Generalized Power Function Research Articles

Синтез квазиоптимальных законов управления на основе принципа декомпозиции и редукции задачи Лагранжа к изопериметрической в условиях неопределенности

The decomposition principle serves as the basis for methods for constructing universal laws of control of mechanical systems that ensure the stability of any target movement from a set of permissible ones and do not contain information about the dynamic parameters of the control object. It is known that the use of reduction of the Lagrange problem to an isoperimetric one makes it possible to obtain an effective solution to the problem of synthesis of nonlinear control laws, the structure of which determines the variant of nonlinear correction of the control laws of the decomposition principle, which provides an increase in performance. This happens due to the fact that the solution of the game problem is obtained under the assumption of the worst variant of disturbing forces. With a known structure of the controlled system or the availability of information about external forces based on their measurement, the correction of the control law makes it possible to improve the quality of control in comparison with the traditional solution. The purpose of this work is to increase the efficiency of control of nonlinear dynamic systems under uncertainty conditions based on the use of a quasi-optimal control structure obtained on the basis of the maximum condition of the generalized power function and the principle of release, and to analyze the effectiveness of the resulting solution in terms of speed using numerical simulation.

Gastric evacuation in European seabass Dicentrarchus labrax (Linnaeus, 1758), forced-fed on commercial pellets

The effects of meal size and body size on gastric evacuation rates were parameterised for European seabass Dicentrarchus labrax (Linnaeus, 1758). A total of three gastric evacuation experiments were performed on small (15.7±0.8 cm) and large (21.5±0.4) size fish forced-fed with meals of 0.5 and 1.5 g composed of commercial pellets. The stomach contents were then recovered by serial slaughtering the fish at predetermined post-prandial times. The surface-area dependent function adequately describes the gastric evacuation in European seabass independently of meal size. A power function of fish length L was then employed to evaluate the impact of body size, revealing its notable effect on gastric evacuation rates of European seabass. Keywords: Aquaculture, Feeding regimes, General power function, Surface-area dependent

On Some Properties of a New Truncated Model With Applications to Lifetime Data

This research explored the exponentiated left truncated power distribution which is a bounded model. Various statistical properties which include the moments and their associated measures, Bonferroni and Lorenz curves, reliability measures, shapes, quantile function, entropy, and order statistics were discussed in detail. A simulation study was provided and applications to two real-world data were considered. The performance of the exponentiated left truncated power distribution over other bounded models like Topp-Leone distribution, Beta distribution, Kumaraswamy distribution, Lehmann type–I distribution, Lehmann type–II distribution, generalized power function, Weibull power function, and Mustapha type–II distribution is quite commendable.

Temperature, meal size and body size effects on the gastric evacuation of rainbow trout: modelling optimum and upper thermal limits.

This study examined the rate and course of gastric evacuation (GE) in rainbow trout Oncorhynchus mykiss in relation to meal size, body size and temperature. The GE experiments were performed on small (mean ± 95% C.I., 17.7 ± 0.5cm total length), medium (22. 9 ± 0.2cm) and large (28.3 ± 0.3cm) rainbow trout fed meals of different sizes using commercial food pellets at water temperatures T ranging from 7.8°C to 19.2°C. Estimating the shape parameter of a general power function suggested that the square root function adequately described the GE in rainbow trout independently of meal size. The effects of total body length L and weight W on gastric evacuation rate (GER) were described by simple power functions. The square root function was further expanded by a temperature function with temperature optimum to describe the effect of temperature. The expanded square root function revealed a considerable effect of body size and temperature on the GER of rainbow trout. The GER increased exponentially with rising temperature, reached an optimum at c. 18.5°C and then declined abruptly to zero at c. 21°C. The GER of rainbow trout could thus be described by (g h-1 ) or (g h-1 ), where St is the current stomach content mass (g), and at post-prandial time t (h). These functions should prove useful to calculate total GE time as well as stomach fullness at different post-prandial times and therefore provide valuable information to develop optimal feeding strategies for farming of rainbow trout.

Vehicle Platooning Impact on Drag Coefficients and Energy/Fuel Saving Implications

In this paper, empirical data from the literature are used to develop general power models that capture the impact of a vehicle position, in a platoon of homogeneous vehicles, and the distance gap to its lead (and following) vehicle on its drag coefficient. These models are developed for light duty vehicles, buses, and heavy duty trucks. The models were fit using a constrained optimization framework to fit a general power function using either direct drag force or fuel measurements. The model is then used to extrapolate the empirical measurements to a wide range of vehicle distance gaps within a platoon. Using these models we estimate the potential fuel reduction associated with homogeneous platoons of light duty vehicles, buses, and heavy duty trucks. The results show a significant reduction in the vehicle fuel consumption when compared with those based on a constant drag coefficient assumption. Specifically, considering a minimum time gap between vehicles of $0.5 \; secs$ (which is typical considering state-of-practice communication and mechanical system latencies) running at a speed of $100 \; km/hr$, the optimum fuel reduction that is achieved is $4.5 \%$, $15.5 \%$, and $7.0 \%$ for light duty vehicle, bus, and heavy duty truck platoons, respectively. For longer time gaps, the bus and heavy duty truck platoons still produce fuel reductions in the order of $9.0 \%$ and $4.5 \%$, whereas light duty vehicles produce negligible fuel savings.

Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

The aim of this work is to schedule the charging of electric vehicles (EVs) at a single charging station such that the temporal availability of each EV as well as the maximum available power at the station are considered. The total costs for charging the vehicles should be minimized w.r.t. time-dependent electricity costs. A particular challenge investigated in this work is that the maximum power at which a vehicle can be charged is dependent on the current state of charge (SOC) of the vehicle. Such a consideration is particularly relevant in the case of fast charging. Considering this aspect for a discretized time horizon is not trivial, as the maximum charging power of an EV may also change in between time steps. To deal with this issue, we instead consider the energy by which an EV can be charged within a time step. For this purpose, we show how to derive the maximum charging energy in an exact as well as an approximate way. Moreover, we propose two methods for solving the scheduling problem. The first is a cutting plane method utilizing a convex hull of the, in general, nonconcave SOC–power curves. The second method is based on a piecewise linearization of the SOC–energy curve and is effectively solved by branch-and-cut. The proposed approaches are evaluated on benchmark instances, which are partly based on real-world data. To deal with EVs arriving at different times as well as charging costs changing over time, a model-based predictive control strategy is usually applied in such cases. Hence, we also experimentally evaluate the performance of our approaches for such a strategy. The results show that optimally solving problems with general piecewise linear maximum power functions requires high computation times. However, problems with concave, piecewise linear maximum charging power functions can efficiently be dealt with by means of linear programming. Approximating an EV’s maximum charging power with a concave function may result in practically infeasible solutions, due to vehicles potentially not reaching their specified target SOC. However, our results show that this error is negligible in practice.

Shallow Layer Destruction Law of Expansive Soil Slope under Rainfall and the Application of Geogrid Reinforcement

A large number of instability cases and laboratory tests of expansive soil slopes show that its shallow layer destruction happens because of the insufficient shear strength under the usual action of low stress and repeated dry-wet cycles. We can obtain the strength nonlinear distribution law fitted by generalized power function based on a series of shear strength tests of expansive soil considering low stress and can construct the numerical model considering the nonlinear strength distribution by FISH, to realize the shear strength dynamic distribution with the vertical stress. Based on the numerical model, the whole-process contrastive analysis has been conducted on the stress field, the slip surface depth, and the seepage field of plain soil and reinforced expansive soil cut slope under different rainfall conditions. Besides, the mechanics characteristic of the geogrid under various design schemes has been compared and analyzed. A further explanation has been given for the expansive soil cut slope prone to shallow layer failure after rainfall and on the effect of geogrid reinforcement. The numerical results provide a reference for slope stability analysis in rainy expansive soil areas.

Supersymmetric generalized power functions

Complex-valued functions defined on a finite interval [a, b] generalizing power functions of the type (x−x0)n for n ≥ 0 are studied. These functions called Φ-generalized powers, Φ being a given nonzero complex-valued function on the interval, were considered to construct a general solution representation of the Sturm–Liouville equation in terms of the spectral parameter [V. V. Kravchenko and R. M. Porter, Math. Methods Appl. Sci. 33(4), 459–468 (2010)]. The Φ-generalized powers can be considered as natural basis functions for the one-dimensional supersymmetric quantum mechanics systems taking Φ=ψ02, where the function ψ0(x) is the ground state wave function of one of the supersymmetric scalar Hamiltonians. Several properties are obtained such as Φ-symmetric conjugate and antisymmetry of the Φ-generalized powers, a supersymmetric binomial identity for these functions, a supersymmetric Pythagorean elliptic (hyperbolic) identity involving four Φ-trigonometric (Φ-hyperbolic) functions, as well as a supersymmetric Taylor series expressed in terms of the Φ-derivatives. We show that the first n Φ-generalized powers are a fundamental set of solutions associated with nonconstant coefficient homogeneous linear ordinary differential equations of order n + 1. Finally, we present a general solution representation of the stationary Schrödinger equation in terms of geometric series where the Volterra compositions of the first type are considered.

The condition for the maximum of the generalized power function in the problem of forming a multi-mode control law with limitation

A quasi-optimal control law is developed based on the condition for the maxi-mum of the generalized power function taking into account the stationarity of the Hamiltonian on the switching line for control objects that can be represented by the Lagrange equations of the second kind. The comparative analysis is carried out based on the mathematical simulation using the optimal nonlinear control laws with respect to several criteria. We found that the modes of the proposed control law provide high accuracy of approximation to the optimal performance laws and the Fuller laws, reducing energy costs for control by eliminating more frequent switching. The choice of the parameters of the developed control law makes it possible to implement a wide range of both nonlinear and linear operating modes, which allows to classify the obtained control law as multimode law.

Quasi-optimal synthesis of an adaptive filter in the problem of estimating the state of dynamic systems

The problem of synthesis of filters to estimate the state of dynamical systems is considered based on the condition for the maximum of the generalized power function and stationarity of the generalized Lagrangian and Hamiltonian of the estimated system model. The paper demonstrates that the use of invariants in combination with the decomposition principle makes it possible to simplify the equations of controlled motion and reduce them to a system of independent equations in terms of the number of degrees of freedom. This approach reduces the number of unknown parameters of the motion model, which greatly simplifies the adaptation process when developing filters for quasi-optimal estimation of the state parameters of dynamic systems. Comparative analysis of the results of the mathematical simulation shows that the application of the proposed method increases the efficiency of filters of the Kalman structure.

Measures of linear type lead to a characterization of Zipf functions

In this contribution we introduce the notion of a measure (or indicator) of linear type. Combining ideas related to power functions, in particular Zipf’s function, and h-type indices, we come to a novel characterization of general power functions and Zipf’s functions.

The Extended Matrix-Variate Beta Probability Distribution on Symmetric Matrices

The notion of generalized power function in the space of real symmetric matrices is used to introduce a kind of extended matrix-variate beta function. With the aid of this, we define a different versions of extended matrix-variate beta distributions. Some fundamental properties of these distributions are established. We show that using a linear transformation on the extended matrix-variate beta distributions of the first and second kind, we can generalize these distributions. We also show that the distribution of the sum of two independent inverse Riesz matrices introduced by Tounsi and Zine (J Multivar Anal 111:174–182, 2012) can be written in terms of the generalized extended matrix-variate beta function. Finally, using Fixed point iterative method, we provide a calculable maximum a posteriori (MAP) estimator for the unknown covariance matrix of a multivariate normal distribution based on the class of the extended matrix-variate beta prior distribution. Additionally, we evaluated the Gaussian finite sample performance by calculating such evaluation criteria as Mean Square Error (MSE) and Hilbert-Schmidt distance (DHS). The obtained results confirm the performance of the proposed prior.

Singular Generalized Analytic Functions

In this paper, we consider solution spaces for some class of singular elliptic systems on Riemann surfaces and boundary-value problems for solution spaces of such systems. We also discuss some relations for the kernels of the Carleman–Vekua equation. In particular, representations of these kernels in the form of generalized power functions are completely analogous to the classical Cauchy kernel expansion. The obtained results are applied to some problems of the theory of generalized analytic functions.

The descriptive statistics for the generalized power function distribution

This paper, introduces the power function distribution considers some of the important descriptive statistics that provide an accurate measures of central tendency and dispersion based on moment-generating functions and provided some special cases related to the power function distribution.

Special cases in order statistics for the alternative parametrization of the Generalized Power Function Distribution

ABSTRACTThis paper investigates the order statistics based on the moment-generating function for the Generalized Power Function Distribution for the two different forms of this distribution. In this paper, we continue our investigation on the distribution of order statistics assuming that the original sample of size n is taken from a population that follows the Generalized Power Function Distribution. Two different forms of the Generalized Power Function Distribution with its special cases are presented and some order statistics related to these different forms are discussed. The main technique is the consideration of the moment-generating function.

Bayesian Estimation Using (Linex) for Generalized Power Function Distribution

This paper introduced the Bayesian estimation when the loss function is a linear exponential (LINEX) for shape parameters from a generalized power function distribution. A numerical application is used to prove the accuracy of this method by comparing it with other non-Bayesian methods of estimation as the maximum likelihood.

Energy efficient scheduling of parallelizable jobs

This paper considers scheduling parallelizable jobs in the non-clairvoyant speed scaling setting to minimize the objective of weighted flow time plus energy. Previously, strong lower bounds were shown on this model in the unweighted setting even when the algorithm is given a constant amount of resource augmentation over the optimal solution. However, these lower bounds were given only for certain families of algorithms that do not recognize the parallelizability of alive jobs. In this work, we circumvent previous lower bounds shown and give a scalable algorithm under the natural assumption that the algorithm can know the current parallelizability of a job. When a general power function is considered, this is also the first algorithm that has a constant competitive ratio for the problem using any amount of resource augmentation.

Conjugation of Rational Functions to Power Functions and Applications to Iteration

In this paper we investigate normalization of rational functions, reducing in the sense of conjugation to monomials or more general power functions. We give conditions for the normalization by computing minimal irreducible decomposition of algebraic varieties. We use those conditions to compute the general n-th order iterates and iterative roots for those rational functions.

Surficial Failure of Expansive Soil Cutting Slope and Its Flexible Support Treatment Technology

The surficial failure of most expansive soil cutting slopes, subjected to the repeated wet‐dry cycles, often occurs during or after rainfall following a long drought. The reason for this, however, is still unclear. Therefore, the laboratory tests were conducted to gain the saturated drained shear strength of the natural Nanning expansive soil considering the combined effects of swelling with loading and wet‐dry cycles. The findings indicate that the envelope of shear strength, which significantly drops close or equal to zero, can be well fitted by the generalized power function. At the same time, the effect of shear strength parameters on the stability of the expansive soil cutting slope was investigated. The reasons for the shear strength attenuation of the natural expansive soil and the surficial failure of the expansive soil cutting slopes were analyzed. It is evident that the effective cohesion being small is a vital factor influencing the occurrence of surficial failure of an expansion soil slope. Moreover, an effective flexible support treatment measure was provided.

Characterization for Generalized Power Function Distribution Using Recurrence Relations Based on General Progressively Type-II Right Censored Order Statistics

Characterization for Generalized Power Function Distribution Using Recurrence Relations Based on General Progressively Type-II Right Censored Order Statistics