L-functions of second-order cusp forms

We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we investigate the effect of adding an assumption of periodicity to this criterion. 2000 Mathematics Subject Classification Primary—11F12, 11F66 G. Mason: Research supported in part by NSF Grant DMS 0245225. C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34.     

The Picard Theorem on S-metric spaces

Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new generalization of the classical "Picard Theorem".     

H2/air autoignition: The nature and interaction of the developing explosive modes

Appropriate algorithmic tools are employed for the analysis of the explosive modes developing during the autoignition of homogeneous mixtures. The ability of these tools to provide significant physical understanding is demonstrated in the case of the homogeneous ignition of a stoichiometric H₂/air mixture, modelled by two different chemical kinetics mechanisms. It is shown that the ignition process evolves in two stages. The first stage is characterised by the development of two explosive timescales (one fast and one slow), that lead the system away from equilibrium. As the end of the first stage is approached, the two explosive timescales converge, they merge and then they disappear. In the second stage only dissipative timescales develop, which drive the system all the way to equilibrium. It is shown that throughout the first stage the fast explosive timescale is generated by chain reactions. The slow explosive timescale is initially generated by an initiation reaction that produces the radicals required for the start-up of the fast mode, while later on it is generated by reactions that are responsible for the heat released. These findings are validated with sensitivity analysis results for the ignition delay time and are employed in order to clarify the discrepancies in the solution provided by the two different chemical kinetics mechanisms considered.     

Issues arising in the construction of QSSA mechanisms: the case of reduced n-heptane/air models for premixed flames

A model reduction methodology, based on the quasi steady-state approximation (QSSA), is employed for the construction of reduced mechanisms in the case of an n-heptane/air premixed flame. Several issues related to the construction of these reduced mechanisms are discussed; such as the influence of the size of the starting skeletal mechanism, the stiffness reduction, and the truncation/simplification of (i) the expressions of the global rates and (ii) the steady-state relations. The starting point for the reduction is two skeletal mechanisms that involve 177/768 and 66/326 species/reactions, respectively [J. Prager, H.N. Najm, M. Valorani, and D.A. Goussis, Skeletal mechanism generation with CSP and validation for premixed n-heptane flames, Proc. Combust. Inst. 32 (2009), pp. 509–517] and which were derived from the detailed mechanism of Curran et al. [H.J. Curran, P. Gaffuri, W.J. Pitz, and C.K. Westbrook, A comprehensive modeling study of iso-octane oxidation, Combust. Flame 129 (2002), pp. 253–280], which involves 561/2538 species/reactions. From these two skeletal mechanisms, a number of reduced mechanisms of various sizes are produced and analysed. The validity of the reduced mechanism with the minimum size is demonstrated by considering its accuracy regarding the mass fractions of major and minor species, the temperature, and the flame speed, over a wide range of equivalence ratios and pressures.     

Anti-Ageing Potential of S. euboea Heldr. Phenolics

In recent years, the use of Sideritis species as bioactive agents is increasing exponentially. The present study aimed to investigate the chemical constituents, as well as the anti-ageing potential of the cultivated Sideritis euboea Heldr. The chemical fingerprinting of the ethyl acetate residue of this plant was studied using 1D and 2D-NMR spectra. Isomeric compounds belonging to acylated flavone derivatives and phenylethanoid glycosides were detected in the early stage of the experimental process through 2D-NMR techniques. Overall, thirty-three known compounds were isolated and identified. Some of them are reported for the first time not only in S. euboea, but also in genus Sideritis L. The anti-ageing effect of the ethyl acetate residue and the isolated specialized products was assessed as anti-hyaluronidase activity. In silico docking simulation revealed the interactions of the isolated compounds with hyaluronidase. Furthermore, the in vitro study on the inhibition of hyaluronidase unveiled the potent inhibitory properties of ethyl acetate residue and apigenin 7-O-β-d-glucopyranoside. Though, the isomers of apigenin 7-O-p-coumaroyl-glucosides and also the 4′-methyl-hypolaetin 7-O-[6′′′-O-acetyl-β-d-allopyranosyl]-(1→2)-β-d-glucopyranoside exerted moderate hyaluronidase inhibition. This research represents the first study to report on the anti-hyaluronidase activity of Sideritis species, confirming its anti-inflammatory, cytotoxic and anti-ageing effects and its importance as an agent for cosmetic formulations as also anticancer potential.     

The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology

In this paper we answer a question of Zagier and find the dimensions of spaces of holomorphic second-order forms of even weight. We also establish a cohomological interpretation and prove an Eichler-Shimura-type isomorphism.

     

Experimental study of thermal development in a rotating square-ended U-bend

This paper reports an experimental study of the thermal development in an idealized model of a blade cooling passage of smooth inner surfaces, comprising a square-ended U-bend with a cross-section that changes from a square upstream to a 2:1 rectangle downstream of the turn. The two flat walls are heated electrically, while the outer wall and the splitter plate are thermally insulated. The steady state liquid crystal technique is used to map the local Nusselt number variation. Measurements are obtained using a stationary air flow facility and also a rotating water flow facility. This enables us to investigate the effects on the thermal development of the variation in Reynolds from 30,000 to 100,000, in Prandtl number from 0.7 to 5.8 (both for static conditions) and in rotation number, from 0 to 0.4. The effects of minor modifications in the cross-sectional area at the bend exit, on the thermal development, under both stationary and rotating conditions, are also explored.     

Temperature-responsive photoluminescence of quinoline-labeled poly(N-isopropylacrylamide) in aqueous solution

The pH- and temperature-responsive optical properties of a quinoline-labeled poly(N-isopropylacrylamide) copolymer are explored in aqueous solution and compared to the respective behavior of a similar quinoline-labeled poly(N,N-dimethylacrylamide) copolymer. These copolymers, P(NIPAM-co-SDPQ) and P(DMAM-co-SDPQ), were prepared through free radical copolymerization of 2,4-diphenyl-6-(4-vinylphenyl)quinoline (SDPQ) with the thermosensitive N-isopropylacrylamide (NIPAM) and the hydrophilic N,N-dimethylacrylamide (DMAM), respectively. Both copolymers exhibit the well-known pH-controlled optical response of quinoline unit in aqueous solution and the emitted color changes from blue to green upon decreasing pH. Nevertheless, a ～20 nm emission shift is observed upon heating the aqueous P(NIPAM-co-SDPQ) solution, regardless of pH, due to the formation of hydrophobic microdomains (Nile Red probing), as a consequence of the Lower Critical Solution Temperature (LCST) behavior of this copolymer in water. Interestingly, this LCST behavior also imposes the partial deprotonation of the otherwise protonated SDPQ unit at pH = 2 and the emission of the basic form appears upon increasing temperature, suggesting that the acid/base equilibrium of the quinoline unit is significantly temperature-controlled, when introduced in the thermosensitive poly(N-isopropylacrylamide) chain.     

Optimization of an Active Noise Control System Inside an Aircraft, Based on the Simultaneous Optimal Positioning of Microphones and Speakers, with the Use of a Genetic Algorithm

In the last decade, Active Noise Control (ANC) has become a very popular technique for controlling low-frequency noise. The increase in its popularity is a consequence of the rapid development in the fields of computers in general, and more specifically in digital signal processing boards. ANC systems are application specific and therefore they should be optimally designed for each application. Even though the physical background of the ANC systems is well known and understood, efficient tools for the optimization of the sensor and actuator configurations of the ANC system, based on classical optimization methods, do not exist. This is due to the nature of the problem that allows the calculation of the effect of the ANC system only when the sensor and actuator configurations are specified. An additional difficulty in this problem is that the sensor and the actuator configurations cannot be optimized independently, since the effect of the ANC system directly depends on the combined sensor and actuator configuration. For the solution of this problem several other optimization techniques were applied, such as simulated annealing for example. In this paper the successful application of a Genetic Algorithm, an optimization technique that belongs to the broad class of evolutionary algorithms, is presented. The results obtained from the application of the GA are very promising. The GA was able to identify various configurations that achieved a reduction of 6.3 dBs to 6.5 dBs, which corresponds to an actual reduction of 50% of the initial acoustic pressure.