Deformation Control Analysis of Unequal-Length Bridge Piles of Urban Rail Transit Tunnel Crossing Urban Expressway Elevated Bridge

Taking the viaduct project of the main road bridge of Fushi road between Jinding Street station and Jinanqiao Station of line 11 of Beijing subway as the background, due to geological reasons, the length of the pile of the main road bridge of Fushi road is 60m to the west of Xin’an road in the north, the pile length of the bridge east of North Xin’an road is 21.5m, and line 11 of Beijing subway passes between two piles of unequal length. This paper simulates the whole construction process with the method of numerical analysis, analyzes the causes of the deformation of the bridge piles by calculation, puts forward the measures of grouting reinforcement in the whole section, sums up the deformation rules of the unequal length bridge piles, and puts forward the deformation control values, in order to ensure the safety of Rail Transit Construction, for the follow-up similar projects to provide a basis and reference.

ELASTOPLASTIC PROBLEM FOR PERFORATED PLATE IN TRANSVERSE SHEAR

A solution is given to the problem of transverse shear of a thin plate clamped along the edges of the holes and weakened by a doubly periodic system of rectilinear through cracks with plastic end zones collinear to the abscissa and ordinate axes of unequal length. General representations of solutions are constructed that describe the class of problems with a doubly periodic stress distribution outside circular holes and rectilinear cracks with end zones of plastic deformations. Satisfying the boundary conditions, the solution of the problem of the theory of shear plates is reduced to two infinite systems of algebraic equations and two singular integral equations. Then each singular integral equation is reduced to a finite system of linear algebraic equations. Keywords: perforated thin plate, straight cracks with end zones, transverse bending, plastic deformation zones.

Rhythm (Exercises 41–60)

Rhythm in this chapter is conceived as the pace at which music unfolds in time. Note values, rests, and other sources of rhythmic notation are a way to control the temporal evolution of a new composition. Exercise 41 proposes a series of simple mathematical transformations to given rhythmic structures; 42 and 43 use segments of equal and unequal length. Numbers 44 and 45 incorporate the concept of non-retrogradable rhythmic structures, the goal of 46 is to extract the rhythm of a given text using its syllables and accents, 47 uses groupings to generate meter, and 48 uses a Morse code translator to extract the durations from a given text. Exercise 49 brings back the concept of rhythmic ostinato; 50 and 51 employ hemiolas. Number 52 is based on the use of several time signatures simultaneously (polymeter), 53 incorporates metric modulations, and 54 uses rhythmic motifs as building blocks. Number 55 continues with the use of motifs, shifting them in time. The concepts of talea and color from isorhythmic motets are included in exercise 56. Looping and composing using repeat signs are included in number 57; 58 is about indeterminate pauses and fermatas. Rhythmic transformations using eliminations are at the core of 59; exercise 60 proposes an experimentation with the perception of pulse.

Learning by Doing: The Use of Distance, Corners and Length in Rewarded Geometric Tasks by Zebrafish (Danio rerio)

Zebrafish spontaneously use distance and directional relationships among three-dimensional extended surfaces to reorient within a rectangular arena. However, they fail to take advantage of either an array of freestanding corners or an array of unequal-length surfaces to search for a no-longer-present goal under a spontaneous cued memory procedure, being unable to use the information supplied by corners and length without some kind of rewarded training. The present study aimed to tease apart the geometric components characterizing a rectangular enclosure under a procedure recruiting the reference memory, thus training zebrafish in fragmented layouts that provided differences in surface distance, corners, and length. Results showed that fish, besides the distance, easily learned to use both corners and length if subjected to a rewarded exit task over time, suggesting that they can represent all the geometrically informative parts of a rectangular arena when consistently exposed to them. Altogether, these findings highlight crucially important issues apropos the employment of different behavioral protocols (spontaneous choice versus training over time) to assess spatial abilities of zebrafish, further paving the way to deepen the role of visual and nonvisual encodings of isolated geometric components in relation to macrostructural boundaries.

Laparoscopic excision of congenital choledochal cyst in children and modified hepaticojejunostomy with an unequal length of the jejunal loop

Introduction: Complete excision biliary-enteric reconstruction is necessary for a congenital choledochal cyst (CC) to prevent recurrent cholangitis, acute pancreatitis, and cholangiocarcinoma. Among various reconstructions, this study aims to evaluate the therapeutic effect of unequal length jejunal loop for the biliary reconstruction of congenital choledochal cyst. Method: The clinical data of 56 cases of congenital choledochal cyst treated in the pediatric surgery department of Children's Hospital Affiliated to Zheng Zhou University were retrospectively analyzed. All cases were treated with choledochal cyst resection and unequal length jejunal loop biliary reconstruction, including 51 cases with laparoscopic surgery and 5 cases with traditional surgery. Result: Choledochal cyst resection and unequal length jejunal loop biliary reconstruction were successfully completed in all cases. One case of laparoscopic operation developed biliary fistula on the 3rd day after the operation, and the biliary fistula healed after conservative treatment for 8 days. The other cases recovered smoothly without obvious complications. No contrast agent bile loop reflux was found in upper gastrointestinal angiography. Conclusion: The modified jejunal loop biliary reconstruction has many advantages over the traditional biliary reconstruction, which is worthy of clinical application.

The evaluation of COVID-19 prediction precision with a Lyapunov-like exponent

In the field of machine learning, building models and measuring their performance are two equally important tasks. Currently, measures of precision of regression models’ predictions are usually based on the notion of mean error, where by error we mean a deviation of a prediction from an observation. However, these mean based measures of models’ performance have two drawbacks. Firstly, they ignore the length of the prediction, which is crucial when dealing with chaotic systems, where a small deviation at the beginning grows exponentially with time. Secondly, these measures are not suitable in situations where a prediction is made for a specific point in time (e.g. a date), since they average all errors from the start of the prediction to its end. Therefore, the aim of this paper is to propose a new measure of models’ prediction precision, a divergence exponent, based on the notion of the Lyapunov exponent which overcomes the aforementioned drawbacks. The proposed approach enables the measuring and comparison of models’ prediction precision for time series with unequal length and a given target date in the framework of chaotic phenomena. Application of the divergence exponent to the evaluation of models’ accuracy is demonstrated by two examples and then a set of selected predictions of COVID-19 spread from other studies is evaluated to show its potential.

The Pentateuch: Five Books, One Canon

This essay investigates the division of the Pentateuch into five scrolls of unequal length. It considers the dating of this division and the structuring that it creates, especially in relation to the Pentateuch’s narrative cycles; it also considers the ways that the combined text reflects its earlier compositional history. Finally, the essay considers the evidence for understanding each pentateuchal scroll/book as well as the Pentateuch overall as a literary unit. In the latter discussion, it gives special attention to the book of numbers.