The aim of this survey is to introduce Waring's problem and some related topics including mean value theorems and Diophantine equations in prime variables.
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil...In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.展开更多
In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the G...In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the Gleason’s problem is solvable on F(p,μ,s).展开更多
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.
This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 i...This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.展开更多
In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally ...In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally (r, s)-stability is proven when (?) is a compact finite Lie group .Transversality condition is used to characterize the stability.展开更多
In the following pages I will try to give a solution to this very known unsolved problem of theory of numbers. The solution is given here with an important analysis of the proof of formula (4.18), with the introductio...In the following pages I will try to give a solution to this very known unsolved problem of theory of numbers. The solution is given here with an important analysis of the proof of formula (4.18), with the introduction of special intervals between square of prime numbers that I call silver intervals . And I make introduction of another also new mathematic phenomenon of logical proposition “In mathematics nothing happens without reason” for which I use the ancient Greek term “catholic information”. From the theorem of prime numbers we know that the expected multitude of prime numbers in an interval is given by formula ?considering that interval as a continuous distribution of real numbers that represents an elementary natural numbers interval. From that we find that in the elementary interval around of a natural number ν we easily get by dx=1 the probability that has the ν to be a prime number. From the last formula one can see that the second part of formula (4.18) is absolutely in agreement with the above theorem of prime numbers. But the benefit of the (4.18) is that this formula enables correct calculations in set N on finding the multitude of twin prime numbers, in contrary of the above logarithmic relation which is an approximation and must tend to be correct as ν tends to infinity. Using the relationship (4.18) we calculate here the multitude of twins in N, concluding that this multitude tends to infinite. But for the validity of the computation, the distribution of the primes in a random silver interval is examined, proving on the basis of catholic information that the density of primes in the same random silver interval is statistically constant. Below, in introduction, we will define this concept of “catholic information” stems of “information theory” [1] and it is defined to use only general forms in set N, because these represent the set N and not finite parts of it. This concept must be correlated to Riemann Hypothesis.展开更多
In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we der...In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.展开更多
This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geom...This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geometric Theory of Phyl-lotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci -Goniometry ( is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scien-tific ideas—The “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—The “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.展开更多
Objectives:Near misses happen more frequently than actual errors,and highlight system vulnerabilities without causing any harm,thus provide a safe space for organizational learning.Second-order problem solving behavio...Objectives:Near misses happen more frequently than actual errors,and highlight system vulnerabilities without causing any harm,thus provide a safe space for organizational learning.Second-order problem solving behavior offers a new perspective to better understand how nurses promote learning from near misses to improve organizational outcomes.This study aimed to explore frontline nurses’perspectives on using second-order problem solving behavior in learning from near misses to improve patient safety.Methods:A qualitative exploratory study design was employed.This study was conducted in three tertiary hospitals in east China from June to November 2015.Purposive sampling was used to recruit 19 frontline nurses.Semi-structured interviews and a qualitative directed content analysis was undertaken using Crossan’s 4I Framework of Organizational Learning as a coding framework.Results:Second-order problem solving behavior,based on the 4I Framework of Organizational Learning,was referred to as being a leader in exposing near misses,pushing forward the cause analysis within limited capacity,balancing the active and passive role during improvement project,and promoting the continuous improvement with passion while feeling low-powered.Conclusions:4I Framework of Organizational Learning can be an underlying guide to enrich frontline nurses’role in promoting organizations to learn from near misses.In this study,nurses displayed their pivotal role in organizational learning from near misses by using second-order problem solving.However,additional knowledge,skills,and support are needed to maximize the application of second-order problem solving behavior when near misses are recognized.展开更多
通过分析欧拉所给出Knight’s Tour Problem的解法,结合哈密尔顿路和哈密尔顿圈的相关知识,得出其解法对应着二部图中的一条哈密尔顿圈.由此再充分利用8×8棋盘所对应的8×8表格的对称性及同格图的特性,对欧拉所给出的Knight’s...通过分析欧拉所给出Knight’s Tour Problem的解法,结合哈密尔顿路和哈密尔顿圈的相关知识,得出其解法对应着二部图中的一条哈密尔顿圈.由此再充分利用8×8棋盘所对应的8×8表格的对称性及同格图的特性,对欧拉所给出的Knight’s Tour Problem的解法作了进一步的探讨,得出了以欧拉的解法为基础的以任一棋格为骑士周游起点的另外一系列解法.最后,把Knight’sTour Problem推广到m×n棋盘上,考虑到移动规则的特殊性,利用图论的相关知识,得到3×4,8×16和16×16棋盘上的Knight’s Tour Problem的解法,同时给出8m×8n(m>2,n>2)棋盘上Knight’s Tour Problem的猜想.展开更多
The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the...The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.展开更多
This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only o...This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in the part A of Introduction, here, you will find simple and useful definitions and the strategy we are going to follow as well useful new theorems (also and in Section 5, which have been produced in this solution). So the published solution of twin’s problem can now be easily understood. The inequalities (4.17), (4.18) of Article A are proved here in Section 4 by a new clear method, without the possible ambiguity of the text between the relations (4.14), (4.16) of the Article A. Also we complete the proof for the twin’s distri-bution which we use. At the end here are presented the Conclusions, the No-menclatures and the numerical control of the proof, which is probably useful as well in coding methods. For a general and convincing picture is sufficient, a study from the beginning of this article B until the end of the part A of the In-troduction here as well a general glance on the Section 5 and on the Conclu-sions below.展开更多
This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to t...This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.展开更多
基金Supported by the NKRDPC(Grant No.2021YFA1000701)。
文摘The aim of this survey is to introduce Waring's problem and some related topics including mean value theorems and Diophantine equations in prime variables.
基金supported by the National Natural Science Foundation of China(No.12461086)the Natural Science Foundation of Hubei Province(No.2022CFC016)。
文摘In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.
基金Supported by the National Natural Science Foundation of China(11942109)the Natural Science Foundation of Hunan Province in China(2022JJ30369)。
文摘In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the Gleason’s problem is solvable on F(p,μ,s).
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
文摘This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.
基金Project supported by the NSF of China! (19971O62)the NSF of Fujian Province!(A97020) the NSF of Educational Committee of
文摘This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.
基金Supported by the National Nature Science Foundation of China (10261002)
文摘In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally (r, s)-stability is proven when (?) is a compact finite Lie group .Transversality condition is used to characterize the stability.
文摘In the following pages I will try to give a solution to this very known unsolved problem of theory of numbers. The solution is given here with an important analysis of the proof of formula (4.18), with the introduction of special intervals between square of prime numbers that I call silver intervals . And I make introduction of another also new mathematic phenomenon of logical proposition “In mathematics nothing happens without reason” for which I use the ancient Greek term “catholic information”. From the theorem of prime numbers we know that the expected multitude of prime numbers in an interval is given by formula ?considering that interval as a continuous distribution of real numbers that represents an elementary natural numbers interval. From that we find that in the elementary interval around of a natural number ν we easily get by dx=1 the probability that has the ν to be a prime number. From the last formula one can see that the second part of formula (4.18) is absolutely in agreement with the above theorem of prime numbers. But the benefit of the (4.18) is that this formula enables correct calculations in set N on finding the multitude of twin prime numbers, in contrary of the above logarithmic relation which is an approximation and must tend to be correct as ν tends to infinity. Using the relationship (4.18) we calculate here the multitude of twins in N, concluding that this multitude tends to infinite. But for the validity of the computation, the distribution of the primes in a random silver interval is examined, proving on the basis of catholic information that the density of primes in the same random silver interval is statistically constant. Below, in introduction, we will define this concept of “catholic information” stems of “information theory” [1] and it is defined to use only general forms in set N, because these represent the set N and not finite parts of it. This concept must be correlated to Riemann Hypothesis.
基金supported by the National Natural Science Foundation of China (11061023)
文摘In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.
文摘This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geometric Theory of Phyl-lotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci -Goniometry ( is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scien-tific ideas—The “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—The “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.
文摘Objectives:Near misses happen more frequently than actual errors,and highlight system vulnerabilities without causing any harm,thus provide a safe space for organizational learning.Second-order problem solving behavior offers a new perspective to better understand how nurses promote learning from near misses to improve organizational outcomes.This study aimed to explore frontline nurses’perspectives on using second-order problem solving behavior in learning from near misses to improve patient safety.Methods:A qualitative exploratory study design was employed.This study was conducted in three tertiary hospitals in east China from June to November 2015.Purposive sampling was used to recruit 19 frontline nurses.Semi-structured interviews and a qualitative directed content analysis was undertaken using Crossan’s 4I Framework of Organizational Learning as a coding framework.Results:Second-order problem solving behavior,based on the 4I Framework of Organizational Learning,was referred to as being a leader in exposing near misses,pushing forward the cause analysis within limited capacity,balancing the active and passive role during improvement project,and promoting the continuous improvement with passion while feeling low-powered.Conclusions:4I Framework of Organizational Learning can be an underlying guide to enrich frontline nurses’role in promoting organizations to learn from near misses.In this study,nurses displayed their pivotal role in organizational learning from near misses by using second-order problem solving.However,additional knowledge,skills,and support are needed to maximize the application of second-order problem solving behavior when near misses are recognized.
文摘通过分析欧拉所给出Knight’s Tour Problem的解法,结合哈密尔顿路和哈密尔顿圈的相关知识,得出其解法对应着二部图中的一条哈密尔顿圈.由此再充分利用8×8棋盘所对应的8×8表格的对称性及同格图的特性,对欧拉所给出的Knight’s Tour Problem的解法作了进一步的探讨,得出了以欧拉的解法为基础的以任一棋格为骑士周游起点的另外一系列解法.最后,把Knight’sTour Problem推广到m×n棋盘上,考虑到移动规则的特殊性,利用图论的相关知识,得到3×4,8×16和16×16棋盘上的Knight’s Tour Problem的解法,同时给出8m×8n(m>2,n>2)棋盘上Knight’s Tour Problem的猜想.
文摘The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.
文摘This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in the part A of Introduction, here, you will find simple and useful definitions and the strategy we are going to follow as well useful new theorems (also and in Section 5, which have been produced in this solution). So the published solution of twin’s problem can now be easily understood. The inequalities (4.17), (4.18) of Article A are proved here in Section 4 by a new clear method, without the possible ambiguity of the text between the relations (4.14), (4.16) of the Article A. Also we complete the proof for the twin’s distri-bution which we use. At the end here are presented the Conclusions, the No-menclatures and the numerical control of the proof, which is probably useful as well in coding methods. For a general and convincing picture is sufficient, a study from the beginning of this article B until the end of the part A of the In-troduction here as well a general glance on the Section 5 and on the Conclu-sions below.
基金partially supported by Ministerio de Educación y Ciencia,Spain,and FEDER,Projects MTM2013-43014-P and MTM 2016-75140-P
文摘This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.
