Positive Solutions Research Articles

Crowdsourcing RTK: a new GNSS positioning framework for building spatial high-resolution atmospheric maps based on massive vehicle GNSS data

High-quality spatial atmospheric delay correction information is essential for achieving fast integer ambiguity resolution (AR) in precise positioning. However, traditional real-time precise positioning frameworks (i.e., NRTK and PPP-RTK) depend on spatial low-resolution atmospheric delay correction through the expensive and sparsely distributed CORS network. This results in limited public appeal. With the mass production of autonomous driving vehicles, more cost-effective and widespread data sources can be explored to create spatial high-resolution atmospheric maps. In this study, we propose a new GNSS positioning framework that relies on dual base stations, massive vehicle GNSS data, and crowdsourced atmospheric delay correction maps (CAM). The map is easily produced and updated by vehicles equipped with GNSS receivers in a crowd-sourced way. Specifically, the map consists of between-station single-differenced ionospheric and tropospheric delays. We introduce the whole framework of CAM initialization for individual vehicles, on-cloud CAM maintenance, and CAM-augmented user-end positioning. The map data are collected and preprocessed in vehicles. Then, the crowdsourced data are uploaded to a cloud server. The massive data from multiple vehicles are merged in the cloud to update the CAM in time. Finally, the CAM will augment the user positioning performance. This framework forms a beneficial cycle where the CAM’s spatial resolution and the user positioning performance mutually improve each other. We validate the performance of the proposed framework in real-world experiments and the applied potency at different spatial scales. We highlight that this framework is a reliable and practical positioning solution that meets the requirements of ubiquitous high-precision positioning.

Global higher regularity and decay estimates for positive solutions of fractional equations in RN *

In the paper, we study the global higher regularity and decay estimates of the positive solutions for the following fractional equations {(−Δ)su+u=|u|p−2uin RN,lim|x|→∞u(x)=0,u∈Hs(RN),(0.1) where s∈(0,1) , N>2s , 2<p<2s∗:=2NN−2s and (−Δ)s is the fractional Laplacian. Let Q be a positive solution of (). We prove that Q∈Ck,γ(RN)∩Hk(RN) and obtain the decay estimates of D k Q as |x|→∞ for all k∈N+ and γ∈(0,1) . The argument relies on the Bessel kernel, comparison principle, Fourier analysis and iteration methods.

Quantum approach to bound states in field theory

It is well known that (possibly nonunique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In [R. M. Wald, ], Wald derived a conserved energy functional for each prescribed dynamics. This conserved energy is related to the positive self-adjoint extensions of the spatial part A of the wave equation ∂2Φ/∂t2=−AΦ (A may not be, in principle, essentially self-adjoint). This is quite surprising since the canonical energy is not conserved in these cases. In this paper, we rederive this energy functional from an action principle (with appropriate boundary terms) following [A. A. Saharian, ] and consider field dynamics arising from nonpositive self-adjoint extensions of A. The spectrum of the resulting theory fails to be positive and unstable mode solutions for classical fields come to light. By studying fields in half-Minkowski spacetime, we illustrate that these unstable classical solutions come as a consequence of an inverted parabolic potential governing their dynamics. From the quantum mechanical point of view, this leads to an effective inverted harmonic oscillator at the boundary. We then explore these unstable modes behavior, as well as their instabilities, at the quantum level. Published by the American Physical Society 2024

Modelling the impact of precaution on disease dynamics and its evolution.

In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction number . For , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics.

Multiple positive solutions for a critical fractional p-Laplacian system with concave nonlinearities

The aim of this paper is to study the following nonlinear fractional p-Laplacian system with critical exponents: { ( − Δ ) p s u + | u | p − 2 u = λg ( x ) | u | q − 2 u + α α + β f ( x ) | u | α − 2 u | v | β  in  Ω , ( − Δ ) p s v + | v | p − 2 v = μh ( x ) | v | q − 2 v + β α + β f ( x ) | u | α | v | β − 2 v  in  Ω , u = v = 0  in  R N ∖Ω , where Ω is a smooth bounded set in R N , 0<s<1, 0 $ ]]> λ , μ > 0 are two parameters, 1 < q < p < p s ∗ , N>ps, 1 $ ]]> α , β > 1 satisfy α + β = p s ∗ with p s ∗ = np n − ps is the fractional Sobolev critical exponent and ( − Δ ) p s is the fractional p-Laplacian operator. Using the Nehari manifold and Ljusternik–Schnirelmann category, we study the topology of the global maximum set Θ of f ( x ) , and show that the system has at least at least ca t Θ δ ( Θ ) + 1 distinct positive solutions.

Threshold for existence, non-existence and multiplicity of positive solutions with prescribed mass for an NLS with a pure power nonlinearity in the exterior of a ball

Threshold for existence, non-existence and multiplicity of positive solutions with prescribed mass for an NLS with a pure power nonlinearity in the exterior of a ball

Nonlinear elliptic problem in exterior domains: exact boundary behavior of blow-up positive solutions

Nonlinear elliptic problem in exterior domains: exact boundary behavior of blow-up positive solutions

Second-order, Positive, and Unconditional Energy Dissipative Scheme for Modified Poisson–Nernst–Planck Equations

First-order energy dissipative schemes in time are available in literature for the Poisson–Nernst–Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite volume discretization in space for modified PNP equations that incorporate effects arising from ionic steric interactions and dielectric inhomogeneity. A multislope method on unstructured meshes is proposed to reconstruct positive, accurate approximations of mobilities on faces of control volumes. Numerical analysis proves that the proposed numerical schemes are able to unconditionally ensure the existence of positive numerical solutions, original energy dissipation, mass conservation, and preservation of steady states at discrete level. Extensive numerical simulations are conducted to demonstrate numerical accuracy and performance in preserving properties of physical significance. Applications in ion permeation through a 3D nanopore show that the modified PNP model, equipped with the proposed schemes, has promising applications in the investigation of ion selectivity and rectification. The proposed second-order discretization can be extended to design temporal second-order schemes with original energy dissipation for a type of gradient flow problems with entropy.

Observing Majorana Fermion dynamic properties on a NISQ computer

Majorana particles are of particular interest due to their profound property of being their own anti-particles and potential applications for quantum computers. However, studying the dynamics of Majorana particles experimentally has proven to be challenging, with many unanswered questions about their behaviors. In this paper, we demonstrate that an improved discrete-time quantum walks (DTQW) on a Noisy Intermediate-Scale Quantum (NISQ) computer can be used to construct a well-defined Majorana fermion. Through this approach, we can observe the behaviors of Majorana particle propagation both in (1+1)- and (3+1)-dimensions. A counter-intuitive dynamic behavior of the non-vanishing expectation value of velocity and position with zero expectation value of momentum from the superposition of positive and negative energy solution is observed for the first time in NISQ. Our findings provide a promising avenue for experimentally studying the dynamical properties of Majorana particles.

A periodic reaction-diffusion model of hospital infection with crowding effects

In this paper, we propose a periodic reaction-diffusion model of hospital infection with crowding effects. We introduce the basic reproduction number R0 for this model and show that the infection-free periodic solution is globally asymptotically stable if R0≤1, while the system admits a globally asymptotically stable positive periodic solution if R0>1. We also obtain the asymptotic behavior of the basic reproduction number when the diffusion rates go to infinity and zero, respectively. Further, we numerically study the effects of diffusion rates, the outflow rate by patient crowding and other parameters on R0 with and without seasonality, and found that the neglect of seasonality does overestimate the infection risk and the disease may be well controlled by avoiding overcrowding of patients rather than increasing the mobility of individuals or bacteria.

ХИРУРГИЧЕСКАЯ ТАКТИКА ПРИ ИНФЕКЦИИ В РЕКОНСТРУКТИВНОЙ ХИРУРГИИ НА АОРТЕ И АРТЕРИЯХ НИЖНИХ КОНЕЧНОСТЕЙ

Background. The relevance of the literature review is explained by the frequent development of purulent-septic complications after reconstructive operations on the abdominal aorta and arteries of the lower extremities. Objective. To analyze the literature covering the problem of purulent-septic complications after reconstructive surgery on the aorto-femoral-popliteal arterial segment. Material and methods. A total of 50 literature sources were analyzed. Results. Purulent-septic complications after reconstructive operations on the abdominal aorta and arteries of the lower extremities are caused by many factors. There are various types of purulent and septic complications arising after arterial surgery, and several algorithms of their treatment have been proposed. However, the results of their practical use do not allow us to claim a positive solution to this problem in angiosurgery. Conclusions. With the development of purulent-septic complications after reconstructive operations on the abdominal aorta and arteries of the lower extremities, individual surgical solutions are required.

LEGAL ASPECTS OF IMPLEMENTING THE KYOTO CONVENTION IN UZBEKISTAN’S CUSTOMS ACTIVITY AND IMPLICATIONS FOR WTO ACCESSION

In this article, the legal significance of the revised Kyoto Convention in the modernization of the customs procedures of Uzbekistan was analyzed. The issues of compliance of customs procedures with Convention standards, trade facilitation, efficiency, preservation of freedom, and a positive solution to the WTO membership process were discussed. The current customs legislation framework of Uzbekistan was reviewed, the necessary directions for compliance were determined, and the impact of implementation and WTO membership was studied. In the process of analysis, legal texts, international agreements, and literature were relied upon.

The Lane-Emden System on Cartan-Hadamard Manifolds: Asymptotics and Rigidity of Radial Solutions

Abstract We investigate existence and qualitative properties of globally defined and positive radial solutions of the Lane-Emden system, posed on a Cartan-Hadamard model manifold $ {{\mathbb{M}}}^{n} $. We prove that, for critical or supercritical exponents, there exists at least a one-parameter family of such solutions. Depending on the stochastic completeness or incompleteness of $ {{\mathbb{M}}}^{n} $, we show that the existence region stays one dimensional in the former case, whereas it becomes two dimensional in the latter. Then, we study the asymptotics at infinity of solutions, which again exhibit a dichotomous behavior between the stochastically complete (where both components are forced to vanish) and incomplete cases. Finally, we prove a rigidity result for finite-energy solutions, showing that they exist if and only if is isometric to $ {\mathbb{R}}^{n} $.

High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity

This article deals with the study of the following Kirchhoff–Choquard problem: M∫RN|∇u|p(-Δp)u+V(x)|u|p-2u=∫RNF(u)(y)|x-y|μdyf(u),inRN,u>0,inRN,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\begin{array}{cc} \\displaystyle M\\left( \\, \\int \\limits _{{\\mathbb {R}}^N}|\ abla u|^p\\right) (-\\Delta _p) u + V(x)|u|^{p-2}u = \\left( \\, \\int \\limits _{{\\mathbb {R}}^N}\\frac{F(u)(y)}{|x-y|^{\\mu }}\\,dy \\right) f(u), \\;\\;\ ext {in} \\; {\\mathbb {R}}^N,\\\\ u > 0, \\;\\; \ ext {in} \\; {\\mathbb {R}}^N, \\end{array} \\end{aligned}$$\\end{document}where M models Kirchhoff-type nonlinear term of the form M(t)=a+btθ-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M(t) = a + bt^{\ heta -1}$$\\end{document}, where a,b>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a, b > 0$$\\end{document} are given constants; 1<p<N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p<N$$\\end{document}, Δp=div(|∇u|p-2∇u)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta _p = \ ext {div}(|\ abla u|^{p-2}\ abla u)$$\\end{document} is the p-Laplacian operator; potential V∈C2(RN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V \\in C^2({\\mathbb {R}}^N)$$\\end{document}; f is monotonic function with suitable growth conditions. We obtain the existence of a positive high energy solution for θ∈1,2N-μN-p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta \\in \\left[ 1, \\frac{2N-\\mu }{N-p}\\right) $$\\end{document} via the Pohožaev manifold and linking theorem. Apart from this, we also studied the radial symmetry of solutions of the associated limit problem.

Dynamic analysis of a fuzzy Bobwhite quail population model under g-division law

This paper is concerned with a kind of Bobwhite quail population model xn+1=A+Bxn+xnxn-1xn-2,n=0,1,⋯,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} x_{n+1}=A+Bx_n+\\frac{x_n}{x_{n-1}x_{n-2}},\\ \\ n=0,1,\\cdots , \\end{aligned}$$\\end{document}where the parameters and initial values are positive parabolic fuzzy numbers. According to g-division of fuzzy sets and based on the symmetrical parabolic fuzzy numbers, the conditional stability of this model is proved. Besides the existence, boundedness and persistence of its unique positive fuzzy solution. When some fuzzy stability conditions are satisfied, the model evolution exhibits oscillations with return to a fixed fuzzy equilibrium no matter what the initial value is. This phenomena provided a vivid counterexample to Allee effect in density-dependent populations of organisms. As a supplement, two numerical examples with data-table are interspersed to illustrate the effectiveness. Our findings have been verified precise with collected northern bobwhite data in Texas, and will help to form some efficient density estimates for wildlife populations of universal applications.

Spectral stability of periodic traveling wave solutions for a double dispersion equation

ABSTRACT In this article, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method, we find explict periodic waves and we also present a characterization for all positive and periodic solutions for the model using the monotonicity of the period map in terms of the energy levels. The monotonicity of the period map is also useful to obtain the quantity and multiplicity of non-positive eigenvalues for the associated linearized operator and to do so, we use tools of the Floquet theory. Finally, we prove the spectral stability by analyzing the difference between the number of negative eigenvalues of a convenient linear operator restricted to the space constituted by zero-mean periodic functions and the number of negative eigenvalues of the matrix formed by the tangent space associated to the low order conserved quantities of the evolution model.

Improved Information Fusion for Agricultural Machinery Navigation Based on Context-Constrained Kalman Filter and Dual-Antenna RTK

Automatic navigation based on dual-antenna real-time kinematic (RTK) positioning has been widely employed for unmanned agricultural machinery, whereas GNSS inevitably suffers from signal blocking and electromagnetic interference. In order to improve the reliability of an RTK-based navigation system in a GNSS-challenged environment, an integrated navigation system is preferred for autonomous navigation, which increases the complexity and cost of the navigation system. The information fusion of integrated navigation has been dominated by Kalman filter (KF) for several decades, but the KF cannot assimilate the known knowledge of the navigation context efficiently. In this paper, the geometric characteristics of the straight path and path-tracking error were employed to formulate the constraint measurement model, which suppresses the position error in the case of RTK-degraded scenarios. The pseudo-measurements were then imported into the KF framework, and the smoothed navigation state was generated as a byproduct, which improves the reliability of the RTK positioning without external sensors. The experiment result of the mobile vehicle automatic navigation indicates that the tracking error-constrained KF (EC-KF) outperforms the trajectory-constrained KF (TC-KF) and KF when the RTK system outputs a float or single-point position (SPP) solution. In the case where the duration of the SPP solution was 20 s, the positioning errors of the EC-KF and TC-KF were reduced by 38.50% and 24.04%, respectively, compared with those of the KF.

THE APPLICABILITY OF LOW-COST MULTI-FREQUENCY MULTI-GNSS RECEIVERS FOR GEODETIC CONTROL SURVEYING

Abstract. In geodetic surveys, survey-grade receivers are conventionally used due to their accuracy. However, expensive survey-grade receivers deter users from performing geodetic surveys utilizing the technology. Considerably, multi-system and multi-frequency low-cost GNSS receivers are available today, which can already provide good positioning accuracy output. This paper evaluates the performance of low-cost GNSS receivers in single-point positioning, relative positioning, and network solutions compared to survey-grade GNSS receivers. The study used a survey-grade antenna to test the u-blox C099-F9P evaluation kit equipped with the ZED-F9P module, a low-cost GNSS receiver. Simultaneously, the survey-grade GNSS receiver utilizes the same antenna using a GPS splitter to ensure simultaneous observation. Based on the results, the low-cost GNSS receiver is comparable to the survey-grade GNSS receiver for single and relative positioning. For single-point positioning, the low-cost GNSS receiver achieved 1- and 1.5-meter accuracy in horizontal and vertical components at a 95% confidence level, respectively. In relative positioning, it achieved an accuracy of 1 millimeter on average at a 95% confidence level. The network solution utilizes four (4) Active Geodetic Stations of the National Mapping and Resource Information Authority within the National Capital Region, used as reference stations. The low-cost GNSS receiver achieved an average accuracy of 8 millimeters. In summary, the ublox C099-F9P low-cost GNSS receiver achieved better than 1:100,000 or first-order survey accuracy stipulated in DAO 2007-29 surveying standards. Results show that the u-blox C099-F9P is possible for geodetic and other land surveying applications, even for high-accuracy requirements surveys.

Positive solutions for parametric equations with unbalanced growth and indefinite perturbation

Positive solutions for parametric equations with unbalanced growth and indefinite perturbation

Estimating potential functions with applications to elliptic problems in half space

We first derive sharp estimates on some potential functions on the half space 0 \\} $ ]]> R + n := { x = ( x 1 , … , x n ) ∈ R n ; x n > 0 } ,   n ≥ 3 . Then, these estimates are applied to demonstrate the existence of a positive solution with an explicit asymptotic behavior for a semi-linear elliptic problem in the half space. Our approach is founded on Karamata's theory for regularly varying functions, complemented by the use of monotonicity methods.