Solution Of Problem Research Articles

Periodic fractional Ambrosetti–Prodi for one-dimensional problem with drift

We prove Ambrosetti–Prodi type results for periodic solutions of some one-dimensional nonlinear problems that can have drift term whose principal operator is the fractional Laplacian of order s∈(0,1). We establish conditions for the existence and nonexistence of solutions of those problems. The proofs of the existence results are based on the sub-supersolution method combined with topological degree type arguments. We also obtain a priori bounds in order to get multiplicity results. We also prove that the solutions are C1,α under some regularity assumptions in the nonlinearities, that is, the solutions of the mentioned equations are classical. We finish the work obtaining Ambrosetti-Prodi-type results for a problem with singular nonlinearities.

Ulam Stability for Boundary Value Problems of Differential Equations—Main Misunderstandings and How to Avoid Them

Ulam type stability is an important property studied for different types of differential equations. When this type of stability is applied to boundary value problems, there are some misunderstandings in the literature. In connection with this, initially, we give a brief overview of the basic ideas of the application of Ulam type stability to initial value problems. We provide several examples with simulations to illustrate the main points in the application. Then, we focus on some misunderstandings in the application of Ulam stability to boundary value problems. We suggest a new way to avoid these misunderstandings and how to keep the main idea of Ulam type stability when it is applied to boundary value problems of differential equations. We present one possible way to connect both the solutions of the given problem and the solutions of the corresponding inequality. In addition, we provide several examples with simulations to illustrate the ideas for boundary value problems and we also show the necessity of the new way of applying the Ulam type stability. To illustrate the theoretical application of the suggested idea to Ulam type stability, we consider a linear boundary value problem for nonlinear impulsive fractional differential equations with the Caputo fractional derivative with respect to another function and piecewise-constant variable order. We define the Ulam–Hyers stability and obtain sufficient conditions on a finite interval. As partial cases, integral presentations of the solutions of boundary value problems for various types of fractional differential equations are obtained and their Ulam type stability is studied.

Second order discrete boundary value problem with the $(p_1(k); p_2(k))$-Laplacian

In this paper we investigate existence and non-existence of solutions for a Dirichlet boundary value problem involving the $(p_1(k), p_2(k))$-Laplacian operator when variational methods are applied to obtain the results.

A Necessary Optimality Condition on the Control of a Charged Particle

We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute an adjoint problem by a Lagrange multiplier that is related to constraints of theory on symmetries and conservation laws. The adjoint problem obtained is a boundary value problem with a nonhomogeneous boundary condition. We prove the existence and uniqueness of the solution of the adjoint problem. Then, we demonstrate the differentiability of the objective functional in the sense of Frechet and get a formula for its gradient. Finally, we give a necessary optimality condition in the form of a variational inequality.

Chaotic-quasi-oppositional-phasor based multi populations gorilla troop optimizer for optimal power flow solution

This paper proposes an efficient modified Gorilla Troops Optimizer (MGTO) to address the problem of prone to local optima and stagnation possibility in the standard Gorilla Troops Optimizer (GTO). The proposed MGTO is based on multiple strategies including chaotic initialization, quasi-oppositional based learning, phasor motion, and multi-populations strategy. The proposed MGTO is applied to resolve the non-convex single objectives optimal power flow (OPF) problem to reduce the fuel cost without and with vple, the emissions, the fuel cost considering prohibted zones (POZs) and piecewise functions, while for multiple objective cases the fuel cost is optimized with the power losses, the voltage deviation and the emissions. To validate the effectiveness of the proposed optimizer, it is tested on IEEE 30-bus and 57-bus systems, as well as 23 standard benchmark functions and the obtained outcomes are compared with the other seven well-known optimization techniques such as SCSO, GWO, WOA, SCA, PF, BWO and GTO. The simulation results verified that the proposed MGTO provides a remarkable and robust solution for the OPF problem solution compared to the other state-of-the-arts algorithms.

Development of the thermal hydraulic analysis code, TASS/SMR-S, under multi-dimensional motion for a reactor under inclination and rolling conditions

The development of a thermal hydraulic analysis code that considers ship motion is important because it would adjust for additional motion effects that are not present in a land-based system analysis code. The TASS/SMR-S code, a one-dimensional system analysis code, was modified to predict the thermal hydraulic behavior of a nuclear reactor under the conditions of an ocean environment. To validate the improved TASS/SMR-S code, the calculation results were compared with the analytical solutions for a conceptual problem involving swaying, rolling, and compounded motions; experimental data were collected under inclination and rolling conditions. The modified TASS/SMR-S code exhibited good agreement with analytical solutions for the conceptual problem and experimental results obtained under ship motion conditions. In conclusion, the modified code was able to simulate thermal hydraulic behavior under ship motion conditions.

Numerical Solution of Natural Convection Problems Using Radial Point Interpolation Meshless (RPIM) Method Combined with Artificial-Compressibility Model

A numerical method is used to solve the thermal analysis of natural convection in enclosures. This paper proposes the use of an implicit artificial-compressibility model in conjunction with the Radial Point Interpolation Meshless (RPIM) method to mimic laminar natural convective heat transport. The technique couples the pressure with the velocity components using an artificial compressibility model. The RPIM is used to discretize the spatial terms of the governing equation. We solve the semi-algebraic system implicitly in backward Euler pseudo-time. The proposed method solves two test problems—natural convection in the annulus of concentric circular cylinders and trapezoidal cavity. Additionally, the results are validated using experimental and numerical data available in the literature. Excellent agreement was seen between the numerical results acquired with the suggested method and those obtained through the standard techniques found in the literature.

Eduction of coherent structures from schlieren images of twin jets using SPOD informed with momentum potential theory in the spectral domain

Abstract This work presents a methodology to extract coherent structures from high-speed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequency-wavenumber domain instead of the time-space domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twin-jet configuration with a small jet separation at two supersonic operation conditions: a perfectly-expanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation, together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lower-rank decomposition than schlieren-based SPOD and provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twin-jet wavepacket models available in the literature than those originally obtained with direct schlieren-based SPOD, facilitating their interpretation and comparison against theoretical analyses. Graphical abstract

Some Boundary Problems, in Sobolev Spaces with Constant Exponents, Governed by the Nonlinear Operator of Plate Vibrations

In this paper, we aim to investigate certain nonlinear boundary problems within Sobolev spaces, where the exponents remain constant. We focus on the dynamically modified operator, incorporating a viscosity term into the nonlinear vibrations of plates. Vibrating plates have a broad range of applications. To address user requirements comprehensively, we've taken into account factors such as the geometric configuration, material density, plate thickness, and Poisson's ratio. After formulating the problems, our method involves converting them into hyperbolic-type nonlinear problems. In this study, we examine six boundary value problems, establishing existence and uniqueness theorems for each. Lastly, we establish the existence of a solution for the stationary problem by employing a variation of Brouwer's fixed point theorem.

An exactly divergence-free hybridized discontinuous Galerkin method for the generalized Boussinesq equations with singular heat source

The purpose of this work is to propose and analyze a hybridized discontinuous Galerkin (HDG) method for the generalized Boussinesq equations with singular heat source. We use polynomials of order k, k−1 and k to approximate the velocity, the pressure and the temperature. By introducing Lagrange multipliers for the pressure, the approximate velocity field obtained by the HDG method is shown to be exactly divergence-free and H(div)-conforming. Under a smallness assumption on the problem data and solutions, we prove by Brouwer’s fixed point theorem that the discrete system has a solution in two dimensions. If the viscosity and thermal conductivity are further assumed to be positive constants, a priori error estimates with convergence rate O(h) and efficient and reliable a posteriori error estimates are derived. Finally numerical examples illustrate the theoretical analysis and show the performance of the obtained a posteriori error estimator. 1991 Mathematics Subject Classification 65N12, 65N30, 65N50, 76N05.

BOTANICAL GARDEN NAMED AFTER JÓZSEF SZIKURA

Objective is to study and analyse the history of the creation of the József Szikura Botanical Garden, the results of its scientific, educational and environmental work. Materials and methods of the study. The collections of the natural flora plants established by Professor József Szikura in 2011 in the village of Velyki Berehy, located 8 km northeast of the city of Berehove, Zakarpattya region were studied. The main criteria for assessing the plants diversity in the botanical garden were the following: the qualitative and quantitative composition of the collections, their condition, the results of plant propagation, the possibility of repatriating them to natural ecosystems, the effects of research work, and educational activities. The plant compositions were analyzed, and the species composition of the plots was studied. The role of the botanical garden in preserving the gene pool of flora was also assessed by the qualitative and quantitative composition of the long-lived seed bank. The results of the cultivation and acclimatisation of species of the world flora and the Carpathians have been evaluated since 2012. The evaluation of the results, cultivation and acclimatization of species of the world flora and the Carpathians has been carried out since 2012. Scientific novelty. For the first time, the compositional and systematic composition of the József Szikura Botanical Garden was analysed in the context of successful solution of problems related to the conservation of plant diversity in artificially created phytocoenoses of Transcarpathia. Based on the results of the study, an electronic catalogue (EC) of the Bank of long-lived seeds was created for the first time. Conclusions. According to the results of the inventory analysis, it was determined that the area of 0,82 ha is represented by plants of different natural flora, the taxonomic composition of the collection of which includes 89 families, 468 species, 149 varieties and cultivars. The most numerous families in the collection are Amaryllidaceae J.St.-Hil., Iridaceae Juss., Poaceae Barnhart, Caryophyllaceae Juss., Lamiaceae Martinov, Asteraceae Giseke, Cupressaceae Gray. Three Allium L. species and two Iris L. species are listed in the Red Data Book of Ukraine. The collection contains plants listed in the IUCN Red List (Allium - 5 species, Iris - 2 species) and the relict Syringa josikaea J.Jacq. ex Rchb. The analysis of the composition of the Seed Bank showed the following distribution between taxa – 249 species belonging to 47 families. The József Szikura Botanical Garden effectively combines research work on the study and protection of biodiversity, introduction and acclimatisation, reproduction and efficient use of plants, and functioning as an educational regional centre for the dissemination of ecological and ethnographic knowledge, education and upbringing of the population in the traditions of caring for nature and preserving the cultural heritage of the region.

Flow modeling and structural characterization in fungal pellets

Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for Laccaria trichodermophora based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (i.e., assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems.

Человек - мессия

This lecture is dedicated to the messianic activity of Louis Pasteur, one of the most outstanding figures in humane and veterinary medicine, the founder of microbiology and immunology, who made the most significant fundamental contribution to the scientific solution of microbiological problems of global significance. Together with his colleagues and followers, he was the first to establish the role of microbes in life on Earth, including in pathology, the bacterial etiology of infectious diseases and the universal nature of anti-infective immunity, discovered the phenomenon of artificially attenuation the pathogenic properties of infectious agents and created means and methods of protection against the most malignant diseases of animals and humans - vaccines against anthrax and rabies, immediately, even during his lifetime, which found wide application in veterinary and medical practice around the world with outstanding socio-economic efficiency.

Relationship between the Significant Solutions of Static Traffic Assignment Problems for Mixed Traffic Flow of Connected and Automated Vehicles and Human-Driven Vehicles

Connected and automated vehicles can reduce the traffic congestion level of the entire network through platoon-driving technologies compared to human-driven vehicles. One promising approach to enhancing platoon-driving technology’s efficiency is deploying dedicated lanes or roads for connected and automated vehicles. Since asymmetric interactions between different vehicle types increase road congestion, it is necessary to distinguish routes for efficient traffic management. However, the traditional traffic assignment problem, which uses only user equilibrium as a constraint with no difference in travel time between users, could not be proposed as a globally optimal solution because it generates an infinite number of locally optimal solutions. Recent studies have attempted to overcome the limitations by considering the sum of system-wide travel times as an additional constraint. Their research sought to help propose optimal deployment strategies through the lowest total travel time solution (best-case) or design robust transport planning strategies through the highest total travel time solution (worst-case). However, past studies have not focused on the possibility of the best/worst case appearing in reality. This study focused on the relationship between the two solutions pointed out in past studies and traffic patterns likely to appear in reality. This study interprets the Karush–Kun–Tucker condition of the static traffic assignment problem, considering the asymmetric interaction, and proposes a solution algorithm using discrete dynamics. The proposed algorithm extends the most widely used method in transportation planning research, which can overcome the limitations of asymmetric interaction problems through simple variations. The proposed algorithm can reliably derive two solutions, and entropy theory shows that both solutions are unlikely to appear in reality without additional policies such as dedicated lanes or roads.

A new identification of Lagrange multipliers to study solutions of nonlinear Caputo–Fabrizio fractional problems

This research aims to provide a new identification of Lagrange multipliers using a novel hybrid method based on the Khalouta transform method and the variational iteration method and to study the solutions of nonlinear fractional problems. This method is called Khalouta variational iteration method (KHVIM). The fractional derivative is considered in Caputo–Fabrizio sense. The uniqueness and convergence results are investigated using Banach fixed point theorem. The results are obtained in the form of successive approximations corresponding to the proposed problem. To demonstrate the accuracy and effectiveness of the proposed method, three different nonlinear fractional partial differential equations are provided. Approximate solutions of the fractional equations were obtained. These solutions quickly converged to exact solutions with lower computational cost. Furthermore, the method used in this study is more generalized and allows our results to be more extensive and cover several new and existing fractional problems in the literature.

“Being a Girl Has Become a Public Health Problem!”: Feminist Organizations Both Resisting and Reproducing Postfeminist Mental Health Discourses

ABSTRACT An apparent decline in youth mental health in the Nordic countries has received a lot of attention over the last decade, and young women have been described as a particularly vulnerable group. To combat the problem, political debate has centred on solutions at the individual level, despite significant evidence of the associations between structural factors and adverse mental health. In this article, I explore how two feminist support organizations working for young women in Sweden (tjejjourer) frame and address girls’ mental health as a problem of feminist concern. Interviews with staff, organizational documents, websites, social media, and other communications were analysed following Snow and Benford’s theory on collective action frames, to identify the organizations’ problem diagnoses, solutions, and motivational frames for action. The results show that the organizations both reiterate and resist a postfeminist discourse on mental health. There is notable friction between structural problem diagnoses, based on intersectional analyses of power, and political demands and support oriented towards the individual. In conclusion, I argue that this friction may be a result of the organizations’ adoption of discourses on risk, vulnerability, and mental health itself, but also that the complex relationship between structural critique and individual care is indispensable for feminist organizing.

Terminal Synergetic Control for Plate Heat Exchanger

Terminal synergetic control (TSC) is proposed as a control strategy for the temperature management of a plate heat exchanger. The controller is designed by incorporating a selected macro variable with a time-varying sliding surface. The primary objective is to maintain precise control over the outlet temperature of the cold water. To assess the convergence characteristics of the newly proposed TSC approach, the simulation results achieved using TSC featuring a time-varying macro variable are compared to those obtained from the conventional synergetic control (SC) method. With an appropriate macro variable, the simulation results indicate a notable improvement in the convergence rate provided by our designed TSC method, compared to the conventional one. The desirable property of control input, the chattering-free condition, achieved by both TSC and SC approaches emphasizes the advantage of the synergetic control-based techniques over the conventional sliding mode controller. In conclusion, synergetic control-based techniques offer superior potential solutions for nonlinear feedback control problems.

Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities

In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary control for the specified hyperbolic system is given. A difference scheme is constructed for the numerical solution of the considered initial boundary value problem. The definition of the exponential stability of the numerical solution in ℓ2-norm with respect to a discrete perturbation of the equilibrium state of the initial boundary value difference problem is given. A discrete Lyapunov function for a numerical solution is constructed, and a theorem on the exponential stability of a stationary solution of the initial boundary value difference problem in ℓ2-norm with respect to a discrete perturbation is proved.

A new method for determining crack propagation

This paper presents a new method for obtaining approximate closed-form solutions for crack propagation problems. In general, it is not possible to obtain explicit solutions of the parameters and elementary functions of these problems, due to their terms complexity, present in their definitions. In this way, we used numerical methods to obtain approximate numerical solutions. The method presented in this article provides a proposal, which, when defined by differential equations, is applicable and extensible to other problems. The approximate solutions are obtained as an exact solution of a modified initial value problem. The performance is evaluated in relation to problems with known exact solution.

Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions

Abstract In this work, we establish a theorem concerning the extension of positive weak solutions for a stationary fractional Laplacian problem featuring weight functions that change sign. Additionally, we introduce novel conditions to ensure the existence of a positive solution for the given problem. These conditions are derived utilizing the approach of sub-super solutions, thereby extending and complementing existing results in the literature.