movements by minimizing the time taken up by unproductive movements (so-called deadhead) and waiting time between movements. Some practical aspects of the implementation of the approach are discussed.     

Spectral analysis for the Gauss problem on continued fractions

We present a new derivation of the formula appearing in Babenko (1978) and Mayer and Roepstorff (1987) that gives the probability distribution of τ⁻ⁿ${\tau }^{-n}$ in terms of the eigenvalues of a symmetric operator. Here τ$\tau$ is the well-known Gauss-map.     

Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls

We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty , $ with measurable coefficients in a punctured ball B _R \{0} of ? ^N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a _{i j} ) and (b _i ) stabilize at zero, and we provide some optimal conditions in this setting.     

Continuous fields of C*-algebras over finite dimensional spaces

Let X be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of C(X)-algebras by C(X)-subalgebras with controlled complexity. The following applications are given. All unital separable continuous fields of C*-algebras over X with fibers isomorphic to a fixed Cuntz algebra On, n∈{2,3,…,∞}, are locally trivial. They are trivial if n=2 or n=∞. For n?3 finite, such a field is trivial if and only if (n−1)[A₁]=0 in K₀(A), where A is the C*-algebra of continuous sections of the field. We give a complete list of the Kirchberg algebras D satisfying the UCT and having finitely generated K-theory groups for which every unital separable continuous field over X with fibers isomorphic to D is automatically locally trivial or trivial. In a more general context, we show that a separable unital continuous field over X with fibers isomorphic to a KK-semiprojective Kirchberg C*-algebra is trivial if and only if it satisfies a K-theoretical Fell type condition.     

Vectorial penalization for generalized functional constrained problems

In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.     

Computational Insights of Selective Intramolecular O-atom Transfer Mediated by Bioinspired Copper Complexes

The stereoselective copper-mediated hydroxylation of intramolecular C−H bonds from tridentate ligands is reinvestigated using DFT calculations. The computational study aims at deciphering the mechanism of C−H hydroxylation obtained after reaction of Cu(I) precursors with dioxygen, using ligands bearing either activated ( L¹ ) or non-activated ( L² ) C−H bonds. Configurational analysis allows rationalization of the experimentally observed regio- and stereoselectivity. The computed mechanism involves the formation of a side-on peroxide species ( P ) in equilibrium with the key intermediate bis-(μ-oxo) isomer ( O ) responsible for the C−H activation step. The P/O equilibrium yields the same activation barrier for the two complexes. However, the main difference between the two model complexes is observed during the C−H activation step, where the complex bearing the non-activated C−H bonds yields a higher energy barrier, accounting for the experimental lack of reactivity of this complex under those conditions.     

Characterizing Methyl‐Bearing Side Chain Contacts and Dynamics Mediating Amyloid β Protofibril Interactions Using 13Cmethyl‐DEST and Lifetime Line Broadening

Many details pertaining to the formation and interactions of protein aggregates associated with neurodegenerative diseases are invisible to conventional biophysical techniques. We recently introduced ¹⁵N dark‐state exchange saturation transfer (DEST) and ¹⁵N lifetime line‐broadening to study solution backbone dynamics and position‐specific binding probabilities for amyloid β (Aβ) monomers in exchange with large (2–80 MDa) protofibrillar Aβ aggregates. Here we use ¹³C_methyl DEST and lifetime line‐broadening to probe the interactions and dynamics of methyl‐bearing side chains in the Aβ‐protofibril‐bound state. We show that all methyl groups of Aβ40 populate direct‐contact bound states with a very fast effective transverse relaxation rate, indicative of side‐chain‐mediated direct binding to the protofibril surface. The data are consistent with position‐specific enhancements of ¹³C_methyl‐${R{{{\rm tethered}\hfill \atop 2\hfill}}}$ values in tethered states, providing further insights into the structural ensemble of the protofibril‐bound state.     

Polylactide (PLA)-CaSO4 composites toughened with low molecular weight and polymeric ester-like plasticizers and related performances

Large amounts of stable β-anhydrite II (AII), a specific type of dehydrated gypsum and a by-product of lactic acid production process, can be melt-blended with bio-sourced and biodegradable polylactide (PLA) to produce economically interesting novel composites with high tensile strength and thermal stability.To enhance their toughness, while preserving an optimal stiffness, selected low molecular weight plasticizers (bis(2-ethylhexyl) adipate and glyceryl triacetate) and polymeric adipates with different molecular weights have been mixed with a specific PLA (l/d isomer ratio of 96/4) and 40 wt% of AII using an internal kneader. Addition of up to 10 wt% plasticizer into these highly filled compositions can trigger a fourfold increase of the impact strength with respect to the compositions without any modifier, cold crystallization properties and a significant decrease of their glass transition temperature. Moreover, these ternary compositions (PLA-AII-plasticizer) are clearly characterized by easier processing, notable thermo-mechanical performances and good filler dispersion. This study represents a new approach in formulating novel melt-processable polyester grades with improved characteristic features using PLA as biodegradable polymer matrix.