A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Harmonic Calculus on Fractals - A Measure Geometric Approach I

Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights.     

Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

Bargaining over the division of a shrinking pie: An axiomatic approach

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).     

A few points on omnidirectional band gaps in one-dimensional photonic crystals

The universal condition for the formation of omnidirectional band gaps (OBG) in photonic crystal (PC) was derived with consideration of permeability of the materials. And it was found that there are four kinds of PCs: one of them has no OBG, and one always possesses OBG. For the other two kinds of PCs, there are OBG for only TM or TE waves respectively. Moreover, in all PCs, the OBG can be broadened by decreasing the refractive index of the ambient medium or/and increasing the contrast between the wave impedances of the component materials of the PC. PACS 42.70.Qs; 71.20.Tx     

Potential for micromachined actuation of ultra-wide continuously tunable optoelectronic devices

Tailored scaling represents a principle of success that, both in nature and in technology, allows the effectiveness of physical effects to be enhanced. Mutation and selection in nature are imitated in technology, e.g. by model calculation and design. Proper scaling of dimensions in natural photonic crystals and our fabricated artificial 1D photonic crystals (DBRs, distributed Bragg reflectors) enable efficient diffractive interaction in a specific spectral range. For our optical microsystems we illustrate that tailored miniaturization may also increase the mechanical stability and the effectiveness of spectral tuning by thermal and electrostatic actuation, since the relative significance of the fundamental physical forces involved considerably changes with scaling. These basic physical principles are rigorously applied in micromachined 1.55-μm vertical-resonator-based devices. We modeled, implemented and characterized 1.55-μm micromachined optical filters and vertical-cavity surface-emitting laser devices capable of wide, monotonic and kink-free tuning by a single control parameter. Tuning is achieved by mechanical actuation of one or several air-gaps that are part of the vertical resonator including two ultra-highly reflective DBR mirrors of strong refractive index contrast: (i) Δn=2.17 for InP/air-gap DBRs (3.5 periods) using GaInAs sacrificial layers and (ii) Δn=0.5 for Si₃N₄/SiO₂ DBRs (12 periods) with a polymer sacrificial layer to implement the air-cavity. In semiconductor multiple air-gap filters, a continuous tuning of >8% of the absolute wavelength is obtained. Varying the reverse voltage (U=0–5 V) between the membranes (electrostatic actuation), a tuning range of >110 nm was obtained for a large number of devices. The correlation of the wavelength and the applied voltage is accurately reproducible without any hysteresis. In two filters, tuning of 127 and 130 nm was observed for about ΔU=7 V. The extremely wide tuning range and the very small voltage required are record values to the best of our knowledge. For thermally actuated dielectric filters based on polymer sacrificial layers, Δλ/ΔU=-7 nm/V is found. Received: 10 May 2002 / Published online: 8 August 2002     

Creation of a donor-acceptor pair for studying intraprotein electron transfer with the participation of amino-acid derivatives of fullerene C60

Efficient quenching of eosin phosphorescence by amino-acid derivatives of fullerene (AADFs) such as C₆₀-alanine and C₆₀-glycine in aqueous solutions indicates the possibility of transferring electrons from eosin to fullerene upon collisions or in the exciplex state. To investigate electron transfer in the protein structure, we studied the process of incorporation of C₆₀-alanine and C₆₀-glycine into the heme pocket of myoglobin by controlling Förster quenching. The dissociation constant for the protein-AADF complex was estimated.     

Ultrasonic evaluation of anisotropic damage in multiaxially textile-reinforced thermoplastic composites made from hybrid yarns

The basic damage and failure models of multiaxially reinforced composites with a thermoplastic matrix are presented and verified. Within the framework of continuum damage mechanics, a phenomenological model is introduced, where the damage is defined as a change in the elasticity tensor. For damage identification, a specific ultrasonic device was developed. A combination of an immersion set-up and a contact coupling device formed a system for an efficient determination of stiffness-tensor components from convenient sets of velocity measurements. Linked to a tensile machine, it allowed us to measure the anisotropic damage of the new materials group caused by tensile loading. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 221–234, March–April, 2006.