BACKGROUND Cardiac sarcoidosis(CS)is an infiltrative disease with manifestations such as nonsustained ventricular tachycardia(NSVT)and heart failure(HF).Antiphospholipid syndrome(APS)and antiphospholipid positivity(AP...BACKGROUND Cardiac sarcoidosis(CS)is an infiltrative disease with manifestations such as nonsustained ventricular tachycardia(NSVT)and heart failure(HF).Antiphospholipid syndrome(APS)and antiphospholipid positivity(APP)are prothrombotic phenomena which elevate risk for thromboembolism.CS with active systemic sarcoid and APS/APP is a rare combination of diseases.CASE SUMMARY A 54 year old male with HF presented with several cardiopulmonary symptoms.Chest imaging showed bilateral patchy and reticulonodular infiltrates.Subsequent lung biopsy confirmed pulmonary sarcoidosis.Positron emission tomography revealed active systemic sarcoidosis(SS)and fibrotic CS.Positive antiphospholipid antibodies without thromboembolism confirmed APP.HF and APP were managed with medical therapy.Fibrotic CS and NSVT required permanent cardiac device and antiarrhythmic therapy.SS was managed with early taper of steroids and transition to biologics.CONCLUSION Fibrotic CS with active SS and APS/APP has not been previously described in literature.This case utilized a modified approach for the management of this combination of diseases.As immunosuppressants such as steroids have limited utility in fibrotic sarcoidosis and a potential for thromboembolic complications in the presence of APP,an accelerated transition to non-thrombotic immunosuppressants can be advantageous in the long term treatment of this combination of diseases.展开更多
To evaluate the apoptosis positivity, the expression of Bcl-2, bax proteinsin 30 patients with squamous cell cervix carcinoma before and after radiotherapy. Methods: By usingimmuno-histochemical and TDT-dUTP nick end ...To evaluate the apoptosis positivity, the expression of Bcl-2, bax proteinsin 30 patients with squamous cell cervix carcinoma before and after radiotherapy. Methods: By usingimmuno-histochemical and TDT-dUTP nick end labelling techniques, 30 cases of squamous cell cervicalcarcinoma were analyzed. Results: The apoptosis positivity before and after irradiation was 76.7%and 100% respectively, with the difference being significant (P 【 0.05); The positive rates of Bcl-2protein before and after irradiation were 73.3% and 46.7% respectively, with the difference beingsignificant (P 【 0.05); The positive rates of bax protein before and after irradiation were 86% and100% respectively, with the difference being significant (P 【 0.05). Conclusion: bax and Bcl-2protein play an important role in apoptosis induced by fractionated radiation therapy. Apoptosisinduced by irradiation is contributed to upregulation of bax protein or downregulation of Bcl-2protein.展开更多
A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By usi...A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By using a kind of special interpolation, the high resolution Boltzmann type difference scheme is constructed. Finally, numerical tests show that the schemes are effective and useful.展开更多
Convalescent plasma therapy has been implemented in a few cases of severe coronavirus disease 2019.No report about convalescent plasma therapy in treating patients with prolonged positivity of SARS-CoV-2 RNA has been ...Convalescent plasma therapy has been implemented in a few cases of severe coronavirus disease 2019.No report about convalescent plasma therapy in treating patients with prolonged positivity of SARS-CoV-2 RNA has been published.In this study,we conducted a retrospective observational study in 27 patients with prolonged positivity of SARS-CoV-2 RNA,the clinical benefit of convalescent plasma therapy were analyzed.q RT-PCR test of SARS-CoV-2 RNA turned negative(B 7 days)in a part of patients(early negative group,n=15)after therapy,others(late negative group,n=12)turned negative in more than 7 days.Pulmonary imaging improvement was confirmed in 7 patients in early negative group and 8 in late negative group after CP therapy.Viral load decreased in early negative group compared with late negative group at day 3,5,7 after implementing convalescent plasma therapy.Patients in early negative group had a shorter median length of hospital stay.In conclusion,convalescent plasma therapy might help eliminate virus and shorten length of hospital stay in patients with prolonged positivity of SARS-CoV-2 RNA.展开更多
With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+...With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.展开更多
The Wilson coefficients of the standard model effective field theory are subject to a series of positivity bounds.It has been shown that while the positivity part of the ultraviolet(UV)partial wave unitarity leads to ...The Wilson coefficients of the standard model effective field theory are subject to a series of positivity bounds.It has been shown that while the positivity part of the ultraviolet(UV)partial wave unitarity leads to the Wilson coefficients living in a convex cone,further including the nonpositivity part caps the cone from above.For Higgs scattering,a capped positivity cone was obtained using a simplified,linear unitarity condition without utilizing the full internal symmetries of Higgs scattering.Here,we further implement stronger nonlinear unitarity conditions from the UV,which generically gives rise to better bounds.We show that,for the Higgs case in particular,while the nonlinear unitarity conditions per se do not enhance the bounds,the fuller use of the internal symmetries do shrink the capped positivity cone significantly.展开更多
The prevalence of TB in sub-Sahara Africa has been reported as 511 per 100,000 populations and a mortality of 74 per 100,000 in year 2009. In the same period, incidence was estimated at 350 cases per 100,000. In this ...The prevalence of TB in sub-Sahara Africa has been reported as 511 per 100,000 populations and a mortality of 74 per 100,000 in year 2009. In the same period, incidence was estimated at 350 cases per 100,000. In this regard, the health system requires strengthening to respond to the rising cases of infection, drug resistance and quality of life lost while continuing to seek interventions that improve adherence to medication and case detection among those infected. Methods: This study sought to determine factors that are associated with sputum positivity after intensive phase of chemotherapy in people with tuberculosis. It was a retrospective case-control study conducted in Rhodes chest clinic, a City Council health unit in Nairobi that specializes in treatment of chest infections. The participants were sampled from clinic attendants who had completed two months of intensive phase TB chemotherapy and met inclusion criteria. Results: Seventy participants of whom 25 (36%) were sputum positive at the end of two (2) months intensive phase were included in the study. Skipping medication doses was significantly associated with sputum positivity (p = 0.01). Patients who were sputum positive at the end of the two-month period were more likely to have taken longer time before seeking treatment compared to those who were sputum negative by median (IQR) 8 (3 - 12) and 4 (3 - 8) weeks respectively although this difference was not significant (p = 0.09). Patients who had not disclosed their infection status had a two-fold possibility of remaining sputum positive at the end of intensive phase. Conclusion: Early diagnosis and treatment of TB, and adherence to medication were important factors that affect sputum conversion during intensive phase of TB treatment. Therefore, public health practitioners should advise patients to seek prompt diagnosis and treatment of signs and symptoms of tuberculosis.展开更多
Let E(x) = be an elementary operator on a C-algebra A. We prove that if A is prime with soc(A) = 0, or there is a family of irreducible representation of A such that is faithful and (A) does not contain compact operat...Let E(x) = be an elementary operator on a C-algebra A. We prove that if A is prime with soc(A) = 0, or there is a family of irreducible representation of A such that is faithful and (A) does not contain compact operator,or A has a faithful repre sentation π such that π(A)″with no central portions of type In for n>1 then E is positive if and only if E is completely positive.展开更多
Two studies examined the question of whether photograph taking of an event influences the positivity of the evaluations of the event at a later point in time.Memories of photographed events yielded higher positivity r...Two studies examined the question of whether photograph taking of an event influences the positivity of the evaluations of the event at a later point in time.Memories of photographed events yielded higher positivity ratings than memories that were not photographed.Although we expected fading of positivity ratings to occur more slowly over a period of two months for memories of photographed events,we found faster affect fading for those memories in Study 2 instead.The findings of the two studies support the idea that taking photographs of events sustains the affective reconstruction of autobiographical memories,regardless of whether these events are special,such as vacation memories,or more mundane,such as memories of the past weekend.展开更多
A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of th...A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.展开更多
The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ens...The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.展开更多
The aim of this paper is to introduce a new 2D fractional hybrid linear system described by the Roesser model with the conformable fractional derivative in the continuous time variables and the fractional difference i...The aim of this paper is to introduce a new 2D fractional hybrid linear system described by the Roesser model with the conformable fractional derivative in the continuous time variables and the fractional difference in the discrete part.The solution of the considered model is derived.The positivity conditions are then extracted and the Cayley±Hamilton theorem is extended.A new necessary and sufficient conditions for the asymptotic stability of the proposed positive fractional 2D hybrid linear model are then established.Finally,some numerical examples are presented to show the applicability and the effectiveness of the presented methods.展开更多
We develop a numerical method for the Keller-Segel chemotaxis system that is designed to(i)preserve the model’s fundamental structural properties(positivity/bound preservation,mass conservation,and energy dissipation...We develop a numerical method for the Keller-Segel chemotaxis system that is designed to(i)preserve the model’s fundamental structural properties(positivity/bound preservation,mass conservation,and energy dissipation),(ii)efficiently and accurately resolve the near-singular dynamics associated with spike formation and finite-time blow-up.Our approach combines a linear,positivity-preserving scalar auxiliary variable(SAV)scheme(following the framework in[15])with a Fourier spectral spatial discretization and an moving-mesh PDE-based method.The SAV reformulation provides a convenient platform for stable,linear time stepping while maintaining energy dissipation;the Fourier spectral discretization delivers high accuracy in smooth regions;and the moving-mesh PDE mesh redistribution concentrates collocation points in regions of large gradients so that sharp,localized structures can be resolved without prohibitive cost.We show that the proposed moving mesh SAV scheme inherits positivity preservation,mass conservation,and discrete energy dissipation provided the mesh motion avoids element overlap.Two-dimensional tests demonstrate the method’s ability to capture fine spike profiles and estimate blow-up times with substantially reduced computational effort;the formulation extends straightforwardly to three spatial dimensions.Numerical results show that the proposed method is a practical and effective method for accurate simulation of chemotactic aggregation.展开更多
Background Plasmodium vivax is the predominant malaria species in many Southeast Asian countries.Eliminating all human malaria species by 2030 requires greater focus on P.vivax,with targeted measures to address its un...Background Plasmodium vivax is the predominant malaria species in many Southeast Asian countries.Eliminating all human malaria species by 2030 requires greater focus on P.vivax,with targeted measures to address its unique challenges.This study evaluated slide positivity rates,temporal trends,and risk factors associated with febrile P.vivax infections in a malaria-endemic district along the Thailand-Myanmar border.Methods This study employed a community-based longitudinal surveillance design over six years(January 2018-December 2023).Data were collected through routine passive case detection at field malaria clinics using extended,standardized case record forms.Malaria diagnosis was conducted via microscopy examination.Descriptive statistics and logistic regression models were used for data analysis.Results Among 13,347 febrile malaria-suspected patients,the cumulative slide positivity rate for P.vivax was 11.0%.Although no distinct seasonal peaks were observed,P.vivax cases generally increased in April and again in November and December.Multivariable logistic regression analysis identified several significant risk factors for febrile P.vivax infection,including school-aged children(5-14 years)(aOR:1.56,95%CI:1.24-1.97),working-age adults(15-34 years)(aOR:1.43,95%CI:1.02-2.00),males(aOR:1.19,95%CI:1.06-1.35),Myanmar nationals(aOR:2.37,95%CI:2.01-2.80),and other non-Thai nationals,such as individuals from Laos and Cambodia(aOR:5.50,95%CI:3.36-8.90).A history of malaria(aOR:1.59,95%CI:1.38-1.83),recent travel within two weeks(aOR:2.38,95%CI:1.94-2.92),and engagement in livestock-related occupations(aOR:2.49,95%CI:1.14-5.35)were also associated with higher odds of infection.In contrast,being unemployed(aOR:0.55,95%CI:0.36-0.81),working in occupations such as maid,driver,or teacher(aOR:0.78,95%CI:0.66-0.93),and consistent use of bed nets(aOR:0.39,95%CI:0.30-0.51)significantly reduced infection risk.Conclusions This study identified a relatively high slide positivity rate of febrile P.vivax infection in a malaria-endemic district in western Thailand along the Myanmar border.Strengthening malaria surveillance,targeting high-risk populations,ensuring treatment adherence,and promoting early care-seeking behavior are crucial for reducing P.vivax transmission and advancing malaria elimination efforts.展开更多
The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-a...The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-associated with a pair of special standard processes which are in weak duality.展开更多
The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution wi...The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.展开更多
This article focuses on the positivity and the asymptotic stability of fractional-order linear time-delay systems(FOLTDSs)which are composed of N(N≥2)subsystems.Firstly,a sufficient and necessary condition is given t...This article focuses on the positivity and the asymptotic stability of fractional-order linear time-delay systems(FOLTDSs)which are composed of N(N≥2)subsystems.Firstly,a sufficient and necessary condition is given to ensure the positivity of FOLTDSs.The solutions of the studied systems are obtained by using the Laplace transform method,and it can be observed that the positivity of FOLTDSs is completely determined by the series of matrices and independent of the magnitude of time-delays.Secondly,a theorem is given to prove the asymptotic stability of positive FOLTDSs.By considering the monotonicity and asymptotic properties of systems with constant time-delay,it is further shown that the asymptotic stability of positive FOLTDSs is independent of the time-delay.Next,a state-feedback controller,whose gain matrix is derived by resolving a linear programming question,is designed such that the state variables of the systems are nonnegative and asymptotically convergent.When the order of the FOLTDSs is greater than one,by utilizing a proposed property of Caputo derivative,a sufficient condition for the positivity of FOLTDS is presented.Finally,simulation examples are presented to verify the validity and practicability of the theoretical analysis.展开更多
In this paper, we design a semi-implicit scheme for the scalar time fractional reaction-diffusion equation. We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time a...In this paper, we design a semi-implicit scheme for the scalar time fractional reaction-diffusion equation. We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes, and numerically show that the convergence orders are 1 in time and 2 in space. As a concrete model, the subdiffusive predator-prey system is discussed in detail. First, we prove that the analytical solution to the system is positive and bounded. Then, we use the provided numerical scheme to solve the subdiffusive predator-prey system, and theoretically prove and numerically verify that the numerical scheme preserves the positivity and boundedness.展开更多
Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Her...Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from the eventual positive-definiteness of an associated integral operator. Their arguments involve asymptotic expansions of the Bergman kernel. The goal of this article is to give an elementary proof of the positive-definiteness of this integral operator.展开更多
文摘BACKGROUND Cardiac sarcoidosis(CS)is an infiltrative disease with manifestations such as nonsustained ventricular tachycardia(NSVT)and heart failure(HF).Antiphospholipid syndrome(APS)and antiphospholipid positivity(APP)are prothrombotic phenomena which elevate risk for thromboembolism.CS with active systemic sarcoid and APS/APP is a rare combination of diseases.CASE SUMMARY A 54 year old male with HF presented with several cardiopulmonary symptoms.Chest imaging showed bilateral patchy and reticulonodular infiltrates.Subsequent lung biopsy confirmed pulmonary sarcoidosis.Positron emission tomography revealed active systemic sarcoidosis(SS)and fibrotic CS.Positive antiphospholipid antibodies without thromboembolism confirmed APP.HF and APP were managed with medical therapy.Fibrotic CS and NSVT required permanent cardiac device and antiarrhythmic therapy.SS was managed with early taper of steroids and transition to biologics.CONCLUSION Fibrotic CS with active SS and APS/APP has not been previously described in literature.This case utilized a modified approach for the management of this combination of diseases.As immunosuppressants such as steroids have limited utility in fibrotic sarcoidosis and a potential for thromboembolic complications in the presence of APP,an accelerated transition to non-thrombotic immunosuppressants can be advantageous in the long term treatment of this combination of diseases.
文摘To evaluate the apoptosis positivity, the expression of Bcl-2, bax proteinsin 30 patients with squamous cell cervix carcinoma before and after radiotherapy. Methods: By usingimmuno-histochemical and TDT-dUTP nick end labelling techniques, 30 cases of squamous cell cervicalcarcinoma were analyzed. Results: The apoptosis positivity before and after irradiation was 76.7%and 100% respectively, with the difference being significant (P 【 0.05); The positive rates of Bcl-2protein before and after irradiation were 73.3% and 46.7% respectively, with the difference beingsignificant (P 【 0.05); The positive rates of bax protein before and after irradiation were 86% and100% respectively, with the difference being significant (P 【 0.05). Conclusion: bax and Bcl-2protein play an important role in apoptosis induced by fractionated radiation therapy. Apoptosisinduced by irradiation is contributed to upregulation of bax protein or downregulation of Bcl-2protein.
文摘A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By using a kind of special interpolation, the high resolution Boltzmann type difference scheme is constructed. Finally, numerical tests show that the schemes are effective and useful.
基金supported by the Fundamental Research Funds for the Central Universities(2020kfyXGYJ092)。
文摘Convalescent plasma therapy has been implemented in a few cases of severe coronavirus disease 2019.No report about convalescent plasma therapy in treating patients with prolonged positivity of SARS-CoV-2 RNA has been published.In this study,we conducted a retrospective observational study in 27 patients with prolonged positivity of SARS-CoV-2 RNA,the clinical benefit of convalescent plasma therapy were analyzed.q RT-PCR test of SARS-CoV-2 RNA turned negative(B 7 days)in a part of patients(early negative group,n=15)after therapy,others(late negative group,n=12)turned negative in more than 7 days.Pulmonary imaging improvement was confirmed in 7 patients in early negative group and 8 in late negative group after CP therapy.Viral load decreased in early negative group compared with late negative group at day 3,5,7 after implementing convalescent plasma therapy.Patients in early negative group had a shorter median length of hospital stay.In conclusion,convalescent plasma therapy might help eliminate virus and shorten length of hospital stay in patients with prolonged positivity of SARS-CoV-2 RNA.
文摘With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.
基金supported by the Fundamental Research Funds for the Central Universities(WK2030000036)the National Natural Science Foundation of China(12075233).
文摘The Wilson coefficients of the standard model effective field theory are subject to a series of positivity bounds.It has been shown that while the positivity part of the ultraviolet(UV)partial wave unitarity leads to the Wilson coefficients living in a convex cone,further including the nonpositivity part caps the cone from above.For Higgs scattering,a capped positivity cone was obtained using a simplified,linear unitarity condition without utilizing the full internal symmetries of Higgs scattering.Here,we further implement stronger nonlinear unitarity conditions from the UV,which generically gives rise to better bounds.We show that,for the Higgs case in particular,while the nonlinear unitarity conditions per se do not enhance the bounds,the fuller use of the internal symmetries do shrink the capped positivity cone significantly.
文摘The prevalence of TB in sub-Sahara Africa has been reported as 511 per 100,000 populations and a mortality of 74 per 100,000 in year 2009. In the same period, incidence was estimated at 350 cases per 100,000. In this regard, the health system requires strengthening to respond to the rising cases of infection, drug resistance and quality of life lost while continuing to seek interventions that improve adherence to medication and case detection among those infected. Methods: This study sought to determine factors that are associated with sputum positivity after intensive phase of chemotherapy in people with tuberculosis. It was a retrospective case-control study conducted in Rhodes chest clinic, a City Council health unit in Nairobi that specializes in treatment of chest infections. The participants were sampled from clinic attendants who had completed two months of intensive phase TB chemotherapy and met inclusion criteria. Results: Seventy participants of whom 25 (36%) were sputum positive at the end of two (2) months intensive phase were included in the study. Skipping medication doses was significantly associated with sputum positivity (p = 0.01). Patients who were sputum positive at the end of the two-month period were more likely to have taken longer time before seeking treatment compared to those who were sputum negative by median (IQR) 8 (3 - 12) and 4 (3 - 8) weeks respectively although this difference was not significant (p = 0.09). Patients who had not disclosed their infection status had a two-fold possibility of remaining sputum positive at the end of intensive phase. Conclusion: Early diagnosis and treatment of TB, and adherence to medication were important factors that affect sputum conversion during intensive phase of TB treatment. Therefore, public health practitioners should advise patients to seek prompt diagnosis and treatment of signs and symptoms of tuberculosis.
文摘Let E(x) = be an elementary operator on a C-algebra A. We prove that if A is prime with soc(A) = 0, or there is a family of irreducible representation of A such that is faithful and (A) does not contain compact operator,or A has a faithful repre sentation π such that π(A)″with no central portions of type In for n>1 then E is positive if and only if E is completely positive.
文摘Two studies examined the question of whether photograph taking of an event influences the positivity of the evaluations of the event at a later point in time.Memories of photographed events yielded higher positivity ratings than memories that were not photographed.Although we expected fading of positivity ratings to occur more slowly over a period of two months for memories of photographed events,we found faster affect fading for those memories in Study 2 instead.The findings of the two studies support the idea that taking photographs of events sustains the affective reconstruction of autobiographical memories,regardless of whether these events are special,such as vacation memories,or more mundane,such as memories of the past weekend.
基金Supported by the National Science Foundation of China (60970079 and 60933008)
文摘A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.
文摘The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.
基金This paper presents research results of the ACSY-Team(Analysis&Control systems team)and of the doctorial training on the Operational Research from the Pure and Applied mathematics Laboratory,UMABDecision Support funded by the General Directorate for Scientific Research and Technological Development of Algeria(DGRSDT)+1 种基金supported by National Higher School of Mathematics(NHSM),University of Mostaganem Abdelhamid Ibn Badis(UMAB)initiated by the concerted research project on Control and Systems theory(PRFU Project Code C00L03UN270120200003)。
文摘The aim of this paper is to introduce a new 2D fractional hybrid linear system described by the Roesser model with the conformable fractional derivative in the continuous time variables and the fractional difference in the discrete part.The solution of the considered model is derived.The positivity conditions are then extracted and the Cayley±Hamilton theorem is extended.A new necessary and sufficient conditions for the asymptotic stability of the proposed positive fractional 2D hybrid linear model are then established.Finally,some numerical examples are presented to show the applicability and the effectiveness of the presented methods.
基金supported by the Hong Kong RGC Grant(Project No.17300325)by the Seed Funding Programme for Basic Research(HKU).
文摘We develop a numerical method for the Keller-Segel chemotaxis system that is designed to(i)preserve the model’s fundamental structural properties(positivity/bound preservation,mass conservation,and energy dissipation),(ii)efficiently and accurately resolve the near-singular dynamics associated with spike formation and finite-time blow-up.Our approach combines a linear,positivity-preserving scalar auxiliary variable(SAV)scheme(following the framework in[15])with a Fourier spectral spatial discretization and an moving-mesh PDE-based method.The SAV reformulation provides a convenient platform for stable,linear time stepping while maintaining energy dissipation;the Fourier spectral discretization delivers high accuracy in smooth regions;and the moving-mesh PDE mesh redistribution concentrates collocation points in regions of large gradients so that sharp,localized structures can be resolved without prohibitive cost.We show that the proposed moving mesh SAV scheme inherits positivity preservation,mass conservation,and discrete energy dissipation provided the mesh motion avoids element overlap.Two-dimensional tests demonstrate the method’s ability to capture fine spike profiles and estimate blow-up times with substantially reduced computational effort;the formulation extends straightforwardly to three spatial dimensions.Numerical results show that the proposed method is a practical and effective method for accurate simulation of chemotactic aggregation.
基金provided by Mahidol University.This study is financially supported by the National Institute of Allergy and Infectious Diseases(NIAID),National Institutes of Health(NIH),USA(U19AI089672,U19AI181583,and TW011509)support from Mahidol University。
文摘Background Plasmodium vivax is the predominant malaria species in many Southeast Asian countries.Eliminating all human malaria species by 2030 requires greater focus on P.vivax,with targeted measures to address its unique challenges.This study evaluated slide positivity rates,temporal trends,and risk factors associated with febrile P.vivax infections in a malaria-endemic district along the Thailand-Myanmar border.Methods This study employed a community-based longitudinal surveillance design over six years(January 2018-December 2023).Data were collected through routine passive case detection at field malaria clinics using extended,standardized case record forms.Malaria diagnosis was conducted via microscopy examination.Descriptive statistics and logistic regression models were used for data analysis.Results Among 13,347 febrile malaria-suspected patients,the cumulative slide positivity rate for P.vivax was 11.0%.Although no distinct seasonal peaks were observed,P.vivax cases generally increased in April and again in November and December.Multivariable logistic regression analysis identified several significant risk factors for febrile P.vivax infection,including school-aged children(5-14 years)(aOR:1.56,95%CI:1.24-1.97),working-age adults(15-34 years)(aOR:1.43,95%CI:1.02-2.00),males(aOR:1.19,95%CI:1.06-1.35),Myanmar nationals(aOR:2.37,95%CI:2.01-2.80),and other non-Thai nationals,such as individuals from Laos and Cambodia(aOR:5.50,95%CI:3.36-8.90).A history of malaria(aOR:1.59,95%CI:1.38-1.83),recent travel within two weeks(aOR:2.38,95%CI:1.94-2.92),and engagement in livestock-related occupations(aOR:2.49,95%CI:1.14-5.35)were also associated with higher odds of infection.In contrast,being unemployed(aOR:0.55,95%CI:0.36-0.81),working in occupations such as maid,driver,or teacher(aOR:0.78,95%CI:0.66-0.93),and consistent use of bed nets(aOR:0.39,95%CI:0.30-0.51)significantly reduced infection risk.Conclusions This study identified a relatively high slide positivity rate of febrile P.vivax infection in a malaria-endemic district in western Thailand along the Myanmar border.Strengthening malaria surveillance,targeting high-risk populations,ensuring treatment adherence,and promoting early care-seeking behavior are crucial for reducing P.vivax transmission and advancing malaria elimination efforts.
文摘The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-associated with a pair of special standard processes which are in weak duality.
基金The project is supported by NSFC(10371050,10571072)by the 985 program of Jilin University
文摘The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.
基金the National Natural Science Foundation of China under Grant Nos.61967001,12062004,and 11771263the Innovation Project of Guangxi University for Nationalities Graduate Education(gxun-chxps201908 and gxun-chxkc201903)the Guangxi Natural Science Foundation(2019GXNSFAA185007 and 2020GXNSFAA297240)。
文摘This article focuses on the positivity and the asymptotic stability of fractional-order linear time-delay systems(FOLTDSs)which are composed of N(N≥2)subsystems.Firstly,a sufficient and necessary condition is given to ensure the positivity of FOLTDSs.The solutions of the studied systems are obtained by using the Laplace transform method,and it can be observed that the positivity of FOLTDSs is completely determined by the series of matrices and independent of the magnitude of time-delays.Secondly,a theorem is given to prove the asymptotic stability of positive FOLTDSs.By considering the monotonicity and asymptotic properties of systems with constant time-delay,it is further shown that the asymptotic stability of positive FOLTDSs is independent of the time-delay.Next,a state-feedback controller,whose gain matrix is derived by resolving a linear programming question,is designed such that the state variables of the systems are nonnegative and asymptotically convergent.When the order of the FOLTDSs is greater than one,by utilizing a proposed property of Caputo derivative,a sufficient condition for the positivity of FOLTDS is presented.Finally,simulation examples are presented to verify the validity and practicability of the theoretical analysis.
基金supported by New Century Excellent Talents in University(Grant No.NCET-09-0438)National Natural Science Foundation of China(Grant Nos.10801067 and 11271173)the Fundamental Research Funds for the Central Universities(Grant Nos.lzujbky-2010-63 and lzujbky-2012-k26)
文摘In this paper, we design a semi-implicit scheme for the scalar time fractional reaction-diffusion equation. We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes, and numerically show that the convergence orders are 1 in time and 2 in space. As a concrete model, the subdiffusive predator-prey system is discussed in detail. First, we prove that the analytical solution to the system is positive and bounded. Then, we use the provided numerical scheme to solve the subdiffusive predator-prey system, and theoretically prove and numerically verify that the numerical scheme preserves the positivity and boundedness.
文摘Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from the eventual positive-definiteness of an associated integral operator. Their arguments involve asymptotic expansions of the Bergman kernel. The goal of this article is to give an elementary proof of the positive-definiteness of this integral operator.
