A NOTE ON MODIFIED BASKAKOV TYPE OPERATORS

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.

ON THE CONVERGENCE OF THE MODIFIED SZASZ-MIRAKJAN OPERATOR

A necessary and sufficient condition of convergence for the modified Szasz-Mirakjan operator is estab- lished.

SOME APPROXIMATION THEOREMS FOR MODIFIED BERNSTEIN-DURRMEYER OPERATORS

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.

On Weighted Approximation by Modified Bernstein Operators for Functions with Singularities

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.

Modeling on a Modified Feeding Mode of Simulated Moving Bed for Improving Productivity

A new feeding mode for a simulated moving bed(SMB) is proposed.The outlet stream from zone II is collected at regular intervals.The concentration of the solution is increased by dissolving raw materials and then fed to zone III as the feed stream during the next collection interval.In this feeding mode,the concentration of the stream fed to zone III is identical to that of original feed,while in a conventional SMB,the feed is diluted by mix-ing with the outlet stream of zone II before feeding to zone III.The new feeding mode increases the inlet concentra-tion of zone III.A modeling investigation shows that higher inlet concentration of zone III increases the height of concentration band in SMB,improving the separation performance significantly.In comparison with the traditonal feeding mode,the new feeding mode increases the productivity by 23.52%and decreases the solvent consumption by 22.56%,so as to increase the raffinate and extract concentrations by 53.17%and 20.38%,respectively.The col-lection interval for the outlet stream from zone II has no effect on the separation performance after reaching the steady state,so that the collection interval can be increased to make the operation more convenient.

Extracorporeal membrane oxygenation in curing a young man after modified Fontan operation:A case report

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.

ON CERTAIN PROPERTIES OF THE COMBINATIONS OF SZáSZ-DURRMEYER OPERATORS

In the present paper we study properties of Szaisz-Durrmeyer operators. These operators are introduced in [5] and generalize the integral operators proposed by S.M.Mazhar and V.Totik in [ 12]. We also generalize some results obtained by M. Heilmann[6] and D.-X. Zhou[16].

The applied value of modified POSSUM score in evaluating lung cancer surgery’s risk

Objective: The aim of this study was to explore the modified physiological and operative severity score for the enumeration of mortality and morbidity (POSSUM) scoring system and the relationship between predicted data and actual data of complication and surgical mortality of lung cancer radical surgery made by such score system. Methods: Retrospective analysis on the 86 cases of the clinical materials of patients with primary lung cancer radical surgery for thoracic surgery of line lung cancer in the 81st Hospital of PLA from October 2010 to October 2011 and using the POSSUM scoring system to predict the cases of postoperative complication and death toll, then making a comparison with the actual cases. Results: The POSSUM scoring system predicting 29 cases of postoperative complications, but 32 cases of practical complications, the difference between them has no statistical significance (P﹥0.05), 8 cases of predicted postoperative deaths, 2 cases of practical deaths, by comparison, there was statistical significance (P﹤0.05). Conclusion: The modified POSSUM scoring system can be used to predict the postoperative complication of lung surgery patients, but sometimes overestimates the postoperative death cases.

Modified Appleby operation for carcinoma of the pancreatic body and tail

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.

Strong Converse Inequality for Modified Szasz Operators

In this paper, we show the direct and converse theorems of strong type of approximation for modified Szasz operators. Rom these theorems, the characterization of approximation for these operators is derived. The obtained results are similar to the corresponding ones of the Szasz operators.

Simultaneous Approximation by Modified Bernstein-Durrmeyer Operators *

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.

H^m-Modified Wave Operator for Nonlinear Hartree Equation in Space of Dimension n≥2

We consider the scattering problem for the Hartree equation with potential|x|-1in a space of dimension n≥2.We prove the existence of Hm-modified wave operator for Hartree equation on a dense set of a neighborhood of zero in Hm（Rn）,meanwhile,we obtain also the global existence for the Cauchy problem of Hartree equation in a space of dimension n≥2.

New Subclasses of Biholomorphic Mappings and the Modified Roper-Suffridge Operator

The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B^n in C^n is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ_(G,γ)(f)](z) preserves the properties of S_Ω~*(A, B), as well as strong and almost spirallikeness of type β and order α on B^n. Thus, the mappings in S_Ω~*(A, B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.

Results of Fontan in Patients with Apicocaval Juxtaposition or/and Separated Hepatic Venous Drainage

Objective:Modifications of the Fontan operation,which are also known as total cavopulmonary connection(TCPC),are widely applied for patients with functionally univentricular hearts(FUH).Herein,we summed up the different surgical pathways and clinical outcomes in FUH patients with apicocaval juxtaposition(ACJ)or/and separated hepatic venous(SHV)drainage.Methods:Between January 2009 and December 2019,123 patients who undergone TCPC in our institute were included in this retrospective study.We have included 70 patients with ACJ(Group 1)and 53 patients with SHV(Group 2).Moreover,Group 2 included 17 cases combing with ACJ(32.1%).In Group 1,three different TCPC methods were conducted.While 45 cases were conducted with the extracardiac conduit-TCPC(EC-TCPC)method,24 cases used the intracardiac conduit-TCPC(IC-TCPC)method,and only one case used the lateral tunnel-TCPC(LT-TCPC).In Group 2,four TCPC methods were conducted on patients.Forty cases used the EC-TCPC-common open technique,6 cases with IC-TCPC technique,4 cases with LT-TCPC,and 3 cases with intra-extracardiac conduit-TCPC(IEC-TCPC).Results:There were 7 patients in Group 1 and 14 patients in Group 2 who required early re-operation during hospitalization(p<0.05).Postoperative mean pulmonary artery pressure(mPAP)greater than 15 mmHg emerged as a predictor for early re-operation(p<0.01)and early death(p<0.001)in univariate analysis.Conclusions:TCPC can be performed in these patients and shows beneficial results.Under the Fontan principle of connecting systemic venous to the pulmonary vasculature unimpededly,surgeons should carefully evaluate three components when choosing for the surgical technique:The distance between inferior vena cava(IVC)and the apex;the site of the vertebrae relative to the ACJ;the distance between ACJ and SHV if coexisting.However,the technique should be altered when the postoperative mPAP was greater than 15 mmHg.

Estimation of Energy Consumption in COREX Process Using a Modified Rist Operating Diagram

Fuel consumption in the COREX-3000 process run in Baosteel is currently higher than the design index. Therefore, mass and heat balance equations for the COREX process were established using the basic principles in- cluded in the Rist operating diagram for blast furnace （BF） as a reference. Thermodynamic calculations were then used to modify the Rist operating diagram so that it was suitable for the COREX process. The modified Rist operating dia- gram was then applied for the evaluation of metallization rate （MR） and fuel structure to reduce the energy consump- tion in the COREX process. The modified Rist operating diagram for the shaft furnace （SF） provided a nearly ideal value for the restriction point W when the metallization rate was increased, while the point P on the operating line for the melter gasifier （MG） moved upward due to reduction in the heat required in hearth. The feasibility of reduc- ing the energy consumption during the COREX process by changing the fuel structure was also demonstrated.

Modified Bentall procedure for aortic prosthetic detachment due to Behcet's disease

Background Severe aortic regurgitation is a rare clinical presentation of Behcet＇s disease,but the valve detachment after valve replacement presents challenges to cardiac surgeons.Methods Five patients with prosthetic detachment after aortic valve replacement attributable to Behcet＇s disease were surgically treated between January 2007 and December 2010.These 5 patients （all male） were from 24 to 50 years of age （mean,38.8 ± 9.8）.Mean follow-up duration from index operations was 19.2 ± 12.5 months （range,3-36 months）.Results There was no early death and pseudoaneurysm of the aortic root occurred at index operations.But one patient suffered Ⅲ° AVB and had pacemaker implanted.All the patients were administered immunosuppressive therapies after operation.Conclusion Modified Bentall operation and postoperative immunosuppressive therapy may be helpful for the patients with valve detachment after valve surgery due to Behcet＇s disease.

Pareto optimal allocation of fault current limiter based on immune algorithm considering cost and mitigation effect

This paper presents a multi-objective Pareto optimal method for allocation of fault current limiters based on an immune algorithm, which takes into account two objectives of the cost and fault current mitigation effect. A sensitivity factor calculation method based on the rate of fault current mitigation is proposed to reduce the search space and improve the efficiency of the algorithm.In this approach, the objective functions related to the cost and fault current mitigation effect are established. A modified inversion operator based on equal cost is proposed to converge to global optimal solutions more effectively. The proposed algorithm is tested on the IEEE39-bus system, and obtains the Pareto optimal solutions,from which the user can select the most suitable solutions according to the preferences and relative importance of the objective functions. Simulation results are used to verify the proposed method.

Scattering Map for the Vlasov-Poisson System

We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified wave operators,but we also obtain a new simple proof of modified scattering.Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system.Via a pseudo-conformal inversion,we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.