On the bounds of the trajectories of differential systems†

The behaviour of differential systems is investigated by considering the stability and instability of such systems with respect to certain sub-sets of the state space These Sets may in general be time-varying, and their properties do not only yield information about the stability of a system but also estimates of the bounds of the system trajectories. In all cases the results which are established yield sufficient conditions for stability and instability, and in general involve the existence of Lyapunov-like functions which do not appear to possess the usual definiteness requirements on V and [Vdot].

The developed theory is applied to two special cases: in one case, only time-invariant sub-sets are considered: in the second case, the time interval [t₀, ∞) over which the systems me defined is truncated to [t ₀, t _a  + T), T < ∞, So the that case of stability over a finite time interval may be considered.     

Endurance time,pain and resumption in passive loading of the elbow joint

This study investigated reactions in passively loaded, fully extended elbow joints in 13 men. Pain reactions during and after loading were studied, as were endurance time, T _end, and resumption time, T _r. The loading moment on the elbow joint, M _n, varied between 7 and 100% of maximum elbow moment. Discomfort/pain was estimated with Borg's CR-10 scale. T _end decreased with increasing load level. The opposite was found for the resumption time: the higher the load, held until T _end, the shorter the T _r. The pain limiting the working capability originated mainly from muscle tissue and not from the joint itself. It is concluded that the relation between load and endurance time for passively loaded, fully extended elbow joints resembles that for muscular loading in more ‘normal’ postures. Equations for estimation of endurance and resumption times (in minutes) for fully extended joints are proposed: T _end = 20.6e^{?6.04M _n} and T _r = 0.0167e^{8.84/(1.46+0.346M _n)}, respectively.     

Covariation in subskin‐bulk temperature difference with environmental parameters in the north Indian Ocean

This study aims to explore the dependence of the ocean subskin–bulk temperature difference ΔT (T _subskin?T _2.5m) on environmental parameters over the north Indian Ocean. This was possible because of the fortuitous concurrence of two parallel programmes, viz., the Tropical Rainfall Measuring Mission (TRMM) carrying a Microwave Imager (TMI) and the Indian moored buoy programme, over 6 years (1998–2003). The environmental parameters considered in this study are total water vapour (TWV), cloud liquid water content (CLW), sea surface wind speed, bulk temperature (T _2.5m) and T _2.5m?T _air temperature difference, consisting of a composite data matrix of more than 3000 sets. The study revealed absence of any perceptible dependence on TWV and CLW. For T _2.5m between 24°C and 28°C, the mean Δ T is a decreasing function of T _2.5m. Data classification indicates that most of the cases of T _2.5m<28°C belong to Bay of Bengal during December to February. For the T _2.5m>28°C, Δ T is very small. Our results on the variation of Δ T with T _2.5m?T _air are linear and in opposite phase. The daytime Δ T variation over the north Indian Ocean displays a decreasing trend with increasing wind. The night‐time Δ T pattern, especially over the Bay of Bengal, is found to be very unusual: it remains insensitive to the variations in wind speed, and it is predominantly positive. Diurnal variation of Δ T under wind speed below 6 m s^?1 is studied for overall data set as well as for the individual season data set. The low wind cases reproduce onset of warming at 9 h local time and a peak around 15 h local time. The average maximum amplitude of Δ T is more than 0.34°C with a standard deviation of greater than 0.7°C. Diurnal warming during pre‐monsoon (post‐monsoon) is highest (lowest).     

On stability analysis of systems featuring a multiplicative combination of nonlinear and linear time‐invariant feedback

We show that sufficient conditions for the finite‐gain stability of certain systems featuring a multiplicative combination of memoryless nonlinear feedback and linear time‐invariant feedback, as encountered in some systems' biology prototype applications, can be obtained by building on the Rantzer multipliers. These results are obtained by observing that for all finite energy signals x, the time‐truncated inner product 〈x, H(x)N(x)〉_T is positive for all T>0 if N belongs to a subclass of positive memoryless monotone nonlinearities and if, in addition, H is a Rantzer multiplier. Copyright © 2011 John Wiley & Sons, Ltd.     

Use of remote sensing for drought stress monitoring,yield prediction and varietal evaluation in castor beans (Ricinus communis L.)

The current study was taken up to investigate the utility of remote sensing tools like infrared thermometer and spectral radiometer for screening of germplasm, stress monitoring and yield prediction in castor beans (Ricinus communis L.). The study was carried out through field experiments conducted for six years (1994–1999) at Hayatnagar Research Farm, Hyderabad, India. In each year, four cultivars of castor beans, viz. VP‐1, 48‐1, GCH‐4 and Aruna, were planted on two different dates maintaining an interval of 6–8 weeks so as to expose the crop to different environments. The infrared thermometric observations like canopy–air temperature differential (T _c–T _a) explained 50–60% variation in soil moisture status and showed a significant relationship with soil moisture. Yield of castor beans exhibited significant inverse relationship with T _c–T _a, which explained 59% of variation in yield. The hybrid GCH‐4, registering comparatively lesser mean T _c–T _a over the entire growing period, established itself as a better cultivar. The spectrometer observations also proved GCH‐4 to be a superior genotype in view of its higher reflectance in near‐infrared region of the spectrum. The significant negative relationship of T _c–T _a of GCH‐4 with saturation vapour pressure deficit brought out its drought tolerance trait over the other genotypes studied. These findings at field level can be extended to wider spatial level using satellite imageries.     

An evaluation method of computer usability based on human-to-computer information transmission model

Abstract

This paper proposes a new evaluation and prediction method for computer usability. This method is based on our two previously proposed information transmission measures created from a human-to-computer information transmission model. The model has three information transmission levels: the device, software, and task content levels. Two measures, called the device independent information measure (DI) and the computer independent information measure (CI), defined on the software and task content levels respectively, are given as the amount of information transmitted. Two information transmission rates are defined as DI/T and CI/T, where T is the task completion time: the device independent information transmission rate (R _DI), and the computer independent information transmission rate (R _CI). The method utilizes the R _DI and R _CI rates to evaluate relatively the usability of software and device operations on different computer systems. Experiments using three different systems, in this case a graphical information input task, confirm that the method offers an efficient way of determining computer usability.     

Estimation of instantaneous air temperature using remote sensing data

In arid areas, the variation of air temperature can be considerable, so instantaneous air temperature (T_ai) estimation is needed in different environmental researches. In this research, two different remote sensing data are used for estimating T_ai for clear sky days in 2009 in Fars Province, Iran, including atmospheric temperature profile and land surface temperature (LST) data from Moderate Resolution Imaging Spectroradiometer. The T_ai from a number of surface weather sites is used to judge the best T_ai estimation. Stations’ elevation, latitude, and land cover type are considered to show their effect on T_ai estimation. The estimated T_ai evaluation focuses on daily and seasonal timescales in the daytime and night time separately. Both LST and vertical temperature profile data produced relatively high coefficient of determination values and small root mean square error value for T_ai estimation, especially during the night time. Land cover and elevation vary the error values in T_ai estimation more, when LST data is used. In comparison atmospheric temperature profile indicates a smaller error in T_ai estimation in spring and summer and in urban land cover type, while using LST data presents a better result in fall and winter especially at night time.     

Evaluation of MODIS land surface temperature products for daily air surface temperature estimation in northwest Vietnam

Recently, the MODerate resolution Imaging Spectroradiometer (MODIS) land surface temperature (LST) is considered one of the most suitable ways to retrieve air surface temperature (T_a) – one of the most important and widely used climate variables for a wide range of applications. In fact, many successful studies have been reported in many regions of the world. Each day, four MODIS LST data are available; from two sensors (Terra and Aqua) at two local overpass times (daytime and night-time). However, due to their different overpass times, most studies have used LST daytime and night-time for daily maximum (T_max) and minimum (T_min) air surface temperature estimation, respectively. Therefore, the performance of each individual LST data, the effect of the dynamic combination of these four LST data, the effect of land surface characteristics, and the effect of LST quality on the same estimation in the same region on the accuracy of estimated T_a remains unclear. In this study, we evaluated and tested all individual LST data as well as all possible combinations of the four MODIS LST data from two separate stations with distinct land surface characteristics in northwest Vietnam for 10 years (from 2004 to 2013) under two sky conditions (all clear sky conditions and only good data – i.e. Quality Control (QC) value of 0) for daily T_a (T_max, T_min, and T_mean) estimations. In addition, the mixed data of the two stations were also evaluated. Our results showed that Terra LST data have a higher correlation with T_a than Aqua LST; which is consistent for both stations and both quality conditions (all clear sky and only good data). A closer overpass time with T_max or T_min occurrence time did not guarantee a higher accuracy of T_a estimation. Using only good LST data produced a higher accuracy of T_a estimation than using all clear sky data. However, if the percentage of good data is low (i.e. less than 30%), then the all clear sky data will provide better results for T_max estimation. Comparing the performance of the different combinations when using the single station and mixed station data, combinations including at least one night-time LST produced stable and high accuracy T_min and T_mean estimates, while the combinations with only daytime LST produced very low accuracy results. For T_max estimation, the results were less impacted by LST quality; however, they were strongly impacted by different combinations and land surface characteristics.     

Estimation of air temperature from MODIS data in east China

Air temperature, T _a, with high spatial and temporal resolution is desired for global change, agricultural disaster, land surface studies, and modelling applications. A statistical algorithm for Moderate Resolution Imaging Spectroradiometer (MODIS) data is developed for daytime T _a retrievals over east China at a resolution of 0.05° × 0.05°. The approach first applies a statistical regression of the first guess, i.e. the preliminary estimate, of T _a to MODIS 11 μm and 12 μm brightness temperature (T _11μm and T _12μm) and site data (longitude, latitude and altitude) for east China. Then the first guess of T _a is further corrected with a series of bias equations for different latitude zones in east China. Further quantitative validation with measured T _a using 335 synoptic weather stations for the whole of 2006 indicates that the algorithm performs well with overall statistics of R = 0.96, RMSE = 3.23°C, and bias = ?0.09°C. 75% of the estimated T _a is within 3°C of the actual T _a and 92% of the estimated T _a is within 5°C of the actual T _a. This bias correction algorithm can be applied to other geostationary and sun-synchronous satellite instruments for T _a retrieval.     

d-Dimensional Range Search on Multicomputers

The range tree is a fundamental data structure for multidimensional point sets, and, as such, is central in a wide range of geometric and database applications. In this paper we describe the first nontrivial adaptation of range trees to the parallel distributed memory setting (BSP-like models). Given a set of n points in d -dimensional Cartesian space, we show how to construct on a coarse-grained multicomputer a distributed range tree T in time O( s / p + T _c (s,p)) , where s = n log ^d-1 n is the size of the sequential data structure and T _c (s,p) is the time to perform an h -relation with h=Θ (s/p) . We then show how T can be used to answer a given set Q of m=O(n) range queries in time O((s log m)/p + T _c (s,p)) and O((s log m)/p + T _c (s,p) + k/p) , where k is the number of results to be reported. These parallel construction and search algorithms are both highly efficient, in that their running times are the sequential time divided by the number of processors, plus a constant number of parallel communication rounds. Received June 1, 1997; revised March 10, 1998.     

Progress in the remote sensing of land surface temperature and ground emissivity using NOAA-AVHRR data

The extensive requirement of landsurface temperature (LST) for environmental studies and management activities of the Earth's resources has made the remote sensing of LST an important academic topic during the last two decades. Many studies have been devoted to establishing the methodology for the retrieval of LST from channels 4 and 5 of Advanced Very High Resolution Radiometer (AVHRR) data. Various split-window algorithms have been reviewed and compared in the literature to understand their differences. Different algorithms differ in both their forms and the calculation of their coefficients. The most popular form of split-window algorithm is T _s=T ₄+A(T ₄-T ₅)+B , where T _s is land surface temperature, T ₄ and T ₅ are brightness temperatures of AVHRR channels 4 and 5, A and B are coefficients in relation to atmospheric effects, viewing angle and ground emissivity. For the actual determination of the coefficients, no matter the complexity of their calculation formulae in various algorithms, only two ways are practically applicable, due tothe unavailability of many required data on atmospheric conditions and ground emissivities in situ satellite pass. Ground data measurements can be used to calibrate the brightness temperature obtained by remote sensing into the actual LST through regression analysis on a sample representing the studied region. The other way is standard atmospheric profile simulationusing computer software such as LOWTRAN7. Ground emissivity has a considerable effect on the accuracy of retrieving LST from remote sensing data. Generally, it is rational to assume an emissivity of 0.96 for most ground surfaces. However, the difference of ground emissivity between channels 4 and 5 also has a significant impact on the accuracy of LST retrieval. By combining the data of AVHRR channels 3, 4 and 5, the difference can be directly calculated from remote sensing data. Therefore, much more study is required on how to accurately determine the coefficients of split-window algorithms in the application of remote sensing to examine LST change and distribution in the real world.     

Approximations of the principal eigenelements inK-positive non-selfadjoint eigenvalue problems

LetT be a compact linearK-positive irreducible operator on a Banach spaceY with a coneK and letT _h be aK-positive approximation ofT on a subspaceY _h Y. It is shown that the principal eigenelements ofT _h approximate the corresponding eigenelements ofT with the same accuracy as the exact normalized positive eigenvector can be approximated by elements inY _h. This result is then extended to eigenvalue problems of the typeMu = Nu with generally unboundedM and compact irreducibleK-positiveT = M ^–1N.     

Lumped model of a non-linear distributed system by finite element method

The finite element method has been used to find an approximate lumped parameter model of a non-linear distributed parameter system. A one dimensional non-linear dispersion system is considered. The space domain is divided into a finite set of k elements. Each element, has n nodes. Within each element the concentration is represented by C(x,t)^(e) = [N][C] ^T where [N] = [n₁(x),n₂(x), [tdot] n_n(x)] and [C] = [C₁(t),C₂(t), [tdot] C_n(t)]. By using Galerkin's criterion a set of (k × n ? n+ 1) first order differential equations are obtained for C_i(t). These equations are solved by an iterative method. The concepts are illustrated by an example taking five three-node elements in the space domain. The results are compared with those obtained by a finite difference method. It is shown that the finite element method can be used effectively in modelling of a distributed system by a lumped system.     

On the group of automorphisms of strongly connected automata

LetA = (S, I, M) be a strongly connected finite automaton withn states. Weeg has shown that ifA has a group of automorphisms of orderm, then there is a partition of the setS inton/m blocks each withm states. Furthermore ifs _i ands _j are in the same block of, thenT _ii =T _jj , whereT _ii = {x|x ^* and thenM(s _i , x) =s _i }. It will be shown that the partition also must have the substitution property and that these two conditions are sufficient for ann state strongly connected automaton to have a group of automorphisms of orderm.Necessary and sufficient conditions for twon-state strongly connected automata to have isomorphic automorphism groups are given. Also, it is demonstrated that forT _ii to equalT _jj it is necessary to check only a finite number of tapes and consequently provide an algorithm for determining whether or notA has a group of automorphisms of orderm. This research was partially supported by the National Science Foundation under Grant No. G.P. 7077.     

The effects of hyperoxia on performance during simulated firefighting work

This study evaluated the effects of hyperoxia (inspired oxygen fraction=40%) on performance during a simulated firefighting work circuit (SFWC) consisting of five events. On separate days, 17 subjects completed at least three orientation trials followed by two experimental trials while breathing either normoxic (NOX) and hyperoxic (HOX) gas mixtures that were randomly assigned in double-blind, cross-over design. Previously, ventilatory threshold (Tvent) and VO₂max had been determined during graded exercise (GXT) on a cycle ergometer. Lactate concentration in venous blood was assessed at exactly 5 min after both the experimental trials and after the GXT. Total time to complete the SFWC was decreased by 4% (p< 0.05) with HOX. No differences were observed in individual event times early in the circuit, however HOX resulted in a 12% improvement (p< 0.05) on the final event. A significantly decreased rating of perceived exertion (RPE) was also recorded immediately prior to the final event. No differences were observed in mean heart rate or post-exercise blood lactate when comparing NOX to HOX. Heart rates during the SFWC (both conditions) were higher than HR at Tvent, but lower than HR at VO₂max (p< 0.05). Post-SFWC lactate values were higher (p< 0.05) than post-VO₂max. These results demonstrate that hyperoxia provided a small but significant increase in performance during short duration, high intensity simulated firefighting work.     

Generalized age-dependent model for estimation of mean survival time in the presence of two competing risks

The paper is motivated towards developing a generalized probability model describing the longevity of a system exposed to paired risks R₁ and R₂ which are dependent. The bivariate exponential model of Freund (1961) with failure times X and Y under risks R₁ and R₂ with a time-independent hazard rate set-up has been generalized by incorporating an additional age factor, t, as a variable. The hazard rates due to R₁ and R₂ have been changed from a to α(t) = αt^α?1, and from β to β(f) = βt^β?1 where α,β > 0 which are Weibull hazard functions for α,β > 1. Further conditions are imposed such that α is changed to α' when R₂ is off and β is changed to β' when R₁ is off. The trivariate distribution of Freund so generalized has again been doubly truncated in the range a  t  b, for a, b > 0; and the conditional distribution of X and Y given t has been used to study the role of the component's age in the context of the system's survival under paired dependent risks in the finite age range.     

On the Cross‐Migrativity with Respect to Continuous t‐Norms

Depending on whether α is an idempotent element of the t‐norm T₀ or not, we study and characterize the structure of a continuous crossmigrative t‐norm T with respect to a fixed and continuous t‐norm T₀, which is indeed the conjecture presented by Fodor et al. (Int J Intell Syst 2012;27:411–428) Results of this paper show that the ‐cross‐migrativity is completely determined by the restriction on a portion of domain of T and have nothing to do with the remaining of [0, 1]². Moreover, we also clarify the relations between our present results and the previous results.     

Thermodynamic Properties of a q-Boson Gas Trapped in an n-Dimensional Harmonic Potential

The thermodynamic properties of an ideal q-boson gas trapped in an n-dimensional harmonic potential are studied, based on the distribution function of q-bosons. The critical temperature T _c,q of Bose-Einstein condensation (BEC) and the heat capacity C of the system are derived analytically. It is shown that for the q-boson gas trapped in a harmonic potential, BEC may occur in any dimension when q 1, the critical temperature is always higher than that of an ordinary Bose gas (q = 1), and the heat capacity is continuous at T _c,q for a one-dimensional system but discontinuous at T _c,q for a two- or multi-dimensional system.     

Minimizing Mean Flow Time with Error Constraint

We consider the problem of minimizing mean flow time for the Imprecise Computation Model introduced by Lin et al. A task system TS=({T _i },{r(T _i )},{d(T _i )},{m(T _i )},{o(T _i )}) consists of a set of n independent tasks, where r(T _i ),d(T _i ),m(T _i ) , and o(T _i ) denote the ready time, deadline, execution time of the mandatory part, and execution time of the optional part of T _i , respectively. Given a task system TS and an error threshold K , our goal is to find a preemptive schedule on one processor such that the average error is no more than K and the mean flow time of the schedule is minimized. Such a schedule is called an optimal schedule. In this article we show that the problem of finding an optimal schedule is NP-hard, even if all tasks have identical ready times and deadlines. A pseudopolynomial-time algorithm is given for a set of tasks with identical ready times and deadlines, and oppositely ordered mandatory execution times and total execution times (i.e., there is a labeling of tasks such that m(T _i )≤ m(T _i+1 ) and m(T _i )+o(T _i )≥ m(T _i+1 )+o(T _i+1 ) for each 1≤ i<n ). Finally, polynomial-time algorithms are given for (1) a set of tasks with identical ready times, and similarly ordered mandatory execution times and total execution times and (2) a set of tasks with similarly ordered ready times, deadlines, mandatory execution times, and total execution times. Received January 19, 1995; revised August 2, 1996.     

Relationships between the three components of air temperature and remotely sensed land surface temperature of agricultural areas in Morocco

In this article, correlations to derive minimum (T_min), mean (T_mean), and maximum (T_max) air temperatures from land surface temperature (T_s) in Morocco are studied. Land surface temperature was derived from 349 decadal cloud-free images acquired by the Advanced Very High Resolution Radiometer sensor, onboard the National Oceanic and Atmospheric Administration’s satellites. T_s was first compared with T_min, T_mean, and T_max, at the level of nine meteorological stations between 1995 and 2012. This first step showed the existence of good linear correlations between T_s and air temperatures. The coefficient of determination, R², varied between 0.59 and 0.79 for T_s versus T_min, between 0.60 and 0.76 for T_s versus T_max, and between 0.67 and 0.79 for T_s versus T_mean. The root mean square error (RMSE) varied between 2.4°C and 3.9°C for T_s versus T_min, between 2.5°C and 4.6°C for T_s versus T_max, and between 2.2°C and 3.8°C for T_s versus T_mean. The mean absolute error (MAE) varied between 2°C and 3.1°C for T_s versus T_min, between 1.9°C and 3.6°C for T_s versus T_max, and between 1.8°C and 3°C for T_s versus T_mean. Second, T_s was compared with T_min, T_max, and T_mean gridded at the level of agricultural areas of 46 provinces in Morocco. For 42 provinces, the mean value of R² was 0.71 for both T_min versus T_s and T_max versus T_s, and 0.76 for T_mean versus T_s. The mean values of the RMSE and the MAE were 3.1°C and 2.4°C for T_s versus T_min, 3.6°C and 2.8°C for T_max versus T_s, and 3°C and 2.3°C for T_mean versus T_s, respectively. Finally, the accuracy of the regression models between air and surface temperatures was tested using a k-fold cross-validation method that showed high stability of these models. The relationships obtained in this work could be very useful for further monitoring and modelling agriculture and meteorological parameters.