General Functional Form Research Articles

Dark Energy Constraints on Red-Shift-Based Gravity

We have studied cosmological dynamics in gravity theory via cosmographic parameters. We have changed variables of field equations from time to red-shift and solved the achieved differential equation analytically for . Then we have used Taylor expansion to find general form of function around the present day value of scalar curvature. By introducing we would simplify our calculations; if we consider as a given function we would restrict our answers of . In this paper we offer a linear form of which leads us to a specific function, where is a constant which depends on the present day value of deceleration parameter. As an example, using Taylor expansion coefficients, we have compared our analytically calculated function with reconstructed function for Dark Energy models. To reconstruct action for Dark Energy models, we have used corresponding of each Dark Energy model for calculating Taylor expansion coefficients. As our function is linear, the Taylor expansion coefficients would be a function of present day value of deceleration parameter.

Electromagnetic decay of X(3872) as the 11D2(2−+) charmonium

The recent BaBar results raise the possibility that X(3872) has negative parity; reassigning it to the state should therefore be considered. In this paper we give a general form of the wave function of 2−+ mesons. By solving the instantaneous Bethe–Salpeter equation, we get the mass spectrum and corresponding wave functions. We calculate the electromagnetic decay widths of the first 2−+ state which we assume to be the X(3872) particle. The results are Γ(2−+(3872) → J/ψγ) = 1.59+0.53−0.42 keV, Γ(2−+(3872) → ψ(2S)γ) = 2.87+1.46−0.97 eV and Γ(2−+(3872) → ψ(3770)γ) = 0.135+0.066−0.047 keV. The ratio of the branch fractions of the second and the first channels is about 0.002, which is inconsistent with the experimental value 3.4 ± 1.4. Therefore X(3872) is unlikely to be a 2−+ charmonium state. In addition, we obtain a relatively large decay width for the 2−+(3872) → hcγ channel, 392+62−111 keV.

Control of error in the homotopy analysis of nonlinear Klein–Gordon initial value problems

In the present paper, we discuss the application of homotopy analysis to general nonlinear Klein–Gordon type equations. We first outline the method for general forms of the nonlinearity, as well as for general functional forms of the initial conditions. In particular, we discuss a method of controlling the residual error in approximate solutions which may be found via homotopy analysis, through adequate selection of the convergence control parameter. With the general problem outlined, we apply the method to various equations, including the quasilinear cubic Klein–Gordon equation, the modified Liouville equation, the sinh-Gordon equation, and the tanh-Gordon equation. For each of these equations and related initial data, we obtain residual error minimizing solutions which demonstrate the qualitative behavior of the true solutions in each case.

Robust Error Specification in a Production System

Economists estimating demand and supply systems face the question of using shares or quantities as dependent variables. This article finds that inconsistent estimates are obtained if one makes the wrong choice. A robust structure is presented to let the data choose the preferred form. Empirical applications to U.S. and Texas agriculture using the generalized method of moments suggest that shares and quantities are rejected in favor of a more general functional form. The Texas application provides some evidence for fixed capital but not for labor.

Adaptive Wave Filtering for Dynamic Positioning of Marine Vessels using Maximum Likelihood Identification: Theory and Experiments

This paper addresses a filtering problem that arises in the design of dynamic positioning systems for ships and offshore rigs subjected to the influence of sea waves. The dynamic model of the vessel captures explicitly the sea state as an uncertain parameter. The proposed adaptive wave filter borrows from maximum likelihood identification techniques. The general form of the logarithmic likelihood function is derived and the dominant wave frequency (the uncertain parameter) is identified by maximizing this function. To this effect, a bank of Kalman filters is used to evaluate the log-likelihood function for different values of the uncertain parameter. After each identification step a new set of Kalman filters is designed to estimate the dominant wave frequency with better accuracy. The proposed sea state identification technique enables adaptive Wave Filtering (WF) and Dynamic Positioning (DP) systems to operate in different operational conditions and hence, it is a step forward to the development of a so-called all-year marine estimation and control system. The results are experimentally verified by model testing a DP operated ship, the Cybership III, under different sea conditions in a towing tank equipped with a hydraulic wave maker.

A Degree-Distance-Based Connections Model with Negative and Positive Externalities

We develop a modification of the connections model by Jackson and Wolinsky (1996) that takes into account negative externalities arising from the connectivity of direct and indirect neighbors, thus combining aspects of the connections model and the co-author model. We consider a general functional form for agents' utility that incorporates both the effects of distance and of neighbors' degree. Consequently, we introduce a framework that can be seen as a degree-distance-based connections model with both negative and positive externalities. Our analysis shows how the introduction of negative externalities modifies certain results about stability and efficiency compared to the original connections model. In particular, we see the emergence of new stable structures, such as a star with links between peripheral nodes. We also identify structures, for example, certain disconnected networks, that are efficient in our model but which could not be efficient in the original connections model. While our results are proved for the general utility function, some of them are illustrated by using a specific functional form of the degree-distance-based utility.

Model selection rates of information based criteria

Model selection criteria proposed over the years have become common procedures in applied research. This article examines the true model selection rates of any model selection criteria; with true model meaning the data generating model. The rate at which model selection criteria select the true model is important because the decision of model selection criteria affects both interpretation and prediction. This article provides a general functional form for the mean function of the true model selection rates process, for any model selection criteria. Until now, no other article has provided a general form for the mean function of true model selection rate processes. As an illustration of the general form, this article provides the mean function for the true model selection rates of two commonly used model selection criteria, Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC). The simulations reveal deeper insight into properties of consistency and efficiency of AIC and BIC. Furthermore, the methodology proposed here for tracking the mean function of model selection procedures, which is based on accuracy of selection, lends itself for determining sufficient sample size in linear models for reliable inference in model selection.

Expected value multiobjective portfolio rebalancing model with fuzzy parameters

In this paper we develop a multicriteria credibilistic framework for portfolio rebalancing. We use an expected value model with fuzzy parameters considering return, risk and liquidity as key financial criteria. The transaction costs are assumed to be paid on the basis of incremental discounts and are adjusted in the net return of the portfolio. A solution procedure based on fuzzy goal programming and a hybrid intelligent algorithm that combines fuzzy simulation with a real-coded genetic algorithm is presented to solve the portfolio rebalancing problem. The approach adopted here has the advantage of handling the multicriteria portfolio rebalancing problem where the fuzzy parameters are characterized by general functional forms. An empirical study is included to demonstrate the effectiveness of the solution approach and efficiency of the model in practical applications of rebalancing an existing portfolio.

Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints

In this paper, we propose a multiobjective credibilistic model with fuzzy chance constraints of the portfolio selection problem. The key financial criteria used are short-term return, long-term return, risk and liquidity. The model generates portfolios which are optimal to the extent of achieving the highest credibility values for the objective functions. The problem is solved using a hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm. The approach adopted here has advantage of handling the multiobjective portfolio selection problem where fuzzy parameters are characterized by general functional forms. Numerical examples are provided to demonstrate effectiveness of the solution approach and efficiency of the model.

A multicriteria optimization model of portfolio rebalancing with transaction costs in fuzzy environment

In this paper we propose multicriteria credibilistic framework for portfolio rebalancing (adjusting) problem with fuzzy parameters considering return, risk and liquidity as key financial criteria. The portfolio risk is characterized by a risk curve that represents each likely loss of the portfolio return and the corresponding chance of its occurrence rather than a single pre-set level of the loss. Furthermore, we consider an investment market scenario where, at the end of a typical time period, the investor would like to modify his existing portfolio by buying and/or selling assets in response to changing market conditions. We assume that the investor pays transaction costs based on incremental discount schemes associated with the buying and/or selling of assets, which are adjusted in the net return of the portfolio. A hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm is developed to solve the portfolio rebalancing (adjusting) problem. The proposed solution approach is useful particularly for the cases where fuzzy parameters of the problem are characterized by general functional forms.

Tensor structure function $b_{1}^{d}(x,Q^{2})$ of the deuteron at NLO and NNLO at small-x

The precision of the contemporary experimental data demands that the parton distribution functions (PDF’s) should be corrected at least up to next-to-leading order (NLO) and preferably up to next-to-next-to-leading order (NNLO). A general form of tensor structure function \(b_{1}^{d}(x,Q^{2})\) of the deuteron at NLO and NNLO is obtained by using the solution of Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP) equation for singlet structure function at small-x. Results are compared with HERA Experiment data.

The dynamic performance of simply-supported rigid-plastic circular steel plates subjected to localised blast loading

Near-field explosive charges, such as buried land mines, produce localised blast loadings which can potentially cause damage to property and/or loss of life in both military and civil structures. As the localised short duration blast pulse affects most severely a small area of a plated structure, boundary effects are not as significant as they are when a quasi-static or global blast loading is applied and full plate action may not be utilised.Many common structural forms are composed of individual plated elements and thus the investigation of localised blast loading effects on plates is a prerequisite to understanding the integral behaviour. Typically, plates are made of ductile materials such as steel, which exhibit considerable post-yield deformation capacity when subjected to such extreme dynamic loads. Analytical study of the dynamic plastic response of rigid-plastic plated structures is the aim of the present study.A circular plate is studied in the present work and a general form of a localised blast loading function with a spatial variation having a central radial zone with constant pressure and exponentially decaying profile outside the zone is assumed. Assuming that steel exhibits perfectly plastic behaviour and ignoring membrane action, transverse shear and rotatory inertia effects, the static plastic collapse pressure is initially found and the analysis is extended to take into account the inertial effects arising from dynamic loading. Results for the permanent transverse displacements are found for rectangular and linearly and exponentially decaying pulse loads.For high loads and/or loads of short duration, it was found that the permanent transverse displacement can be found by replacing the applied pulse load by means of an impulsive velocity without great loss of accuracy. Good correlation with numerical simulations obtained from ABAQUS/Explicit is achieved (within 15% accuracy) for plate geometries falling within the identified limits where membrane and shear effects are negligible.The predicted final transverse displacements are found to be dependent on the loading pulse shape, but the pulse-shape effects are eliminated by using the correlation parameters (effective impulse and pressure) advocated by Youngdahl (1971) [52] to give a single pulse shape-independent curve for the final plate deflection as a function of the effective pressure and effective impulse.

Position-momentum Heisenberg uncertainty in Gaussian enfoldments of Euclidian space

Gaussian enfoldments have been derived from the form of general Gaussian functions centered at arbitrary positions in Euclidian space. Every point of Euclidian space acts in this way as the center of a Gaussian function defined in position space. Using the position-momentum Fourier transform in the quantum mechanical way and applied into the position functions of the Gaussian Euclidian enfoldment, the transform result provides a unique momentum Gaussian function, centered at the origin. In this way, the Euclidian enfoldment disappears in momentum space. Further analysis of the position-momentum relationship indicates that the product of the variances of the enfoldment in position and the corresponding momentum Fourier transform produces some kind of Heisenberg’s uncertainty relation.

Multiobjective expected value model for portfolio selection in fuzzy environment

In this paper, we propose a credibilistic framework for portfolio selection problem using an expected value multiobjective model with fuzzy parameters. We consider short term return, long term return, risk and liquidity as key financial criteria. A solution procedure comprising fuzzy goal programming and fuzzy simulation based real-coded genetic algorithm is developed to solve the model. The proposed solution approach is considered advantageous particularly for the cases where the fuzzy parameters of the problem may assume any general functional form. An empirical study is included to illustrate the usefulness of the proposed model and solution approach in real-world applications of portfolio selection.

Lie group of transformations to study anisotropic diffusion of scalar images

Lie group of transformations associated with anisotropic diffusion equation is derived using the invariance properties. The equation is of great importance in the study of geometrical diffusion of scalar images. Infinitesimals of Lie group of transformations with respect to independent and dependent variables along with invariant surface conditions are used to obtain a general form of edge stopping function. The edge stopping functions used by Perona & Malik and their successors are obtained in particular cases. The equation in three independent variables reduced in terms of fewer independent variables.

A Study on the Bi-Rayleigh ROC Curve Model

Receiver Operating Characteristic (ROC) curves are used to describe and compare the accuracy of diagnostic test or the ability of a continuous biomarker in discriminating between the subjects into healthy or diseased cases in medical field. The most familiar form of ROC curve is Bi-normal (Gaussian) ROC curve model, which assumes that the test scores or a monotone transformation of the test scores are from two normal populations (i.e. healthy and diseased). It may not be true all the time, it may violate the assumptions of normal distribution in some situations and also we cannot adopt the model as it is when the sample size is small. In this paper, we have proposed ROC curve model for Rayleigh distribution which can be used even when sample size is small. The properties of Bi-Rayleigh ROC model are studied and Area Under the ROC Curve (AUC) are derived. The proposed model is supported by real life example as well as simulation studies. The confidence interval for the population parameter is studied with simulation studies of varying sample sizes. It is found that Bi-Rayleigh ROC model provides better accuracy of classification than the conventional bi-normal ROC model. In the ROC model section, Bi-Rayleigh ROC model and its AUC are derived and its properties are discussed. In application section, two real life example viz. Head trauma data and Multiple Sclerosis data were used for the proposed model and then these are compared with the conventional bi- normal model. In the simulation section, simulation studies have been carried out for different values of parameters to support the Bi-Rayleigh ROC model. In the last section, the confidence intervals for the parameter σi, i=0,1 are discussed for real life example and simulated data sets. II. ROC MODEL AND AREA UNDER THE CURVE Let the scores (S) be a random variable in healthy (H) and diseased (D) populations respectively. The ROC curve is plotted over values of threshold value (t) and is given by y(t) = h (x(t)) where x(t) is the False positive rate which is given by x(t) = P(S>t|H) and y(t) is True positive rate which is given by y(t) = P (S>t|D) The general functional form of ROC can be represented as

Description and measurement of observables in the optical tomographic probability representation of quantum mechanics

Explicit expressions for most interesting quantum observable operators in optical tomography representation are found. A general formalism of the symbols of the operators is presented in the optical tomography representation. The symbols of the operators in the form of singular and regular generalized functions are found, and suggestions for their use in experimental data processing in quantum tomography are given.

Derivation of Relationships between Spectral Vegetation Indices from Multiple Sensors Based on Vegetation Isolines

An analytical form of relationship between spectral vegetation indices (VI) is derived in the context of cross calibration and translation of vegetation index products from different sensors. The derivation has been carried out based on vegetation isoline equations that relate two reflectance values observed at different wavelength ranges often represented by spectral band passes. The derivation was first introduced and explained conceptually by assuming a general functional form for VI model equation. This process is universal by which two VIs of different sensors and/or different model equations can be related conceptually. The general process was then applied to the actual case of normalized difference vegetation index (NDVI) from two sensors in a framework of inter-sensor continuity. The derivation results indicate that the NDVI from one sensor can be approximated by a rational function of NDVI from the other sensor as a parameter. Similar result was obtained for the case of soil adjusted VI, enhanced VI, and two-band variance of enhanced VI.

Point Load Weight Functions for Semi-Elliptical Cracks in Finite Thickness Plate

Abstract This paper presents the application of the weight function method for the calculation of stress intensity factors for surface semi-elliptical cracks in finite thickness plates subjected to arbitrary two-dimensional stress fields. A new general mathematical form of point load weight function has been formulated by taking advantage of the knowledge of a few specific weight functions for two-dimensional planar cracks available in the literature and certain properties of the weight function in general. The existence of the generalized form of the weight function simplifies the determination of a specific weight function for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalized weight function expression. These unknown parameters can be determined from reference stress intensity factor solutions. This method is used to derive the weight functions for semi-elliptical surface cracks in finite thickness plates. The derived weight functions are then validated against stress intensity factor solutions for several linear and non-linear two-dimensional stress distributions. The derived weight functions are particularly useful for the fatigue crack growth analysis of planar surface cracks subjected to fluctuating nonlinear stress fields resulting from surface treatment (shot peening), stress concentration, or welding (residual stress)

Introduction to the angular functions in euclidian 2D-space

The Angular functions are new mathematical functions introduced by the author, they produce rectangular signals, in which period is function of angles and not of time as the previous functions. Similar to trigonometric functions, the angular functions have the same properties as the precedent, but the difference is that a rectangular signal is obtained instead of a sinusoidal signal, and moreover, one can change the width of each positive and negative alternate in the same period. This is not the case of any other trigonometric function. In other hand, one can change the frequency, the amplitude and the width of any period of the signal at any position by using the general form of the angular function. In this paper, an original study is introduced. Thus, the definition of the original part is presented. The angular functions are also defined. These functions are very important in technical subjects. They will be widely used in mathematics and in engineering domains, especially in power electronics, signal theory, propagation of signals and many other topics. Moreover, the Angular functions are the basis of the Elliptical trigonometry and the rectangular trigonometry in which they are new domains introduced in mathematics by the author.