In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).A...In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.展开更多
Concerned that fewer than 20%of adolescents meet the World Health Organization(WHO)’s physical activity(PA)guidelines of engaging in≥60 min each day of the week of moderate-to-vigorous PA(MVPA),classifying them as i...Concerned that fewer than 20%of adolescents meet the World Health Organization(WHO)’s physical activity(PA)guidelines of engaging in≥60 min each day of the week of moderate-to-vigorous PA(MVPA),classifying them as insufficiently active,1 Araujo et al.2 sought to identify the global prevalence of adolescents reporting less frequent MVPA(≥60 min per day of MVPA≥1 days per week)and identify differences in this prevalence by age,gender.展开更多
Background:Congenital heart disease(CHD)remains a significant global health concern,with considerable heterogeneity across age groups,genders,and regions.Objective:This study aimed to investigate the global epidemiolo...Background:Congenital heart disease(CHD)remains a significant global health concern,with considerable heterogeneity across age groups,genders,and regions.Objective:This study aimed to investigate the global epidemiological patterns,inequalities,and socio-demographic determinants of CHD burden from 1990 to 2021 to inform targeted interventions.Methods:We utilized data from the Global Burden of Disease 2021 study to assess CHD prevalence,incidence,and mortality rates.Trends were analyzed using Joinpoint regression,age-period-cohort models and autoregressive integrated moving average(ARIMA)forecasting.Health inequality was quantified using the slope index of inequality(SII)and the concentration index(CI),and associations with the Socio-Demographic Index(SDI)were explored.Results:CHD burden increased with age,peaking among individuals aged 70 years and older.This does not reflect new-onset disease,but rather the accumulation of late diagnoses,long-term complications,and healthcare encounters in aging individuals with CHD.Males consistently exhibited higher incidence and mortality rates than females.From 1990 to 2010,global age-standardized prevalence and incidence rates increased steadily and declined slightly thereafter.Joinpoint and age-period-cohort analyses revealed inflection points post-2010 and suggested cohort-related effects.Although SII trends indicated rising inequality over time,that disease burden has become more concentrated in low-SDI regions.ARIMA projections estimated a stable or marginally declining CHD burden by 2030.Regional analyses showed that high-SDI countries experienced significant reductions in CHD mortality,whereas low-SDI regions continued to bear a disproportionate burden.Conclusions:CHD burden has shifted in recent decades,influenced by demographic transitions,healthcare access,and socio-economic development.Despite progress,persistent health inequalities remain.Continued investment in early detection,maternal care,and public health infrastructure is essential to reduce CHD disparities globally.展开更多
By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several propertie...By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.展开更多
Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitr...Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.展开更多
The manuscript's authors examine some Milne-type inequalities for various function classes.Firstly,some Milne-type inequalities are established for diferentiable convex functions by using Riemann-Liouville integra...The manuscript's authors examine some Milne-type inequalities for various function classes.Firstly,some Milne-type inequalities are established for diferentiable convex functions by using Riemann-Liouville integrals.Secondly,we provide some fractional Milne-type inequalities for bounded functions by fractional integrals.Afterwards,we ofer several Milne-type inequalities for Lipschitzian functions.Likewise,we ofers Milne-type inequalities by fractional integrals of bounded variation.Finally,we demonstrate the correctness of our results by using special cases and examples of the obtained theorems.展开更多
In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by ...In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.展开更多
Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all re...Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all real numbers N1_(1)and N_(2)satisfying N_(1)>N_(1)^((0)),N_(2)>N_(2)^((0))andα≤N_(2)/N_(1)^(d=c)≤β,the system of two Diophantine inequalities|p_^(1)+…+p_(6)^(c)-N_(1)|<N_(1)^(−(1=c)(14=13−c))logN_(1),|p_(1)^(d)+…+p_(6)^(d)|N_(2)^(−(1=d)(14=13−d))logN_(2)has solutions in prime variables p_(1)…,p6.展开更多
In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which gi...In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.展开更多
In this paper, we point out a fault in Theorem B in , generalize Hua Wang type inequalities given by Theorem A in , and prove them by using elementary mean value inequalities. It also makes the improved Theorem B its...In this paper, we point out a fault in Theorem B in , generalize Hua Wang type inequalities given by Theorem A in , and prove them by using elementary mean value inequalities. It also makes the improved Theorem B its corollary.展开更多
In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmoni...In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmonic Prékopa-Leindler inequality is used.We prove that these new inequalities are more efficient in estimating the variance and entropy for some functions with exponential terms.展开更多
In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field...In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.展开更多
In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat eq...In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.展开更多
Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient c...Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.展开更多
We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan d...We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.展开更多
A parametrization of density matrices of ddimensions in terms of the raising J+and lowering J−angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann paramete...A parametrization of density matrices of ddimensions in terms of the raising J+and lowering J−angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta j1and j2is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the X-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel’son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell’s inequality.展开更多
Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
In this study,we propose a novel method for establishing Milne’s rule-type inequalities within the context of quantum calculus applied to differentiable convex functions.Initially,we obtain a quantum integral identit...In this study,we propose a novel method for establishing Milne’s rule-type inequalities within the context of quantum calculus applied to differentiable convex functions.Initially,we obtain a quantum integral identity,which serves as the foundation for deriving several new Milne’s rule inequalities tailored for quantum differentiable convex functions.These inequalities are particularly relevant in Open-Newton’s Cotes formulas,facilitating the determination of bounds for Milne’s rule in both classical and q-calculus domains.Additionally,we conduct computational analysis on these inequalities for convex functions and present mathematical examples and graphical representation to demonstrate the validity of our newly established results within the realm of q-calculus.展开更多
Dear Editor,The global population of individuals aged 65 and older is projected to reach 1.6 billion by 2050[1].Given that urinary tumors,such as bladder cancer(BCa),kidney cancer(KCa),and prostate cancer(PCa),are mor...Dear Editor,The global population of individuals aged 65 and older is projected to reach 1.6 billion by 2050[1].Given that urinary tumors,such as bladder cancer(BCa),kidney cancer(KCa),and prostate cancer(PCa),are more common in older adults,the burden on the healthcare system is increasing[2].Recently,Zi et al.[3]conducted a comprehensive assessment of the global burden of 6 urinary diseases from 1990 to 2021,based on the Global Burden of Diseases,Injuries,and Risk Factors Study 2021.展开更多
This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we esta...This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.展开更多
基金supported by the National Natural Science Foundation of China(12371327)the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0107).
文摘In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.
文摘Concerned that fewer than 20%of adolescents meet the World Health Organization(WHO)’s physical activity(PA)guidelines of engaging in≥60 min each day of the week of moderate-to-vigorous PA(MVPA),classifying them as insufficiently active,1 Araujo et al.2 sought to identify the global prevalence of adolescents reporting less frequent MVPA(≥60 min per day of MVPA≥1 days per week)and identify differences in this prevalence by age,gender.
文摘Background:Congenital heart disease(CHD)remains a significant global health concern,with considerable heterogeneity across age groups,genders,and regions.Objective:This study aimed to investigate the global epidemiological patterns,inequalities,and socio-demographic determinants of CHD burden from 1990 to 2021 to inform targeted interventions.Methods:We utilized data from the Global Burden of Disease 2021 study to assess CHD prevalence,incidence,and mortality rates.Trends were analyzed using Joinpoint regression,age-period-cohort models and autoregressive integrated moving average(ARIMA)forecasting.Health inequality was quantified using the slope index of inequality(SII)and the concentration index(CI),and associations with the Socio-Demographic Index(SDI)were explored.Results:CHD burden increased with age,peaking among individuals aged 70 years and older.This does not reflect new-onset disease,but rather the accumulation of late diagnoses,long-term complications,and healthcare encounters in aging individuals with CHD.Males consistently exhibited higher incidence and mortality rates than females.From 1990 to 2010,global age-standardized prevalence and incidence rates increased steadily and declined slightly thereafter.Joinpoint and age-period-cohort analyses revealed inflection points post-2010 and suggested cohort-related effects.Although SII trends indicated rising inequality over time,that disease burden has become more concentrated in low-SDI regions.ARIMA projections estimated a stable or marginally declining CHD burden by 2030.Regional analyses showed that high-SDI countries experienced significant reductions in CHD mortality,whereas low-SDI regions continued to bear a disproportionate burden.Conclusions:CHD burden has shifted in recent decades,influenced by demographic transitions,healthcare access,and socio-economic development.Despite progress,persistent health inequalities remain.Continued investment in early detection,maternal care,and public health infrastructure is essential to reduce CHD disparities globally.
文摘By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.
文摘Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.
文摘The manuscript's authors examine some Milne-type inequalities for various function classes.Firstly,some Milne-type inequalities are established for diferentiable convex functions by using Riemann-Liouville integrals.Secondly,we provide some fractional Milne-type inequalities for bounded functions by fractional integrals.Afterwards,we ofer several Milne-type inequalities for Lipschitzian functions.Likewise,we ofers Milne-type inequalities by fractional integrals of bounded variation.Finally,we demonstrate the correctness of our results by using special cases and examples of the obtained theorems.
文摘In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.
文摘Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all real numbers N1_(1)and N_(2)satisfying N_(1)>N_(1)^((0)),N_(2)>N_(2)^((0))andα≤N_(2)/N_(1)^(d=c)≤β,the system of two Diophantine inequalities|p_^(1)+…+p_(6)^(c)-N_(1)|<N_(1)^(−(1=c)(14=13−c))logN_(1),|p_(1)^(d)+…+p_(6)^(d)|N_(2)^(−(1=d)(14=13−d))logN_(2)has solutions in prime variables p_(1)…,p6.
文摘In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.
文摘In this paper, we point out a fault in Theorem B in , generalize Hua Wang type inequalities given by Theorem A in , and prove them by using elementary mean value inequalities. It also makes the improved Theorem B its corollary.
基金Supported in part by the NSFC(12071378,12461009)the Natural Science Basic Research Program of Shaanxi(2023-JC-YB-036)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSQ033).
文摘In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmonic Prékopa-Leindler inequality is used.We prove that these new inequalities are more efficient in estimating the variance and entropy for some functions with exponential terms.
文摘In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.
基金Partially supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province(Nos.KYCX22-2211,KYCX22-2205)。
文摘In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.
基金supported by the project Disuguaglianze analitiche e geometriche,funded by the Gruppo per Analisi Matematica la Probabilitàe le loro Applicazioni.
文摘Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.
文摘We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.
文摘A parametrization of density matrices of ddimensions in terms of the raising J+and lowering J−angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta j1and j2is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the X-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel’son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell’s inequality.
文摘Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
文摘In this study,we propose a novel method for establishing Milne’s rule-type inequalities within the context of quantum calculus applied to differentiable convex functions.Initially,we obtain a quantum integral identity,which serves as the foundation for deriving several new Milne’s rule inequalities tailored for quantum differentiable convex functions.These inequalities are particularly relevant in Open-Newton’s Cotes formulas,facilitating the determination of bounds for Milne’s rule in both classical and q-calculus domains.Additionally,we conduct computational analysis on these inequalities for convex functions and present mathematical examples and graphical representation to demonstrate the validity of our newly established results within the realm of q-calculus.
基金supported by the Chinese Scholarship Council(202206240086,202406240158).
文摘Dear Editor,The global population of individuals aged 65 and older is projected to reach 1.6 billion by 2050[1].Given that urinary tumors,such as bladder cancer(BCa),kidney cancer(KCa),and prostate cancer(PCa),are more common in older adults,the burden on the healthcare system is increasing[2].Recently,Zi et al.[3]conducted a comprehensive assessment of the global burden of 6 urinary diseases from 1990 to 2021,based on the Global Burden of Diseases,Injuries,and Risk Factors Study 2021.
文摘This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.
