Fundamental Solution Research Articles

Two soliton interaction of Zakharov–Mikhailov spinor models

We outline the spectral properties of their Lax operators for the Zakharov-Mikhailov spinor model (ZMm) and construct their fundamental analytic solutions (FAS). Using the dressing Zakahrov-Shabat method we derive the dressing factors for the one-soliton u 1(z 1, Φ1) and u 2(z 1 , z 2, Φ1, Φ2) for the two-soliton solutions. Next we calculate the asymptotics of the dressing factors of u 1(z 1, Φ1) for z 1 → ±∞. Inserting them into u 2(z 1 , z 2, Φ1, Φ2) we find that for z 1 → ±∞ u 2(z 1 , z 2, Φ1, Φ2) goes into one-soliton solutions but with shifted center of mass and shifted phase. Thus we conclude that the 2-soliton interactions of ZMm are purely elastic and are characterized by the above mentioned shifts.

Method of Fundamental Solutions without Fictitious Boundary in Elastodynamic Behavior Using Dual Reciprocity Method

Method of Fundamental Solutions without Fictitious Boundary in Elastodynamic Behavior Using Dual Reciprocity Method

Wave Analysis and Representation of Fundamental Solution in Modified Couple Stress Thermoelastic Diffusion with Voids, Nonlocal and Phase Lags

Wave Analysis and Representation of Fundamental Solution in Modified Couple Stress Thermoelastic Diffusion with Voids, Nonlocal and Phase Lags

Asymptotics of Fundamental Solutions of Parabolic Problems

Asymptotics of Fundamental Solutions of Parabolic Problems

Archetypal representations of dilemmas concerning invasive alien species management—A case of invasive Lantana camara in the protected areas of Nilgiri Biosphere Reserve, India

AbstractThis multi‐site case study on the invasive alien plant Lantana camara in protected areas of Nilgiri Biosphere Reserve, India, addresses the reasons for inadequate institutional responses from stakeholders in managing the species despite the seriousness. The study uses thematic analysis and qualitative systems approach. The themes are converted into a qualitative‐system‐dynamics model and are then abstracted into system archetypes. The study identified three major themes: the dilemma involving stakeholders, the dilemma of alternative and commercial use of Lantana, and the Lantana management conundrum. The study translated these dilemmas into four generalisable archetypes: ‘drifting goals’, ‘modified‐shifting‐the‐burden’, ‘fixes‐that‐fail’ and ‘substitution rebound’. The latest is a novel contribution to the systems literature. Practically, the study helps understand the recurring undesired behavioural patterns in invasive species management and suggests policy and governance changes to tackle them. The study also points towards building stakeholder relationship protocols, focussing on fundamental solutions and having clear Lantana management targets.

건강소양 향상을 위한 전략

Health literacy is emerging as an important public health issue in the 21st century. Strengthening people's health literacy is the only and most powerful way to not only improve the health and wellness of each individual, but also to solve the problem of health inequality caused by social and economic disparities and the problem of rapidly increasing medical costs as the population ages. However, research on health literacy is still insufficient in Korea, and in particular, there is little research on practical measures to improve health literacy in adults.
 Lifestyle medicine, which has emerged as a fundamental solution to prevent and treat chronic diseases, which are called diseases of the 21st century, has already systematized the knowledge and technology of health literacy, so if a route to disseminate this is secured, projects to promote national health literacy can be carried out quickly.
 This study examines the definition and significance of health literacy and the background of the emergence of lifestyle medicine and its effects, then explores specific routes for implementing national health literacy education centered on lifestyle medicine, with online universities and religious facilities as the promising routes proposed.
 Since health literacy education must be conducted as part of lifelong education, formal educational institutions, social welfare facilities, religious facilities, workplaces, etc. can all serve as sites for health literacy education and practice. In particular, online universities are expected to play the most central role in many aspects, including their purpose, capability for content development, and operating system. Religious facilities are also social capital that can make a significant contribution as a center of health literacy education and mutual care in regional communities.

A Short Examination of the Measures to Protect a Commercial Building Lessee’s De Facto-Marriage Spouse After His or Her Death

The birthrate in Korea continues to decline. A phenomenon like this can pose a risk to the existence of a state. For this reason, a number of policies are being proposed to increase the birthrate. Among other things, I propose that marriage, including a de facto marriage, should be protected more thoroughly. For it is common to become a couple through marriage and as a result, children are born.
 The Commercial Building Lease Protection Act, as opposed to the Housing Lease Protection Act, has no provision on a de facto-marriage spouse’s succession to right of lease of commercial building. Like the Housing Lease Protection Act, the Commercial Building Lease Protection Act is a social law. Social law means the law in order to protect the socially or economically disadvantaged, the state intervenes in the relation between individuals which falls under the domain of private law. If it is the only means of living to make a living by running a small store, the death of the commercial building lessee puts his or her de facto-marriage spouse at risk of livelihood. Of course, a fundamental solution to this problem is to put provisions such as provisions of the Housing Lease Protection Act in the Commercial Building Lease Protection Act.
 By the way, until the Commercial Building Lease Protection Act is supplemented, as a second-best solution, this legislative gap in the Commercial Building Lease Protection Act should be filled with the interpretation of the inheritance system in the Civil Act, the system of apportionment for person having special connection in the Civil Act, etc.
 In particular, I’d maintain that the commercial building lessee’s de facto-marriage spouse has a right to inheritance. Even if the commercial building lessee died, his or her de facto-marriage spouse can file a lawsuit to confirm the existence of the de facto marriage concerned because there is standing. Only if the court decision to confirm the existence of de facto marriage becomes final and conclusive, the de facto marriage turns into a legal marriage under customary law retroactively when there was a substance of marriage which can objectively be recognized as a marital cohabitation. A spouse stipulated in Article 1003 of the Civil Act refers to a legal-marriage spouse. A legal marriage includes not only a legal marriage under statutory law but also a legal marriage under customary law. As a result, the commercial building lessee’s spouse has a right to inheritance.

Identifying the Heat Source in Radially Symmetry and Axis-Symmetry Problems

This paper solves the inverse source problem of heat conduction in which the source term only varies with time. The application of the discrete regularization method, a kind of effective radial symmetry and axisymmetric heat conduction problem source identification that does not involve the grid integral numerical method, is put forward. Taking the fundamental solution as the fundamental function, the classical Tikhonov regularization method combined with the L-curve criterion is used to select the appropriate regularization parameters, so the problem is transformed into a class of ill-conditioned linear algebraic equations to solve with an optimal solution. Several numerical examples of inverse source problems are given. Simultaneously, a few numerical examples of inverse source problems are given, and the effectiveness and superiority of the method is shown by the results.

New Types of Derivative Non-linear Schrödinger Equations Related to Kac–Moody Algebra A2(1)

We derive a new system of integrable derivative non-linear Schrödinger equations with an L operator, quadratic in the spectral parameter with coefficients belonging to the Kac–Moody algebra A2(1). The construction of the fundamental analytic solutions of L is outlined and they are used to introduce the scattering data, thus formulating the scattering problem for the Lax pair L,M.

Redesign of Anode Catalyst for Sustainable Survival of Fuel Cells.

Polymer electrolyte membrane fuel cells (PEMFCs) suffer from severe performance degradation when operating under harsh conditions such as fuel starvation, shut-down/start-up, and open circuit voltage. A fundamental solution to these technical issues requires an integrated approach rather than condition-specific solutions. In this study, an anode catalyst based on Pt nanoparticles encapsulated in a multifunctional carbon layer (MCL), acting as a molecular sieve layer and protective layer is designed. The MCL enabled selective hydrogen oxidation reaction on the surface of the Pt nanoparticles while preventing their dissolution and agglomeration. Thus, the structural deterioration of a membrane electrode assembly can be effectively suppressed under various harsh operating conditions. The results demonstrated that redesigning the anode catalyst structure can serve as a promising strategy to maximize the service life of the current PEMFC system.

Parabolicity on Graphs

Large scale properties of Riemannian manifolds, in particular, those properties preserved by quasi-isometries, can be studied using discrete structures which approximate the manifolds. In a sequence of papers, M. Kanai proved that, under mild conditions, many properties are preserved by a certain (quasi-isometric) graph approximation of a manifold. One of these properties is p-parabolicity. A manifold M (respectively, a graph G) is said to be p-parabolic if all positive p-superharmonic functions on M (resp. G) are constant. This is equivalent to not having p-Green’s function (i.e. a positive fundamental solution of the p-Laplace-Beltrami operator). Herein we study directly the p-parabolicity on graphs. We obtain some characterizations in terms of graph decompositions. Also, we give necessary and sufficient conditions for a uniform hyperbolic graph to be p-parabolic in terms of its boundary at infinity. Finally, we prove that if a uniform hyperbolic graph satisfies the (Cheeger) isoperimetric inequality, then it is non-p-parabolic for every 1<p<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p<\\infty $$\\end{document}.

Improved dynamic analysis of shear deformable shells using the hybrid displacement boundary element method

In this paper, the dynamic analysis of shear deformable shells was conducted using the hybrid displacement boundary element method (HD-BEM). The approach involved utilizing the fundamental solution as a trial function to derive the 8-node element stiffness matrix, while approximating the boundary variables with quadratic shape functions. To ensure efficient computations and avoid singular integrals, the source points were strategically positioned outside the domain. For accurate calculations of the proposed 8-node element mass matrix, only four Gauss points were relied upon. It is important to note that both the element mass and stiffness matrices demonstrate symmetry. Throughout the study, free, forced, and harmonic analyses were considered. Encouragingly, the results obtained from the study exhibited exceptional accuracy levels, even when employing a coarse discretization approach.

3D stress concentration around circular hole under remote biaxial loading

In this study, a theoretical model is proposed to analyze the stress concentration in a plate of finite thickness containing a circular hole under remote biaxial loading. The stresses in a plate with a circular hole under remote biaxial loading is a superposition of the stresses in the unperforated plate and the released stresses induced by opening the hole. For the latter, the stresses at the edge of the hole can be further decomposed into a spherical component and a deviatoric component. The solution due to a spherical component can be readily obtained but the solution due to a deviatoric component is hard to find. According to the literature, the solution of three-dimensional stress distributions in a plate of finite thickness containing a circular hole can be found by four potential functions. The available fundamental solutions of the potential functions satisfying the boundary conditions on the surfaces of the plate contain numerous complicated integrals, which limits their application to the current problem. Nevertheless, these fundamental solutions can be found explicitly by constructing the orthogonal function, which is composed of the Bessel functions. A system of linear equations is established to satisfy the boundary conditions at the edge of the hole. Therefore, the stresses due to a deviatoric component are obtained by solving the linear simultaneous equations. The stress concentration factor calculated by the proposed model is validated with the available numerical and theoretical solutions. It is concluded that the stress ratio, the thickness of the plate, and Poisson's ratio have an important influence on the distribution of the stress concentration factor along the thickness of the plate, especially on the distribution near the surface. Moreover, the proposed model can be extended to analyze the stress concentration at the edge of a circular hole in a plate of finite thickness under remote bending. The model is efficient and reliable, and it can provide a powerful analytical method to analyze three-dimensional stress concentrations around holes under various remote loading in engineering.

Evaluation of mixed-mode stress intensity factors for anisotropic elastic solids with interface singularity

Abstract When a structure is composed of many different parts and each part is made of different materials, it is very possible that many interface corners appear in several local fields of the structure. Due to the mismatch of elastic properties, stress singularity may occur at the interface corners. The singular orders of stresses and their associated stress intensity factors (SIFs) are two important parameters for understanding failure initiation. Since the singular orders of general interface corners may be real or complex, distinct or repeated, several different definitions of SIFs have been proposed for different types of interfaces. In order to build a direct connection among all general interface corners (including cracks and interface cracks), a unified definition of SIFs was proposed in our previous studies. To calculate the uni-defined SIF accurately and efficiently, a special boundary element using the fundamental solution satisfying interface continuity conditions is established. The singular integrals involved in the associated boundary integral equations are solved by the setting of proper rigid body motions and the approximation through interpolation of nearby non-singular solutions. To avoid the unstable and inaccurate region near the corners, in this study we employ the path-independent H-integral, and derive the relations between H-integral and SIFs. Moreover, the auxiliary solutions of displacements and tractions required in the H-integral are provided for different integral paths. Several numerical examples, such as interface cracks, interface corners, single lap joints and delamination, are presented to demonstrate the methodology employed in this paper.

Integrating ball milling assisted enzymatic hydrolysis of bamboo cellulose for controllable production of xylo-oligosaccharides, monosaccharides and cellulose nanofibrils

Green bioconversion technology has been regarded as a fundamental solution to energy challenges and environmental issues. During bioconversion, a combination of mechanical and enzymatic treatment on lignocellulosic biomass can not only conformity with environmental concepts but also enable efficient conversion. In this study, a ball milling assisted enzymatic treatment was applied for full utilization of bamboo cellulose. In addition to the production of soluble saccharides, the residues that remained after enzymatic hydrolysis were collected for producing high-quality nanocellulose. Ball milling efficiently broke the hydrogen bonding interactions between glucan chains thus promoting the following xylanase and cellulase conversion. The highest Xylo-oligosaccharides (XOS) yield reached 21.6%. Meanwhile, xylanase facilitated cellulase hydrolysis by separation of hemicellulose on cellulose. With a low commercial cellulase loading of 5 FPU/g glucan, a maximum yield of 76.6% glucose and 53.3% xylose was reached. Finally, nanocellulose was extracted from the enzymatic hydrolyzate residue with a minimum width of 3.5 nm and an average size of 294.8 nm. The present study proposed an efficient combination of mechanical treatment assisted enzymatic digestion, which is not only environmentally friendly but also allows for complete bioconversion of bamboo cellulose.

The semi-discrete diffusion convection equation with decay

In this paper we find the fundamental solution of the semi-discrete diffusion convection equation with decay, and we show that under a certain combination of the parameters of the equation said fundamental solution constitutes a uniformly continuous semigroup of operators in the Lebesgue spaces ℓp(Z),1≤p≤∞.

Physics-informed kernel function neural networks for solving partial differential equations

This paper proposes an improved version of physics-informed neural networks (PINNs), the physics-informed kernel function neural networks (PIKFNNs), to solve various linear and some specific nonlinear partial differential equations (PDEs). It can also be considered as a novel radial basis function neural network (RBFNN). In the proposed PIKFNNs, it employs one-hidden-layer shallow neural network with the physics-informed kernel functions (PIKFs) as the customized activation functions. The PIKFs fully or partially contain PDE information, which can be chosen as fundamental solutions, green's functions, T-complete functions, harmonic functions, radial Trefftz functions, probability density functions and even the solutions of some linear simplified PDEs and so on. The main difference between the PINNs and the proposed PIKFNNs is that the PINNs add PDE constraints to the loss function, and the proposed PIKFNNs embed PDE information into the activation functions of the neural network. The feasibility and accuracy of the proposed PIKFNNs are validated by some benchmark examples.

On fundamental solution of the Cauchy problem for ultra-parabolic equations in the Asian options models

Paper studies ultra-parabolic equations with three groups of spatial variables appearing in Asian options problems. The class of these equations which satisfy some conditions was denoted by EB22. This class is a generalization of the well-known class of degenerate parabolic Kolmogorov type equations E22. So called L-type fundamental solutions have been constructed for the equations from the class EB22 previously, and some their properties have been established as well. The main feature of the research was the establishing of an one-to-one correspondence between the classes EB22 and E22. The Cauchy problem classic fundamental solutions for the equations from the class EB22 are considered. Special H\"older conditions with respect to spatial variables are applied to the coefficients of the equations.

Technological Impact on Tertiary Level Students’ Writing Skills in the Post-COVID Era

The incorporation of technology with writing has become the fundamental solution in developing writing skills in the crisis of the COVID-19 era. This research aims to examine and describe how technology impacts the writing process. Based on technology after the post-COVID situation, this study focuses on positive and negative concepts of writing skills employing both qualitative and quantitative methods. Information was gathered via observational surveys, interviews, and peer-reviewed journal articles. The outcome shows that the use of various technology-based apps, the development of strategy, and a variety of online evaluation methods contributed to the impact of technology on writing skills. According to the findings, incorporating technology with writing can enhance critical and creative thinking, as well as foster a positive outlook. This research recommends that using the right technology for writing skills can maximize the positive outcomes.

CAUCHY PROBLEM FOR ULTRA-PARABOLIC EQUATIONS OF KOLMOGOROV TYPE WITH BLOCK STRUCTURE

The investigation is devoted to ultra-parabolic equations which appear in Asian options problems. Unlike the European option, the payout of Asian derivative depends on the entire trajectory of the price value, not the final value only. Among methods of researching of the Asian options, the one is to include dependent on the price trajectory variables in the state space. The expansion of the state space by including of dependent on the price trajectory variables transforms the path-dependent problem for the Asian option into an equivalent path-independent Markov problem. However, the increasing of the dimension usually leads to partial differential equations which are not uniformly parabolic. The class of these equations under some conditions is a generalization of the well-known degenerate parabolic A.N.Kolmogorov's equation of diffusion with inertia. Mathematical models of the options have been studied in many works. It has been constructed so called L-type fundamental solutions for considered equations previously, some their properties have been established, the Cauchy problem has been researched. In current work, for the given equations we study the classical solutions of the Cauchy problem. For the coefficients of the equations we apply special Hölder conditions with respect to spatial variables. Under these conditions, we prove the wellposedness of the Cauchy problem in special weighed spaces, obtained integral presentation of classic solutions of the Cauchy problem for homogeneous equations. Classes of well-posedness of the Cauchy problem were described. The results obtained in the work are realization of well-known Eidelman-Ivasyshen approach. Ones can be used to advanced studying of the Cauchy problem and boundary value problems for linear and quasi-linear degenerated parabolic equations, as well as in the theory of stochastic processes when studying Markov processes, the transition probability density of which is the fundamental solution of the Cauchy problem for these equations.