Singer cycles in 2-modular representations of the group $$GL_{n+1}(2)$$

We determine the irreducible 2-modular representations of the group \(G=GL_{n+1}(2)\) in which a Singer cycle has eigenvalue 1, and show that in these representations every element \(g\in G\) has eigenvalue 1.     

Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.     

Finding representations for an unconstrained bi-objective combinatorial optimization problem

Typically, multi-objective optimization problems give rise to a large number of optimal solutions. However, this information can be overwhelming to a decision maker. This article introduces a technique to find a representative subset of optimal solutions, of a given bounded cardinality for an unconstrained bi-objective combinatorial optimization problem in terms of \(\epsilon \)-indicator. This technique extends the Nemhauser–Ullman algorithm for the knapsack problem and allows to find a representative subset in a single run. We present a discussion on the representation quality achieved by this technique, both from a theoretical and numerical perspective, with respect to an optimal representation.     

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional.     

Simple ℤ<Subscript>2</Subscript>-actions twisted by aperiodic automorphisms

We construct a simple transformation whose centralizer is isomorphic to (?)² ? _A ?, where A is an aperiodic automorphism of ?². As a corollary we obtain an example of a ?²-action \({({T_g})_{g \in {Z^2}}}\) with minimal self-joinings which is conjugate to the (twisted by A) action \({({T_{Ag}})_{g \in {Z^2}}}\). This answers a question of E. Glasner.     

Functional nonparametric estimation of conditional extreme quantiles

We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such “extreme” quantiles can be located in the range of the data or near and even beyond the boundary of the sample, depending on the convergence rate of their order to one. Nonparametric estimators of these functional extreme quantiles are introduced, their asymptotic distributions are established and their finite sample behavior is investigated.     

On the use of phosphoramidite ligands in copper-catalyzed asymmetric transformations with trialkylaluminum reagents

[reaction: see text] Phosphoramidites based on BINOL readily react with trimethylaluminum in "noncoordinating" solvents, leading to the corresponding aminophosphine which is the real ligand in copper-catalyzed asymmetric transformations. This artifact explains the experimental differences in the asymmetric ring opening of meso bicyclic hydrazines using dialkylzinc or trialkylaluminum reagents as nucleophiles.     

Potential energy landscape of monolayer-surface systems governed by repulsive lateral interactions: the case of (3 x 3)-I-Pt(111)

Combined density functional theory (DFT) and Monte Carlo (MC) approach is applied to study the potential energy landscape of four iodine atoms adsorbed on the Pt(111) surface in a (3 x 3) unit cell. Three critical points were identified: (3 x 3)-sym and (3 x 3)-asym, corresponding to structures well known from experimental studies, while the third one (3 x 3)-zigzag is a new structure not reported before. An interaction model fitted to DFT calculations allows us to explain the difference between arrangements of iodine monolayer in vacuum, air, and solution environments as a result of different repulsion regimes.     

Mechanically controlled DNA extrusion from a palindromic sequence by single molecule micromanipulation

A magnetic tweezers setup is used to control both the stretching force and the relative linking number DeltaLk of a palindromic DNA molecule. We show here, in absence of divalent ions, that twisting negatively the molecule while stretching it at approximately 1 pN induces the formation of a cruciform DNA structure. Furthermore, once the cruciform DNA structure is formed, the extrusion of several kilo-base pairs of palindromic DNA sequence is directly and reversibly controlled by varying DeltaLk. Indeed the branch point behaves as a nanomechanical gear that links rotation with translation, a feature related to the helicity of DNA. We obtain experimentally a very good linear relationship between the extension of the molecule and DeltaLk. We use then this experiment to obtain a precise measurement of the pitch of B-DNA in solution: 3.61 +/- 0.03 nm/turn.     

Synthesis and properties of a functionalized heterobimetallic Re(I)–Gd(III) complex as a potential dual-contrast agent for molecular imaging

In the design of dual-imaging probes, the first functionalized and neutral heterobimetallic Re(I)–Gd(III) complex, highly soluble in aqueous solutions, has been prepared. This system exhibits interesting photophysical properties (λ_em = 578 nm, ? = 1.4%) for optical imaging and substantial higher relaxivity (r₁ = 6.6 mM⁻¹ s⁻¹ at 0.47 T and 37 °C) than the clinically used MRI contrast agents. Moreover, this system incorporates an aromatic ester functionality suitable for bioconjugation.