Unit Time Interval Research Articles

Delay Equations with Rapidly Oscillating Stable Periodic Solutions

We prove analytically that there exist delay equations admitting rapidly oscillating stable periodic solutions. Previous results were obtained with the aid of computers, only for particular feedback functions. Our proofs work for stiff equations with several classes of feedback functions. Moreover, we prove that for negative feedback there exists a class of feedback functions such that the larger the stiffness parameter is, the more stable rapidly oscillating periodic solutions there are. There are stable periodic solutions with arbitrarily many zeros per unit time interval if the stiffness parameter is chosen sufficiently large.

Dynamic Bandwidth Allocation Scheme for Video Streaming in Wireless Cellular Networks

In this paper, we propose a novel dynamic bandwidth allocation scheme for the downlink real-time video streaming in the wireless cellular networks. Our scheme is able to maximize the bandwidth utilization, while satisfying the required packet loss probability, a QoS constraint, by dynamically determining the amount of bandwidth to be allocated at each unit time interval by measuring the queue length and the packet loss probability. The simulation results show that, without the need of a priori knowledge about the traffic traces, our scheme is able to achieve the same level of performance as what can be accomplished with the pre-calculated effective bandwidth in terms of the bandwidth utilization and the packet loss rate.

Some Scheduling Problem with Fuzzy Resource Constraints

Resource constrained scheduling problems cover a wide range of problems which captures many variations of the model. But in realistic situations, many uncertainties exist and the fuzzy methodology is employed to deal with situations that are expressed in vague or ambiguous terms. In this paper, the available resource limit of each job is flexible as we propose the following bi criteria scheduling problem: There are n jobs to be processed on one of identical parallel machines. Each job has unit processing time and its processing requires the number of resource types. Resource requirement of each job for each type of resource is fixed but available limit of each type of resource to be used by job processing in each unit time interval is flexible. That is, fuzzy limit with membership function describing non-decreasing satisfaction degree about setting limit quantity. Under above setting, maximum completion time is to be minimized and minimal satisfaction degree about upper limits of resource quantity of all types to be maximized. But usually we cannot optimize two objectives at a time. So we seek non-dominated schedule after defining dominance between schedules by proposing an efficient algorithm.

EFFECTIVE DETERMINATION OF POISSON NOISE

We give an effective definition of higher dimensional parameter Poisson noise. The idea comes from the observation of the conditional probablistic behavior of a Poisson process under the condition that it jumps over the unit time interval exactly as many times as n. Also, taking the optimality into account we can give effective determination of a Poisson noise with multi-dimensional parameter, which is in agreement with the formal generalization of a Poisson noise in terms of the characteristic functional.

Prey selection by greenback flounder Rhombosolea tapirina (Günther) larvae

The potential for greenback flounder ( Rhombosolea tapirina), as a new species for aquaculture in temperate Australia, is currently under investigation. Isolation of an endemic temperate rotifer, Testudinella sp., provided the opportunity to assess this genus against standard live prey species used in aquaculture. Greenback flounder larvae were offered a range of rotifer prey species ( Testudinella sp., Brachionus rotundiformis, Brachionus plicatilis) and the brine shrimp Artemia, either in isolation or combination, in order to test the hypothesis that factors besides prey size affect prey selection. From first-feeding to approximately day 13 post-hatching, greenback flounder larvae preferentially consumed the rotifer Testudinella sp. over the larger width rotifer B. plicatilis and to a lesser extent the rotifer of similar width dimension, B. rotundiformis. From day 15 post-hatching, consumption (number of prey consumed per larva per unit time interval) and selection ( α) of B. plicatilis was significantly higher than of Testudinella sp. and Artemia, but by day 18 post-hatching, there was a shift of feeding preference to Artemia. This indicated that size of prey ingested increased with age, likely reflecting an ontogenetic increase in larval sensory function, mouth gape and prey capture and handling ability. Significant selection of Testudinella sp. over the larger rotifer B. plicatilis occurred despite greenback flounder larvae being able to consume B. plicatilis. This along with significant selection (day 11 post-hatching) and consumption (days 11 and 12 post-hatching) of Testudinella sp. over the rotifer of similar width B. rotundiformis, indicates that prey size is not the sole determinant of prey consumption and suggests that greenback flounder larvae exhibit both species-specific and size-specific prey selection. Understanding the basis of prey selection by larval fish predators is essential for enhancing prey consumption in culture, especially in the context of ontogenetic shifts in prey species preference.

A Basic System of Equations for the Motion of a Fluid with Variable Flow Rate in the Bilateral Flow Offtake

All theoretical studies conducted in modern hydrodynamics are based on a system of Eulerian equations, a continuity equation, and a characteristic equation [1]. In the area of hydraulics that is concerned with a one-dimensional motion, the basis for all theoretical investigations is a system of three equations: (i) a Bernoulli equation, which is a particular solution of the Eulerian system, (ii) a flow equation, which is an analog of the continuity equation, and (iii) a characteristic equation. These equations are used to study the motion of a fluid at a constant flow rate. For the case of motion of a fluid at a variable flow rate, these equations must be modified and augmented with new equations to make the system complete. Most studies were mainly concerned with formulating a “basic equation” for the motion of a fluid at a variable flow rate. For the first time, the problem of constructing a general complete system of equations for the motion of a fluid at a variable flow rate for unilateral division of the flow was brought to a logical conclusion by Kiselev [2]. To follow suit, it was our goal in this study to set up a general complete system of equations for the motion of a fluid at a variable flow rate for bilateral division of the flow. General equations for the fluid motion at a variable flow rate for bilateral flow offtake. We consider a model for constructing general equations. From the main stream flowing through a constraint space (a river, a channel, etc.), part of the fluid is uniformly and simultaneously diverted. Within an infinitesimal time interval At, the masses m lo and m ro moving with the velocities u lo and u ro are instantaneously diverted from the main stream of mass m moving with the velocity u (here the subscripts “lo” and “ro” denote the left-side offtake and right-side offtake, respectively). At the instant of diversion, the remaining mass m – m lo – m ro has the velocity u + Au = u. The lapse of time from At to dt is is a continuous process involving the change in mass. One can assume that at any instant of the unit time interval within the volume of fluid AW, the system in question can be partitioned into two parts: one is the mass of the main stream m, and the other is the diverted masses m lo and m ro . The space of volume AW is filled with fluid masses of the main and diverted flows. The fluid motion is assumed to be uninter

The experimental study on freezing of supercooled water using metallic surface

Freezing of supercooled water on a metallic plate was studied, experimentally. First of all, a gold plated surface was selected as a metallic surface because the surface has very little change in the characteristics of the surface against time. The experiments on freezing under various cooling rates were carried out and the probability of freezing per unit surface area per unit time interval was calculated. It was found that the probability was independent of the cooling rate. Secondly, in order to clarify the effect of oxidation on freezing of supercooled water, an electrolytically polished copper surface was selected and a time variation of the probability of freezing was investigated. A large number of experimental data is required to obtain an accurate value for the probability, but it is impossible to perform it before the characteristics of the surface changes. Hence, in order to cover a wide range of the degree of supercooling at freezing in a short period of time, experiments were carried out under various cooling rates. It was found that the oxidation of the surface restrained the supercooled water on the surface from freezing. By comparing the results with the one for a gold plated surface, a parameter was obtained to express the characteristics of the surface.

The Convex Minorant of the Cauchy Process

We determine the law of the convex minorant $(M_s, s\in [0,1])$ of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. In particular, this enables us to deduce that the paths of $M$ have a continuous derivative, and that the support of the Stieltjes measure $dM'$ has logarithmic dimension one.

Quasi-Steady-State Solutions of Some Population Models

We consider a class of first-order differential equations generalizing the logistic equation of population growth, together with a two-point boundary condition of the form y(0)=η(y(1)) (where y(t) is the size of the population at time t). Thus the population, defined for t∈[0,1], resets itself at the end of the unit time interval to its initial value. If y satisfies the boundary condition and we define Y(t+n)=y(t) for t∈[0,1) and n=0,1,…, then Y is a 1-periodic solution of the differential equation (extended to t∈[0,∞ by periodicity) for t≠1,2,… and Y has a jump of magnitude η(y(1))−y(0) at t=1,2,…. This quasi-steady-state solution corresponds to a population growing or declining on n−1<t<n (n=1,2,…) and decreasing or increasing impulsively at t=1,2,…. Y plays a role for the jump condition y(n+)=η(y(n−)) analogous to that played by constant solutions to the differential equation with zero jump condition (i.e., y(n+)=y(n−)). We show, under hypotheses motivated by biological considerations, that a strictly positive solution exists, is unique, and is monotone and continuous in its dependence on η.

Effects of Dynamics on the Properties of Feedback Adjustment Schemes With Dead Band

Bounded adjustment schemes—also called dead-band schemes—are analyzed assuming that delayed elfects of the adjustments occur. The disturbance model is allowed to show a deterministic process drift per unit time interval, The resulting average adjustment interval and mean squared deviation from target are obtained under this general framework.

Effects of Dynamics on the Properties of Feedback Adjustment Schemes with Dead Band

Bounded adjustment schemes—also called dead-band schemes—are analyzed assuming that delayed elfects of the adjustments occur. The disturbance model is allowed to show a deterministic process drift per unit time interval, The resulting average adjustment interval and mean squared deviation from target are obtained under this general framework.

Multiplicities of eigenvalues of some linear search schemes

We consider the problem of dynamically reorganizing a linear list when the list is subject to a random number of requests during a unit time interval. Three different heuristics are considered in which the selected items are moved to the front of the list in random order, the same order and finally the opposite order to the previous one. We find the eigenvalues and their multiplicities for the corresponding transition probability matrices. These are given in terms of the weights representing the probability of selection of the individual items. The methods employed are purely algebraic, being based on properties of permutations, and so our results are valid for arbitrary complex weights.

Intraday Lead-Lag Relationships Between the Futures-, Options and Stock Market *

In rational, efficiently functioning and complete markets, returns on derivative and underlying securities should be perfectly contemporaneously correlated.Due to market imperfections, one of these markets may reflect information faster.The use of high-frequency data and the choice for a small unit time interval to measure these lead-lag relations comes at the cost of some or many missing observations, causing traditional estimators to either under- or overestimate covariances and correlations.We use a new estimator to estimate lead-lag relationships between the cash AEX index, options and futures.We find that futures returns lead both options and cash index returns by approximately 10 minutes.The relationship between options and the cash market is not completely unidirectional

Groundwater head sampling based on stochastic analysis

The problem of determining a uniform sampling time interval for monitoring serially correlated groundwater heads is the main subject discussed here. The problem is approached by stochastic time series analysis and modeling. An autoregressive integrated moving average model is assumed to fit the underlying series. Given that groundwater head data can be sampled at different time intervals and that the same stochastic model must represent the time series regardless of the sampling timescale, the parameters of the underlying model for the series sampled at a given arbitrary time interval h are obtained as a function of h and as a function of the model parameters for the series sampled at a unit time interval. This is accomplished by linking the derived variances and autocovariances at the two sampling scales. The derived equations and the sampling design procedure are tested and illustrated using the groundwater head data of Collier County, Florida.

A Computer Simulation Study of Isometric Contraction of Latissimus Dorsi Muscle Used for Cardiac Assistance

This study was designed to investigate the feasibility of a skeletal muscle pump employing latissimus dorsi muscle (LDM) for cardiac assistance. We developed and used a 2-dimensional mathematical model for LDM to investigate how the size of pneumatic balloons (30, 38, and 45 ml) and the three different locations (proximal, center, and distal) affect the pressure applied to the balloon by LDM. The computer simulation was performed by coding a visco-elastic and nonlinear 2-dimensional program that employed the finite element method (FEM). The muscle specific parameters of LDM were obtained from animal experiment results. The model is based on Hill's characteristic equation and composed of a contractile component and a passive element. The simulation results indicated that the intermediate and largest sized balloon lead to the highest and the lowest power (volume reduction per unit time interval), respectively. On the other hand, when the balloon is inserted in the distal LDM, the power is lower than in the other two positions, regardless of the balloon size. The above results suggest that the optimal size of the balloon should be selected depending on the muscle specific parameters of the actuator, and that the balloon should be inserted either in the proximal portion or center of the actuator.

Recurrence statistics of concentration fluctuations in plumes within a near-neutral atmospheric surface layer

This study examines the statistical properties of the concentration derivative, χ′, for a dispersing plume in a near-neutrally stratified atmospheric surface layer. Towards this goal, the probability density function (pdf) of χ′, and the conditional pdf of χ′ given a fixed concentration level, χ, have been measured. These pdfs are found to be modeled well by a generalizedq-Gaussian (gqG) distribution with intermittency exponent,q, equal to 0.3 and 3/4, respectively. These results highlight the strong intermittency effect (patchiness) of the small-scale concentration eddy structures in the plume. The distribution of time intervals between successive high peaks in the squared derivative process, x′2, is found to be well approximated by a power-law distribution, implying that occurrences of these high peaks are much more clustered than would be predicted by a Poisson or shot-noise process. The results are used to improve models for the joint pdf of χ and χ′, and for the expected number of upcrossings per unit time interval of a fixed concentration level that have been proposed by Kristensenet al. (1989). The predictions of the improved models are in accord with observations, and suggest that the intercorrelation between χ and χ′ must be explicitly incorporated if good estimates of the upcrossing intensity are to be obtained.

Minima of Independent Bessel Processes and of Distances Between Brownian Particles

Consider a large, finite collection of particles performing Brownian motion independently in space. We examine the process obtained by taking the minimum, at each time, of the distances of the particles, either (a) from the origin, or (b) from each other. In both cases, when time and space are suitably renormalized, we obtain a narrow convergence result. We also consider the number of pairs of particles which approach each other closely, over a unit time interval.

Correlation among Si, Ge, and B deposition rates in low-pressure CVD with SiH4−GeH4−B2H6-He mixtures

The deposition process at 500 °C with SiH4–GeH4–B2H6–He mixtures, which yields the amorphous Si–Ge–B alloy, was studied. Although in crystalline Si and Ge the maximum B content is limited to the solid solubility, any amount of B can uniformly be contained in amorphous Si–Ge–B. Thus, films with a B content up to 64 at.% have been prepared. The deposition rate of atoms, defined as the number of atoms deposited in a unit time interval, is obtained for each element by analyzing the growth rate together with the composition and the mass density of the film. When the SiH4 and the B2H6 partial pressures are constant, the Si and the B deposition rates are almost independent of the GeH4 partial pressure. In contrast, the Si deposition rate increases remarkably as the B2H6 partial pressure increases, even when the SiH4 partial pressure is maintained constant. A simple model is proposed for explaining the relationship between the Si and the B deposition rates.

Fundamental research on the supercooling phenomenon on heat transfer surfaces—investigation of an effect of characteristics of surface and cooling rate on a freezing temperature of supercooled water

In relation to the problem of supercooling for ice storage devices, a basic investigation is carried out by performing a number of experiments and a statistical analysis. In the experiments, the freezing temperature of supercooled water on a heat transfer surface is measured. It is observed that the characteristics of the surface and the cooling condition affect the freezing temperature. The probability of the initial appearance of ice within a unit surface area in a unit time interval is introduced as a function of the degree of supercooling and the surface property. Finally, a method to predict the most probable freezing temperature of supercooled water for a given cooling condition and surface property is proposed.

Diffusion approximation for equilibrium distribution of reservoir storage

The Fokker‐Planck equation is used to describe the evolution through time of the probability density function of storage levels between the boundaries of a finite reservoir. Analytical solutions for the equilibrium density function are obtained under the assumption that potential storage displacements are independent stationary Gaussian random variables. The potential storage displacement represents the change in storage that would occur during a unit time interval in a reservoir of infinite capacity. Results show that the storage density function is a mixed truncated exponential distribution with mass concentrations on the lower and upper boundaries corresponding to the steady state probability that the reservoir is empty or full, respectively. Parameters of the equilibrium storage density function are computed from the reservoir capacity and the mean and variance per unit time of the potential storage displacement. A dimensionless parameter, analogous to a Peclet number, identifies conditions for which the finite reservoir effectively behaves as one with semi‐infinite capacity. Analytical solutions from the diffusion approximation show excellent agreement with independent estimates of the storage distribution function obtained using probability matrix methods, Monte Carlo simulation, and numerical methods.