Our paper presents a project that involves two research questions: does the choice of a related problem by the tutorial system allow the problem solving process which is blocked for the student to be restarted? What i...Our paper presents a project that involves two research questions: does the choice of a related problem by the tutorial system allow the problem solving process which is blocked for the student to be restarted? What information about learning do related problems returned by the system provide us? We answer the first question according to the didactic engineering, whose mode of validation is internal and based on the confrontation between an a priori analysis and an a posteriori analysis that relies on data from experiments in schools. We consider the student as a subject whose adaptation processes are conditioned by the problem and the possible interactions with the computer environment, and also by his knowledge, usually implicit, of the institutional norms that condition his relationship with geometry. Choosing a set of good problems within the system is therefore an essential element of the learning model. Since the source of a problem depends on the student’s actions with the computer tool, it is necessary to wait and see what are the related to problems that are returned to him before being able to identify patterns and assess the learning. With the simultaneity of collecting and analysing interactions in each class, we answer the second question according to a grounded theory analysis. By approaching the problems posed by the system and the designs in play at learning blockages, our analysis links the characteristics of problems to the design components in order to theorize on the decisional, epistemological, representational, didactic and instrumental aspects of the subject-milieu system in interaction.展开更多
Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Br...Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.展开更多
A meshfree method namely, element free Gelerkin (EFG) method, is presented in this paper for the solution of governing equations of 2-D potential problems. The EFG method is a numerical method which uses nodal points ...A meshfree method namely, element free Gelerkin (EFG) method, is presented in this paper for the solution of governing equations of 2-D potential problems. The EFG method is a numerical method which uses nodal points in order to discretize the computational domain, but where the use of connectivity is absent. The unknowns in the problems are approximated by means of connectivity-free technique known as moving least squares (MLS) approximation. The effect of irregular distribution of nodal points on the accuracy of the EFG method is the main goal of this paper as a complement to the precedent researches investigated by proposing an irregularity index (II) in order to analyze some 2-D benchmark examples and the results of sensitivity analysis on the parameters of the method are presented.展开更多
The paper provides mathematical analysis of sensitivity of different combination rules in the DS/AHP method when an alternative is added to the set of decision alternatives while solving foresight problems. Different ...The paper provides mathematical analysis of sensitivity of different combination rules in the DS/AHP method when an alternative is added to the set of decision alternatives while solving foresight problems. Different cases of rank reversals are defined and two sets of conditions for these cases using the method DS/AHP are considered. Rank reversals are illustrated when the DS/AHP method is used to solve practical problem of critical technologies of energy conservation and power efficiency evaluation in Ukraine. It is shown that the DS/AHP method is not sensitive to exclusion (or addition) of an irrelevant decision alternative from (or to) the set of decision alternatives.展开更多
Spinal cord injury(SCI) leads generally to an irreversible loss of sensory functions and voluntary motor control below injury level. Cures that could repair SCI and/or restore voluntary walking have not been yet devel...Spinal cord injury(SCI) leads generally to an irreversible loss of sensory functions and voluntary motor control below injury level. Cures that could repair SCI and/or restore voluntary walking have not been yet developed nor commercialized. Beyond the well-known loss of walking capabilities, most SCI patients experience also a plethora of motor problems and health concerns including specific bladder and bowel dysfunctions. Indeed, chronic constipation and urinary retention, two significant life-threatening complications, are typically found in patients suffering of traumatic(e.g., falls or car accidents) or non-traumatic SCI(e.g., multiple sclerosis, spinal tumors). Secondary health concerns associated with these dysfunctions include hemorrhoids, abdominal distention, altered visceral sensitivity, hydronephrosis, kidney failure, urinary tract infections, sepsis and, in some cases, cardiac arrest. Consequently, individuals with chronic SCI are forced to regularly seek emergency and critical care treatments when some of these conditions occur or become intolerable. Increasing evidence supports the existence of a novel experimental approach that may be capable of preventing the occurrence or severity of bladder and bowel problems. Indeed, recent findings in animal models of SCI have revealed that, despite paraplegia or tetraplegia, it remains possible to elicit episodes of micturition and defecation by acting pharmacologically or electrically upon specialized lumbosacral neuronal networks, namely the spinal or sacral micturition center(SMC) and lumbosacral defecation center(LDC). Daily activation of SMC and LDC neurons could potentially become, new classes of minimally invasive treatments(i.e., if orally active) against these dysfunctions and their many lifethreatening complications.展开更多
We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional ...We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.展开更多
Focusing on the Yangtze River economic zone,the previous geological researches are systematically summarized,resources and environment conditions and major geological problems which are needing to be concerned in land...Focusing on the Yangtze River economic zone,the previous geological researches are systematically summarized,resources and environment conditions and major geological problems which are needing to be concerned in land planning and construction are studied.The results show that the resource conditions of cultivated land,shale gas,geotherm,lithium and so on are superior in the Yangtze River economic zone,and the resources and environment conditions are conducive to develop the modern agriculture,clean energy industry and strategic emerging industries.3×1013 m^2 farmlands without heavy metal pollution are concentrated;there are three national level shale gas exploration and development bases with explored reserves of 5.441×1011 m^3;geothermal availability is 2.4×109 t of standard coal each year,equivalent to 19% of the amount of coal in 2014;Asia's largest energy lithium metal ore deposit is found.In some parts of Yangtze River economic zone,there are some major geological problems such as active faults,karst collapse,ground subsidence,landslide-collapse-debris flow,affecting the river-crossing channels,high-speed railway,urban agglomeration and green ecological corridor planning and construction.Those problems should be concerned,and the relevant suggestions and countermeasures are put forward.Meanwhile,the ideas to further support the development of the Yangtze River economic zone are put forward.展开更多
In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper a...In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper and lower solution, the sufficient condition for the existence of the boundary value problem is obtained, and the range of the solution is determined. Then the existence and uniqueness of the solution are proved by the proof by contradiction. Finally, a concrete example is given to illustrate the wide applicability of our main results.展开更多
Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’...Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.展开更多
In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor depos...In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.展开更多
In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener...In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.展开更多
Owing to intensive human activities and the floods of the Huaihe River in historic peiod, the contiguous region of Jiangsu, Shandong, Henan and Anhui provinces is suffering from a variety of environmental problems and...Owing to intensive human activities and the floods of the Huaihe River in historic peiod, the contiguous region of Jiangsu, Shandong, Henan and Anhui provinces is suffering from a variety of environmental problems and naturaldisasters, of which water pollution and drought-flood disasters are most observable. Considering the special location andenvironmental status of the contiguous region, advices are proposed in the paper: perfecting trans-regional managementssystem of water environment incorporating basin management agencies in local government activities; strengthening cooperation of two agencies: water conservancy agency and environment protection agency; enhancing integrated control ofwater pollution and flood-drought disasters; taking the interests of the whole river into acount and paying attention to bothstorage and drainage; broadening sources of water supply and inceasing water delivery; controlling pollutant discharge,developing water saving production system.展开更多
Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet ...Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.展开更多
The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which...The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.展开更多
Nowadays, the success of the new technology development and deployment process depends not only on technical, technological solutions, but also on solving the non-technological problems and crossing the societal and p...Nowadays, the success of the new technology development and deployment process depends not only on technical, technological solutions, but also on solving the non-technological problems and crossing the societal and psychological barriers. A large international European projects, GABRIEL1 had developed a maglev assisted aircraft take-off and landing, that was applied to conceptual design of aircraft and required on-board and ground systems, had analysed all impacts (effects of concept deployment on effectiveness, safety, security, noise, emissions) and had demonstrated the safe applicability by concept validation. The applied methodology, used methods and the results of the Gabriel projects had been described and discussed by 55 project deliverables. This paper has a special goal: investigating the problems and barriers of possible implementing of the radically new technology, aircraft MagLev assisted take-off and landing. The study was started by identification and classification of the problems and barriers. After it, the problems were systematically analysed by use of special methodology containing the understanding (description) of the problems, investigation of the possible solutions and discussing their applicability (mainly by use of the Gabriel project results). The paper has three major sections: 1) description of the Gabriel concept and project results, 2) introducing some related thoughts on general aspects of new technology developments, and 3) discussion on the problems and their solutions. The major classes of the problems are the 1) technical, technological problems as developing a radically new solution, landing the undercarriage-less aircraft on the magnetic tracks, 2) stakeholders’ problems as decision makers kicking against supporting the developments of so radically new technologies and 3) society barriers like society worrying on and fear of future passengers on flying by aircraft have not conventional undercarriage systems. The paper will show that these problems have safe and cost-effective solutions.展开更多
In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary condit...In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.展开更多
This manuscript provides a comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of the Standard Cosmology. The performed analysis of BBM shows that the Four Pillars of the ...This manuscript provides a comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of the Standard Cosmology. The performed analysis of BBM shows that the Four Pillars of the Standard Cosmology are model-dependent and not strong enough to support the model. The angular momentum problem is one of the most critical problems in BBM. Standard Cosmology cannot explain how Galaxies and Extra Solar systems obtained their substantial orbital and rotational angular momenta, and why the orbital momentum of Jupiter is considerably larger than the rotational momentum of the Sun. WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM discusses in detail the Beginning of the World. The Model introduces Dark Epoch (spanning from the Beginning of the World for 0.4 billion years) when only Dark Matter Particles (DMPs) existed, and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in Standard Cosmology is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning Dark Matter (DM) Supercluster’s Cores. WUM envisions Matter carried from the Universe into the World from the fourth spatial dimension by DMPs. Ordinary Matter is a byproduct of DM annihilation. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Diversity of Gravitationally-Rounded Objects in Solar system;some problems in Solar and Geophysics [1]. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.展开更多
The present paper deals with very important practical problems of wide range of applications. The main target of the present paper is to track all moving boundaries that appear throughout the whole process when dealin...The present paper deals with very important practical problems of wide range of applications. The main target of the present paper is to track all moving boundaries that appear throughout the whole process when dealing with multi-moving boundary problems continuously with time up to the end of the process with high accuracy and minimum number of iterations. A new numerical iterative scheme based the boundary integral equation method is developed to track the moving boundaries as well as compute all unknowns in the problem. Three practical applications, one for vaporization and two for ablation were solved and their results were compared with finite element, heat balance integral and the source and sink results and a good agreement were obtained.展开更多
We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurz...We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.展开更多
In this paper, Goursat’s problems for: linear and nonlinear hyperbolic equations of second-order, systems of nonlinear hyperbolic equations and fourth-order linear hyperbolic equations in which the attached condition...In this paper, Goursat’s problems for: linear and nonlinear hyperbolic equations of second-order, systems of nonlinear hyperbolic equations and fourth-order linear hyperbolic equations in which the attached conditions are given on the characteristics curves are transformed in such a manner that the Adomian decomposition method (ADM) can be applied. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.展开更多
文摘Our paper presents a project that involves two research questions: does the choice of a related problem by the tutorial system allow the problem solving process which is blocked for the student to be restarted? What information about learning do related problems returned by the system provide us? We answer the first question according to the didactic engineering, whose mode of validation is internal and based on the confrontation between an a priori analysis and an a posteriori analysis that relies on data from experiments in schools. We consider the student as a subject whose adaptation processes are conditioned by the problem and the possible interactions with the computer environment, and also by his knowledge, usually implicit, of the institutional norms that condition his relationship with geometry. Choosing a set of good problems within the system is therefore an essential element of the learning model. Since the source of a problem depends on the student’s actions with the computer tool, it is necessary to wait and see what are the related to problems that are returned to him before being able to identify patterns and assess the learning. With the simultaneity of collecting and analysing interactions in each class, we answer the second question according to a grounded theory analysis. By approaching the problems posed by the system and the designs in play at learning blockages, our analysis links the characteristics of problems to the design components in order to theorize on the decisional, epistemological, representational, didactic and instrumental aspects of the subject-milieu system in interaction.
文摘Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.
文摘A meshfree method namely, element free Gelerkin (EFG) method, is presented in this paper for the solution of governing equations of 2-D potential problems. The EFG method is a numerical method which uses nodal points in order to discretize the computational domain, but where the use of connectivity is absent. The unknowns in the problems are approximated by means of connectivity-free technique known as moving least squares (MLS) approximation. The effect of irregular distribution of nodal points on the accuracy of the EFG method is the main goal of this paper as a complement to the precedent researches investigated by proposing an irregularity index (II) in order to analyze some 2-D benchmark examples and the results of sensitivity analysis on the parameters of the method are presented.
文摘The paper provides mathematical analysis of sensitivity of different combination rules in the DS/AHP method when an alternative is added to the set of decision alternatives while solving foresight problems. Different cases of rank reversals are defined and two sets of conditions for these cases using the method DS/AHP are considered. Rank reversals are illustrated when the DS/AHP method is used to solve practical problem of critical technologies of energy conservation and power efficiency evaluation in Ukraine. It is shown that the DS/AHP method is not sensitive to exclusion (or addition) of an irrelevant decision alternative from (or to) the set of decision alternatives.
文摘Spinal cord injury(SCI) leads generally to an irreversible loss of sensory functions and voluntary motor control below injury level. Cures that could repair SCI and/or restore voluntary walking have not been yet developed nor commercialized. Beyond the well-known loss of walking capabilities, most SCI patients experience also a plethora of motor problems and health concerns including specific bladder and bowel dysfunctions. Indeed, chronic constipation and urinary retention, two significant life-threatening complications, are typically found in patients suffering of traumatic(e.g., falls or car accidents) or non-traumatic SCI(e.g., multiple sclerosis, spinal tumors). Secondary health concerns associated with these dysfunctions include hemorrhoids, abdominal distention, altered visceral sensitivity, hydronephrosis, kidney failure, urinary tract infections, sepsis and, in some cases, cardiac arrest. Consequently, individuals with chronic SCI are forced to regularly seek emergency and critical care treatments when some of these conditions occur or become intolerable. Increasing evidence supports the existence of a novel experimental approach that may be capable of preventing the occurrence or severity of bladder and bowel problems. Indeed, recent findings in animal models of SCI have revealed that, despite paraplegia or tetraplegia, it remains possible to elicit episodes of micturition and defecation by acting pharmacologically or electrically upon specialized lumbosacral neuronal networks, namely the spinal or sacral micturition center(SMC) and lumbosacral defecation center(LDC). Daily activation of SMC and LDC neurons could potentially become, new classes of minimally invasive treatments(i.e., if orally active) against these dysfunctions and their many lifethreatening complications.
文摘We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.
文摘Focusing on the Yangtze River economic zone,the previous geological researches are systematically summarized,resources and environment conditions and major geological problems which are needing to be concerned in land planning and construction are studied.The results show that the resource conditions of cultivated land,shale gas,geotherm,lithium and so on are superior in the Yangtze River economic zone,and the resources and environment conditions are conducive to develop the modern agriculture,clean energy industry and strategic emerging industries.3×1013 m^2 farmlands without heavy metal pollution are concentrated;there are three national level shale gas exploration and development bases with explored reserves of 5.441×1011 m^3;geothermal availability is 2.4×109 t of standard coal each year,equivalent to 19% of the amount of coal in 2014;Asia's largest energy lithium metal ore deposit is found.In some parts of Yangtze River economic zone,there are some major geological problems such as active faults,karst collapse,ground subsidence,landslide-collapse-debris flow,affecting the river-crossing channels,high-speed railway,urban agglomeration and green ecological corridor planning and construction.Those problems should be concerned,and the relevant suggestions and countermeasures are put forward.Meanwhile,the ideas to further support the development of the Yangtze River economic zone are put forward.
文摘In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper and lower solution, the sufficient condition for the existence of the boundary value problem is obtained, and the range of the solution is determined. Then the existence and uniqueness of the solution are proved by the proof by contradiction. Finally, a concrete example is given to illustrate the wide applicability of our main results.
文摘Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.
文摘In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.
文摘In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
文摘Owing to intensive human activities and the floods of the Huaihe River in historic peiod, the contiguous region of Jiangsu, Shandong, Henan and Anhui provinces is suffering from a variety of environmental problems and naturaldisasters, of which water pollution and drought-flood disasters are most observable. Considering the special location andenvironmental status of the contiguous region, advices are proposed in the paper: perfecting trans-regional managementssystem of water environment incorporating basin management agencies in local government activities; strengthening cooperation of two agencies: water conservancy agency and environment protection agency; enhancing integrated control ofwater pollution and flood-drought disasters; taking the interests of the whole river into acount and paying attention to bothstorage and drainage; broadening sources of water supply and inceasing water delivery; controlling pollutant discharge,developing water saving production system.
基金the National Natural Science Foundation of China (Nos.11571238,11601332,91130014,11471312 and 91430216).
文摘Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.
基金supported by the National Natural Science Foundation of China(51078150)the National Natural Science Foundation of China(11602087)+1 种基金the State Key Laboratory of Subtropical Building Science,South China University of Technology(2017ZB32)National Undergraduate Innovative and Entrepreneurial Training Program(201810561180).
文摘The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.
文摘Nowadays, the success of the new technology development and deployment process depends not only on technical, technological solutions, but also on solving the non-technological problems and crossing the societal and psychological barriers. A large international European projects, GABRIEL1 had developed a maglev assisted aircraft take-off and landing, that was applied to conceptual design of aircraft and required on-board and ground systems, had analysed all impacts (effects of concept deployment on effectiveness, safety, security, noise, emissions) and had demonstrated the safe applicability by concept validation. The applied methodology, used methods and the results of the Gabriel projects had been described and discussed by 55 project deliverables. This paper has a special goal: investigating the problems and barriers of possible implementing of the radically new technology, aircraft MagLev assisted take-off and landing. The study was started by identification and classification of the problems and barriers. After it, the problems were systematically analysed by use of special methodology containing the understanding (description) of the problems, investigation of the possible solutions and discussing their applicability (mainly by use of the Gabriel project results). The paper has three major sections: 1) description of the Gabriel concept and project results, 2) introducing some related thoughts on general aspects of new technology developments, and 3) discussion on the problems and their solutions. The major classes of the problems are the 1) technical, technological problems as developing a radically new solution, landing the undercarriage-less aircraft on the magnetic tracks, 2) stakeholders’ problems as decision makers kicking against supporting the developments of so radically new technologies and 3) society barriers like society worrying on and fear of future passengers on flying by aircraft have not conventional undercarriage systems. The paper will show that these problems have safe and cost-effective solutions.
文摘In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.
文摘This manuscript provides a comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of the Standard Cosmology. The performed analysis of BBM shows that the Four Pillars of the Standard Cosmology are model-dependent and not strong enough to support the model. The angular momentum problem is one of the most critical problems in BBM. Standard Cosmology cannot explain how Galaxies and Extra Solar systems obtained their substantial orbital and rotational angular momenta, and why the orbital momentum of Jupiter is considerably larger than the rotational momentum of the Sun. WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM discusses in detail the Beginning of the World. The Model introduces Dark Epoch (spanning from the Beginning of the World for 0.4 billion years) when only Dark Matter Particles (DMPs) existed, and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in Standard Cosmology is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning Dark Matter (DM) Supercluster’s Cores. WUM envisions Matter carried from the Universe into the World from the fourth spatial dimension by DMPs. Ordinary Matter is a byproduct of DM annihilation. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Diversity of Gravitationally-Rounded Objects in Solar system;some problems in Solar and Geophysics [1]. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.
文摘The present paper deals with very important practical problems of wide range of applications. The main target of the present paper is to track all moving boundaries that appear throughout the whole process when dealing with multi-moving boundary problems continuously with time up to the end of the process with high accuracy and minimum number of iterations. A new numerical iterative scheme based the boundary integral equation method is developed to track the moving boundaries as well as compute all unknowns in the problem. Three practical applications, one for vaporization and two for ablation were solved and their results were compared with finite element, heat balance integral and the source and sink results and a good agreement were obtained.
文摘We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.
文摘In this paper, Goursat’s problems for: linear and nonlinear hyperbolic equations of second-order, systems of nonlinear hyperbolic equations and fourth-order linear hyperbolic equations in which the attached conditions are given on the characteristics curves are transformed in such a manner that the Adomian decomposition method (ADM) can be applied. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.
