New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model arei...New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.展开更多
Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a ...Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.展开更多
The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal...The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.展开更多
While antibiotic resistance is becoming increasingly serious today,there is almost no doubt that more challenging times await us in the future.Resistant microorganisms have increased in the past decades leading to lim...While antibiotic resistance is becoming increasingly serious today,there is almost no doubt that more challenging times await us in the future.Resistant microorganisms have increased in the past decades leading to limited treatment options,along with higher morbidity and mortality.Klebsiella pneumoniae is one of the significant microorganisms causing major public health problems by acquiring resistance to antibiotics and acting as an opportunistic pathogen of healthcare-associated infections.The production of extended spectrumbeta-lactamases(ESBL)is one of the resistance mechanisms of K.pneumoniae against antibiotics.In this study,the future clinical situation of ESBL-producing K.pneumoniae was investigated in order to reflect the future scenarios to understand the severity of the issue and to determine critical points to prevent the spread of the ESBL-producing strain.For evaluation purposes,SIS-type mathematical modeling was used with retrospective medical data from the period from 2016 to 2019.Stability of the disease-free equilibrium and basic reproduction ratios were calculated.Numerical simulation of the SISmodel was conducted to describe the dynamics of non-ESBL and ESBL-producing K.pneumoniae.In order to determine the most impactful parameter on the basic reproduction ratio,sensitivity analysis was performed.A study on mathematical modeling using data on ESBL-producing K.pneumoniae strains has not previously been performed in any health institution in Northern Cyprus,and the efficiency of the parameters determining the spread of the relevant strains has not been investigated.Through this study,the spread of ESBL-producing K.pneumoniae in a hospital environment was evaluated using a different approach.According to the study,in approximately seventy months,ESBL-producing K.pneumoniae strains will exceed non-ESBL K.pneumoniae strains.As a result,the analyses showed that hospital admissions and people infected with non-ESBL or ESBL-producing K.pneumoniae have the highest rate of spreading the infections.In addition,it was observed that the use of antibiotics plays a major role in the spread of ESBL-producing K.pneumoniae compared to other risk factors such as in-hospital transmissions.As amatter of course,recoveries fromKlebsiella infections were seen to be the most effective way of limiting the spread.It can be concluded from the results that although the use of antibiotics is one of themost effective factors in the development of the increasing ESBL-producing K.pneumoniae,regulation of antibiotic use policy could be a remedial step together with effective infection control measures.Such steps may hopefully lead to decreased morbidity and mortality rates as well as improved medical costs.展开更多
From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430...From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.展开更多
In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy ...In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy estimation,we obtain that the trivial solution u=Q=0 is the unique solution.Our theorems correspond to improvements of some recent results and contain some known results as particular cases.展开更多
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where...In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.展开更多
In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled...In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.展开更多
We propose a fractional-order improved Fitz Hugh–Nagumo(FHN)neuron model in terms of a generalized Caputo fractional derivative.Following the existence of a unique solution for the proposed model,we derive the numeri...We propose a fractional-order improved Fitz Hugh–Nagumo(FHN)neuron model in terms of a generalized Caputo fractional derivative.Following the existence of a unique solution for the proposed model,we derive the numerical solution using a recently proposed L1 predictor–corrector method.The given method is based on the L1-type discretization algorithm and the spline interpolation scheme.We perform the error and stability analyses for the given method.We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns,chaotic patterns,and quasi-periodic patterns.The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics,which are inherent to many biological systems.展开更多
In this paper,we study the Cauchy problem of three-dimensional incompressible magnetohydrodynamics with almost symmetrical initial values in the cylindrical coordinates.Here the almost axisymmetric means that(■θu_(0...In this paper,we study the Cauchy problem of three-dimensional incompressible magnetohydrodynamics with almost symmetrical initial values in the cylindrical coordinates.Here the almost axisymmetric means that(■θu_(0)^(r),■θeu_(0)^(θ),■θeu_(θ)^(z))is small.With additional smallness assumption on(u_(0)^(θ),b_(0)^(θ)),we prove the global existence of a unique strong solution(u,b),which keeps close to some axisymmetric vector fields.Moreover,we give the initial data with some special symmetric structures that will persist for all time.展开更多
this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(...this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(2)(R^(3),p,q,r∈(3,∞],and 1/p+1/q+1/r≥2/3, which extends some known results.展开更多
It is well known that the explicit-invariant energy quadratization(EIEQ)approach can generate fully decoupled,linear and unconditionally energy-stable numerical schemes,so it is favored by many researchers.However,the...It is well known that the explicit-invariant energy quadratization(EIEQ)approach can generate fully decoupled,linear and unconditionally energy-stable numerical schemes,so it is favored by many researchers.However,the undeniable fact is that the numerical method obtained by EIEQ approach preserves the“modified”energy law instead of the original energy.This is mainly due to the introduction of some auxiliary variables in EIEQ scheme,and the truncation error will make the auxiliary variables deviate from the original definition in the process of numerical calculation.The primary objective of this paper is to address this gap by providing the accuracy and consistency of the EIEQ method in the context of the CahnHilliard equation.We introduce a relaxation technique for auxiliary variables and construct two numerical schemes based on EIEQ.The analysis results show that the newly constructed schemes are not only unconditionally energy stable,linear and fully decoupled,but also can effectively correct the errors introduced by auxiliary variables and follow the original energy law.Finally,several 2D and 3D numerical examples illustrate the accuracy and efficiency of the newly constructed numerical schemes.展开更多
this paper,we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process.As applications,the optimal uniform Berry-Esseen bound and optimal C...this paper,we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process.As applications,the optimal uniform Berry-Esseen bound and optimal Cramer-type moderate deviations of the Ornstein-Uhlenbeck process andα-Brownian bridge can be obtained.The main methods are the change of measure method and asymptotic analysis technique.展开更多
With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the in...With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the inverted pendulum model as an example,the algebraic Riccati equation is used to solve the optimal control problem,and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix.Then,the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems,with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration.Two methods for solving the Lyapunov equations are introduced,providing references for related research.展开更多
This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator ...This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.展开更多
In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome...In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.展开更多
In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimens...In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.展开更多
Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton...Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.展开更多
This study presents a numerical investigation of shallow water wave dynamics with particular emphasis on the role of surface tension.In the absence of surface tension,shallow water waves are primarily driven by gravit...This study presents a numerical investigation of shallow water wave dynamics with particular emphasis on the role of surface tension.In the absence of surface tension,shallow water waves are primarily driven by gravity and are well described by the classical Boussinesq equation,which incorporates fourth-order dispersion.Under this framework,solitary and shock waves arise through the balance of nonlinearity and gravity-induced dispersion,producing waveforms whose propagation speed,amplitude,and width depend largely on depth and initial disturbance.The resulting dynamics are comparatively smoother,with solitary waves maintaining coherent structures and shock waves displaying gradual transitions.When surface tension is incorporated,however,the dynamics become significantly richer.Surface tension introduces additional sixth-order dispersive terms into the governing equation,extending the classical model to the sixth-order Boussinesq equation.This higher-order dispersion modifies the balance between nonlinearity and dispersion,leading to sharper solitary wave profiles,altered shock structures,and a stronger sensitivity of wave stability to parametric variations.Surface tension effects also change the scaling laws for wave amplitude and velocity,producing conditions where solitary waves can narrow while maintaining large amplitudes,or where shock fronts steepen more rapidly compared to the tension-free case.These differences highlight how capillary forces,though often neglected in macroscopic wave studies,play a fundamental role in shaping dynamics at smaller scales or in systems with strong fluid–interface interactions.The analysis in this work is carried out using the Laplace-Adomian Decomposition Method(LADM),chosen for its efficiency and accuracy in solving high-order nonlinear partial differential equations.The numerical scheme successfully recovers both solitary and shock wave solutions under the sixth-order model,with error analysis confirming remarkably low numerical deviations.These results underscore the robustness of the method while demonstrating the profound contrast between shallow water wave dynamics without and with surface tension.展开更多
GPR has become an important geophysical method in UXO and landmine detection, for it can detect both metal and non-metallic targets. However, it is difficult to remove the strong clutters from surface-layer reflection...GPR has become an important geophysical method in UXO and landmine detection, for it can detect both metal and non-metallic targets. However, it is difficult to remove the strong clutters from surface-layer reflection and soil due to the low signal to noise ratio of GPR data. In this paper, we use the adaptive chirplet transform to reject these clutters based on their character and then pick up the signal from the UXO by the transform based on the Radon-Wigner distribution. The results from the processing show that the clutter can be rejected effectively and the target response can be measured with high SNR.展开更多
基金Lucian Blaga University of Sibiu&Hasso Plattner Foundation Research Grants LBUS-IRG-2020-06.
文摘New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.
文摘Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.
文摘The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.
文摘While antibiotic resistance is becoming increasingly serious today,there is almost no doubt that more challenging times await us in the future.Resistant microorganisms have increased in the past decades leading to limited treatment options,along with higher morbidity and mortality.Klebsiella pneumoniae is one of the significant microorganisms causing major public health problems by acquiring resistance to antibiotics and acting as an opportunistic pathogen of healthcare-associated infections.The production of extended spectrumbeta-lactamases(ESBL)is one of the resistance mechanisms of K.pneumoniae against antibiotics.In this study,the future clinical situation of ESBL-producing K.pneumoniae was investigated in order to reflect the future scenarios to understand the severity of the issue and to determine critical points to prevent the spread of the ESBL-producing strain.For evaluation purposes,SIS-type mathematical modeling was used with retrospective medical data from the period from 2016 to 2019.Stability of the disease-free equilibrium and basic reproduction ratios were calculated.Numerical simulation of the SISmodel was conducted to describe the dynamics of non-ESBL and ESBL-producing K.pneumoniae.In order to determine the most impactful parameter on the basic reproduction ratio,sensitivity analysis was performed.A study on mathematical modeling using data on ESBL-producing K.pneumoniae strains has not previously been performed in any health institution in Northern Cyprus,and the efficiency of the parameters determining the spread of the relevant strains has not been investigated.Through this study,the spread of ESBL-producing K.pneumoniae in a hospital environment was evaluated using a different approach.According to the study,in approximately seventy months,ESBL-producing K.pneumoniae strains will exceed non-ESBL K.pneumoniae strains.As a result,the analyses showed that hospital admissions and people infected with non-ESBL or ESBL-producing K.pneumoniae have the highest rate of spreading the infections.In addition,it was observed that the use of antibiotics plays a major role in the spread of ESBL-producing K.pneumoniae compared to other risk factors such as in-hospital transmissions.As amatter of course,recoveries fromKlebsiella infections were seen to be the most effective way of limiting the spread.It can be concluded from the results that although the use of antibiotics is one of themost effective factors in the development of the increasing ESBL-producing K.pneumoniae,regulation of antibiotic use policy could be a remedial step together with effective infection control measures.Such steps may hopefully lead to decreased morbidity and mortality rates as well as improved medical costs.
文摘From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.
基金Supported by National Natural Science Foundation of China(11871305,11901346).
文摘In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy estimation,we obtain that the trivial solution u=Q=0 is the unique solution.Our theorems correspond to improvements of some recent results and contain some known results as particular cases.
基金supported by the National Natural Science Foundation of China under Grant No.12147115the Discipline(Subject)Leader Cultivation Project of Universities in Anhui Province under Grant Nos.DTR2023052 and DTR2024046+2 种基金the Natural Science Research Project of Universities in Anhui Province under Grant No.2024AH040202the Young Top Notch Talents and Young Scholars of High End Talent Introduction and Cultivation Action Project in Anhui Provincethe Scientific Research Foundation Funded Project of Chuzhou University under Grant Nos.2022qd022 and 2022qd038。
文摘In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.
基金Supported by the National Natural Science Foundation of China(Grant No.12261017)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022ZCZX077)。
文摘In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.
文摘We propose a fractional-order improved Fitz Hugh–Nagumo(FHN)neuron model in terms of a generalized Caputo fractional derivative.Following the existence of a unique solution for the proposed model,we derive the numerical solution using a recently proposed L1 predictor–corrector method.The given method is based on the L1-type discretization algorithm and the spline interpolation scheme.We perform the error and stability analyses for the given method.We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns,chaotic patterns,and quasi-periodic patterns.The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics,which are inherent to many biological systems.
基金supported by the National Natural Science Foundation of China(11871305).
文摘In this paper,we study the Cauchy problem of three-dimensional incompressible magnetohydrodynamics with almost symmetrical initial values in the cylindrical coordinates.Here the almost axisymmetric means that(■θu_(0)^(r),■θeu_(0)^(θ),■θeu_(θ)^(z))is small.With additional smallness assumption on(u_(0)^(θ),b_(0)^(θ)),we prove the global existence of a unique strong solution(u,b),which keeps close to some axisymmetric vector fields.Moreover,we give the initial data with some special symmetric structures that will persist for all time.
基金Supported by the National Natural Science Foundation of China(11871305)。
文摘this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(2)(R^(3),p,q,r∈(3,∞],and 1/p+1/q+1/r≥2/3, which extends some known results.
基金Supported by the National Natural Science Foundation of China(Grant No.11901100)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022XSXMB11).
文摘It is well known that the explicit-invariant energy quadratization(EIEQ)approach can generate fully decoupled,linear and unconditionally energy-stable numerical schemes,so it is favored by many researchers.However,the undeniable fact is that the numerical method obtained by EIEQ approach preserves the“modified”energy law instead of the original energy.This is mainly due to the introduction of some auxiliary variables in EIEQ scheme,and the truncation error will make the auxiliary variables deviate from the original definition in the process of numerical calculation.The primary objective of this paper is to address this gap by providing the accuracy and consistency of the EIEQ method in the context of the CahnHilliard equation.We introduce a relaxation technique for auxiliary variables and construct two numerical schemes based on EIEQ.The analysis results show that the newly constructed schemes are not only unconditionally energy stable,linear and fully decoupled,but also can effectively correct the errors introduced by auxiliary variables and follow the original energy law.Finally,several 2D and 3D numerical examples illustrate the accuracy and efficiency of the newly constructed numerical schemes.
基金supported by the NSFC(12101358,12471095)the Natural Science Foundation of Hubei Province in China(2024AFC020)the Fundamental Research Funds for the Central Universities,South-Central MinZu University(CZY23010)。
文摘this paper,we study the exponential non-uniform Berry-Esseen bound for the maximum likelihood estimator of some time inhomogeneous diffusion process.As applications,the optimal uniform Berry-Esseen bound and optimal Cramer-type moderate deviations of the Ornstein-Uhlenbeck process andα-Brownian bridge can be obtained.The main methods are the change of measure method and asymptotic analysis technique.
基金Supported by National Natural Science Foundation of China(Grant No.12571388)the Visiting Scholar Program of National Natural Science Foundation of China(Grant No.12426616)Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications(Grant No.NY223127).
文摘With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the inverted pendulum model as an example,the algebraic Riccati equation is used to solve the optimal control problem,and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix.Then,the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems,with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration.Two methods for solving the Lyapunov equations are introduced,providing references for related research.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1236108412001130)。
文摘This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.
基金supported by the NSFC(11301297)the Hubei Provincial Natural Science Foundation of China(2024AFB730)+3 种基金the Yichang City Natural Science Foundation(A-24-3-008)the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(NAA2024ORG003)Gu's research was supported by the Zhejiang Provincial Natural Science Foundation(LQ21A010014)the NFSC(12101577).
文摘In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.
基金Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.
文摘Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.
文摘This study presents a numerical investigation of shallow water wave dynamics with particular emphasis on the role of surface tension.In the absence of surface tension,shallow water waves are primarily driven by gravity and are well described by the classical Boussinesq equation,which incorporates fourth-order dispersion.Under this framework,solitary and shock waves arise through the balance of nonlinearity and gravity-induced dispersion,producing waveforms whose propagation speed,amplitude,and width depend largely on depth and initial disturbance.The resulting dynamics are comparatively smoother,with solitary waves maintaining coherent structures and shock waves displaying gradual transitions.When surface tension is incorporated,however,the dynamics become significantly richer.Surface tension introduces additional sixth-order dispersive terms into the governing equation,extending the classical model to the sixth-order Boussinesq equation.This higher-order dispersion modifies the balance between nonlinearity and dispersion,leading to sharper solitary wave profiles,altered shock structures,and a stronger sensitivity of wave stability to parametric variations.Surface tension effects also change the scaling laws for wave amplitude and velocity,producing conditions where solitary waves can narrow while maintaining large amplitudes,or where shock fronts steepen more rapidly compared to the tension-free case.These differences highlight how capillary forces,though often neglected in macroscopic wave studies,play a fundamental role in shaping dynamics at smaller scales or in systems with strong fluid–interface interactions.The analysis in this work is carried out using the Laplace-Adomian Decomposition Method(LADM),chosen for its efficiency and accuracy in solving high-order nonlinear partial differential equations.The numerical scheme successfully recovers both solitary and shock wave solutions under the sixth-order model,with error analysis confirming remarkably low numerical deviations.These results underscore the robustness of the method while demonstrating the profound contrast between shallow water wave dynamics without and with surface tension.
基金This work was supported by U.S. Department of Defense Science Research Fund （Grant No. DAAD 19-03-1-0375） and the National Natural Science Foundation of China （Grant No. 40774055）.
文摘GPR has become an important geophysical method in UXO and landmine detection, for it can detect both metal and non-metallic targets. However, it is difficult to remove the strong clutters from surface-layer reflection and soil due to the low signal to noise ratio of GPR data. In this paper, we use the adaptive chirplet transform to reject these clutters based on their character and then pick up the signal from the UXO by the transform based on the Radon-Wigner distribution. The results from the processing show that the clutter can be rejected effectively and the target response can be measured with high SNR.
