First-order Operators Research Articles

A New Synthetic Aperture Radar (SAR) Imaging Method Combining Match Filter Imaging and Image Edge Enhancement.

In general, synthetic aperture radar (SAR) imaging and image processing are two sequential steps in SAR image processing. Due to the large size of SAR images, most image processing algorithms require image segmentation before processing. However, the existence of speckle noise in SAR images, as well as poor contrast and the uneven distribution of gray values in the same target, make SAR images difficult to segment. In order to facilitate the subsequent processing of SAR images, this paper proposes a new method that combines the back-projection algorithm (BPA) and a first-order gradient operator to enhance the edges of SAR images to overcome image segmentation problems. For complex-valued signals, the gradient operator was applied directly to the imaging process. The experimental results of simulated images and real images validate our proposed method. For the simulated scene, the supervised image segmentation evaluation indexes of our method have more than 1.18%, 11.2% and 11.72% improvement on probabilistic Rand index (PRI), variability index (VI), and global consistency error (GCE). The proposed imaging method will make SAR image segmentation and related applications easier.

Adiabatic approach to large-amplitude collective motion with the higher-order collective-coordinate operator

We propose a new set of equations to determine the collective Hamiltonian including the second-order collective-coordinate operator on the basis of the adiabatic self-consistent collective-coordinate (ASCC) theory. We illustrate, with the two-level Lipkin model, that the collective operators including the second-order one are self-consistently determined. We compare the results of the calculations with and without the second-order operator and show that, without the second-order operator, the agreement with the exact solution becomes worse as the excitation energy increases, but that, with the second-order operator included, the exact solution is well reproduced even for highly excited states. We also reconsider which equations one should adopt as the basic equations in the case where only the first-order operator is taken into account, and suggest an alternative set of fundamental equations instead of the conventional ASCC equations. Moreover, we briefly discuss the gauge symmetry of the new basic equations we propose in this paper.

Classification of the Associativity Equations with A First-Order Hamiltonian Operator

We study the Hamiltonian geometry of systems of hydrodynamic type that are equivalent to the associativity equations in the case of three primary fields and obtain the complete classification of the associativity equations with respect to the existence of a first-order Dubrovin–Novikov Hamiltonian structure.

MEMS Fabry–Pérot Interferometers With Double Membrane Mirrors for Improved Mirror Parallelism

This paper presents surface micromachined MEMS Fabry-Pérot interferometers (FPIs) with two released membrane mirrors. Fabrication of such FPIs with large-area membrane reflectors of up to 5 mm in diameter for first-order operation in the near infrared is shown. The mirrors are distributed Bragg reflectors based on silicon and silicon carbonitride. Single mirror membrane FPIs with the same mirror design are used as a benchmark in order to demonstrate the improvements achievable by the double membrane approach. To that end, the FPIs are characterized with respect to their top surface flatness by white light interferometry as well as to the variations of the optical gap width over the aperture area by spatially resolved transmittance measurements. It is shown that the upper mirror membranes are flat within the nanometer range for both approaches. Nevertheless, single membrane FPIs exhibit strongly increasing gap variations for increasing membrane diameters due to a bow in the substrate wafer, thus decreasing the filter resolution over the full aperture. On the other hand, for double-membrane FPIs, the mirrors are highly parallel with a standard deviation of the gap as low as 2 nm.

Derivatives of the Shape Operator of Real Hypersurfaces in the Complex Quadric

On a real hypersurface in the complex quadric we can consider the Levi-Civita connection and, for any nonnull constant k, the k-th generalized Tanaka-Webster connection. We also have a differential operator of first order of Lie type associated to the k-th generalized Tanaka-Webster connection. We prove non-existence of real hypersurfaces in the complex quadric for which the covariant derivatives associated to both connections coincide or Lie derivative and Lie type differential operator coincide when they act on the shape operator of the real hypersurface.

Generalized discrete q-Hermite I polynomials and q-deformed oscillator

In this paper, we present an explicit realization of q-deformed Calogero-Vasiliev algebra whose generators are first-order q-difference operators related to the generalized discrete q-Hermite I polynomials recently introduced in [14]. Furthermore, we construct the wave functions and we determine the q-coherent states.

Global hypoellipticity for first-order operators on closed smooth manifolds

The main goal of this paper is to address global hypoellipticity issues for the following class of operators: $L = D_t + C(t,x,D_x)$, where $(t,x) \in \mathbb{T} \times M$, $\mathbb{T}$ is the one-dimensional torus, $M$ is a closed manifold and $C(t,x,D_x)$ is a first order pseudo-differential operator on $M$, smoothly depending on the periodic variable $t$. In the case of separation of variables, namely, $C(t,x,D_x) = a(t)p(x,D_x)+ib(t)q(x,D_x)$, we give necessary and sufficient conditions for the global hypoellipticity of $L$. In particular, we show that, under suitable conditions, the famous (P) condition of Niremberg-Treves is neither necessary nor sufficient to guarantee the global hypoellipticity of $L$.

Elliptic complexes of first-order cone operators: ideal boundary conditions

The purpose of this paper is to provide a detailed description of the spaces that can be specified as L2 domains for the operators of a first order elliptic complex on a compact manifold with conical singularities. This entails an analysis of the nature of the minimal domain and of a complementary space in the maximal domain of each of the operators. The key technical result is the nondegeneracy of a certain pairing of cohomology classes associated with the indicial complex. It is further proved that the set of choices of domains leading to Hilbert complexes in the sense of Bruning and Lesch form a variety, as well as a theorem establishing a necessary and sufficient condition for the operator in a given degree to map its maximal domain into the minimal domain of the next operator.

Design of an Optimal Preview Controller for Dual-Rate Linear Discrete-Time Systems

Abstract A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given. Finally, simulation results show the effectiveness of the proposed method.

Multipoint selfadjoint quasi-differential operators for first order

In the present paper, the aim is to described all selfadjoint extensions of the minimal operator generated by first order linear symmetric multipoint quasi-differential operator expression in the direct sum of weighted Hilbert spaces of vector-functions defined at the semi-infinite intervals by using the Calkin-Gorbachuk method. We have also examine the structure of the spectrum of such extensions.

Boundedly solvable degenerate differential operators for first order

Using the methods of operator theory all boundedly solvable extensions of the minimal operator generated by degenerated type differential-operators expression in the weighted Hilbert space of vector-functions in finite interval in terms of boundary conditions. Later on, the structure of spectrum of these type extensions will be investigated.

On semilocal convergence of two step Kurchatov method

ABSTRACTIn this article we present a new semilocal convergence analysis for the two step Kurchatov method by using recurrence relations under Lipschitz type conditions on first-order divided difference operator. The main advantage of this iterative method is that it does not require to evaluate any Fréchet derivative but it includes extra parameters in the first-order divided difference in order to ensure a good approximation to the first derivative in each iteration. The detailed study of the domain of parameters of the method has been carried out and the applicability of the proposed convergence analysis is illustrated by solving some numerical examples. It has been concluded that the present method converges more rapidly than the one step Kurchatov method and two step Secant method.

On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions

For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, we prove a strong Hadamard instability for the associated Cauchy problem, namely an instantaneous defect of Hölder continuity of the flow from Gσ to L2, with 0<σ<σ0, the limiting Gevrey index σ0 depending on the nature of the transition. We restrict here to scalar transitions, and non-scalar transitions in which the boundary of the hyperbolic zone satisfies a flatness condition. As in our previous work for initially elliptic Cauchy problems [B. Morisse, On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, arXiv:1611.07225], the instability follows from a long-time Cauchy–Kovalevskaya construction for highly oscillating solutions. This extends recent work of N. Lerner, T. Nguyen, and B. Texier [The onset of instability in first-order systems, to appear in J. Eur. Math. Soc.].

Robust Visual Tracking Based on Convolutional Features with Illumination and Occlusion Handing

Visual tracking is an important area in computer vision. How to deal with illumination and occlusion problems is a challenging issue. This paper presents a novel and efficient tracking algorithm to handle such problems. On one hand, a target’s initial appearance always has clear contour, which is light-invariant and robust to illumination change. On the other hand, features play an important role in tracking, among which convolutional features have shown favorable performance. Therefore, we adopt convolved contour features to represent the target appearance. Generally speaking, first-order derivative edge gradient operators are efficient in detecting contours by convolving them with images. Especially, the Prewitt operator is more sensitive to horizontal and vertical edges, while the Sobel operator is more sensitive to diagonal edges. Inherently, Prewitt and Sobel are complementary with each other. Technically speaking, this paper designs two groups of Prewitt and Sobel edge detectors to extract a set of complete convolutional features, which include horizontal, vertical and diagonal edges features. In the first frame, contour features are extracted from the target to construct the initial appearance model. After the analysis of experimental image with these contour features, it can be found that the bright parts often provide more useful information to describe target characteristics. Therefore, we propose a method to compare the similarity between candidate sample and our trained model only using bright pixels, which makes our tracker able to deal with partial occlusion problem. After getting the new target, in order to adapt appearance change, we propose a corresponding online strategy to incrementally update our model. Experiments show that convolutional features extracted by well-integrated Prewitt and Sobel edge detectors can be efficient enough to learn robust appearance model. Numerous experimental results on nine challenging sequences show that our proposed approach is very effective and robust in comparison with the state-of-the-art trackers.

Smoothed Particle Hydrodynamics: A consistent model for interfacial multiphase fluid flow simulations

In this work, a consistent Smoothed Particle Hydrodynamics (SPH) model to deal with interfacial multiphase fluid flows simulation is proposed. A modification to the Continuum Stress Surface formulation (CSS) [1] to enhance the stability near the fluid interface is developed in the framework of the SPH method. A non-conservative first-order consistency operator is used to compute the divergence of stress surface tensor. This formulation benefits of all the advantages of the one proposed by Adami et al. [2] and, in addition, it can be applied to more than two phases fluid flow simulations. Moreover, the generalized wall boundary conditions [3] are modified in order to be well adapted to multiphase fluid flows with different density and viscosity. In order to allow the application of this technique to wall-bounded multiphase flows, a modification of generalized wall boundary conditions is presented here for using the SPH method. In this work we also present a particle redistribution strategy as an extension of the damping technique presented in [3] to smooth the initial transient phase of gravitational multiphase fluid flow simulations. Several computational tests are investigated to show the accuracy, convergence and applicability of the proposed SPH interfacial multiphase model.

General first-order mass ladder operators for Klein–Gordon fields

We study the ladder operator on scalar fields, mapping a solution of the Klein–Gordon equation onto another solution with a different mass, when the operator is at most first order in derivatives. Imposing the commutation relation between the d’Alembertian, we obtain the general condition for the ladder operator, which contains a non-trivial case which was not discussed in the previous work (Cardoso et al 2017 Phys. Rev. D 96 024044). We also discuss the relation with supersymmetric quantum mechanics.

On an inverse spectral problem for first-order integro-differential operators with discontinuities

A convolution integro-differential operator of the first order with a finite number of discontinuities is considered. Properties of its spectrum are studied and a uniqueness theorem is proven for the inverse problem of recovering the convolution kernel along with the boundary condition from the spectrum.

A travel time forecasting model based on change-point detection method

Travel time parameters obtained from road traffic sensors data play an important role in traffic management practice. A travel time forecasting model is proposed for urban road traffic sensors data based on the method of change-point detection in this paper. The first-order differential operation is used for preprocessing over the actual loop data; a change-point detection algorithm is designed to classify the sequence of large number of travel time data items into several patterns; then a travel time forecasting model is established based on autoregressive integrated moving average (ARIMA) model. By computer simulation, different control parameters are chosen for adaptive change point search for travel time series, which is divided into several sections of similar state.Then linear weight function is used to fit travel time sequence and to forecast travel time. The results show that the model has high accuracy in travel time forecasting.

Linearity-preserving monotone local projection stabilization schemes for continuous finite elements

This paper presents some new tools for enforcing discrete maximum principles and/or positivity preservation in continuous piecewise-linear finite element approximations to convection-dominated transport problems. Using a linear first-order advection equation as a model problem, we construct element-level bilinear forms associated with first-order artificial diffusion operators and their two-scale counterparts. The underlying design philosophy is similar to that behind local projection stabilization (LPS) techniques and variational multiscale (VMS) methods. The difference lies in the structure of the local stabilization operator and in the way in which the resolved scales are detected. The proposed stabilization term penalizes the difference between the nodal values and cell averages of the finite element solution in a manner which guarantees monotonicity and linearity preservation. The value of the stabilization parameter is determined using a multidimensional limiter function designed to prevent unresolvable fine scale effects from creating undershoots or overshoots. The result is a nonlinear high-resolution scheme capable of resolving moving fronts and internal/boundary layers as sharp localized nonoscillatory features. The use of variational gradient recovery makes it possible to add high-order background dissipation leading to improved approximation properties in smooth regions. The numerical behavior of the constrained schemes is illustrated by a grid convergence study for stationary and time-dependent test problems in two space dimensions.

Efficient higher order derivative-free multipoint methods with and without memory for systems of nonlinear equations

ABSTRACTWe present a family of multipoint methods without memory with sixth-order convergence for solving systems of nonlinear equations. The methods use first-order divided difference operators and are derivative free. Extending the work further, we explore a family of methods with memory with increasing order of convergence from the basic family without memory. The increase in convergence order is attained by varying a free parameter step to step using information available from the previous step. It is proved that the convergence order of the family with memory is increased from 6 to , and in some special cases to and . Computational efficiency of the methods is discussed and compared with existing methods. Numerical examples, including those arise from integral equations and boundary value problems, are considered to verify the theoretical results. A comparison with the existing methods shows that the new methods are more efficient than existing ones and hence use the minimum computing time in multiprecision arithmetic.