'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Small states, great power? Gaining influence through intrinsic, derivative, and collective power

In recent years, scholars have devoted increased attention to the agency of small states in International Relations. However, the conventional wisdom remains that while not completely powerful, small states are unlikely to achieve much of significance when faced by great power opposition. This argument, however, implicitly rests on resource-based and compulsory understandings of power. This article explores the implicit connections between the concept of "small state" and diverse concepts of power, asking how we should understand these states' attempts to gain influence and achieve their international political objectives. By connecting the study of small states with additional understandings of power, the article elaborates the broader avenues for influence that are open to many states but are particularly relevant for small states. The article argues that small states' power can be best understood as originating in three categories: “derivative,” collective, and particular-intrinsic. Derivative power, coined by Michael Handel, relies upon the relationship with a great power. Collective power involves building coalitions of supportive states, often through institutions. Particular-intrinsic power relies on the assets of the small state trying to do the influencing. Small states specialize in the bases and means of these types of power, which may have unconventional compulsory, institutional, structural, and productive aspects.

Salmonella enterica Serovar Typhimurium Vaccine Strains Expressing a Nontoxic Shiga-Like Toxin 2 Derivative Induce Partial Protective Immunity to the Toxin Expressed by Enterohemorrhagic Escherichia coli

Shiga-like toxin 2 (Stx2)-producing enterohemorrhagic Escherichia coli (referred to as EHEC or STEC) strains are the primary etiologic agents of hemolytic-uremic syndrome (HUS), which leads to renal failure and high mortality rates. Expression of Stx2 is the most relevant virulence-associated factor of EHEC strains, and toxin neutralization by antigen-specific serum antibodies represents the main target for both preventive and therapeutic anti-HUS approaches. In the present report, we describe two Salmonella enterica serovar Typhimurium aroA vaccine strains expressing a nontoxic plasmid-encoded derivative of Stx2 (Stx2 Delta AB) containing the complete nontoxic A2 subunit and the receptor binding B subunit. The two S. Typhimurium strains differ in the expression of flagellin, the structural subunit of the flagellar shaft, which exerts strong adjuvant effects. The vaccine strains expressed Stx2 Delta AB, either cell bound or secreted into the extracellular environment, and showed enhanced mouse gut colonization and high plasmid stability under both in vitro and in vivo conditions. Oral immunization of mice with three doses of the S. Typhimurium vaccine strains elicited serum anti-Stx2B (IgG) antibodies that neutralized the toxic effects of the native toxin under in vitro conditions (Vero cells) and conferred partial protection under in vivo conditions. No significant differences with respect to gut colonization or the induction of antigen-specific antibody responses were detected in mice vaccinated with flagellated versus nonflagellated bacterial strains. The present results indicate that expression of Stx2 Delta AB by attenuated S. Typhimurium strains is an alternative vaccine approach for HUS control, but additional improvements in the immunogenicity of Stx2 toxoids are still required.

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the derection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.

Light emitting diodes containing Langmuir-Blodgett films of copolymer of a poly(p-phenylene-vinylene) derivative and poly(octaneoxide)

The properties of Langmuir and Langmuir-Blodgett (LB) films from a block copolymer with polyethylene oxide and phenylene-vinylene moieties are reported. The LB films were successfully transferred onto several types of substrates, with sufficient quality to allow for evaporation of a metallic electrode on top of the LB films to produce polymer light emitting diodes (PLEDs). The photoluminescence and electroluminescence spectra of the LB film and device were similar, featuring an emission at ca. 475 nm, from which we could infer that the emission mechanisms are essentially the same as in poly(p-phenylene) derivatives. Analogously to other PLEDs the current versus voltage characteristics of the LB-based device could be explained with the Arkhipov model according to which charge transport occurs among localized sites. The implications for nanotechnology of the level of control that may be achieved with LB devices will also be discussed.

Molecular conformation of the racemic indan derivative (+/-)-1-trans-3-(3,4-dichlorophenyl)-2,3-dihydro-1H-indene-1-carboxamide

This paper presents the structural characterization of the indan derivative (+/-)-1-trans-3-(3,4-dichlorophenyl)-2,3-dihydro-1H-indene-1-carboxamide, which was unambiguously determined by X-ray diffraction (XRD) to be a racemate (R/S: 50/50) crystallizing in an achiral crystal structure (P2(1)/c, a = 9.3180(1) , b = 7.9070(2) , c = 19.7550(4) , beta = 103.250(1)A degrees, V = 1416.75(5) (3) and Z = 4). The diastereomers are related by the inversion symmetry and linked by H bond forming a dimer. The crystal packing is stabilized by hydrogen bonds, including the classical one responsible for the formation of centrosymmetric dimers, and non-classical ones involving C-H center dot center dot center dot O and C-H center dot center dot center dot pi-aryl interactions. The intra and intermolecular geometry of the title compound is compared to the (+/-)-1-trans-3-(3,4-dichlorophenyl)-2,3-dihydro-1H-indene-1-carboxylic acid one, which also present an achiral crystal structure from racemates (R/S: 50/50). The two indan derivatives crystallize in a very similar unit cell.

De-aggregation of polyfluorene derivative by blending with a series of poly(alkyl methacrylate)s with varying sidegroup sizes

A polyfluorene derivative of the PPV, poly(9,9`-n-dihexyl-2,7-fluorenedilvinylene-alt-1,4-phenylenevinylene), with a strong tendency to aggregation was blended with several members of a series composed by poly(alkyl methacrylate)s with the following substituents in the ester position: methyl, ethyl, isopropyl, isobutyl, n-butyl, and cyclohexyl. The de-aggregation effect in blends was studied by steady-state photoluminescence spectroscopy using several blend compositions. The efficiency of each dispersing phase was discussed in terms of the polymer miscibility, controlled by interaction parameters between the polyfluorene and every poly(alkyl methacrylate)s, here described using Hilde-brand solubility parameters. (c) 2009 Elsevier Ltd. All rights reserved.

Low cost selective sensor for carbonyl compounds in air based on a novel conductive poly(p-xylylene) derivative

A novel poly(p-xylylene), PPX, derivative bearing phenyl side groups was electrochemically synthesized in 85% yield. The polymer, poly(2-phenyl-p-xylylene) (PPPX), presented a major fraction (88%) soluble in common organic solvents. It showed to be thermally resistant up to 140 degrees C. UV-VIS analysis revealed an Egap of similar to 3.0 eV. Gas sensors made from thin films of CSA doped PPPX deposited on interdigitated electrodes exhibited significant changes in electrical conductance upon exposure to five carbonyl compounds: acetaldehyde, propionaldehyde. benzaldehyde, acetone and butanone. Three-dimensional plots of relative response vs. time of half-response vs. time of half-recovery showed good discrimination between the five carbonyl Compounds tested. (C) 2008 Elsevier B.V. All rights reserved.

Intrachain Energy Migration to Weak Charge-Transfer State in Polyfluorene End-Capped with Naphthalimide Derivative

Polyfluorene end-capped with N-(2-benzothiazole)-1 8-naphthalimide (PF-BNI) is a highly fluorescent material with fluorescence emission modulated by solvent polarity Its low energy excited state is assigned as a mixed configuration state between the singlet S(1) of the fluorene backbone (F) with the charge transfer (CI) of the end group BNI The triexponential fluorescence decays of PF-BNI were associated with fast energy migration to form an intrachain charge-transfer (ICCT) state polyfluorene backbone decay and ICCT deactivation Time-resolved fluorescence anisotropy exhibited biexponential relaxation with a fast component of 12-16 ps in addition to a slow one in the range 0 8-1 4 ns depending on the solvent showing that depolarization occurs from two different processes energy migration to form the ICCT state and slow rotational diffusion motion of end segments at a longer time Results from femtosecond transient absorption measurements agreed with anisotropy decay and showed a decay component of about 16 ps at 605 nm in PF BNI ascribed to the conversion of S(1) to the ICCT excited state From the ratio of asymptotic and initial amplitudes of the transient absorption measurement the efficiency of intrachain ICCT formation is estimated in 0 5 which means that on average, half of the excited state formed in a BNI-(F)(n)-BNI chain with n = 32 is converted to its low energy intrachain charge-transfer (ICCT) state

Estimating the term structure of volatility and fixed income derivative pricing

Estimating the parameters of the instantaneous spot interest rate process is of crucial importance for pricing fixed income derivative securities. This paper presents an estimation for the parameters of the Gaussian interest rate model for pricing fixed income derivatives based on the term structure of volatility. We estimate the term structure of volatility for US treasury rates for the period 1983 - 1995, based on a history of yield curves. We estimate both conditional and first differences term structures of volatility and subsequently estimate the implied parameters of the Gaussian model with non-linear least squares estimation. Results for bond options illustrate the effects of differing parameters in pricing.