In the paper [properties defined with semi-continuous functions and some related spaces＇, Houston J. Math., 2015, 41（3）： 1097-1106] properties （UL）m^wl, （UL）mK and （UL）m were defined and it was shown that sp...In the paper [properties defined with semi-continuous functions and some related spaces＇, Houston J. Math., 2015, 41（3）： 1097-1106] properties （UL）m^wl, （UL）mK and （UL）m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces, countably mesocompact spaces and countably metacompact spaces, respectively. In this paper, we continue with the study on the relationship between properties defined with real-valued functions and some covering properties. Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.展开更多
For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving function...For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.展开更多
In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition,...In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbound...Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.展开更多
The volume-time curve change in patients with normal left ventricular （LV） diastolic function and diastolic dysfunction was evaluated by real-time three-dimensional echocardiography （RT3DE）. LV diastolic dysfuncti...The volume-time curve change in patients with normal left ventricular （LV） diastolic function and diastolic dysfunction was evaluated by real-time three-dimensional echocardiography （RT3DE）. LV diastolic dysfunction was defined by E＇〈A＇ in pulse-wave tissue Doppler for inter-ventricular septal （IVS） of mitral annulus. In 24 patients with LV diastolic dysfunction, including 12 patients with delayed relaxation （delayed relaxation group） and 12 patients with pseudo-normal function （pseudo-normal group） and 24 normal volunteers （control group）, data of full-volume image were acquired by real-time three-dimensional echocardiography and subjected to volume-time curve analysis. EDV （end-diastolic volume）, ESV （end-systolic volume）, LVEF （left ventricular ejection fraction）, PER （peak ejection rate）, PFR （peak filling rate） from RT3DE were examined in the three groups. Compared to the control group, PFR （diastolic filling index of RT3DE） was significantly reduced in the delayed relaxation group and pseudo-normal group （P〈0.05）. There were no significant differences in EDV, ESV, LVEE PER （P〉0.05）. It is concluded that PFR, as a diastolic filling index of RT3DE, can reflect the early diastolic function and serve as a new non-invasive, quick and accurate tool for clinical assessment of LV diastolic function.展开更多
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su...In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.展开更多
AIM To define predictors of functional benefit of direct-acting antivirals(DAAs) in patients with chronic hepatitis C virus(HCV) infection and liver cirrhosis.METHODS We analysed a cohort of 199 patients with chronic ...AIM To define predictors of functional benefit of direct-acting antivirals(DAAs) in patients with chronic hepatitis C virus(HCV) infection and liver cirrhosis.METHODS We analysed a cohort of 199 patients with chronic HCV genotype 1, 2, 3 and 4 infection involving previously treated and untreated patients with compensated(76%) and decompensated(24%) liver cirrhosis at two tertiary centres in Germany. Patients were included withtreatment initiation between February 2014 and August 2016. All patients received a combination regimen of one or more DAAs for either 12 or 24 wk. Predictors of functional benefit were assessed in a univariable as well as multivariable model by binary logistic regression analysis.RESULTS Viral clearance was achieved in 88%(175/199) of patients. Sustained virological response(SVR) 12 rates were as follows: among 156 patients with genotype 1 infection the SVR 12 rate was 90%(n = 141); among 7 patients with genotype 2 infection the SVR 12 rate was 57%(n = 4); among 30 patients with genotype 3 infection the SVR 12 rate was 87%(n = 26); and among 6 patients with genotype 4 infection the SVR 12 rate was 67%(n = 4). Follow-up MELD scores were available for 179 patients. A MELD score improvement was observed in 37%(65/179) of patients, no change of MELD score in 41%(74/179) of patients, and an aggravation was observed in 22%(40/179) of patients. We analysed predictors of functional benefit from antiviral therapy in our patients beyond viral eradication. We identified the Child-Pugh score, the MELD score, the number of platelets and the levels of albumin and bilirubin as significant factors for functional benefit.CONCLUSION Our data may contribute to the discussion of potential risks and benefits of antiviral therapy with individual patients infected with HCV and with advanced liver disease.展开更多
Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wave...Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.展开更多
Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the la...Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the last results in the paper highlight analogies between algebraic identities for Hankelians with special entries and asymptotic relations valid for large classes of entries.展开更多
We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly de...We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.展开更多
Lars V.Ahlfors所著的《复分析》教材给出了已知实部或虚部求解析函数的直接方法,但是没有给出证明,且有较大的局限性,后来邵惠民先生在《数学物理方法》中利用线性变换的方法给出了证明,但是难于理解.本文则从解析函数的变量特点出发...Lars V.Ahlfors所著的《复分析》教材给出了已知实部或虚部求解析函数的直接方法,但是没有给出证明,且有较大的局限性,后来邵惠民先生在《数学物理方法》中利用线性变换的方法给出了证明,但是难于理解.本文则从解析函数的变量特点出发给出了易于理解的证明,进而提供了具体应用的例题.展开更多
Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximate...Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup>x </sup>) . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.展开更多
The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szego problem and some othe...The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szego problem and some other for a new subclass of analytic functions, which are defined here by means of linear operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.展开更多
In ordet to maintain the dependability of system and meet the functional needof users dtsire, this paper introduces a survivability mechanism into embedded real-time system,and proposes a general comprehensive, approa...In ordet to maintain the dependability of system and meet the functional needof users dtsire, this paper introduces a survivability mechanism into embedded real-time system,and proposes a general comprehensive, approach based on a rigorous definition of survivability. Thisapproach permits a trade-off between the function and the cost of system development. It emphasizesthe ultradependable implementation of crucial function without demanding that of entire system.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1140126211271178)
文摘In the paper [properties defined with semi-continuous functions and some related spaces＇, Houston J. Math., 2015, 41（3）： 1097-1106] properties （UL）m^wl, （UL）mK and （UL）m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces, countably mesocompact spaces and countably metacompact spaces, respectively. In this paper, we continue with the study on the relationship between properties defined with real-valued functions and some covering properties. Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.
基金supported by Kyungsung University Re-search Grants in 2013.
文摘For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374094 and 61503338)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.
文摘Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.
基金This project was supported by a grant from Guangdong Provincial Natural Sciences Foundation (No 05300738)
文摘The volume-time curve change in patients with normal left ventricular （LV） diastolic function and diastolic dysfunction was evaluated by real-time three-dimensional echocardiography （RT3DE）. LV diastolic dysfunction was defined by E＇〈A＇ in pulse-wave tissue Doppler for inter-ventricular septal （IVS） of mitral annulus. In 24 patients with LV diastolic dysfunction, including 12 patients with delayed relaxation （delayed relaxation group） and 12 patients with pseudo-normal function （pseudo-normal group） and 24 normal volunteers （control group）, data of full-volume image were acquired by real-time three-dimensional echocardiography and subjected to volume-time curve analysis. EDV （end-diastolic volume）, ESV （end-systolic volume）, LVEF （left ventricular ejection fraction）, PER （peak ejection rate）, PFR （peak filling rate） from RT3DE were examined in the three groups. Compared to the control group, PFR （diastolic filling index of RT3DE） was significantly reduced in the delayed relaxation group and pseudo-normal group （P〈0.05）. There were no significant differences in EDV, ESV, LVEE PER （P〉0.05）. It is concluded that PFR, as a diastolic filling index of RT3DE, can reflect the early diastolic function and serve as a new non-invasive, quick and accurate tool for clinical assessment of LV diastolic function.
文摘In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.
文摘AIM To define predictors of functional benefit of direct-acting antivirals(DAAs) in patients with chronic hepatitis C virus(HCV) infection and liver cirrhosis.METHODS We analysed a cohort of 199 patients with chronic HCV genotype 1, 2, 3 and 4 infection involving previously treated and untreated patients with compensated(76%) and decompensated(24%) liver cirrhosis at two tertiary centres in Germany. Patients were included withtreatment initiation between February 2014 and August 2016. All patients received a combination regimen of one or more DAAs for either 12 or 24 wk. Predictors of functional benefit were assessed in a univariable as well as multivariable model by binary logistic regression analysis.RESULTS Viral clearance was achieved in 88%(175/199) of patients. Sustained virological response(SVR) 12 rates were as follows: among 156 patients with genotype 1 infection the SVR 12 rate was 90%(n = 141); among 7 patients with genotype 2 infection the SVR 12 rate was 57%(n = 4); among 30 patients with genotype 3 infection the SVR 12 rate was 87%(n = 26); and among 6 patients with genotype 4 infection the SVR 12 rate was 67%(n = 4). Follow-up MELD scores were available for 179 patients. A MELD score improvement was observed in 37%(65/179) of patients, no change of MELD score in 41%(74/179) of patients, and an aggravation was observed in 22%(40/179) of patients. We analysed predictors of functional benefit from antiviral therapy in our patients beyond viral eradication. We identified the Child-Pugh score, the MELD score, the number of platelets and the levels of albumin and bilirubin as significant factors for functional benefit.CONCLUSION Our data may contribute to the discussion of potential risks and benefits of antiviral therapy with individual patients infected with HCV and with advanced liver disease.
文摘Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.
文摘Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the last results in the paper highlight analogies between algebraic identities for Hankelians with special entries and asymptotic relations valid for large classes of entries.
基金supported by the Faculty Research Project grant of DTU(DTU/Council/BOM-AC/Notification-/31/2018/5738)Research Fellowship from the Department of Science and Technology,New Delhi(IF170272)。
文摘We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.
文摘Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup>x </sup>) . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.
文摘The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szego problem and some other for a new subclass of analytic functions, which are defined here by means of linear operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.
文摘In ordet to maintain the dependability of system and meet the functional needof users dtsire, this paper introduces a survivability mechanism into embedded real-time system,and proposes a general comprehensive, approach based on a rigorous definition of survivability. Thisapproach permits a trade-off between the function and the cost of system development. It emphasizesthe ultradependable implementation of crucial function without demanding that of entire system.
