An Improved Indexing and Matching Method for Mathematical Expressions Based on Inter-Relevant Successive Tree

In recent years, a growing number of math contents are available on the Web. When conventional search engines deal with mathematical expressions, the two-dimen- sion-al structure of mathematical expressions is lost, which results in a low performance of math retrieval. While the retrieval technology specifically designed for mathematical expressions is not mature currently. Aiming at these problems, an improved mathematical expression indexing and matching method was proposed through employing full text index method to deal with the two-dimensional structure of mathematical expressions. Firstly, through the fully consideration of LaTeX formulae’ characteristics, a feature representation method of mathematical expressions and a clustering method of feature keywords were put forward. Then, an improved inter-relevant successive trees index model was applied to the construction of the mathematical expression index, in which the cluster algorithm of mathematical expression features was employed to solve the problem of the quantity growth of the trees in processing large amount of formulae. Finally, the matching algorithms of mathematical expressions were given which provide four query modes called exact matching, compatible matching, sub-expression matching and fuzzy matching. In browser/server mode, 110027 formulae were used as experimental samples. The index file size was 29.02 Mb. The average time of retrieval was 1.092 seconds. The experimental result shows the effectiveness of the method.

Structural Carpentry in Qing Dynasty-A Framework for the Hierarchically Modularized Chinese Timber Structural Design

This article, by using mathematical expressions, offers a scientific framework for understanding how the grading system of Qing′s structural carpentry determines the design and construction in the grand style timber architecture.The Qing′s grand style timber structure, which is ready for prefabrication and assembly, is extremely hierarchical oriented and significantly standardized. The general procedure in designing a grand style timber structure is to start with the grade that defines the basic module (dou kou); next comes with the number of bracket set (cuan), the number of longitudinal bays and the number of purlins which affect its plan and cross section; thirdly choose a roof type that determines its longitudinal section and the facade as well. A series of formulae are conducted to help depict the layout, cross sectional roof curvature and special longitudinal treatments in 4 sloped and 9 spined roofs respectively.

Computer-based Creativity Enhanced Conceptual Design Model for Non-routine Design of Mechanical Systems

Computer-based conceptual design for routine design has made great strides, yet non-routine design has not been given due attention, and it is still poorly automated. Considering that the function-behavior-structure（FBS） model is widely used for modeling the conceptual design process, a computer-based creativity enhanced conceptual design model（CECD） for non-routine design of mechanical systems is presented. In the model, the leaf functions in the FBS model are decomposed into and represented with fine-grain basic operation actions（BOA）, and the corresponding BOA set in the function domain is then constructed. Choosing building blocks from the database, and expressing their multiple functions with BOAs, the BOA set in the structure domain is formed. Through rule-based dynamic partition of the BOA set in the function domain, many variants of regenerated functional schemes are generated. For enhancing the capability to introduce new design variables into the conceptual design process, and dig out more innovative physical structure schemes, the indirect function-structure matching strategy based on reconstructing the combined structure schemes is adopted. By adjusting the tightness of the partition rules and the granularity of the divided BOA subsets, and making full use of the main function and secondary functions of each basic structure in the process of reconstructing of the physical structures, new design variables and variants are introduced into the physical structure scheme reconstructing process, and a great number of simpler physical structure schemes to accomplish the overall function organically are figured out. The creativity enhanced conceptual design model presented has a dominant capability in introducing new deign variables in function domain and digging out simpler physical structures to accomplish the overall function, therefore it can be utilized to solve non-routine conceptual design problem.

Influences affecting the soil-water characteristic curve

The soil-water characteristic curve (SWCC) is the primary partially saturated soil information as its behavior and properties can be derived from it. Although there have been many studies of unsaturated soils and the SWCC, there is still no combined constitutive model that can simulate soil characteristics accurately. In cases when hydraulic hysteresis is dominant (e.g. under cyclic loading) it is particularly important to use the SWCC. In the past decades, several mathematical expressions have been proposed to model the curve. There are various influences on the SWCC as a source of information, so the curves obtained from conventional tests often cannot be directly applied; and the mathematical expressions from one scenario cannot be used to simulate another situation. The effects of void ratio, initial water content, stress state and high suction were studied in this work revealing that water content and stress state are more important than the other effects; but that the influences tend to decrease when suction increases. The van Genuchten model was modified to simulate better the changes in the degree of saturation at low values of suction. Predictions were compared with experimental results to determine the simulation capability of the model.

A New Nonlinear Yield Criterion

Many experimental results show that a wide class of ductile materials obey often nonlinear behavior, thus it is important to propose a nonlinear criterion describing nonlinear behavior of ductile material. A new nonlinear yield criterion was proposed which gives a series of new failure criteria, establishes a relationship among various failure criteria, and encompasses previous yield criteria as special cases or approximations. The criterion is capable of being expressed in a simple mathematical expression and through a particular physical concept, it also agree with some experimental data. It may therefore serve as a possible admissible isotropic yield criterion.

Synthetic Data Generation and Shuffled Multi-Round Training Based Offline Handwritten Mathematical Expression Recognition

Offline handwritten mathematical expression recognition is a challenging optical character recognition(OCR)task due to various ambiguities of handwritten symbols and complicated two-dimensional structures.Recent work in this area usually constructs deeper and deeper neural networks trained with end-to-end approaches to improve the performance.However,the higher the complexity of the network,the more the computing resources and time required.To improve the performance without more computing requirements,we concentrate on the training data and the training strategy in this paper.We propose a data augmentation method which can generate synthetic samples with new LaTeX notations by only using the official training data of CROHME.Moreover,we propose a novel training strategy called Shuffled Multi-Round Training(SMRT)to regularize the model.With the generated data and the shuffled multi-round training strategy,we achieve the state-of-the-art result in expression accuracy,i.e.,59.74%and 61.57%on CROHME 2014 and 2016,respectively,by using attention-based encoder-decoder models for offline handwritten mathematical expression recognition.

The Abbreviated Symbol of Living Forms, Unit and Growth

This essay is written in the form of a mosaic. It intersperses simple language, primary and secondary quotes within text, footnotes and epigraphs from classical thinkers and cutting-edge researchers. It invites readers, be they casual or experienced, to a certain play of irony and fantasy in their reflection on the main thrust of the argument. The essay is divided into two parts. The first seeks to introduce the readers to some of the main concerns of frontier science and the Philosophy of Science at the beginning of this millennium： the Universe Models proposed by scientists from fields related to Physics and Mathematics in their eagerness to explain more and more discoveries and to lay out a solid new scientific paradigm. We are convinced that the leap between sidelines and insides--when confronting straightforward style with systematic contrast--does not lessen the rigor of research, and serves to lighten the density of the topic by projecting nuances and resonance onto the logos and its concatenation. It may also serve to vivify field and figure, in order to recreate the fertile delight that generally comes from a good reading of deep intertext.In the second part, we attempt to subtly demonstrate a fortunate discovery： the validity and solidity of the laws of Nature, upheld on the basis of their abstract mathematical expression （the Number Phi （φ）, the goldennumber or golden section）, which despite having faded into oblivion, buried under centuries of disuse in the fields of Aesthetics and Art, has proven to be useful as a critical instrument and a template for concrete solutions that we wish to share. We believe that this Model may serve not only to answer some of the scientific issues that we have referred to, but to redirect the discussion itself, and break the logjam of many frontier forums that place conditions on the application of the Models pro- duced over the last century. Having glimpsed those realms where analysis and common sense come together for addressing one of the most salient issues of our time, we chose to close the essay by offering practical, concrete findings on the topic of Models, which not only specialists in the field may find useful, but also any reader, especially educators, who are charged with sharing these findings with the present and future generations.