For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial...For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.展开更多
Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple ...Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.展开更多
There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given...There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.展开更多
A famous theorem of Szemer＇edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq（（X^-1）） be the power ...A famous theorem of Szemer＇edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq（（X^-1）） be the power field of formal series with coefficients lying in Fq. In this paper, we concern with the analogous Szemeredi problem for continued fractions of Laurent series： we will show that the set of points x ∈ Fq（（X-1）） of whose sequence of degrees of partial quotients is strictly increasing and contain arbitrarily long arithmetic progressions is of Hausdorff dimension 1/2.展开更多
Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=in...Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=inf{s≥0:∑n≥1an^(-s)(x)<∞}.展开更多
In the paper, firstly, based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form, scattered data interpolating schemes are constructed via bivariate continued fractions...In the paper, firstly, based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form, scattered data interpolating schemes are constructed via bivariate continued fractions with odd and even nodes, respectively. And equivalent identities are also obtained between interpolated functions and bivariate continued fractions. Secondly, by means of three-term recurrence relations for continued fractions, the characterization theorem is presented to study on the degrees of the numerators and denominators of the interpolating continued fractions. Thirdly, some numerical examples show it feasible for the novel recursive schemes. Meanwhile, compared with the degrees of the numera- tors and denominators of bivariate Thiele-typed interpolating continued fractions, those of the new bivariate interpolating continued fractions are much low, respectively, due to the reduc- tion of redundant interpolating nodes. Finally, the operation count for the rational function interpolation is smaller than that for radial basis function interpolation.展开更多
The significant increase in the number of older adults in China,coupled with continuing industrialization and urbanization,has profound social and economic ramifications,including the evolution of major challenges to ...The significant increase in the number of older adults in China,coupled with continuing industrialization and urbanization,has profound social and economic ramifications,including the evolution of major challenges to public health,elder care services,policy-making,and the nation’s healthcare system.While the unprecedented changes in political and economic structures have obviously increased China’s productivity and revenues,what is less well understood is how they展开更多
In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of...In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of variation of Poisson＇s ratio, the one-dimensional ultrasonic technique was adopted to detect the modulus development of concrete under continued hydration. The experimental results indicate the nonlinear characteristics of density and modulus evolution. At the initial stage of continued hydration, the density and modulus increase quickly, and then the increases slow down and finally tend to be constant. The mechanism of modulus enhancement is that the newly produced C-S-H gel in the continued hydration process not only leads to the decrease in porosity, but also repairs the initial defects of concrete. Based on this mechanism, simple differential equations for the density and modulus development of concrete were established by considering the chemical reactions of continued hydration, and new simple models for density and modulus development were proposed.展开更多
An essential prerequisite of any genetherapy technique is the efficient and stable de-livery of transferred DNA into the target cell.Avariety of techniques are available for directly in-troducing DNA into eukaryotic c...An essential prerequisite of any genetherapy technique is the efficient and stable de-livery of transferred DNA into the target cell.Avariety of techniques are available for directly in-troducing DNA into eukaryotic cells,includingcoprecipitation with calcium phosphate,electroporation and microinjection. The efficien-cy of most of these physical transfection tech-niques is less than one in ten thousand, and展开更多
Interpretation of gravity data plays an important role in the study of geologic structure and resource exploration in the deep part of the earth,like the lower crust,the upper mantle(Lüet al.,2013,2019).The gravi...Interpretation of gravity data plays an important role in the study of geologic structure and resource exploration in the deep part of the earth,like the lower crust,the upper mantle(Lüet al.,2013,2019).The gravity anomaly reflects the lateral resolution of the underground mass distribution.展开更多
CLINICAL STUDIES Clinical studies on Chinese herbal medicine(CHM)in lung cancer(LC)have largely been on anumber of basic formulae selected by syndrome(Zheng)differentiation,or specific formula basedon clinical experie...CLINICAL STUDIES Clinical studies on Chinese herbal medicine(CHM)in lung cancer(LC)have largely been on anumber of basic formulae selected by syndrome(Zheng)differentiation,or specific formula basedon clinical experience.There have also been anumber of studies comparing combination ofCHMs with either chemotherapy or radiotherapywith chemotherapy or radiotherapy alone,to as-sess any additional benefits or synergistic outcomesof the combination.展开更多
We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obta...We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obtained from the Laplacian block matrices by means of Gauss partial diagonalization procedure described explicitly by W. Neumann. The linking matrix is an important topological invariant of a graph manifold which is possible to interpret as a matrix of coupling constants of gauge interaction in Kaluza-Klein approach, where 3-dimensional graph manifold plays the role of internal space in topological 7-dimensional BF theory. The Gauss-Neumann method gives us a simple algorithm to calculate the linking matrices of graph manifolds and thus the coupling constants matrices.展开更多
BACKGROUND Percutaneous hepatobiliary drainage(PTCD)is an effective method for the treatment of biliary obstruction and other diseases,but postoperative complications are still one of the important problems faced by p...BACKGROUND Percutaneous hepatobiliary drainage(PTCD)is an effective method for the treatment of biliary obstruction and other diseases,but postoperative complications are still one of the important problems faced by patients.Continuous nursing is a comprehensive nursing model that plays an important role in postoperative recovery.The purpose of this study was to investigate the effect of continuous nursing on the incidence of complications in patients after PTCD surgery through meta-analysis and to evaluate its efficacy and safety.AIM To evaluate the effect of extended nursing on the incidence of complications in discharged patients after percutaneous transhepatic biliary drainage(PTBD).METHODS Randomized controlled studies on PTBD postdischarge extended care were identified in the CNKI,Wanfang,VIP,CBM,PubMed,Cochrane Library,Embase,Web of Science,and other databases.The quality of the included studies was evaluated using the Joanna Briggs Institute of Australia literature quality evaluation tool,and a meta-analysis of the included studies was performed with RevMan 5.4 software.RESULTS Finally,9 studies were included,with a total sample size of 854 patients(425 patients in the control group and 429 patients in the intervention group).Meta-analysis revealed that extended care effectively reduced biliary tract infection(RR:0.42,95%CI:0.30-0.57),puncture wound infection(RR:0.19,95%CI:0.06-0.65),catheter protrusion or displacement in discharged patients after PTBD(RR:0.31,95%CI:0.18-0.54),catheter blockage(RR:0.23,95%CI:0.13-0.42),skin infection around the drainage tube(RR:0.30,95%CI:0.12-0.77),and catheter-related readmissions(RR:0.34,95%CI:0.18-0.65)(P<0.05).CONCLUSION Compared with conventional discharge care,extended care can effectively reduce the occurrence of complications such as biliary tract infection,puncture wound infection,catheter prolapse or displacement,catheter blockage,skin infection around the drainage tube,and catheter-related readmission in discharged patients after PTBD.展开更多
For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by...For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods.展开更多
In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic...In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic).展开更多
CHRONIC CONSTIPATIONTREATED WITHAURICULOACUPUNCTUREChronic constipation is caused mainlyby irregular toilet habits or sluggishintestinal peristalsis,resulting in prolongedretention of feces which become dehydratedand ...CHRONIC CONSTIPATIONTREATED WITHAURICULOACUPUNCTUREChronic constipation is caused mainlyby irregular toilet habits or sluggishintestinal peristalsis,resulting in prolongedretention of feces which become dehydratedand hard and not excreted for days.Some-times the feces may not be very dry,but thedefecation muscles are too weak for展开更多
Europe was the gLobaL magnets center before World War Ⅱ. Afterwards, it had shifted to USA. Till Late 1960s, the center had moved to Japan. EventuaLLy, it moved to China at the beginning of 21st century. Magnet outpu...Europe was the gLobaL magnets center before World War Ⅱ. Afterwards, it had shifted to USA. Till Late 1960s, the center had moved to Japan. EventuaLLy, it moved to China at the beginning of 21st century. Magnet output in different countries （2005） is shown in Table 3.展开更多
A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work e...A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work explores the use of the satellite ground-track vector as the differential correction variable.The geodetic latitude is recovered by well-known elementary means.A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed.Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth’s surface,throughout the LEO-GEO range of applications.As a result,a single iteration of the continued fraction iteration yields a maximum error for the satellite height of 10??11 km.and maximum error for the geodetic anomaly of 10??9 rad.The coordinate transformation is completed by non-iteratively recovering the satellite height and the geodetic anomaly.No Taylor expansions are introduced and no Jacobian sensitivity calculations are required.For all practical applications the new algorithm provides a closed-form solution.The accuracy and algorithmic performance of the proposed approach is compared with other state of the art algorithms.展开更多
基金Supported by Projects from Chongqing Municipal Science and Technology Commission(CSTB2022NSCQ-MSX0445)。
文摘For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.
文摘Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.
基金Supported by the National Natural Science Foundation of china
文摘There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.
文摘A famous theorem of Szemer＇edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq（（X^-1）） be the power field of formal series with coefficients lying in Fq. In this paper, we concern with the analogous Szemeredi problem for continued fractions of Laurent series： we will show that the set of points x ∈ Fq（（X-1）） of whose sequence of degrees of partial quotients is strictly increasing and contain arbitrarily long arithmetic progressions is of Hausdorff dimension 1/2.
基金This research was supported by National Natural Science Foundation of China(11771153,11801591,11971195,12171107)Guangdong Natural Science Foundation(2018B0303110005)+1 种基金Guangdong Basic and Applied Basic Research Foundation(2021A1515010056)Kunkun Song would like to thank China Scholarship Council(CSC)for financial support(201806270091).
文摘Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=inf{s≥0:∑n≥1an^(-s)(x)<∞}.
基金Supported by the Special Funds Tianyuan for the National Natural Science Foundation of China(Grant No.11426086)the Fundamental Research Funds for the Central Universities(Grant No.2016B08714)the Natural Science Foundation of Jiangsu Province for the Youth(Grant No.BK20160853)
文摘In the paper, firstly, based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form, scattered data interpolating schemes are constructed via bivariate continued fractions with odd and even nodes, respectively. And equivalent identities are also obtained between interpolated functions and bivariate continued fractions. Secondly, by means of three-term recurrence relations for continued fractions, the characterization theorem is presented to study on the degrees of the numerators and denominators of the interpolating continued fractions. Thirdly, some numerical examples show it feasible for the novel recursive schemes. Meanwhile, compared with the degrees of the numera- tors and denominators of bivariate Thiele-typed interpolating continued fractions, those of the new bivariate interpolating continued fractions are much low, respectively, due to the reduc- tion of redundant interpolating nodes. Finally, the operation count for the rational function interpolation is smaller than that for radial basis function interpolation.
文摘The significant increase in the number of older adults in China,coupled with continuing industrialization and urbanization,has profound social and economic ramifications,including the evolution of major challenges to public health,elder care services,policy-making,and the nation’s healthcare system.While the unprecedented changes in political and economic structures have obviously increased China’s productivity and revenues,what is less well understood is how they
基金the financial support by the National Natural Science Foundation of China (NSFC#11772164,#11272165,#11572163)the National Basic Research Program of China (973 Program,2009CB623203)+2 种基金the Key Research Program of Society Development of Ningbo (2013C51007)the K.C.Wong Magna Fund in Ningbo Universitysupported by the Research Project Foundation of Zhejiang Educational Department (Y201636745)
文摘In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of variation of Poisson＇s ratio, the one-dimensional ultrasonic technique was adopted to detect the modulus development of concrete under continued hydration. The experimental results indicate the nonlinear characteristics of density and modulus evolution. At the initial stage of continued hydration, the density and modulus increase quickly, and then the increases slow down and finally tend to be constant. The mechanism of modulus enhancement is that the newly produced C-S-H gel in the continued hydration process not only leads to the decrease in porosity, but also repairs the initial defects of concrete. Based on this mechanism, simple differential equations for the density and modulus development of concrete were established by considering the chemical reactions of continued hydration, and new simple models for density and modulus development were proposed.
文摘An essential prerequisite of any genetherapy technique is the efficient and stable de-livery of transferred DNA into the target cell.Avariety of techniques are available for directly in-troducing DNA into eukaryotic cells,includingcoprecipitation with calcium phosphate,electroporation and microinjection. The efficien-cy of most of these physical transfection tech-niques is less than one in ten thousand, and
基金the National Natural Science Foundation(Grant nos.41904122,42004068)China Geological Survey’s project(Grant nos.DD20190012,DD20190435,and DD 20190129)+2 种基金the Special Project for Basic Scientific Research Service(Grant No.JKY202007)the Macao Young Scholars Program(Grant No.AM2020001)the Science and Technology Development Fund,Macao SAR
文摘Interpretation of gravity data plays an important role in the study of geologic structure and resource exploration in the deep part of the earth,like the lower crust,the upper mantle(Lüet al.,2013,2019).The gravity anomaly reflects the lateral resolution of the underground mass distribution.
文摘CLINICAL STUDIES Clinical studies on Chinese herbal medicine(CHM)in lung cancer(LC)have largely been on anumber of basic formulae selected by syndrome(Zheng)differentiation,or specific formula basedon clinical experience.There have also been anumber of studies comparing combination ofCHMs with either chemotherapy or radiotherapywith chemotherapy or radiotherapy alone,to as-sess any additional benefits or synergistic outcomesof the combination.
文摘We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obtained from the Laplacian block matrices by means of Gauss partial diagonalization procedure described explicitly by W. Neumann. The linking matrix is an important topological invariant of a graph manifold which is possible to interpret as a matrix of coupling constants of gauge interaction in Kaluza-Klein approach, where 3-dimensional graph manifold plays the role of internal space in topological 7-dimensional BF theory. The Gauss-Neumann method gives us a simple algorithm to calculate the linking matrices of graph manifolds and thus the coupling constants matrices.
文摘BACKGROUND Percutaneous hepatobiliary drainage(PTCD)is an effective method for the treatment of biliary obstruction and other diseases,but postoperative complications are still one of the important problems faced by patients.Continuous nursing is a comprehensive nursing model that plays an important role in postoperative recovery.The purpose of this study was to investigate the effect of continuous nursing on the incidence of complications in patients after PTCD surgery through meta-analysis and to evaluate its efficacy and safety.AIM To evaluate the effect of extended nursing on the incidence of complications in discharged patients after percutaneous transhepatic biliary drainage(PTBD).METHODS Randomized controlled studies on PTBD postdischarge extended care were identified in the CNKI,Wanfang,VIP,CBM,PubMed,Cochrane Library,Embase,Web of Science,and other databases.The quality of the included studies was evaluated using the Joanna Briggs Institute of Australia literature quality evaluation tool,and a meta-analysis of the included studies was performed with RevMan 5.4 software.RESULTS Finally,9 studies were included,with a total sample size of 854 patients(425 patients in the control group and 429 patients in the intervention group).Meta-analysis revealed that extended care effectively reduced biliary tract infection(RR:0.42,95%CI:0.30-0.57),puncture wound infection(RR:0.19,95%CI:0.06-0.65),catheter protrusion or displacement in discharged patients after PTBD(RR:0.31,95%CI:0.18-0.54),catheter blockage(RR:0.23,95%CI:0.13-0.42),skin infection around the drainage tube(RR:0.30,95%CI:0.12-0.77),and catheter-related readmissions(RR:0.34,95%CI:0.18-0.65)(P<0.05).CONCLUSION Compared with conventional discharge care,extended care can effectively reduce the occurrence of complications such as biliary tract infection,puncture wound infection,catheter prolapse or displacement,catheter blockage,skin infection around the drainage tube,and catheter-related readmission in discharged patients after PTBD.
基金The NNSF(10171026 and 60473114)of Chinathe Research Funds(2005TD03) for Young Innovation Group,Education Department of Anhui Province.
文摘For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods.
文摘In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic).
文摘CHRONIC CONSTIPATIONTREATED WITHAURICULOACUPUNCTUREChronic constipation is caused mainlyby irregular toilet habits or sluggishintestinal peristalsis,resulting in prolongedretention of feces which become dehydratedand hard and not excreted for days.Some-times the feces may not be very dry,but thedefecation muscles are too weak for
文摘Europe was the gLobaL magnets center before World War Ⅱ. Afterwards, it had shifted to USA. Till Late 1960s, the center had moved to Japan. EventuaLLy, it moved to China at the beginning of 21st century. Magnet output in different countries （2005） is shown in Table 3.
文摘A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work explores the use of the satellite ground-track vector as the differential correction variable.The geodetic latitude is recovered by well-known elementary means.A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed.Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth’s surface,throughout the LEO-GEO range of applications.As a result,a single iteration of the continued fraction iteration yields a maximum error for the satellite height of 10??11 km.and maximum error for the geodetic anomaly of 10??9 rad.The coordinate transformation is completed by non-iteratively recovering the satellite height and the geodetic anomaly.No Taylor expansions are introduced and no Jacobian sensitivity calculations are required.For all practical applications the new algorithm provides a closed-form solution.The accuracy and algorithmic performance of the proposed approach is compared with other state of the art algorithms.
