UNIT VECTOR FIELDS ON ANTIPODALLY PUNCTURED SPHERES: BIG INDEX, BIG VOLUME

We establish in this paper a lower bound for the volume of a unit vector field (v) over right arrow defined ou S(n) \ {+/-x}, n = 2,3. This lower bound is related to the sum of the absolute values of the indices of (v) over right arrow at x and -x.

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

Fast and reliable analyses of sulphite in fruit juices using a supramolecular amperometric detector encompassing in flow gas diffusion unit

A new compact system encompassing in flow gas diffusion unit and a wall-jet amperometric FIA detector, coated with a supramolecular porphyrin film, was specially designed as an alternative to the time-consuming Monier-Williams method, allowing fast, reproducible and accurate analyses of free sulphite species in fruit juices. In fact, a linear response between 0.64 and 6.4 ppm of sodium sulphite. LOD = 0.043 ppm, relative standard deviation of +/- 1.5% (n = 10) and analytical frequency of 85 analyses/h were obtained utilising optimised conditions. That superior analytical performance allows the precise evaluation of the amount of free sulphite present in foods, providing an important comparison between the standard addition and the standard injection methods. Although the first one is most frequently used, it was strongly influenced by matrix effects because of the unexpected reactivity of sulphite ions with the juice matrixes, leading to its partial consumption soon after addition. In contrast, the last method was not susceptible to matrix effects yielding accurate results, being more reliable for analytical purposes. (C) 2011 Elsevier Ltd. All rights reserved.

Spatiotemporal Pattern Formation in the Oscillatory Electro-Oxidation of Sulfide on a Platinum Disk

Spatiotemporal pattern formation in the electrocatalytic oxidation of sulfide on a platinum disk is investigated using electrochemical methods and a charge-coupled device (CCD) camera simultaneously. The system is characterized by different oscillatory regions spread over a wide potential range. An additional series resistor and a large electrode area facilitate observation of multiple regions of kinetic instabilities along the current/potential curve. Spatiotemporal patterns on the working electrode, such as fronts, pulses, spirals, twinkling eyes, labyrinthine stripes, and alternating synchronized deposition and dissolution, are observed at different operating conditions of series resistance and sweep rate.

Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach

This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

Testing for Seasonal Unit Roots when Residuals Contain Serial Correlations under HEGY Test Framework

This paper introduces a corrected test statistic for testing seasonal unit roots when residuals contain serial correlations, based on the HEGY test proposed by Hylleberg,Engle, Granger and Yoo (1990). The serial correlations in the residuals of test regressionare accommodated by making corrections to the commonly used HEGY t statistics. Theasymptotic distributions of the corrected t statistics are free from nuisance parameters.The size and power properties of the corrected statistics for quarterly and montly data are investigated. Based on our simulations, the corrected statistics for monthly data havemore power compared with the commonly used HEGY test statistics, but they also have size distortions when there are strong negative seasonal correlations in the residuals.

Motor-unit Coherence During Isometric Contractions Is Greater in a Hand Muscle of Older Adults

The purpose of this study was to quantify the strength of motor-unit coherence from the first dorsal interosseus muscle in young and old adults using data obtained in a previous study, where no differences in motor-unit synchronization between the two groups were observed.

Motor-unit coherence and its relation with synchrony are influenced by training

The purpose of the study was to quantify the strength of motor-unit coherence from the left and right first dorsal interosseous muscles in untrained, skill-trained (musicians), and strength-trained (weightlifters) individuals who had long-term specialized use of their hand muscles. The strength of motor-unit coherence was quantified from a total of 394 motor-unit pairs in 13 subjects using data from a previous study in which differences were found in the strength of motor-unit synchronization depending on training status. In the present study, we found that the strength of motor-unit coherence was significantly greater in the left compared with the right hand of untrained right-handed subjects with the largest differences observed between 21 and 24 Hz. The strength of motor-unit coherence was lower in both hands of skill-trained subjects (21–27 Hz) and the right (skilled) hand of untrained subjects (21–24 Hz), whereas the largest motor-unit coherence was observed in both hands of strength-trained subjects (3–9 and 21–27 Hz). A strong curvilinear association was observed between motor-unit synchronization and the integral of coherence at 10–30 Hz in all motor-unit pairs (r² = 0.77), and was most pronounced in strength-trained subjects (r² = 0.90). Furthermore, this association was accentuated when using synchronization data with broad peaks (>11 ms), suggesting that the 10- to 30-Hz coherence is due to oscillatory activity in indirect branched common inputs. The altered coherence with training may be due to an interaction between cortical inhibition and the number of direct common inputs to motor neurons in skill- or strength-trained hands.

Life-cycle energy analysis of building integrated photovoltaic systems (BiPVs) with heat recovery unit

Building integrated photovoltaic (BiPV) systems generate electricity, but also heat, which is typically wasted and also reduces the efficiency of generation. A heat recovery unit can be combined with a BiPV system to take advantage of this waste heat, thus providing cogeneration. Two different photovoltaic (PV) cell types were combined with a heat recovery unit and analysed in terms of their life-cycle energy consumption to determine the energy payback period. A net energy analysis of these PV systems has previously been performed, but recent improvements in the data used for this study allow for a more comprehensive assessment of the combined energy used throughout the entire life-cycle of these systems to be performed. Energy payback periods between 4 and 16.5 years were found, depending on the BiPV system. The energy embodied in PV systems is significant, emphasised here due to the innovative use of national average input–output (I–O) data to fill gaps in traditional life-cycle inventories, i.e. hybrid analysis. These findings provide an insight into the net energy savings that are possible with a well-designed and managed BiPV system.

Motor unit synchronization measured by cross-correlation is not influenced by short-term strength training of a hand muscle

The purpose of the study was to quantify the strength of motor unit synchronization and coherence from pairs of concurrently active motor units before and after short-term (4–8 weeks) strength training of the left first dorsal interosseous (FDI) muscle. Five subjects (age 24.8 ± 4.3 years) performed a training protocol three times/week that consisted of six sets of ten maximal isometric index finger abductions, whereas three subjects (age 27.3 ± 6.7 years) acted as controls. Motor unit activity was recorded from pairs of intramuscular electrodes in the FDI muscle with two separate motor unit recording sessions obtained before and after strength training (trained group) or after 4 weeks of normal daily activities that did not involve training (control group). The training intervention resulted in a 54% (45.2 ± 8.3 to 69.5 ± 13.8 N, P = 0.001) increase in maximal index finger abduction force, whereas there was no change in strength in the control group. A total of 163 motor unit pairs (198 single motor units) were examined in both subject groups, with 52 motor unit pairs obtained from 10 recording sessions before training and 51 motor unit pairs from 10 recording sessions after training. Using the cross-correlation procedure, there was no change in the strength of motor unit synchronization following strength training (common input strength index; 0.71 ± 0.41 to 0.67 ± 0.43 pulses/s). Furthermore, motor unit coherence z scores at low (0–10 Hz; 3.9 ± 0.3 before to 4.4 ± 0.4 after) or high (10–30 Hz; 1.7 ± 0.1 before to 1.9 ± 0.1 after) frequencies were not influenced by strength training. These motor unit data indicate that increases in strength following several weeks of training a hand muscle are not accompanied by changes in motor unit synchronization or coherence, suggesting that these features of correlated motor unit activity are not important in the expression of muscle strength.