In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exac...In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.展开更多
We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bo...We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.展开更多
First of all, using the relations （2.3）, （2.4）, and （2.5）, we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators δ and δ on Kaehler manifolds w...First of all, using the relations （2.3）, （2.4）, and （2.5）, we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators δ and δ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace opeator is argued. Then, the Borel-Pompeiu formulas for W-valued functions are derived through designing a matrix Dirac operator D and a 2 × 2 matrix-valued invariant integral kernel with the Witt basis.展开更多
In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Lit...In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.展开更多
The purpose of the present paper is to introduce a new subclass of p-valent meromorphic functions by using certain integral operator and to investigate various properties for this subclass.
Abstract： Let L=-△＋V be a SchrSdinger operator on Rn, n 〉 3, where △ is the Laplacian on Rn and V ≠ 0 is a nonnegative function satisfying the reverse HSlder＇s inequality. Let [b, T] be the commutator generated...Abstract： Let L=-△＋V be a SchrSdinger operator on Rn, n 〉 3, where △ is the Laplacian on Rn and V ≠ 0 is a nonnegative function satisfying the reverse HSlder＇s inequality. Let [b, T] be the commutator generated by the Campanatotype function b ∈∧Lβ and the Riesz transform associated with SchrSdinger operator T =△↓（-△ ＋ V）-1/2. In the paper, we establish the boundedness of [b, T] on Lebesgue spaces and Campanato-type spaces.展开更多
We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±,...We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.展开更多
We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representat...We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.展开更多
AIM:To evaluate long-term survival after the Whipple operation with superior mesenteric vein/portal vein resection(SMV/PVR)in relation to resection length.METHODS:We evaluated 118 patients who underwent the Whipple op...AIM:To evaluate long-term survival after the Whipple operation with superior mesenteric vein/portal vein resection(SMV/PVR)in relation to resection length.METHODS:We evaluated 118 patients who underwent the Whipple operation for pancreatic adenocarcinoma at our Department of Hepatobiliary Pancreatic Surgery between 2005 and 2010.Fifty-eight of these patients were diagnosed with microscopic PV/SMV invasion by frozen-section examination and underwent SMV/PVR.In 28 patients,the length of SMV/PVR was≤3 cm.In the other 30 patients,the length of SMV/PVR was>3cm.Clinical and survival data were analyzed.RESULTS:SMV/PVR was performed successfully in 58patients.There was a significant difference between the two groups(SMV/PVR≤3 cm and SMV/PVR>3 cm)in terms of the mean survival time(18 mo vs 11 mo)and the overall 1-and 3-year survival rates(67.9%and14.3%vs 41.3%and 5.7%,P<0.02).However,there was no significant difference in age(64 years vs 58years,P=0.06),operative time(435 min vs 477 min,P=0.063),blood loss(300 mL vs 383 mL,P=0.071)and transfusion volume(85.7 mL vs 166.7 mL,P=0.084)between the two groups.CONCLUSION:Patients who underwent the Whipple operation with SMV/PVR≤3 cm had better long-term survival than those with>3 cm resection.展开更多
The operation of an ideal heat integrated distillation column (HIDiC) is addressed. Five kinds of control configurations, i.e. single-loop control, multi-loop control, multivariable internal model control (IMC), modif...The operation of an ideal heat integrated distillation column (HIDiC) is addressed. Five kinds of control configurations, i.e. single-loop control, multi-loop control, multivariable internal model control (IMC), modified multivariable internal model control (MIMC) and nonlinear process model-based control (NPMC), are designed and applied to the process. Simulation results demonstrate that all of the above control configurations are valid for product quality control. NPMC control configuration is found to be the best one among all the alternatives. It can readily realize setpoint transitions and conduct effectively against external disturbances. MIMC control configuration ranks second in the row for its regulatory responses to feed composition disturbances with relatively extended setting time. Next comes from the multi-loop control configuration, which is more or less handicapped by its greater deviations and overshootings. IMC control configuration can not compete with the multi-loop control configuration because it is extremely sensitive to operating condition changes. Single-loop control configuration is the worst one among all the mentioned control configurations. Its responses for the uncontrolled end products are extremely sluggish.展开更多
AIM:To explore the impact of tumor size on outcomes in patients with advanced gastric cancer in the lower third of the stomach.METHODS:We retrospectively analyzed the clinical records of 430 patients with advanced gas...AIM:To explore the impact of tumor size on outcomes in patients with advanced gastric cancer in the lower third of the stomach.METHODS:We retrospectively analyzed the clinical records of 430 patients with advanced gastric cancer in the lower third of the stomach who underwent distal subtotal gastrectomy and D2 lymphadenectomy in our hospital from January 1998 to June 2004.Receiver-operating characteristic(ROC)curve analysis was used to determine the appropriate cutoff value for tumor size,which was measured as maximum tumor diameter.Based on this cutoff value,patients were divided into two groups:those with large-sized tumors(LSTs)and those with small-sized tumors(SSTs).The correlations between other clinicopathologic factors and tumor size were investigated,and the 5-year overall survival(OS)rate was compared between the two groups.Potential prognostic factors were evaluated by univariate KaplanMeier survival analysis and multivariate Cox's propor-tional hazard model analysis.The 5-year OS rates in the two groups were compared according to pT stage and pN stage.RESULTS:The 5-year OS rate in the 430 patients with advanced gastric cancer in the lower third of the stomach was 53.7%.The mean±SD tumor size was 4.9±1.9 cm,and the median tumor size was 5.0 cm.ROC analysis indicated that the sensitivity and specificity results for the appropriate tumor size cutoff value of 4.8 cm were 80.0%and 68.2%,respectively(AUC=0.795,95%CI:0.751-0.839,P=0.000).Using this cutoff value,222 patients(51.6%)had LSTs(tumor size≥4.8 cm)and 208(48.4%)had SSTs(tumor size<4.8 cm).Tumor size was significantly correlated with histological type(P=0.039),Borrmann type(P=0.000),depth of tumor invasion(P=0.000),lymph node metastasis(P=0.000),tumor-nodes metastasis stage(P=0.000),mean number of metastatic lymph nodes(P=0.000)and metastatic lymph node ratio(P=0.000).Patients with LSTs had a significantly lower 5-year OS rate than those with SSTs(37.1%vs 63.3%,P=0.000).Univariate analysis showed that depth of tumor invasion(c 2=69.581,P=0.000),lymph node metastasis(c 2=138.815,P=0.000),tumor size(c 2=78.184,P=0.000)and metastatic lymph node ratio(c 2=139.034,P=0.000)were significantly associated with 5-year OS rate.Multivariate analysis revealed that depth of tumor invasion(P=0.000),lymph node metastasis(P=0.019)and tumor size(P=0.000)were independent prognostic factors.Gastric cancers were divided into 12 subgroups:pT2N0;pT2N1;pT2N2;pT2N3;pT3N0;pT3N1;pT3N2;pT3N3;pT4aN0;pT4aN1;pT4aN2;and pT4aN3.In patients with pT2-3N3 stage tumors and patients with pT4a stage tumors,5-year OS rates were significantly lower for LSTs than for SSTs(P<0.05 each),but there were no significant differences in the 5-year OS rates in LST and SST patients with pT23N0-2 stage tumors(P>0.05).CONCLUSION:Using a tumor size cutoff value of 4.8cm,tumor size is a prognostic factor in patients with pN3 stage or pT4a stage advanced gastric cancer located in the lower third of the stomach.展开更多
In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich-Forn^ess exponent and its relations with existence of domains with Levi-flat b...In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich-Forn^ess exponent and its relations with existence of domains with Levi-flat boundary in complex manifolds.展开更多
The Orc language is a concurrency calculus pro- posed to study the orchestration patterns in service oriented computing. Its special features, such as high concurrency and asynchronism make it a brilliant subject for ...The Orc language is a concurrency calculus pro- posed to study the orchestration patterns in service oriented computing. Its special features, such as high concurrency and asynchronism make it a brilliant subject for studying web applications that rely on web services. The conventional se- mantics for Orc does not contain the execution status of ser- vices so that a program cannot determine whether a service has terminated normally or halted with a failure after it pub- lished some results. It means that this kind of failure cannot be captured by the fault handler. Furthermore, such a seman- tic model cannot establish an order saying that a program is better if it fails less often. This paper employs UTP methods to propose a denotational semantic model for Orc that con- rains execution status information. A failure handling seman- tics is defined to recover a failure execution back to normal. A refinement order is defined to compare two systems based on their execution failures. Based on this order, a system that introduces a failure recovery mechanism is considered bet- ter than one without. An extended operational semantics is also proposed and proven to be equivalent to the denotational semantics.展开更多
基金supported by the National Natural Science Foundation of China (10901158)
文摘In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
基金supported by the National Science Centre of Poland within the project Opus 2013/09/B/ST1/02057
文摘We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.
基金Project supported in part by the National Natural Science Foundation of China (10771174,10601040,10971170)Scientific Research Foundation of Xiamen University of Technology (700298)
文摘First of all, using the relations （2.3）, （2.4）, and （2.5）, we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators δ and δ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace opeator is argued. Then, the Borel-Pompeiu formulas for W-valued functions are derived through designing a matrix Dirac operator D and a 2 × 2 matrix-valued invariant integral kernel with the Witt basis.
基金The Excellent Young Talent Foundation(2013SQRL080ZD)of Anhui Province
文摘In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.
文摘The purpose of the present paper is to introduce a new subclass of p-valent meromorphic functions by using certain integral operator and to investigate various properties for this subclass.
文摘Abstract： Let L=-△＋V be a SchrSdinger operator on Rn, n 〉 3, where △ is the Laplacian on Rn and V ≠ 0 is a nonnegative function satisfying the reverse HSlder＇s inequality. Let [b, T] be the commutator generated by the Campanatotype function b ∈∧Lβ and the Riesz transform associated with SchrSdinger operator T =△↓（-△ ＋ V）-1/2. In the paper, we establish the boundedness of [b, T] on Lebesgue spaces and Campanato-type spaces.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 11275123)the Key Project of Natural Science Fund of Anhui Province,China(Grant No.KJ2013A261)
文摘We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.
文摘We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.
文摘AIM:To evaluate long-term survival after the Whipple operation with superior mesenteric vein/portal vein resection(SMV/PVR)in relation to resection length.METHODS:We evaluated 118 patients who underwent the Whipple operation for pancreatic adenocarcinoma at our Department of Hepatobiliary Pancreatic Surgery between 2005 and 2010.Fifty-eight of these patients were diagnosed with microscopic PV/SMV invasion by frozen-section examination and underwent SMV/PVR.In 28 patients,the length of SMV/PVR was≤3 cm.In the other 30 patients,the length of SMV/PVR was>3cm.Clinical and survival data were analyzed.RESULTS:SMV/PVR was performed successfully in 58patients.There was a significant difference between the two groups(SMV/PVR≤3 cm and SMV/PVR>3 cm)in terms of the mean survival time(18 mo vs 11 mo)and the overall 1-and 3-year survival rates(67.9%and14.3%vs 41.3%and 5.7%,P<0.02).However,there was no significant difference in age(64 years vs 58years,P=0.06),operative time(435 min vs 477 min,P=0.063),blood loss(300 mL vs 383 mL,P=0.071)and transfusion volume(85.7 mL vs 166.7 mL,P=0.084)between the two groups.CONCLUSION:Patients who underwent the Whipple operation with SMV/PVR≤3 cm had better long-term survival than those with>3 cm resection.
文摘The operation of an ideal heat integrated distillation column (HIDiC) is addressed. Five kinds of control configurations, i.e. single-loop control, multi-loop control, multivariable internal model control (IMC), modified multivariable internal model control (MIMC) and nonlinear process model-based control (NPMC), are designed and applied to the process. Simulation results demonstrate that all of the above control configurations are valid for product quality control. NPMC control configuration is found to be the best one among all the alternatives. It can readily realize setpoint transitions and conduct effectively against external disturbances. MIMC control configuration ranks second in the row for its regulatory responses to feed composition disturbances with relatively extended setting time. Next comes from the multi-loop control configuration, which is more or less handicapped by its greater deviations and overshootings. IMC control configuration can not compete with the multi-loop control configuration because it is extremely sensitive to operating condition changes. Single-loop control configuration is the worst one among all the mentioned control configurations. Its responses for the uncontrolled end products are extremely sluggish.
文摘AIM:To explore the impact of tumor size on outcomes in patients with advanced gastric cancer in the lower third of the stomach.METHODS:We retrospectively analyzed the clinical records of 430 patients with advanced gastric cancer in the lower third of the stomach who underwent distal subtotal gastrectomy and D2 lymphadenectomy in our hospital from January 1998 to June 2004.Receiver-operating characteristic(ROC)curve analysis was used to determine the appropriate cutoff value for tumor size,which was measured as maximum tumor diameter.Based on this cutoff value,patients were divided into two groups:those with large-sized tumors(LSTs)and those with small-sized tumors(SSTs).The correlations between other clinicopathologic factors and tumor size were investigated,and the 5-year overall survival(OS)rate was compared between the two groups.Potential prognostic factors were evaluated by univariate KaplanMeier survival analysis and multivariate Cox's propor-tional hazard model analysis.The 5-year OS rates in the two groups were compared according to pT stage and pN stage.RESULTS:The 5-year OS rate in the 430 patients with advanced gastric cancer in the lower third of the stomach was 53.7%.The mean±SD tumor size was 4.9±1.9 cm,and the median tumor size was 5.0 cm.ROC analysis indicated that the sensitivity and specificity results for the appropriate tumor size cutoff value of 4.8 cm were 80.0%and 68.2%,respectively(AUC=0.795,95%CI:0.751-0.839,P=0.000).Using this cutoff value,222 patients(51.6%)had LSTs(tumor size≥4.8 cm)and 208(48.4%)had SSTs(tumor size<4.8 cm).Tumor size was significantly correlated with histological type(P=0.039),Borrmann type(P=0.000),depth of tumor invasion(P=0.000),lymph node metastasis(P=0.000),tumor-nodes metastasis stage(P=0.000),mean number of metastatic lymph nodes(P=0.000)and metastatic lymph node ratio(P=0.000).Patients with LSTs had a significantly lower 5-year OS rate than those with SSTs(37.1%vs 63.3%,P=0.000).Univariate analysis showed that depth of tumor invasion(c 2=69.581,P=0.000),lymph node metastasis(c 2=138.815,P=0.000),tumor size(c 2=78.184,P=0.000)and metastatic lymph node ratio(c 2=139.034,P=0.000)were significantly associated with 5-year OS rate.Multivariate analysis revealed that depth of tumor invasion(P=0.000),lymph node metastasis(P=0.019)and tumor size(P=0.000)were independent prognostic factors.Gastric cancers were divided into 12 subgroups:pT2N0;pT2N1;pT2N2;pT2N3;pT3N0;pT3N1;pT3N2;pT3N3;pT4aN0;pT4aN1;pT4aN2;and pT4aN3.In patients with pT2-3N3 stage tumors and patients with pT4a stage tumors,5-year OS rates were significantly lower for LSTs than for SSTs(P<0.05 each),but there were no significant differences in the 5-year OS rates in LST and SST patients with pT23N0-2 stage tumors(P>0.05).CONCLUSION:Using a tumor size cutoff value of 4.8cm,tumor size is a prognostic factor in patients with pN3 stage or pT4a stage advanced gastric cancer located in the lower third of the stomach.
基金supported by NSF(Grant No.DMS 1500952)supported by NSF(Grant No.DMS 1700003)
文摘In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich-Forn^ess exponent and its relations with existence of domains with Levi-flat boundary in complex manifolds.
基金This work was supported by the National High Tech- nology Research and Development Program of China （2012AA011205）, the National Natural Science Foundation of China （Grant Nos. 61361136002, 61321064 and 91118007）, Shanghai Knowledge Service Platform Project （ZF1213） and Shanghai Minhang Talent Project.
文摘The Orc language is a concurrency calculus pro- posed to study the orchestration patterns in service oriented computing. Its special features, such as high concurrency and asynchronism make it a brilliant subject for studying web applications that rely on web services. The conventional se- mantics for Orc does not contain the execution status of ser- vices so that a program cannot determine whether a service has terminated normally or halted with a failure after it pub- lished some results. It means that this kind of failure cannot be captured by the fault handler. Furthermore, such a seman- tic model cannot establish an order saying that a program is better if it fails less often. This paper employs UTP methods to propose a denotational semantic model for Orc that con- rains execution status information. A failure handling seman- tics is defined to recover a failure execution back to normal. A refinement order is defined to compare two systems based on their execution failures. Based on this order, a system that introduces a failure recovery mechanism is considered bet- ter than one without. An extended operational semantics is also proposed and proven to be equivalent to the denotational semantics.
