The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a...The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a)), |M_n f-f(x)|≤M(x(1-x)/n+1/_n2)~a/2ω(f,t)=O(t^a), where otherwise.展开更多
The aim of the present paper is to prove direct and converse results for simultaneous approximation by modified Bernstein-Durrmeyer operators. A point-wise equivalence characterization of simultaneous approximation is...The aim of the present paper is to prove direct and converse results for simultaneous approximation by modified Bernstein-Durrmeyer operators. A point-wise equivalence characterization of simultaneous approximation is obtained.展开更多
In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Ba...In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Baskakov operators.展开更多
In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help ...In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.展开更多
The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrm...The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.展开更多
In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w(x)=x^a(1-x)β.All the results involved have no restriction a...In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w(x)=x^a(1-x)β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.展开更多
The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK...The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK(α,β)(x,y):=∑∞k=0 Ck(α,β)(x)Qk(α,β)(y),where Qk(α,β) (x) are the Jacobi polynomials of order k on (0, 1 ), Ck(α,β) 〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β (x, y).展开更多
As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong di...As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.展开更多
In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde...In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0¥ ( hk - 1 ) < + ¥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.展开更多
Della Vecchia et al. (see [2]) introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on [0,1]. In the present paper, we obtain a kind of pointwi...Della Vecchia et al. (see [2]) introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on [0,1]. In the present paper, we obtain a kind of pointwise Stechkin-type inequalities for weighted approximation by the modified Bemsetin operators.展开更多
We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators o...We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .展开更多
With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the...With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.展开更多
We modify Bernstein-Durrmeyer operators by means of digonal matarix which overeome a difficulty in extending a Berens-Lorentz result to the Bernstein-Durrmeyer operators for second order of smoothness. The direct and ...We modify Bernstein-Durrmeyer operators by means of digonal matarix which overeome a difficulty in extending a Berens-Lorentz result to the Bernstein-Durrmeyer operators for second order of smoothness. The direct and converse theorems for these operators in L_p are also presented by Ditzian-Totik, modulus of smoothness.展开更多
A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly wi...A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.展开更多
In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we ob...In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.展开更多
The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some gr...The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some graph operations, such as, composition, join, etc.展开更多
BACKGROUND The Fontan operation is the only treatment option to change the anatomy of the heart and help improve patients’ hemodynamics.After successful operation,patients typically recover the ability to engage in g...BACKGROUND The Fontan operation is the only treatment option to change the anatomy of the heart and help improve patients’ hemodynamics.After successful operation,patients typically recover the ability to engage in general physical activity.As a better ventilatory strategy,extracorporeal membrane oxygenation(ECMO) provides gas exchange via an extracorporeal circuit,and is increasingly being used to improve respiratory and circulatory function.After the modified Fontan operation,circulation is different from that of patients who are not subjected to the procedure.This paper describe a successful case using ECMO in curing influenza A infection in a young man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The special cardiac structure and circulatory characteristics are explored in this case.CASE SUMMARY We report a successful case using ECMO in curing influenza A infection in a 23-year-old man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The man was admitted to the intensive care unit with severe acute respiratory distress syndrome as a result of influenza A infection.He was initially treated by veno-venous(VV) ECMO,which was switched to veno-venous-arterial ECMO(VVA ECMO) 5 d later.As circulation and respiratory function gradually improved,the VVA ECMO equipment was removed on May 1,2018.The patient was successfully withdrawn from artificial ventilation on May 28,2018 and then discharged from hospital on May 30,2018.CONCLUSION After the modified Fontan operation,circulation is different compared with that of patients who are not subjected to the procedure.There are certainly many differences between them when they receive the treatment of ECMO.Due to the special cardiac structure and circulatory characteristics,an individualized liquid management strategy is necessary and it might be better for them to choose an active circulation support earlier.展开更多
The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta functio...The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta function and Bin-Saad generalized double zeta function as particular cases. The results are obtained by suitably applying Riemann-Liouville type and Tremblay fractional integral and differential operators. We derive the expansion formula for the proposed function with some of its properties via fractional operators and discuss the link with known results.展开更多
This is a case of a pancreatic tumor with invasion of the celiac stem treated using the modified Appleby operation.Preoperatively,routine B-ultrasound,computed tomography,and magnetic resonance imaging were performed....This is a case of a pancreatic tumor with invasion of the celiac stem treated using the modified Appleby operation.Preoperatively,routine B-ultrasound,computed tomography,and magnetic resonance imaging were performed.In the perioperative period,the combined gallbladder was excised;the duration of the operation was 5 h and volume of blood loss was approximately 500 ml.Postoperatively,the liver function temporarily returned and after a liver protection treatment,it returned to normal within 2 weeks.The liver had normal arterial blood supply,and the postoperative course was uneventful.It is safe and feasible to resect the whole pancreatic body and tail tumor combined with celiac stem resection.It can improve the resection rate of tumor and relieve pain.展开更多
文摘The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a)), |M_n f-f(x)|≤M(x(1-x)/n+1/_n2)~a/2ω(f,t)=O(t^a), where otherwise.
基金Supported by Natural Science Foundation of Zhejiang Province(102002)
文摘The aim of the present paper is to prove direct and converse results for simultaneous approximation by modified Bernstein-Durrmeyer operators. A point-wise equivalence characterization of simultaneous approximation is obtained.
基金Research supported by Council of ScientificIndustrial Research, India under award no.9/143(163)/91-EMR-1.
文摘In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Baskakov operators.
基金Supported by the NSF of P.R.China(10471130)the NSF of Zhejiang Province(Y604003)
文摘In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.
基金Supported by the Science Foundation of Zhejiang Province(Y604003)
文摘The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.
文摘In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w(x)=x^a(1-x)β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.
基金Supported by the National Natural Science Foundation of China (Grant No. 10871226)
文摘The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK(α,β)(x,y):=∑∞k=0 Ck(α,β)(x)Qk(α,β)(y),where Qk(α,β) (x) are the Jacobi polynomials of order k on (0, 1 ), Ck(α,β) 〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β (x, y).
基金Supported by Foundation of Key Item of Science and Technology of Education Ministry of China (03142)Foundation of Higher School of Ningxia (JY2002107)Nature Science Foundation of Zhejiang Province(102002).
文摘As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.
基金Supported both by the Teaching and Research Award Fund for Outstanding Young Teachers inHigher Educational Institutions of MOEChinaand by the Dawn Program Fund in Shanghai
文摘In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0¥ ( hk - 1 ) < + ¥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.
文摘Della Vecchia et al. (see [2]) introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on [0,1]. In the present paper, we obtain a kind of pointwise Stechkin-type inequalities for weighted approximation by the modified Bemsetin operators.
文摘We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .
基金Supported by the 2007 Year School Grade Plan Item of Inner Mongolia University for Nationalities(MDX2007030)
文摘With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.
基金supported by Zhejiang Provincial Foundation of China
文摘We modify Bernstein-Durrmeyer operators by means of digonal matarix which overeome a difficulty in extending a Berens-Lorentz result to the Bernstein-Durrmeyer operators for second order of smoothness. The direct and converse theorems for these operators in L_p are also presented by Ditzian-Totik, modulus of smoothness.
文摘A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.
文摘In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.
文摘The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some graph operations, such as, composition, join, etc.
基金Supported by the Capital Foundation of Medical Development,No. 2018-1-2171the Seedling Plan from the Beijing Ditan Hospital,Capital Medical University,No. DTYM201802。
文摘BACKGROUND The Fontan operation is the only treatment option to change the anatomy of the heart and help improve patients’ hemodynamics.After successful operation,patients typically recover the ability to engage in general physical activity.As a better ventilatory strategy,extracorporeal membrane oxygenation(ECMO) provides gas exchange via an extracorporeal circuit,and is increasingly being used to improve respiratory and circulatory function.After the modified Fontan operation,circulation is different from that of patients who are not subjected to the procedure.This paper describe a successful case using ECMO in curing influenza A infection in a young man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The special cardiac structure and circulatory characteristics are explored in this case.CASE SUMMARY We report a successful case using ECMO in curing influenza A infection in a 23-year-old man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The man was admitted to the intensive care unit with severe acute respiratory distress syndrome as a result of influenza A infection.He was initially treated by veno-venous(VV) ECMO,which was switched to veno-venous-arterial ECMO(VVA ECMO) 5 d later.As circulation and respiratory function gradually improved,the VVA ECMO equipment was removed on May 1,2018.The patient was successfully withdrawn from artificial ventilation on May 28,2018 and then discharged from hospital on May 30,2018.CONCLUSION After the modified Fontan operation,circulation is different compared with that of patients who are not subjected to the procedure.There are certainly many differences between them when they receive the treatment of ECMO.Due to the special cardiac structure and circulatory characteristics,an individualized liquid management strategy is necessary and it might be better for them to choose an active circulation support earlier.
文摘The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta function and Bin-Saad generalized double zeta function as particular cases. The results are obtained by suitably applying Riemann-Liouville type and Tremblay fractional integral and differential operators. We derive the expansion formula for the proposed function with some of its properties via fractional operators and discuss the link with known results.
文摘This is a case of a pancreatic tumor with invasion of the celiac stem treated using the modified Appleby operation.Preoperatively,routine B-ultrasound,computed tomography,and magnetic resonance imaging were performed.In the perioperative period,the combined gallbladder was excised;the duration of the operation was 5 h and volume of blood loss was approximately 500 ml.Postoperatively,the liver function temporarily returned and after a liver protection treatment,it returned to normal within 2 weeks.The liver had normal arterial blood supply,and the postoperative course was uneventful.It is safe and feasible to resect the whole pancreatic body and tail tumor combined with celiac stem resection.It can improve the resection rate of tumor and relieve pain.