MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

Efficacy and safety analysis of continued nursing of complications in discharged patients after percutaneous transhepatic biliary drainage

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.

China-ASEAN Environmental Cooperation Consensus on eco environmental protection outweighs differences with continued focus on four strategic areas

In response to the severe challenges posed by global climate change and the sustainable development goals of reaching peak carbon emissions and achieving carbon neutrality, green development has become a shared objective and necessity for economic growth and social transformation worldwide. China and the ASEAN countries share extensive common interests and positions on addressing climate change. Both have consistently emphasized green and sustainable development in their pursuit of shared prosperity. They have engaged in extensive practical cooperation in areas such as ecological conservation and clean energy.

Bangladeshi textile and garment sectors defied the global disasters and continued growth

Bangladeshi textile and garment sectors defied the global challenges over the last five years and continued to grow although the growth momentum was not so strong before the COVID-19 pandemic.Before the start of the pandemic,both the textile and garment sectors were growing at a higher rate because of rising demand from the international clothing retailers and brands because of two main reasons including the trade war between USA and China and competitive prices of locally made garment.

National Economy Continued to Recover in May

In May,the policies and measures to stabilize growth,employment and prices continued to take effect,the production and demand recovered steadily,employment and prices were generally stable,and transformation and upgrading was further advanced.The national economy sustained the recovery momentum.

Migration of Healthcare Professionals: Exploring Self-Perception about Midwifery Professional Life and Continued Education

Introduction: International migration has always existed, primarily as a means to find economic opportunity. Recently, the number of health care professionals seeking to work outside Albania is growing rapidly. In 2021 alone, 1073 nurses left Albania. The departure of health care professionals is reflected in education where it can be observed that a good part of the students who finished the bachelor’s level program did not enroll to continue the second level of study in the master’s. The student’s decision not to continue further levels of education has brought consequences from programs shutting down due to lack of students and forcing the university to spread out the few remaining students to other programs. Objective: The purpose of the study was to explore the opinions of Midwifery Students studying at the Bachelor level, regarding their professional future and continuing education. Methodology: This is a cross-sectional study. In this study are included the students of the bachelor level of education. Student participating are studying Midwifery in the 2022-2023 academic year, at the Faculty of Technical Medical Sciences at the University of Medicine, Albania. Results: The students on average believe they can find a job as a midwife. The career is relatively safe and the profession of midwifery will ensure economic well-being for them. Most of the students hope to emigrate and develop their professional career outside of Albania. This was a surprise given that most frequent answers given by the students for not continuing their Master’s level education was the fact that the program was not accredited, their Bachelor’s diploma was also not accredited and so not recognized by other countries, the cost of continuing their studies was too high and their desire for a better economic and social status which they cannot get in Albania. The majority of students participating in the study identified emigration as the main way they plan to further their studies. Conclusions and Recommendations: Although the students had willingly chosen to continue the midwifery diploma, as they thought it would provide them with a proper future, this dignified professional future was seen as unattainable in Albania so they are seeking it out in more developed countries. A significant number of health professionals prefer to continue their second cycle studies in another country. The professional security within their home country does not satisfy the students. As the market demand for nurses around the globe escalates, the changes and consequences associated with nurse migration are increasingly in need of policy solutions that will address the needs of all parties involved. .

The Convergence of 1-Periodic Branched Continued Fraction of the Special Form in Parabolic Regions

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.

ON THE CHOICES OF ACCELERATING CONVERGENCE FACTORS FOR LIMIT PERIODIC CONTINUED FRACTION K(an/1)

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.

ARBITRARILY LONG ARITHMETIC PROGRESSIONS FOR CONTINUED FRACTIONS OF LAURENT SERIES

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.

Physical activity, aging, and health in China: Addressing public health needs in the presence of continued economic growth and urbanization

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

GENE THERAPY (continued) Ⅱ. TECHNIQUES FOR GENE THERAPY

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

Chinese Herbal Medicine for Lung Cancer——A Critical Literature Review(Continued)

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.

MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

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)<∞}.

Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions

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.

The Limiting Case of Blending Differences for Bivariate Blending Continued Fraction Expansions

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.

Continued Fraction Evaluation of the Universal Y’s Functions

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).

AURICULOACUPUNCTURE THERAPY——A TRADITIONAL CHINESE METHOD OF TREATMENT(Continued)

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

Gravity Field Imaging by Continued Fraction Downward Continuation: A Case Study of the Nechako Basin(Canada)

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.

Continued Fraction Cartesian to Geodetic Coordinate Transformation

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.

A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS

In this article, a sufficient condition for a Clifford continued fraction to be convergent is established, and some applications are given.