Detecting perfect powers by factoring into coprimes

This paper presents an algorithm that, given an integer , finds the largest integer such that is a th power. A previous algorithm by the first author took time where ; more precisely, time ; conjecturally, time . The new algorithm takes time . It relies on relatively complicated subroutines--specifically, on the first author's fast algorithm to factor integers into coprimes--but it allows a proof of the bound without much background; the previous proof of relied on transcendental number theory.

The computation of is the first step, and occasionally the bottleneck, in many number-theoretic algorithms: the Agrawal-Kayal-Saxena primality test, for example, and the number-field sieve for integer factorization.

     

Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics.     

Low dose 60Co gamma-irradiation effects on electronic carrier transport and DC characteristics of AlGaN/GaN high-electron-mobility transistors

The impact of internal irradiation with secondary Compton electrons, generated by gamma-photons, on the characteristics of III-N/GaN-based devices was explored. N-channel AlGaN/GaN high-electron-mobility transistors (HEMTs) were exposed to gamma-radiation from a ⁶⁰Co source for doses up to 600?Gy. Temperature-dependent electron beam-induced current (EBIC) was employed to measure minority carrier transport properties. For low doses below ～250?Gy, the minority carrier diffusion length in AlGaN/GaN HEMTs is shown to increase by about 40%. This increase is likely due to longer minority carrier lifetime induced by internal Compton electron irradiation. An associated decrease in activation energy, extracted from temperature-dependent EBIC, was also found. The obtained increase in transconductance and decrease in gate leakage current indicate an improvement in performance of the devices after low doses of irradiation. For high doses of gamma-irradiation, above ～300?Gy, the performance of HEMTs showed a deterioration. The deterioration results from the onset of increased carrier scattering due to additional radiation-induced defects, as is translated in a decrease of minority carrier diffusion length.     

Development of Low-Cost Instrumentation for Single Point Autofluorescence Lifetime Measurements

Autofluorescence lifetime measurements, which can provide label-free readouts in biological tissues, contrasting e.g. different types and states of tissue matrix components and different cellular metabolites, may have significant clinical potential for diagnosis and to provide surgical guidance. However, the cost of the instrumentation typically used currently presents a barrier to wider implementation. We describe a low-cost single point time-resolved autofluorescence instrument, exploiting modulated laser diodes for excitation and FPGA-based circuitry for detection, together with a custom constant fraction discriminator. Its temporal accuracy is compared against a “gold-standard” instrument incorporating commercial TCSPC circuitry by resolving the fluorescence decays of reference fluorophores presenting single and double exponential decay profiles. To illustrate the potential to read out intrinsic contrast in tissue, we present preliminary measurements of autofluorescence lifetime measurements of biological tissues ex vivo. We believe that the lower cost of this instrument could enhance the potential of autofluorescence lifetime metrology for clinical deployment and commercial development.     

Large amplitude oscillatory shear rheology of three different shear-thickening particle dispersions

We present a large amplitude oscillatory shear rheology (LAOS) investigation of three different shear-thickening particle dispersions - fumed silica in polyethylene oxide (FLOC), fumed silica in polypropylene glycol (HydroC), and cornstarch in water (JAM). These systems shear-thicken by three different mechanisms - shear-induced formation of particle clusters flocculated by polymer bridging, hydrocluster formation, and jamming. The viscoelastic non-linearities of the three fluids were studied as a function of strain and strain-rate space through the use of Lissajous-Bowditch curves and local nonlinear viscoelastic moduli of an oscillatory shear cycle. The nonlinear behaviors of the three fluids were compared and contrasted to understand the nonlinear shear-thickening mechanism of each. Both HydroC and JAM dispersions were found to exhibit strong strain stiffening of the elastic moduli and strain thickening of the loss moduli behavior associated with possible hydrocluster formation and particle jamming. However, the FLOC dispersion, in contrast, showed strong strain softening and strain thinning behavior at large strain amplitudes associated with yielding of the microstructure. The expected thickening of the loss modulus of FLOC in LAOS with increasing strain was not observed even though viscosity of FLOC was found to shear-thicken in steady-shear measurements. This disagreement is likely due to very large strain amplitudes required for shear-thickening to occur by shear-induced polymer bridging mechanism. The hypothesis was confirmed through stress growth experiments. Conversely, the HydroC and JAM dispersions required relatively small applied strains for shear-thickening to occur by hydrocluster and jamming mechanism. The comparison of local intra-cycle nonlinearity through Lissajous-Bowditch plots and nonlinear viscoelastic parameters indicated that the elastic nonlinearities of all three systems are primarily driven by a strong dependence on the magnitude of the applied strain-rates within an oscillatory cycle rather than the amplitude of the applied strain. A close inspection of the LAOS data reveals strong differences in the viscoelastic nonlinearities of these three different shear-thickening dispersions which can be used to create a nonlinear rheological fingerprint for each and offers valuable new insights into the nonlinear dynamics associated with each of the shear-thickening mechanisms.     

Mitochondrial BNIP3 upregulation precedes endonuclease G translocation in hippocampal neuronal death following oxygen-glucose deprivation

Background  

Caspase-independent apoptotic pathways are suggested as a mechanism for the delayed neuronal death following ischemic insult. However, the underlying signalling mechanisms are largely unknown. Recent studies imply the involvement of several mitochondrial proteins, including endonuclease G (EndoG) and Bcl-2/adenovirus E1B 19 kDa-interacting protein (BNIP3), in the pathway of non-neuronal cells.     

Optimization of the operational bandwidth in air-core photonic bandgap fibers for IR transmission

We determine the optimal inner glass ring thickness in infrared air-core photonic bandgap fibers (PBGFs) with 19-cell and 7-cell cores. For PBGFs with a 19-cell core, we find that an inner ring thickness of , where Λ is pitch, yields the widest operational bandwidth, which is nearly 6%. The operational bandwidth increases as the refractive index decreases from 2.8 to 2.0. For PBGFs with a 7-cell core, one needs to draw fiber with a ring thickness of less than to achieve a comparable operational bandwidth.     

An L2 model for selfadjoint elliptic differential operators with constant coefficients on bounded domains

The selfadjoint realization of a second order elliptic differential expression with Dirichlet boundary conditions is shown to be unitarily equivalent to the maximal multiplication operator with the independent variable in an explicit L² model space. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The proton‐transfer compounds of strychnine with achiral salicylic acids: strychninium 3,5‐dinitro­salicylate and the strychninium 5‐nitro­salicylate bis­(5‐nitro­salicylic acid) adduct

In the crystal structures of the proton‐transfer compounds of strychnine with 3,5‐dinitro­salicylic acid, namely strychninium 3,5‐dinitro­salicylate, C₂₁H₂₃N₂O₂⁺·C₇H₃N₂O₇⁻, (I), and 5‐nitro­salicylic acid, namely strychninium–5‐nitro­salicylate–5‐nitro­salicylic acid (1/1/2), C₂₁H₂₃N₂O₂⁺·C₇H₄NO₅⁻·2C₇H₅NO₅, (II), protonation of one of the N atoms of the strychnine mol­ecule occurs and this group is subsequently involved in inter­molecular hydrogen‐bonding inter­actions. In (I), this is four‐centred, the primary being with an adjacent strychninium carbonyl O‐atom acceptor in a side‐to‐side inter­action giving linear chains. Other inter­actions are with the phenolate and nitro O‐atom acceptors of the anionic species, resulting in a one‐dimensional polymer structure. In (II), the N⁺—H inter­action is three‐centred, the hydrogen bonding involving carboxyl O‐atom acceptors of the anion and both acid adduct species, giving unique discrete hetero‐tetramer units. The structure of (II) also features π‐bonding inter­actions between the two acid adduct mol­ecules.