A radial estimation of distribution algorithm for the job-shop scheduling problem

The job-shop environment has been widely studied under different approaches. It is due to its practical characteristic that makes its research interesting. Therefore, the job-shop scheduling problem continues being attracted to develop new evolutionary algorithms. In this paper, we propose a new estimation of distribution algorithm coupled with a radial probability function. The aforementioned radial function comes from the hydrogen element. This approach is proposed in order to build a competitive evolutionary algorithm for the job-shop scheduling problem. The key point is to exploit the radial probability distribution to construct offspring, and to tackle the inconvenient of the EDAs, i.e., lack of diversity of the solutions and poor ability of exploitation. Various instances and numerical experiments are presented to illustrate, and to validate this novel research. The results, obtained from this research, permits to conclude that using radial probability distributions is an emerging field to develop new and efficient EDAs.

Products of Toeplitz Operators on the 2-Analytic Bergman Space

Let f and g be bounded functions, and let T f and T g be Toeplitz operators on A 2 2 D . We show that if the product T f T g equals zero and one of f and g is a radial function satisfying a Mellin transform condition, then the other function must be zero.

Perturbation analysis for massless spin fields in accelerating Kerr-Newman-(anti-)de Sitter black holes

We obtain the wave equation of the perturbation theory governing massless fields of spin 0, 1/2, 1, 3/2 and 2 in accelerating Kerr–Newman–(anti-)de Sitter black holes. We show that the wave equation is separable and the radial and angular equations can both be transformed into Heun’s equation. We approximate Heun’s equation and analyze the solution of radial function near the event horizon. It is worth pointing out that all the field equations collapse to a unique equation which means it can provide a possible way for the analog research between the gravitational field and those other fields.

INTERPOLASI DATA BERDIMENSI d>1 DENGAN FUNGSI BASIS RADIAL (RADIAL BASIS FUNCTION)

Radial Basis Function (RBF) is a method typically used to aproximate a function based on information data. A radial function is a real valued function whose depends only on the distance the data input and some fixed point ,called a centre point. Distance between some fixed point/centre and data input is usually Euclidean metric so that . Commonly types of Radial Basis Function using a to indicate a shape parameter to scale the input data of the radial centre. Since this method has been proven effective and flexsibel so that it has been widely used in engineering and science, so in this paper we will discuss how to use Radial basis Function to interpolate 2 dimension data. From the result of discussion it was found that this method was accurate to aproximate actual data or observation.

Scattered Data Interpolation and Approximation with Truncated Exponential Radial Basis Function

Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation effect, this is often accompanied by an ill-conditioned algebraic system. The exceedingly large condition number of the discrete matrix makes the numerical calculation time consuming. The paper introduces a truncated exponential function, which is radial on arbitrary n-dimensional space R n and has compact support. The truncated exponential radial function is proven strictly positive definite on R n while internal parameter l satisfies l ≥ ⌊ n 2 ⌋ + 1 . The error estimates for scattered data interpolation are obtained via the native space approach. To confirm the efficiency of the truncated exponential radial function approximation, the single level interpolation and multilevel interpolation are used for surface modeling, respectively.

Model of Recognition Operators Based on the Formation of Representative Objects

Parametric representations of the model of recognition operators based on the selection of representative objects are considered. The main idea of the proposed model is to build a family of proximity functions in the parameter space. In this case, the proximity function is determined within the framework of the radial function. A distinctive feature of the proposed model is the formation of preferred features with respect to selected representative objects when constructing recognition operators. To verify the performance of the proposed model, experimental studies were carried out to solve the model problem.

Extended Target Tracking and Feature Estimation for Optical Sensors Based on the Gaussian Process

A problem of tracking surface shape-shifting extended target by using gray scale pixels on optical image is considered. The measurement with amplitude information (AI) is available to the proposed method. The target is regarded as a convex hemispheric object, and the amplitude distribution of the extended target is represented by a solid radial function. The Gaussian process (GP) is applied and the covariance function of GP is modified to fit the convex hemispheric shape. The points to be estimated on the target surface are selected reasonably in the hemispheric space at the azimuth and pitch directions. Analytical representation of the estimated target extent is provided and the recursive process is implemented by the extended Kalman filter (EKF). In order to demonstrate the algorithm’s ability of tracking complex shaped targets, a trailing target characterized by two feature parameters is simulated and the two feature parameters are extracted with the estimated points. The simulations verify the validity of the proposed method with compared to classical algorithms.

ON NONLOCAL NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN

In this paper, we study the existence of positive solutions to a semilinear nonlocal elliptic problem with the fractional α-Laplacian on Rn, 0 < α < n. We show that the problem has infinitely many positive solutions in $ {C^\tau}({R^n})\bigcap H_{loc}^{\alpha /2}({R^n}) $. Moreover, each of these solutions tends to some positive constant limit at infinity. We can extend our previous result about sub-elliptic problem to the nonlocal problem on Rn. We also show for α ∊ (0, 2) that in some cases, by the use of Hardy’s inequality, there is a nontrivial non-negative $ H_{loc}^{\alpha /2}({R^n}) $ weak solution to the problem $$ {( - \Delta )^{\alpha /2}}u(x) = K(x){u^p} \quad {\rm{ in}} \ {R^n}, $$ where K(x) = K(|x|) is a non-negative non-increasing continuous radial function in Rn and p > 1.