Stability of Runge–Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments

AbstractThis paper deals with the numerical properties of Runge–Kutta methods for the solution of u′(t)=au(t)+a0u([t+12]). It is shown that the Runge–Kutta method can preserve the convergence order. The necessary and sufficient conditions under which the analytical stability region is contained in the numerical stability region are obtained. It is interesting that the θ-methods with 0⩽θ<12 are asymptotically stable. Some numerical experiments are given

Botanical composition, production and nutrient status of an originally Lolium perenne-dominant cut grass sward receiving long-term manure applications

Effects of long-term applications (50, 100 and 200 m(3) ha(-1)y(-1)) of pig and cow slurries on yield, botanical composition and nutrient content of herbage of an original perennial ryegrass sward were assessed in a three-cut silage system and compared with unamended and fertilized controls in the 36th year of the experiment. Cow slurry at 50 m(3) ha(-1) produced similar annual herbage DM yield to 200 kg ha(-1) fertilizer N in 2006, whereas about 100 m(3) ha(-1) pig slurry were required to produce a similar amount of DM. The highest slurry application rate significantly influenced sward botanical composition without depressing DM yield. The principal invading species were creeping bent and meadow grasses (similar to findings at a previous assessment in 1981) except in the unamended control (which were common bent and Yorkshire fog). Perennial ryegrass remained a main species in plots receiving fertilizer (31 % annual DM yield) and low slurry rates (38 %) but declined to 3 % annual DM yield at the highest slurry rate where the ability of ryegrass to utilize slurry N and P may have been affected by chemically or physically induced deficiencies of other nutrients (e.g. Ca) or direct physical effects such as smothering

Identification of a candidate gene for Rc-D1, a locus controlling red coleoptile colour in wheat

Red coleoptile is an easily observed agronomic trait of wheat and has been extensively studied. However, the molecular mechanism of this trait has not yet been revealed. In this study, the MYB gene TaMYB-D1 was isolated from the wheat cultivar ‘Gy115’, which possesses red coleoptiles. This gene resided at the short arm of the homoelogous group 7 chromosomes. TaMYB-D1 was the only gene expressed in the coleoptiles of ‘Gy115’ and was not expressed in ‘Opata’ and ‘CS’, which have uncoloured coleoptiles. Phylogenetic analysis placed TaMYB-D1 very close to ZmC1 and other MYB proteins regulating anthocyanin biosynthesis. The encoded protein of TaMYB-D1 had an integrated DNA binding domain of 102 amino acids and a transcription domain with 42 amino acids, similar to the structure of ZmC1. Transient expression analysis in onion epidermal cells showed that TaMYB-D1 was located at the plant nucleus, which suggested its role as a transcription factor. The expression of TaMYB-D1 was accompanied with the expression of TaDFR and anthocyanin biosynthesis in the development of the coleoptile of ‘Gy115’. Transient expression analysis showed that only TaMYB-D1 induced a few ‘Opata’ coleoptile cells to synthesize anthocyanin in light, and the gene also induced a colour change to red in many cells with the help of ZmR. All of these results suggested TaMYB-D1 as the candidate gene for the red coleoptile trait of ‘Gy115’

A note on "The Economic Lot Sizing Problem with Inventory Bounds"

In a recent paper, Liu (2008) considers the lot-sizing problem with lower and upper bounds on the inventory levels. He proposes an O(n^2) algorithm for the general problem, and an O(n) algorithm for the special case with non-speculative motives. We show that neither of the algorithms provides an optimal solution in general. Furthermore, we propose a fix for the former algorithm that maintains the O(n^2) complexity

Roles Of Cell Compartments in the Variation of Firing Patterns Generated by Reduced Pacemaker Models of the Crustacean Stomatogastric Ganglion

Endogenous bursters in central pattern generators (CPGs) generate rhythmic firing patterns controlling regular movements in the organism. Based on a pacemaker kernel model of the stomatogastric ganglion (SGG) of crustaceans, we constructed three reduced models, (i) dendrite-reduced model (DRM), (ii) axon-reduced model (ARM), and (iii) primary neuritereduced model (PNRM). Similar firing patterns were observed in two models except the axonreduced one. Perturbing of various parameters in the models induced bifurcation phenomena in the occurrence of interspike intervals (ISIs), which depicted variation of the firing patterns. By comparing and analyzing two-dimensional parameter planes derived from the above different models, the effects of compartments on varying firing patterns were detected. In particular, a different kind of period-doubling transition mode of firing patterns, which varied via a ring-shape mode, was found.Ендогенні компоненти центральних генераторів патернів (ЦГП), відповідальні за контроль певних стандартних моторних феноменів в організмі, генерують ритмічні групи розрядів. Базуючись на ядерній моделі пейсмекерів у стоматогастричному ганглії (СГГ) ракоподібних, ми сконструювали три редуковані моделі – модель з редукованими дендритами (ДРМ), модель з редукованим аксоном (АРМ) та модель з редукованим первинним нейритом (ПНРМ). У двох моделях, за виключенням АРМ, спостерігались однакові патерни розрядів. Змини різних параметрів моделей призводили до появи біфуркаційних феноменів у послідовностях міжімпульсних інтервалів, що віддзеркалювалось у варіаціях патернів розрядів. У перебігу порівняння двовимірних площин параметрів, отриманих для різних моделей, вдалось ідентифікувати впливи компартментів на варіацію параметрів розрядів. Зокрема, було встановлено специфічний вид перехідного режиму подвоєння періоду в патернах, варіації якого мали кільцеподібний характер

Ammonium uptake and assimilation are required for rice defense against sheath blight disease

Nitrogen (N) is an important nutrient for plant growth and yield production, and rice grown in paddy soil mainly uses ammonium (NH4+) as its N source. Previous studies have shown that N status is tightly connected to plant defense; however, the roles of NH4+ uptake and assimilation in rice sheath blight disease response have not been studied previously. Here, we analyzed the effects of different N sources on plant defense against Rhizoctonia solani. The results indicated that rice plants grown in N-free conditions had higher resistance to sheath blight than those grown under N conditions. In greater detail, rice plants cultured with glutamine as the sole N source were more susceptible to sheath blight disease compared to the groups using NH4+ and nitrate (NO3–) as sole N sources. N deficiency severely inhibited plant growth; therefore, ammonium transporter 1;2 overexpressors (AMT1;2 OXs) were generated to test their growth and defense ability under low N conditions. AMT1;2 OXs increased N use efficiency and exhibited less susceptible symptoms to R. solani and highly induced the expression of PBZ1 compared to the wild-type controls upon infection of R. solani. Furthermore, the glutamine synthetase 1;1 (GS1;1) mutant (gs1;1) was more susceptible to R. solani infection than the wild-type control, and the genetic combination of AMT1;2 OX and gs1;1 revealed that AMT1;2 OX was less susceptible to R. solani and required GS1;1 activity. In addition, cellular NH4+ content was higher in AMT1;2 OX and gs1;1 plants, indicating that NH4+ was not directly controlling plant defense. In conclusion, the present study showed that the activation of NH4+ uptake and assimilation were required for rice resistance against sheath blight disease

Tibetan sheep are better able to cope with low energy intake than Small-tailed Han sheep due to lower maintenance energy requirements and higher nutrient digestibilities

Tibetan sheep are indigenous to the Qinghai-Tibetan Plateau (QTP) and are well-adapted to and even thrive under the harsh alpine conditions. Small-tailed Han sheep were introduced to the plateau because of their high prolificacy and are maintained mainly in feedlots. Because of their different backgrounds, we hypothesised that Tibetan and Small-tailed Han sheep would differ in their utilization of energy intake and predicted that Tibetan sheep would cope better with low energy intake than Small-tailed Han sheep. To test this prediction, we determined nutrient digestibilities, energy requirements for maintenance and blood metabolite and hormone concentrations involved in energy metabolism in these breeds. Sheep of each breed (n = 24 of each, all wethers and 1.5 years of age) were distributed randomly into one of four groups and offered ad libitum diets of different digestible energy (DE) densities: 8.21, 9.33, 10.45 and 11.57 MJ DE/kg Dry matter (DM). Following 42 d of measuring feed intake, a 1-week digestion and metabolism experiment was done. DM intakes did not differ between breeds nor among treatments but, by design, DE intake increased linearly in both breeds as dietary energy level increased (P < 0.001). The average daily gain (ADG) was significantly greater in the Tibetan than Small-tailed Han sheep (P = 0.003) and increased linearly in both breeds (P < 0.001). In addition, from the regression analysis of ADG on DE intake, daily DE maintenance requirements were lower for Tibetan than for Small-tailed Han sheep (0.41 vs 0.50 MJ/BW0.75, P < 0.05). The DE and metabolizable energy (ME) digestibilities were higher in the Tibetan than Small-tailed Han sheep (P < 0.001) and increased linearly as the energy level increased in the diet (P < 0.001). At the lowest energy treatment, Tibetan sheep when compared with Small-tailed Han sheep, had: 1) higher serum glucose and glucagon, but lower insulin concentrations (P < 0.05), which indicated a higher capacity for gluconeogenesis and ability to regulate glucose metabolism; and 2) higher non-esterified fatty acids (NEFA) and lower very low density lipoprotein (VLDL) and triglyceride (TG) concentrations (P < 0.05), which indicated a higher capacity for NEFA oxidation but lower ability for triglyceride (TG) synthesis. We concluded that our prediction was supported as these differences between breeds conferred an advantage for Tibetan over Small-tailed Han sheep to cope better with low energy diets

Design and fabrication of indium phosphide air-bridge waveguides with MEMS functionality

We present the design and fabrication of a dual air-bridge waveguide structure integrated with MEMS functionality. The structure is designed to function as a tunable optical buffer for telecommunication application. The optical buffer structure is based on two parallel waveguides made of high refractive index material with subwavelength dimensions. They are suspended in air, and are separated by a sub-micron air gap. Due to the fact that the size of the waveguides is much smaller than the wavelength of light that propagates in the structure, a significant fraction of the optical mode is in the air gap between the waveguides. By changing the size of the air gap using MEMS techniques, we can vary this fraction and hence the effective refractive index of the waveguide structure, thus generating tunable optical delay.The optical buffer structure was grown on an InP substrate by molecular beam epitaxy, and the device layer was made of InGaP. An InGaAs layer was sandwiched between the device layer and the substrate to serve as a sacrificial layer. The sub-micron waveguides, their supports in the form of side pillars with tapered shapes in order to minimize optical losses, and the MEMS structures were patterned using electron beam lithography and plasma etching. Electrodes were integrated into the structure to provide electrostatic actuation. After the sample patterning, the waveguide structure was released using HF etch. Our simulations predict that by varying the waveguide separation from 50 nm to 500 nm, we could achieve a change in propagation delay by a factor of two

An Artificial Intelligence Approach for Tackling Conformational Energy Uncertainties in Chiroptical Spectroscopies

Determination of the absolute configuration of chiral molecules is a prerequisite for obtaining a fundamental understanding in any chirality-related field. The interaction with polarised light has proven to be a powerful means to determine this absolute configuration, but its application rests on the comparison between experimental and computed spectra for which the inherent uncertainty in conformational Boltzmann factors has proven to be extremely hard to tackle. Here we present a novel approach that overcomes this issue by combining a genetic algorithm that identifies the relevant conformers by accounting for the uncertainties in DFT relative energies, and a hierarchical clustering algorithm that analyses the trends in the spectra of the considered conformers and identifies on-the-fly when a given chiroptical technique is not able to make reliable predictions. The effectiveness of this approach is demonstrated by considering the challenging cases of papuamine and haliclonadiamine, two bis-indane natural products with eight chiral centres and considerable conformational heterogeneity that could not be assigned unambiguously with current approaches.</p