26 research outputs found

    Lifting of vector-valued automorphic forms

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    Recently, the first author [1] showed that the admissible vector-valued automorphic forms lift to the admissible ones. In this article, we study the lifts for the logarithmic vector-valued automorphic forms and explicitly compute the Fourier coefficients of the lifted vector-valued automorphic forms.Comment: 20 pages, revised following referee's suggestion

    Multi-scale analysis for transport of fine settling particles through an ice-covered channel in a laminar flow condition

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    The current research deals with the dispersion of fine settling particles in a fluid flowing through an ice-covered channel under the laminar flow condition. An analytical solution of the two-dimensional convection–diffusion equation, based on the multi-scale homogenization technique, is obtained. To validate the current study, analytical results for the dispersion coefficient are compared with the available earlier research work. Moreover, the proposed analytical solutions for mean concentration distributions of the tracers are compared with the numerical results obtained from the finite difference technique. From the industrial and environmental points of view, the vertical concentration distribution provides a very significant information. The downstream evolution of the concentration distribution also is shown for typical time periods at different values of the settling velocity. The approach to the vertical uniformity shows that it is too slow a process in comparison to that of longitudinal normality. It was found that settling velocities of particles disturb the vertical uniformity and the centroid of the solute cloud rises due to the increase in settling velocity. Results illustrate that in the downstream direction, the vertical concentration distribution increases near the bed surface and it decreases in the proximity of the ice-covered surface of the channel with the increase of settling velocity, but the mean concentration of the solute increases. The current study may play an important role to understand the mechanism of the sedimentation process in a closed channel system

    Coupled effects of wind shear and bed absorption on sediment transport in wetland

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    Wetlands play a vital role in sustaining ecosystems, supporting biodiversity, and controlling environmental degradation. Sedimentation in wetlands has emerged as a critical research area due to its relevance in flood management, water purification, and geophysical applications. Despite its importance, the combined effects of wind shear and bed absorption on sediment transport remain underexplored. This study investigates sediment removal efficiency in wetland flow influenced by wind shear, absorbent beds, and particle settling. The time-dependent convection-diffusion equation is solved using a hybrid approach, combining Aris's method of integral moments with a finite difference implicit scheme. Analytical expressions for two-dimensional spatial concentration distributions are derived via Gill's series expansion. Key parameters, including wind direction (W), relative wind strength (⁠ Er⁠), bed absorption coefficient (⁠ β⁠), vegetation parameter (⁠ α⁠), and settling velocity (⁠ ω⁠), are analyzed to determine their impact on dispersion characteristics like the dispersion coefficient, concentration distribution, skewness, and kurtosis. Results show that wind shear enhances sediment dispersion when aligned with the flow (⁠ W=+1⁠) but induces backflow and reduces dispersion within a certain wind strength range when opposing it (⁠ W=−1⁠). Bed absorption accelerates stabilization by trapping particles, limiting their dispersion capacity. Settling velocity further influences dispersion by reducing the suspension of the particles, with higher ω accelerating stabilization but suppressing long-term dispersion. Dense vegetation reduces wind-induced variations, improving flow stability by dampening momentum transfer. This study provides new insights into coupled wind-absorbent bed-settling velocity interactions, offering a framework for optimizing wetland design, pollutant removal, and environmental sustainability. This proposed model can be applied to optimize wetland restoration strategies, enhance sediment management in aquatic ecosystems, and improve pollutant filtration efficiency in natural and engineered water systems.The authors wish to express their sincere thanks to the Chief Editor, Associate Editor, and anonymous reviewers for their constructive comments and suggestions for the improvement of the present research. The first author, Saugata Dutta (NTA Ref. No. 211610066362), expresses sincere gratitude to the University Grants Commission (UGC), India, for providing financial support to undertake this work. The author, Nanda Poddar, gratefully acknowledges the financial support from the Irish Research Council (now Research Ireland) (Project No. GOIPD/2024/226) for this research work.peer-reviewe

    A filtration method for rapid preparation of conjugates for immunoassay

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    Modification of protein and other biopolymers by labeling them with small or macromolecules has become a very powerful research tool in biochemistry, molecular biology, diagnostics, and therapeutics. However, current methodologies available for their preparations are not straightforward and take several hours of incubation time. In this paper, we describe a new filtration-assisted technique for covalent conjugation between the reactive functional groups of two different molecules (small or macromolecules). Compared to the current method, this new approach significantly reduces the total reaction time from several hours to just a few minutes. The technique has been used for the preparation of conjugates of a small molecule to a protein such as biotin–BSA conjugate or small molecules to a small molecule such as biotin– tyramine conjugate or protein–protein conjugation such as antibody-horseradish peroxidase conjugate. The procedure consists of filtering the reaction mixture multiple times through membrane micropores with the help of two syringes, which make the cross filtration process less laborious. The method saves time, allows conjugation of less than 1 mg protein and produces conjugates better than those obtained by the current methods. Although the present technique has been applied on some common conjugation methods, it provides a potentially generalmethod, and may further be expanded for the synthesis of several other macromolecular conjugate

    Early Breast Cancer Detection Using Flexible Microstrip Antenn

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    Women’s across the world are influenced by Breast cancer and conclude on a fatal note if it doesn't cure correctly. When the cases of Breast cancer gaining its pace among young age group the recent technology asks for advance early detection methods apart from the available methods as MRI &amp;amp; breast imaging system, Mammography. Keeping in mind the principles of our society and to bring on a feasible environment the technology can be developed with precise detection of the type of breast tumor cells with help of an antenna among the young age group while still, the age limit for diagnosis by mammography remains at 35 years. Developing a breast cancer exposure system that helps us predict the type of tumor cell present in the breast volume will ease the patients from initial clinical diagnosis.</jats:p
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