Minimum altitude variation orbits. Analysis of characteristics and stability

The article discusses the regularities of satellite motion in almost circular orbits under the influence of the second zonal harmonic of the geopotential. The aim of the research is to determine the parameters of orbits with a minimum change in radius and to study the properties of these orbits. It is shown that the problem of determining the parameters of orbits with a minimum change in radius is of theoretical and practical interest. These orbits are the closest to Keplerian circular orbits. The practical interest in such orbits is determined by the possibility of using them for scientific research and Earth observation systems. Based on the analysis of the literature, it was concluded that the solution of the problem under consideration is not complete by now: the algorithm for determining the parameters of the orbits are not well founded and unnecessarily complicated; there is no analytical analysis of the stability of the orbits of the minimum change in radius. The efficiency of application of the previously developed theory of describing the motion of satellites in almost circular orbits for determining the parameters of orbits with a minimum change in radius is shown. For this purpose, the solutions of the first approximation of the motion of satellites in almost circular orbits under the influence of the second zonal harmonic of the geopotential have been improved. These solutions make it easy to determine the parameters of the orbits of the minimum change in radius. The averaged equations of the second approximation of the influence of the second zonal harmonic on the satellite motion are constructed and, on their basis, the stability of the orbits with a minimum change in radius is proved. It is shown that the second approximation in small parameters completely describes the main regularities of the long-period satellite motion under the influence of the second zonal harmonic of the geopotential. With the help of numerical studies, the instability of orbits with a minimum change in radius is shown with allowance for the effect of higher order harmonics of the geopotential. Analysis of the area of possible application of orbits with a minimum change in radius showed that such orbits can be of practical importance for very low and ultra low orbits, where the control action on the satellite movement is carried out at least once every two days.

Solution of boundary value problems with moving boundaries by using an approximate method for constructing solutions of integro – differential equations

The problem of oscillations of objects with moving boundaries, formulated as a differential equation with boundary and initial conditions, is a non-classical generalization of a problem of hyperbolic type. To facilitate the construction of a solution to this problem and justify the choice of a solution form, equivalent integro-differential equations are constructed with symmetric and time-dependent kernels and integration limits varying in time. The method for constructing solutions of integro-differential equations is based on the direct integration of differential equations in combination with the standard replacement of the desired function with a new variable. The method is extended to a wider class of model boundary value problems that take into account the bending stiffness of an oscillating object, the resistance of the environment, and the rigidity of the substrate. Particular attention is paid to the consideration of the most common in practice case when external disturbances act at the boundaries. The solution is made in dimensionless variables accurate to second-order values of smallness with respect to small parameters characterizing the speed of the border.

Convergence estimates for abstract second order differential equations with two small parameters and Lipschitzian nonlinearities

In a real Hilbert space $H$ we consider the following singularly perturbed Cauchy problem ... We study the behavior of solutions $u_{\varepsilon\delta}$ in two different cases: $\varepsilon\to 0$ and $\delta \geq \delta_0>0;$ $\varepsilon\to 0$ and $\delta \to 0,$ relative to solution to the corresponding unperturbed problem.We obtain some {\it a priori} estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of $t=0.$

Two parameter singular perturbation problems for sine-Gordon type equations

In the real Sobolev space $H_0^1(\Omega)$ we consider the Cauchy-Dirichlet problem for sine-Gordon type equation with strongly elliptic operators and two small parameters. Using some {\it a priori} estimates of solutions to the perturbed problem and a relationship between solutions in the linear case, we establish convergence estimates for the difference of solutions to the perturbed and corresponding unperturbed problems. We obtain that the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of $t=0.$

ANINet: a deep neural network for skull ancestry estimation

Background Ancestry estimation of skulls is under a wide range of applications in forensic science, anthropology, and facial reconstruction. This study aims to avoid defects in traditional skull ancestry estimation methods, such as time-consuming and labor-intensive manual calibration of feature points, and subjective results. Results This paper uses the skull depth image as input, based on AlexNet, introduces the Wide module and SE-block to improve the network, designs and proposes ANINet, and realizes the ancestry classification. Such a unified model architecture of ANINet overcomes the subjectivity of manually calibrating feature points, of which the accuracy and efficiency are improved. We use depth projection to obtain the local depth image and the global depth image of the skull, take the skull depth image as the object, use global, local, and local + global methods respectively to experiment on the 95 cases of Han skull and 110 cases of Uyghur skull data sets, and perform cross-validation. The experimental results show that the accuracies of the three methods for skull ancestry estimation reached 98.21%, 98.04% and 99.03%, respectively. Compared with the classic networks AlexNet, Vgg-16, GoogLenet, ResNet-50, DenseNet-121, and SqueezeNet, the network proposed in this paper has the advantages of high accuracy and small parameters; compared with state-of-the-art methods, the method in this paper has a higher learning rate and better ability to estimate. Conclusions In summary, skull depth images have an excellent performance in estimation, and ANINet is an effective approach for skull ancestry estimation.

A window on infrared QCD with small expansion parameters

Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector — defined, e.g., in the Taylor scheme— remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with ab-initio lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

Survey of Eight Modern Methods of Hamiltonian Mechanics

Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them. The methods allow to find families of periodic solutions and families of invariant n-dimensional tori by means of analytic computation near a stationary solution, near a periodic solution and near an invariant torus, using the corresponding normal form of a Hamiltonian. Then we can continue the founded families by means of numerical computation. In a Hamiltonian system without parameters, only periodic solutions and invariant n-dimensional tori form one-parameter families. The last two methods are intended for systems with not small parameters, which do not depend on time. They allow computing sets of parameters, which guarantee the stability of some solutions for linear (method seven) and nonlinear (method eight) systems. We do not consider chaotic behaviors, but only regular ones.

Efficient Shot Detector: Lightweight Network Based on Deep Learning Using Feature Pyramid

Convolutional-neural-network (CNN)-based methods are continuously used in various industries with the rapid development of deep learning technologies. However, an inference efficiency problem was reported in applications that require real-time performance, such as a mobile device. It is important to design a lightweight network that can be used in general-purpose environments such as mobile environments and GPU environments. In this study, we propose a lightweight network efficient shot detector (ESDet) based on deep training with small parameters. The feature extraction process was performed using depthwise and pointwise convolution to minimize the computational complexity of the proposed network. The subsequent layer was formed in a feature pyramid structure to ensure that the extracted features were robust to multiscale objects. The network was trained by defining a prior box optimized for the data set of each feature scale. We defined an ESDet-baseline with optimal parameters through experiments and expanded it by gradually increasing the input resolution for detection accuracy. ESDet training and evaluation was performed using the PASCAL VOC and MS COCO2017 Dataset. Moreover, the average precision (AP) evaluation index was used for quantitative evaluation of detection performance. Finally, superior detection efficiency was demonstrated through the experiment compared to the conventional detection method.