In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A ...In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.展开更多
In recent years,there has been a backlash of sorts and the authenticity of images has been routinely questioned.Seeing is no longer believing.There is an urgent need for robust image forensic techniques to expose phot...In recent years,there has been a backlash of sorts and the authenticity of images has been routinely questioned.Seeing is no longer believing.There is an urgent need for robust image forensic techniques to expose photo forgery.This paper proposed a novel and effective technique to expose image forgery using inconsistent reflection.More specifically,a new technique was presented to calculate reflection line midpoint,the definition of midpoint ratio was given,and three standards were proposed and employed to detect image forgery.Accuracy and effectiveness of the proposed technique were evaluated using a data set consisting of 200 authentic and forged images.Experimental results indicate that the proposed method can detect image forgery with very high success rate.展开更多
A new family of numerical integration formula is presented, which uses the function evaluation at the midpoint of the interval and odd derivatives at the endpoints. Because the weights for the odd derivatives sum to z...A new family of numerical integration formula is presented, which uses the function evaluation at the midpoint of the interval and odd derivatives at the endpoints. Because the weights for the odd derivatives sum to zero, the derivative calculations cancel out for the interior points in the composite form, so that these derivatives must only be calculated at the endpoints of the overall interval of integration. When using N subintervals, the basic rule which uses the midpoint function evaluation and the first derivative at the endpoints achieves fourth order accuracy for the cost of N/2 function evaluations and 2 derivative evaluations, whereas the three point open Newton-Cotes method uses 3N/4 function evaluations to achieve the same order of accuracy. These derivative-based midpoint quadrature methods are shown to be more computationally efficient than both the open and closed Newton-Cotes quadrature rules of the same order. This family of derivative-based midpoint quadrature rules are derived using the concept of precision, along with the error term. A theorem concerning the order of accuracy of quadrature rule using the concept of precision is provided to justify its use to determine the leading order error term.展开更多
BACKGROUND The midpoint transverse process to pleura(MTP)block,a novel technique for thoracic paravertebral block(TPVB),was first employed in laparoscopic renal cyst decortication.CASE SUMMARY Thoracic paravertebral n...BACKGROUND The midpoint transverse process to pleura(MTP)block,a novel technique for thoracic paravertebral block(TPVB),was first employed in laparoscopic renal cyst decortication.CASE SUMMARY Thoracic paravertebral nerve block is frequently employed for perioperative analgesia during laparoscopic cyst decortication.To address safety concerns associated with TPVBs,we administered MTP blocks in two patients prior to administering general anesthesia for laparoscopic cyst decortication.The MTP block was performed at the T9 level under ultrasound guidance,with 20 mL of 0.5%ropivacaine injected.Reduced sensation to cold and pinprick was observed from the T8 to T11 dermatome levels.Immediately postoperative Numeric Pain Rating Scale scores were 0/10 at rest and on movement,with none exceeding a mean 24 h numeric rating scale>3.CONCLUSION MTP block was effective technique for providing postoperative analgesia for patients undergoing laparoscopic renal cyst decortication.展开更多
In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending ...In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending on the number of subintervals ＂n＂ are calculated by using Maple 18 and presented. These results are demonstrated graphically in a particular numerical example. An algorithm of this application is given by using Maple 18.展开更多
基金supported by the National Natural Science Foundation of China(11671252)supported by the National Natural Science Foundation of China(11771278)
文摘In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.
基金Fundamental Research Funds for the Central Universities,China
文摘In recent years,there has been a backlash of sorts and the authenticity of images has been routinely questioned.Seeing is no longer believing.There is an urgent need for robust image forensic techniques to expose photo forgery.This paper proposed a novel and effective technique to expose image forgery using inconsistent reflection.More specifically,a new technique was presented to calculate reflection line midpoint,the definition of midpoint ratio was given,and three standards were proposed and employed to detect image forgery.Accuracy and effectiveness of the proposed technique were evaluated using a data set consisting of 200 authentic and forged images.Experimental results indicate that the proposed method can detect image forgery with very high success rate.
文摘A new family of numerical integration formula is presented, which uses the function evaluation at the midpoint of the interval and odd derivatives at the endpoints. Because the weights for the odd derivatives sum to zero, the derivative calculations cancel out for the interior points in the composite form, so that these derivatives must only be calculated at the endpoints of the overall interval of integration. When using N subintervals, the basic rule which uses the midpoint function evaluation and the first derivative at the endpoints achieves fourth order accuracy for the cost of N/2 function evaluations and 2 derivative evaluations, whereas the three point open Newton-Cotes method uses 3N/4 function evaluations to achieve the same order of accuracy. These derivative-based midpoint quadrature methods are shown to be more computationally efficient than both the open and closed Newton-Cotes quadrature rules of the same order. This family of derivative-based midpoint quadrature rules are derived using the concept of precision, along with the error term. A theorem concerning the order of accuracy of quadrature rule using the concept of precision is provided to justify its use to determine the leading order error term.
基金Supported by Self-funded Research Projects of Guangxi Zhuang Autonomous Region Health Commission of China,No.Z20210063。
文摘BACKGROUND The midpoint transverse process to pleura(MTP)block,a novel technique for thoracic paravertebral block(TPVB),was first employed in laparoscopic renal cyst decortication.CASE SUMMARY Thoracic paravertebral nerve block is frequently employed for perioperative analgesia during laparoscopic cyst decortication.To address safety concerns associated with TPVBs,we administered MTP blocks in two patients prior to administering general anesthesia for laparoscopic cyst decortication.The MTP block was performed at the T9 level under ultrasound guidance,with 20 mL of 0.5%ropivacaine injected.Reduced sensation to cold and pinprick was observed from the T8 to T11 dermatome levels.Immediately postoperative Numeric Pain Rating Scale scores were 0/10 at rest and on movement,with none exceeding a mean 24 h numeric rating scale>3.CONCLUSION MTP block was effective technique for providing postoperative analgesia for patients undergoing laparoscopic renal cyst decortication.
文摘In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending on the number of subintervals ＂n＂ are calculated by using Maple 18 and presented. These results are demonstrated graphically in a particular numerical example. An algorithm of this application is given by using Maple 18.
