Positive Solutions Research Articles

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

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.

Investigating the Dynamics of Bayoud Disease in Date Palm Trees and Optimal Control Analysis

The fungus Fusarium oxysporum (f.sp. albedinis) causes Bayoud disease. It is one of the epiphytotic diseases that affects a wide range of palm species and has no known cure at present. However, preventive measures can be taken to reduce the effects of the disease. Bayoud disease has caused enormous economic losses due to decreased crop yield and quality. Therefore, it is essential to develop a mathematical model for the dynamics of the disease to propose some affordable methods for disease management. In this study, we propose a novel mathematical model that describes the transmission dynamics of the disease in date palm trees. The model incorporates various factors such as the contact rate of the fungi with date palm trees, the utilization of fungicides, and the introduction of a quarantine compartment to prevent disease dissemination. We first prove a few key properties of the proposed model to ensure that the model is well-posed and suitable for numerical investigations. We establish that the model has a unique positive solution that is bounded and stable over time. We use sensitivity analysis to identify the parameters that have the greatest effect on the reproduction number R0 and illustrate this effect graphically. We then formulate an optimal control problem to identify the most suitable and cost-effective disease control approaches. As a first approach, we solely focus on the application of fungicide to susceptible trees and determine the best spray rates for a greater decrease in exposed and infected trees. Secondly, we emphasize quarantining exposed and infected trees at optimal quarantine rates. Finally, we explore the combined effect of fungicide spraying and isolating infected trees on disease control. The findings of the last approach turn out to be the most rewarding and cost-effective for minimizing infections in date palm trees.

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.

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.

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.

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

Bifurcation analysis of fractional Kirchhoff problems with singular exponential nonlinearity

This paper deals with the bifurcation results of (weak) solutions for the Kirchhoff fractional p-Laplacian equation { M ( x , [ u ] s , p p ) ( − Δ ) p s u = f ( λ , x , u ) in Ω , u = 0 in R N ∖ Ω , where ( − Δ ) p s denotes the fractional operator, with sp = N, and the nonlinearity f exhibits the singular exponential growth at infinity. Moreover, the existence of unbounded components of (weak) solutions emanating from the trivial solution, is treated via the fix point result and the global bifurcation theorem due to Rabinowitz. Finally, the main feature of this paper consists of the existence of positive solutions to the above equation for λ small enough.

Multiple positive solutions of the quasilinear Schrödinger–Poisson system with critical exponent in D1,p(R3)

This paper is concerned with the quasilinear Schrödinger–Poisson system −Δpu−l(x)ϕ|u|p−2u=|u|p*−2u+μh(x)|u|q−2u in R3 and −Δϕ = l(x)|u|p in R3, where μ &amp;gt; 0, p*=3p3−p and Δpu = div(|∇u|p−2∇u). By using the Ekeland’s variational principle and the mountain pass theorem, we prove that the system admits two positive solutions for 1 ⩽ q &amp;lt; p and 1 &amp;lt; p &amp;lt; 3, and the system admits one positive solution for p ⩽ q &amp;lt; p* and 32&amp;lt;p&amp;lt;3.

Dynamics of a stochastic food chain chemostat model with Monod–Haldane functional response and Ornstein–Uhlenbeck process

In the present paper, a novel stochastic food chain chemostat model with Monod–Haldane functional response is proposed and studied, incorporating the mean-reversion Ornstein–Uhlenbeck process to simulate stochastic perturbation on the growth of microorganisms by environmental fluctuations. Firstly, the existence and uniqueness of the global positive solution are proved, and the stochastic boundedness of the solution is obtained. Secondly, the conditions for controlling exponential extinction and persistence in the mean of microorganisms are delved. Finally, a large number of representative numerical examples are provided to validate the theoretical results. The results show that the stochastic noise measured by the regression speed and the fluctuation intensity has significant effects on the dynamics of the model.

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.

Delving a stochastic SEQAIJR COVID-19 model with hexa delayed and copious control strategies

The actual ideal of the literature is to probe the effect of external undulation on prevalence of COVID-19. Owing to some environmental influences, we enhanced our model to the stochastic perturbations. In this article, we scrutinize a stochastic epidemic COVID-19 model with seven states of epidemiological classification. Incipiently, a sophisticated biological system with the effect of time lags put forward copious strategies. At the outset, aim of this work is to explore the existence and uniqueness of global positive solution. Moment exponential stability are upheld. By fabricating a suitable lyapunov function, the sufficient conditions for the persistence of the disease and the existence of an ergodic stationary distribution are established. To regulate the widespread of COVID-19 infection, the main intent is to curb the disease with the succor of three control measures. Finally, the theoretical results bring into being alive in the form of graphical visualization. By nurturing the comparison study, the parameters of the model system come up with real data of most afflicted countries that layout premier consequences.

On a class of quasilinear Schrödinger equations with superlinear terms

In this paper, we consider a class of quasilinear Schrödinger equations arising from a model of a self-trapped electrons in quadratic or hexagonal lattices. By variational methods, we prove that this problem admits a positive solution for any positive parameter.

Long-term effect of SARS-CoV-2 variant : Challenging issues and controlling strategies

In this study, a latest version of COVID-19 pandemic is hand overed. A Stochastic post COVID-19 delayed model is developed to explore the spread of COVID-19 as well as omicron variant with the correlation of heart attack. This article provides an eradication of the COVID-19 and omicron variant as well as the population who have heart attack after post COVID-19 of these epidemic diseases. Then the existence and uniqueness of global positive solution are studied. Ensuing, In this article, we classify COVID-19 virus and omicron variant which go to extinction and become persistent in mean. By using Lyapunov function, the existence of ergodic stationary distribution are established. Later from the persistent disease as well as extinction, heart disease are ready to develop in the human body. By Eventually, an optimal control strategies are introduced in the form of stochastic post COVID-19 delayed model to control two different types of virus. Finally, the numerical simulation are presented to determine the behavior of dynamical system by utilizing the real data of United Kingdom.

Bias-constrained integer least squares estimation: distributional properties and applications in GNSS ambiguity resolution

To accommodate the presence of bounded biases in mixed-integer models, Khodabandeh (2022) extended integer estimation theory by introducing a new admissible integer estimator. The estimator follows the principle of integer least squares estimation and is computed via the integer search method of BEAT. In this contribution, we present the probability distributions of a class of estimators to which the proposed bias-constrained integer least squares estimation belongs. Some important interferometric measuring systems, whose estimation problems can be covered by BEAT, are identified. To show the proposed estimator at work, we apply BEAT to the problem of GLONASS single-differenced (SD) ambiguity resolution. Numerical results of several short-baseline datasets are presented to illustrate why one can achieve more accurate positioning solutions when considering between-receiver SD ambiguity resolution for the cases where carrier phase data are captured on frequency-varying signals with bounded SD receiver phase delays.

Positive solutions for a Hadamard-type fractional p-Laplacian integral boundary value problem

In this paper we study the existence of positive solutions to a Hadamard-type fractional integral boundary value problem using fixed point index. We construct a new linear operator and obtain our main results under some conditions concerning the spectral radius of this linear operator. Our method improves and generalizes some results in the literature.

A study on positive solutions for evolution equation with delay in Banach space

A study on positive solutions for evolution equation with delay in Banach space

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.