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804 results on '"Murthy, Sudhir"'

2. Three Classical Theorems on Interchanging Limits With Integrals in Calculus

Author

Murthy, Sudhir and Gavosto, Estela

Subjects
Real Analysis, Riemann Integrals, Arzel`a’s Dominated Convergence Theorem, Monotone Convergence Theorem, Uniform Convergence Theorem
Abstract

The interchange of the ‘limit of an integral’ with the ‘integral of a limit’ for sequenc- es of functions is crucial in relevant applications, such as Fourier series for decom- posing periodic functions into sinusoidal components, and Fubini’s theorem for changing the order of integration of multivariable functions. This expository paper reviews three classical results in real analysis for cases where the limit of an integral of a sequence of functions equals the integral of the limiting function: (1) Mono- tone Convergence Theorem, (2) Uniform Convergence Theorem, and the broad- est result, (3) Dominated Convergence Theorem. While proofs of (2) are typically studied in undergraduate analysis, the proofs of (1) and (3) are usually reserved for graduate-level measure theory, where they are taught in a more general context. The purpose of this paper is to summarize and adapt W. A. J. Luxembourg’s un- dergraduate-friendly proof [7] of (3) Arzel`a’s Dominated Convergence Theorem, to demonstrate the nontrivial direction of (1) Monotone Convergence Theorem for Riemann Integrals. Our aim is to demystify the hidden logic involved in these well-established theorems, making them more accessible for undergraduate analysis.

Published
2023

3. A proof‐of‐concept experimental study for vacuum‐driven anaerobic biosolids fermentation using the IntensiCarb technology

Author

Okoye, Frances, Kakar, Farokh Laqa, Elbeshbishy, Elsayed, Bell, Kati, Muller, Christopher, Jimenez, Jose, Al‐Omari, Ahmed, Santoro, Domenico, Jang, Eunkyung, Walton, John, Bahreini, Gholamreza, Zaman, Masuduz, Nakhla, George, Hazi, Ferenc, Takacs, Imre, Murthy, Sudhir, and Rosso, Diego

Subjects
Chemical Engineering, Engineering, Environmental Engineering, fermentation, intensification, resource recovery, sludge treatment, thickening, vacuum evaporation, Chemical Sciences, Biological Sciences, Biological sciences, Chemical sciences
Abstract

This study demonstrates the potential of an innovative anaerobic treatment technology for municipal biosolids (IntensiCarb), which relies on vacuum evaporation to decouple solids and hydraulic retention times (SRT and HRT). We present proof-of-concept experiments using primary sludge and thickened waste activated sludge (50-50 v/v mixture) as feed for fermentation and carbon upgrading with the IntensiCarb unit. IntensiCarb fully decoupled the HRT and SRT in continuously stirred anaerobic reactors (CSAR) to achieve two intensification factors, that is, 1.3 and 2, while keeping the SRT constant at 3 days (including in the control fermenter). The intensified CSARs were compared to a conventional control system to determine the yields of particulate hydrolysis, VFA production, and nitrogen partitioning between fermentate and condensate. The intensified CSAR operating at an intensification factor 2 achieved a 65% improvement in particulate solubilization. Almost 50% of total ammonia was extracted without pH adjustment, while carbon was retained in the fermentate. Based on these results, the IntensiCarb technology allows water resource recovery facilities to achieve a high degree of plant-wide intensification while partitioning nutrients into different streams and thickening solids. PRACTITIONER POINTS: The IntensiCarb reactor can decouple hydraulic (HRT) and solids (SRT) retention times in anaerobic systems while also increasing particulate hydrolysis and overall plant capacity. Using vacuum as driving force of the IntensiCarb technology, the system could achieve thickening, digestion, and partial dewatering in the same unit-thus eliminating the complexity of multi-stage biosolids treatment lines. The ability to partition nutrients between particulate, fermentate, and condensate assigns to the IntensiCarb unit a key role in recovery strategies for value-added products such as nitrogen, phosphorus, and carbon, which can be recovered separately and independently.

Published
2022

28. Marks & Spencer

Author

Murthy, Sudhir Rama, primary, Barry, Mike, additional, and Ellis, Justine Esta, additional

Published
2021
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