Self-adjoint extensions for linear Hamiltonian systems with two singular endpoints

We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Holder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1).

On the rank of the matrix radius of the limiting set for a singular linear Hamiltonian system

The paper is concerned with singular Hamiltonian systems of arbitrary order with arbitrary equal defect indices. It is proved that the minimal operator generated by the Hamiltonian system is simple. As a consequence, a sufficient condition is obtained for the continuous spectrum of every self-adjoint extension of the minimal operator to be empty in some interval and for the spectrum to be nowhere dense in this interval in terms of the numbers of linearly independent square integrable solutions.

Many important properties, such as the absence of essential spectrum, follow when an ordinary differential operator comes from a differential expression such that the minimal operator has completely continuous inverse. This always happens in the case of a compact interval. On infinite intervals it happens much less frequently, however. To assure that the minimal operator is 1-1, we analyze the question only on intervals of type 1= [a, oo). By an ordinary differential expression r we mean an expression of type EOakDk, where ak,EzCk(I), and an is nonvanishing on I. With 1 <p< oo and 1 <q< oo, we define the minimal operator To,p,q in the usual fashion. (See Goldberg's book for details.) Our main result shows roughly that for formally selfadjoint differential expressions, To,2,2 has compact inverse if and only if the spectra of its selfadjoint extensions are completely dependent on the boundary conditions. A weaker result holds for To,p,p with p$2.

Generalized uncertainty principle and self-adjoint operators

Spectral analysis of dissipative Dirac operators with general boundary conditions

Investigation on the thermodynamic performance and machinery mass in the N2O-based mixtures recompression Brayton cycle for a nuclear-powered spacecraft

Eigenvalue problems of linear Hamiltonian systems arising from H∞ filtering

Rotordynamics prediction in engineering (second edition)

To address the issues of low accuracy and significant noise impact in edge continuity detection of art and design images, this paper proposes a visual attention-based edge continuity detection method for art and design images. Determine the edge position points of art and design images using the Laplace operator, and obtain the horizontal and vertical gradients of the image edges by calculating the first-order difference method to determine the amplitude of the image edge gradient; By using the maximum and minimum operations in binary morphology instead of intersection and union operations, the image grayscale is determined, and the HSI color space features are determined to complete the edge feature extraction of art and design images. Using the SUSAN operator to clarify the kernel similarity zone of the edges of art and design images, removing similar edge image pixels, using spatial domain denoising and frequency domain denoising to reduce the edge noise of art and design images, and achieving edge preprocessing of art and design images. Introducing visual attention mechanism to transform the pixel space of edge features in art and design images, performing threshold segmentation on the edges of art and design images, and continuously annotating the segmented edge pixels. Introducing loss function to improve the convergence speed of detection, constructing an art and design image edge continuity detection model based on visual attention mechanism, outputting detection results, and implementing research. The experimental results show that the proposed method has better continuity due to the successful avoidance of noise interference by introducing visual attention mechanisms and other operations. As the number of detected pixels increases, the detection deviation rate of the proposed method remains between 0.02% and 0.03%. The proposed method has a lower detection bias rate and can effectively improve the performance of edge continuity detection in art and design images.

In recent years, the usage of ensemble learning in applications has grown significantly due to increasing computational power allowing the training of large ensembles in reasonable time frames. Many applications, e.g., malware detection, face recognition, or financial decision-making, use a finite set of learning algorithms and do aggregate them in a way that a better predictive performance is obtained than any other of the individual learning algorithms. In the field of Post-Silicon Validation for semiconductor devices (PSV), data sets are typically provided that consist of various devices like, e.g., chips of different manufacturing lines. In PSV, the task is to approximate the underlying function of the data with multiple learning algorithms, each trained on a device-specific subset, instead of improving the performance of arbitrary classifiers on the entire data set. Furthermore, the expectation is that an unknown number of subsets describe functions showing very different characteristics. Corresponding ensemble members, which are called outliers, can heavily influence the approximation. Our method aims to find a suitable approximation that is robust to outliers and represents the best or worst case in a way that will apply to as many types as possible. A ‘softmax’ or ‘soft-min’ function is used in place of a maximum or minimum operator. A Neural Network (NN) is trained to learn this ‘soft-function’ in a two-stage process. First, we select a subset of ensemble members that is representative of the best or worst case. Second, we combine these members and define a weighting that uses the properties of the Local Outlier Factor (LOF) to increase the influence of non-outliers and to decrease outliers. The weighting ensures robustness to outliers and makes sure that approximations are suitable for most types.

The minimal and maximal operators generated by the Bessel differential expression on a finite interval and a half-line are studied. All nonnegative self-adjoint extensions of the minimal operator are described. We obtain a description of the domain of the Friedrichs extension of the minimal operator in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding Weyl functions, and by using the quadratic form method.

Optical implementation of pattern fuzzy logic based on shadow casting is reported. In particular, a new spatial encoding method for fuzzy logic variables is proposed to optically realize the maximization and minimization operations needed by fuzzy logic. Experimental results are also given. © 1992 John Wiley & Sons, Inc.

In this paper, we study matrix-valued Hahn–Sturm–Liouville equations. We give an existence and uniqueness result. We introduce the corresponding maximal and minimal operators for this system, and some properties of these operators are investigated. Finally, we characterize extensions (maximal dissipative, maximal accumulative and self-adjoint) of the minimal symmetric operator.

This paper considers a Legendre polynomials spectral approximation for the infinite‐dimensional Hamiltonian systems. As a consequence, the Legendre polynomials spectral semidiscrete system is a Hamiltonian system for the Hamiltonian system whose Hamiltonian operator is a constant differential operator.