Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

Anionic metabolic profiling of urine from antibiotic-treated rats by capillary electrophoresis–mass spectrometry

A recently developed capillary electrophoresis (CE)-negative-ionisation mass spectrometry (MS) method was used to profile anionic metabolites in a microbial-host co-metabolism study. Urine samples from rats receiving antibiotics (penicillin G and streptomycin sulfate) for 0, 4, or 8 days were analysed. A quality control sample was measured repeatedly to monitor the performance of the applied CE-MS method. After peak alignment, relative standard deviations (RSDs) for migration time of five representative compounds were below 0.4 %, whereas RSDs for peak area were 7.9–13.5 %. Using univariate and principal component analysis of obtained urinary metabolic profiles, groups of rats receiving different antibiotic treatment could be distinguished based on 17 discriminatory compounds, of which 15 were downregulated and 2 were upregulated upon treatment. Eleven compounds remained down- or upregulated after discontinuation of the antibiotics administration, whereas a recovery effect was observed for others. Based on accurate mass, nine compounds were putatively identified; these included the microbial-mammalian co-metabolites hippuric acid and indoxyl sulfate. Some discriminatory compounds were also observed by other analytical techniques, but CE-MS uniquely revealed ten metabolites modulated by antibiotic exposure, including aconitic acid and an oxocholic acid. This clearly demonstrates the added value of CE-MS for nontargeted profiling of small anionic metabolites in biological samples.

Transport timescales and tracer properties in the extratropical UTLS

A comprehensive evaluation of seasonal backward trajectories initialized in the northern hemisphere lowermost stratosphere (LMS) has been performed to investigate the factors that determine the temporal and spatial structure of troposphere-to-stratosphere-transport (TST) and it's impact on the LMS. In particular we explain the fundamental role of the transit time since last TST (tTST) for the chemical composition of the LMS. According to our results the structure of the LMS can be characterized by a layer with tTST<40 days forming a narrow band around the local tropopause. This layer extends about 30 K above the local dynamical tropopause, corresponding to the extratropical tropopause transition layer (ExTL) as identified by CO. The LMS beyond this layer shows a relatively well defined separation as marked by an aprupt transition to longer tTST indicating less frequent mixing and a smaller fraction of tropospheric air. Thus the LMS constitutes a region of two well defined regimes of tropospheric influence. These can be characterized mainly by different transport times from the troposphere and different fractions of tropospheric air. Carbon monoxide (CO) mirrors this structure of tTST due to it's finite lifetime on the order of three months. Water vapour isopleths, on the other hand, do not uniquely indicate TST and are independent of tTST, but are determined by the Lagrangian Cold Point (LCP) of air parcels. Most of the backward trajectories from the LMS experienced their LCP in the tropics and sub-tropics, and TST often occurs 20 days after trajectories have encountered their LCP. Therefore, ExTL properties deduced from CO and H2O provide totally different informations on transport and particular TST for the LMS.

Mobile-to-mobile MIMO transmit-receive diversity systems: analysis and performance in three-dimensional double-correlated channels

Mobile-to-mobile (M-to-M) communications are expected to play a crucial role in future wireless systems and networks. In this paper, we consider M-to-M multiple-input multiple-output (MIMO) maximal ratio combining system and assess its performance in spatially correlated channels. The analysis assumes double-correlated Rayleigh-and-Lognormal fading channels and is performed in terms of average symbol error probability, outage probability, and ergodic capacity. To obtain the receive and transmit spatial correlation functions needed for the performance analysis, we used a three-dimensional (3D) M-to-M MIMO channel model, which takes into account the effects of fast fading and shadowing. The expressions for the considered metrics are derived as a function of the average signal-to-noise ratio per receive antenna in closed-form and are further approximated using the recursive adaptive Simpson quadrature method. Numerical results are provided to show the effects of system parameters, such as distance between antenna elements, maximum elevation angle of scatterers, orientation angle of antenna array in the x–y plane, angle between the x–y plane and the antenna array orientation, and degree of scattering in the x–y plane, on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.

Analysis and compensation of I/Q imbalance in MIMO transmit-receive diversity systems

In wireless communication systems, all in-phase and quadrature-phase (I/Q) signal processing receivers face the problem of I/Q imbalance. In this paper, we investigate the effect of I/Q imbalance on the performance of multiple-input multiple-output (MIMO) maximal ratio combining (MRC) systems that perform the combining at the radio frequency (RF) level, thereby requiring only one RF chain. In order to perform the MIMO MRC, we propose a channel estimation algorithm that accounts for the I/Q imbalance. Moreover, a compensation algorithm for the I/Q imbalance in MIMO MRC systems is proposed, which first employs the least-squares (LS) rule to estimate the coefficients of the channel gain matrix, beamforming and combining weight vectors, and parameters of I/Q imbalance jointly, and then makes use of the received signal together with its conjugation to detect the transmitted signal. The performance of the MIMO MRC system under study is evaluated in terms of average symbol error probability (SEP), outage probability and ergodic capacity, which are derived considering transmission over Rayleigh fading channels. Numerical results are provided and show that the proposed compensation algorithm can efficiently mitigate the effect of I/Q imbalance.

Performance analysis of MIMO MRC in 3D mobile-to-mobile double-correlated channels

In this paper, we consider multiple-input multiple- output (MIMO) maximal ratio combining (MRC) systems and assess the system performance in terms of average symbol error probability (SEP), outage probability and ergodic capacity in double-correlated Rayleigh-and-Lognormal fading channels. In order to derive the receive and transmit correlation functions needed for the performance analysis, a three-dimensional (3D) MIMO mobile-to-mobile (M-to-M) channel model, which takes into account the effects of fast fading and shadowing is used. Numerical results are provided to show the effects of system parameters, such as maximum elevation angle of scatterers, orientation angle of antenna array in the x-y plane, angle between x-y plane and the antenna array orientation, and degree of scattering in the x-y plane, on the system performance.

Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Nonpsychotropic plant cannabinoids, cannabidivarin (CBDV) and cannabidiol (CBD), activate and desensitize transient receptor potential vanilloid 1 (TRPV1) channels in vitro: potential for the treatment of neuronal hyperexcitability

Epilepsy is the most common neurological disorder, with over 50 million people worldwide affected. Recent evidence suggests that the transient receptor potential cation channel subfamily V member 1 (TRPV1) may contribute to the onset and progression of some forms of epilepsy. Since the two nonpsychotropic cannabinoids cannabidivarin (CBDV) and cannabidiol (CBD) exert anticonvulsant activity in vivo and produce TRPV1-mediated intracellular calcium elevation in vitro, we evaluated the effects of these two compounds on TRPV1 channel activation and desensitization and in an in vitro model of epileptiform activity. Patch clamp analysis in transfected HEK293 cells demonstrated that CBD and CBDV dose-dependently activate and rapidly desensitize TRPV1, as well as TRP channels of subfamily V type 2 (TRPV2) and subfamily A type 1 (TRPA1). TRPV1 and TRPV2 transcripts were shown to be expressed in rat hippocampal tissue. When tested on epileptiform neuronal spike activity in hippocampal brain slices exposed to a Mg2+-free solution using multielectrode arrays (MEAs), CBDV reduced both epileptiform burst amplitude and duration. The prototypical TRPV1 agonist, capsaicin, produced similar, although not identical effects. Capsaicin, but not CBDV, effects on burst amplitude were reversed by IRTX, a selective TRPV1 antagonist. These data suggest that CBDV antiepileptiform effects in the Mg2+-free model are not uniquely mediated via activation of TRPV1. However, TRPV1 was strongly phosphorylated (and hence likely sensitized) in Mg2+-free solution-treated hippocampal tissue, and both capsaicin and CBDV caused TRPV1 dephosphorylation, consistent with TRPV1 desensitization. We propose that CBDV effects on TRP channels should be studied further in different in vitro and in vivo models of epilepsy.

Temporality, cultural biography and seasonality: rethinking time in wetland archaeology

Wetland archaeology is uniquely well placed to investigate questions of chronology, temporality, life-cycles and seasonality. Beyond the usual archaeological approaches to time (eg seriation, typology and stratigraphy), most wetland archaeological investigations have access to a ready supply of samples (ie wood, peat and organic deposits) for absolute scientific dating, particularly radiocarbon and dendrochronology. Indeed, the success of dendrochronology in revealing dynamic sequences of site and regional occupation, use and abandonment are well known. Investigating wetland archaeological sites, environmental archaeologists have used the evidence of insects' plant remains, seeds and even testate amoeba to establish the season, or months, of a site's occupation. Soil micromorphologists have carried out innovative studies of settlement deposits to reconstruct the chronological sequences of processes and events leading to their formation. In brief, wetland archaeology has become adept at calibrating past times.

Observations at the magnetopause and in the auroral ionosphere of momentum transfer from the solar wind

Recent radar studies of field-perpendicular flows in the auroral ionosphere, in conjunction with observations of the interplanetary medium immediately upstream of the Earth's bow shock, have revealed direct control of dayside convection by the Bz component of the interplanetary magnetic field (IMF). The ionospheric flows begin to respond to both northward and southward turnings of the IMF impinging upon the magnetopause after a delay of only a few minutes in the early afternoon sector, rising to about 15 minutes nearer dawn and dusk. In both the polar cap and the auroral oval, the subsequent rise and decay times are of order 5–10 minutes. We conclude there is very little convection “flywheel” effect in the dayside polar ionosphere and that only newly-opened flux tubes impart significant momentum to the ionosphere, in a relatively narrow region immediately poleward of the cusp. These findings concerning the effects of quasi-steady reconnection have important implications for any ionospheric signatures of transient reconnection which should be considerably shorter-lived than thought hitherto. In order to demonstrate the difficulty of uniquely identifying a Flux Transfer Event (FTE) in ground-based magnetometer data, we present observations of an impulsive signature, identical with that expected for an FTE if data from only one station is studied, following an observed magnetopause compression when the IMF was purely northward. We also report new radar observations of a viscous-like interaction, consistent with an origin on the flanks of the magnetotail and contributing an estimated 15–30kV to the total cross-cap potential during quiet periods.

Exploration of relational factors: Sino-foreign joint-venture partnering

Purpose – Despite recent threats of economic contraction, China still offers attractive opportunities for foreign companies seeking to expand their business activities through joint venturing (JV) partnering entry strategies. Recent research has indicated a growing recognition of the importance of relational factors in JV partnering. The purpose of this paper is to build on recent research findings that identify critical relation success factors in JVs and explores these in the context of a Hong Kong-based civil aviation services company seeking to expand business activities in Greater China. Design/methodology/approach – While the extant management literature focuses primarily on factors relevant to the inter-partner relationship between partners in the formation stage of a joint venture, this research takes a dynamic stakeholder perspective in respect of the relevant relational factors over the evolution of a partnership. The research described in this paper is based on a case-based study that identifies and examines the relevance and importance of uniquely Chinese factors such as guanxi, renqing and mianzi in the specific context of a strategic partnering relationship. Findings – This phenomenological study provides empirical evidence of critical linkages of these to intrinsically Chinese notions of guanxi, mianzi and renqing – it links these to key strategic partnering success factors identified to be trust, conflict resolution, commitment and cooperation. This study thereby reinforces the importance of the uniquely Chinese relational context in cross-border JVs. Moreover, the research findings suggest that these factors underpin the dynamic bi-directional stakeholder relationship in a Sino-foreign strategic partnership. Originality/value – This study conceptually links the uniquely Chinese relational factors (guanxi, mianzi and renqing) to key success factors supporting the establishment of a strategic partnership in a Sino-foreign context; moreover, it contributes empirical evidence substantiating the proposed conceptual linkage.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.