Free energy and states of fractional-order hereditariness

Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.     

On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus.     

On duality concepts in fractional programming

The paper (Part I) describes an approach to duality in fractional programming on the basis of another kind of conjugate functions. The connections to some duality concepts (the Lagrange-duality and duality concepts of Craven and Schaible) are investigated and some new proofs of strong duality theorems are given.     

Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PID controller

Oustaloup recursive approximation (ORA) is widely used to find a rational integer-order approximation for fractional-order integrators and differentiators of the form s^v, v ∈ (−1, 1). In this method the lower bound, the upper bound and the order of approximation should be determined beforehand, which is currently performed by trial and error and may be inefficient in some cases. The aim of this paper is to provide efficient rules for determining the suitable value of these parameters when a fractional-order PID controller is used in a stable linear feedback system. Two numerical examples are also presented to confirm the effectiveness of the proposed formulas.     

An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems

Structural redundancies in mathematical programming models are nothing uncommon and nonlinear programming problems are no exception. Over the past few decades numerous papers have been written on redundancy. Redundancy in constraints and variables are usually studied in a class of mathematical programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective function(s) and redundant constraint(s) simultaneously in multi-objective nonlinear stochastic fractional programming problems is provided. A solution procedure is also illustrated with numerical examples. The proposed algorithm reduces the number of nonlinear fractional objective functions and constraints in cases where redundancy exists.     

Scale-space point spread function based framework to boost infrared target detection algorithms

Small target detection is one of the major concern in the development of infrared surveillance systems. Detection algorithms based on Gaussian target modeling have attracted most attention from researchers in this field. However, the lack of accurate target modeling limits the performance of this type of infrared small target detection algorithms. In this paper, signal to clutter ratio (SCR) improvement mechanism based on the matched filter is described in detail and effect of Point Spread Function (PSF) on the intensity and spatial distribution of the target pixels is clarified comprehensively. In the following, a new parametric model for small infrared targets is developed based on the PSF of imaging system which can be considered as a matched filter. Based on this model, a new framework to boost model-based infrared target detection algorithms is presented. In order to show the performance of this new framework, the proposed model is adopted in Laplacian scale-space algorithms which is a well-known algorithm in the small infrared target detection field. Simulation results show that the proposed framework has better detection performance in comparison with the Gaussian one and improves the overall performance of IRST system. By analyzing the performance of the proposed algorithm based on this new framework in a quantitative manner, this new framework shows at least 20% improvement in the output SCR values in comparison with Laplacian of Gaussian (LoG) algorithm.