Handwritten Mathematical Expression Recognition (HMER) remains challenging because mathematical notation is both spatially structured and highly variable across writers. Existing methods either operate on offline raster images, thereby discarding pen-stroke dynamics, or rely on modular online pipelines in which segmentation and relation errors propagate downstream. We present STRAMER (Structural Tree-Aware Mathematical Expression Recognizer), an end-to-end multi-modal architecture that integrates a DenseNet image encoder and a BiLSTM stroke encoder through bidirectional cross-modal fusion, combines a coverage-augmented Transformer decoder with a tree-aware biaffine dependency module for explicit syntactic supervision, and appends a spatial relation head that yields a complete Stroke Label Graph (SLG). To ensure globally valid structure, tree decoding is performed with maximum spanning arborescence inference and SLG relation labels are obtained with constrained CRF decoding. The model is trained with a triple joint objective comprising sequence, tree, and relation losses. Over five independent runs, STRAMER achieves ExpRate on CROHME 2019 while additionally producing interpretable SLG outputs. We further report an inference latency of per expression on a single GPU and provide a full complexity analysis of the relation component. These results indicate that jointly modelling visual appearance, stroke dynamics, and explicit structure is a promising direction for robust HMER.
A high-precision spectral implementation framework is presented for computing eigenvalues of second- and fourth-order Sturm–Liouville problems on finite intervals. The framework employs the trigonometric substitution to assemble all derivative operations on Chebyshev polynomials entry-by-entry from closed-form trigonometric identities, bypassing the repeated matrix multiplication that causes the standard Chebyshev differentiation matrix (CDM) approach to accumulate roundoff at large , high derivative order, and in clustered spectral regimes. By reformulating the differential problem as a generalised eigenvalue system solved via the QZ algorithm, the framework combines numerical reliability with high-order geometric convergence. Multiple boundary conditions at the same endpoint are incorporated through a node-reduction procedure; an empirical condition-number study is included to characterise its stability. All numerical experiments are conducted in MATLAB at 34-digit precision, enabling eigenvalue errors at the level of and providing self-convergence verification independent of double-precision saturation. The framework is benchmarked across six problems including the Coffey–Evans equation and free vibration of exponentially functionally graded beams, demonstrating good accuracy beyond double-precision references.
Introduction: Dynamic capabilities implies the professional functions by which an organization initiates carrying out self-adjustment and self-improvement thereby improving the efficiency and growth of the organization itself. Higher education institutions can be described as complex adaptive systems that change their behaviour as needed in order to survive, thrive & avoid deterioration. HEI in developing countries are required to increase performance to enlarge their contribution to socio-economic development. Organizational capacity is considered a pre-requisite for this performance. Organizational dynamics is enhanced by capacity development processes and activities. Performance measures must be based on a set of objectives that are linked to the mission of the organisation and its vision for the future. Objectives: The research aims to find out the relationship between perception of the respondents on their organisational dynamics and performances and course stream. This study investigates the role of organizational dynamics in the performance of the respondents. Methods: Organisational Leadership & Organisational Culture was considered to be the precedents of Organisational Dynamics and Organisational Capacity, Organisational Competency, Organisational Environment, Organisational Development and Organisational Motivation were taken as the measures of Organisational Dynamics. The primary data were collected through questionnaire and analysed using statistical tools. Results: Based on SEM analysis using data from 203 respondents studying in arts and science colleges in Tirunelveli, it is shown that that measures of Organisational Dynamics has a mediating role on the performance of students. Conclusions: The study aimed at analysing the influence of measures of organisational dynamics on the performance of students specifically academic and research performance. It opens ground for further research in the dimension of the relationship between organisational dynamics and faculty performance which is relatively focussed less.
To investigate the effects of side ratio and turbulent characteristics on the spatial correlation of along-wind fluctuating wind loads on rectangular tall buildings,synchronization pressure wind tunnel tests for rectangular tall buildings with side ratios ranging from 1/9～9 were carried out in four wind fields.Based on the experimental findings,the coherence function and vertical correlation coefficient of along-wind fluctuating wind loads were examined in relation to the effects of side ratio,turbulence intensity,and turbulence integral scale.The mathematical model of vertical correlation of rectangular high-rise buildings with a side ratio of 1/9～9 was obtained by the nonlinear least square method.The results show that the correlation coefficient of along-wind fluctuating wind load is affected by both the side ratio and separation distance,and decreases exponentially with the increase of separation distance.The along-wind fluctuating coherence function decays exponentially with the increase of frequency,and the decay rate of the coherence function is roughly positively related to the ratio of separation distance to average wind speed.The effects of turbulence integral scale and turbulence intensity on the correlation of along-wind fluctuating wind loads are different for buildings with different side ratios.It can serve as a guide for structural design and load code revision since the coherence functions and correlation coefficients of along-wind fluctuating wind loads on rectangular high-rise buildings suggested in this work correspond well with the experimental data.
Around the world, concrete is widely used as an essential building material, however it can fracture and let water and salts in, which can cause corrosion and shorten the structure's lifespan. In particular, the robustness of bacterial concrete in marine environments where it is exposed to more extreme conditions is examined in this extensive study. Making use of the special properties of bacteria that may produce calcium carbonate, bacterial concrete, also known as Bio-Concrete, takes advantage of this. Sealing the cracks helps the concrete self-heal, hence increasing the structure's lifespan. The goal of the study is to shed light on how bacterial concrete might lessen the negative impacts of environmental stressors on concrete structures in maritime environments. The study highlights how crucial it is to take into account the sustainability and economic viability of bacterial concrete in coastal environments before implementing it widely. The study immersed bacterial concrete beams in seawater for 365 days, showing no rebar corrosion, a common issue with normal concrete. It also compared the strength of normal and bacterial concrete. The research explored using RHA to strengthen M40-grade concrete and adding 5% to 10% corn starch to improve flowability and setting time without compromising strength and durability. Additionally, 0.5% silica fume was introduced to enhance concrete strength and durability. Concrete's capacity to survive weathering, chemical abrasion, and other difficulties throughout time is largely dependent on its durability. Crack prevention is essential for maintaining structural integrity, water tightness, and aesthetic appeal. Moreover, concrete structures' longevity and functioning could be greatly improved by the development of a trustworthy automated crack repair system. For this reason, maintaining the longevity of concrete structures depends critically on controlling the fracture widths. The study also examines the sustainability over the long run and the difficulties involved in using bacterial concrete in marine construction, providing important information for researchers and engineers and advancing our knowledge of the material's potential for durable and robust marine applications.
