Ideal spaces

[EN] Let C∞ (X) denote the family of real-valued continuous functions which vanish at infinity in the sense that {x ∈ X : |f(x)| ≥ 1/n} is compact in X for all n ∈ N. It is not in general true that C∞ (X) is an ideal of C(X). We define those spaces X to be ideal space where C∞ (X) is an ideal of C(X). We have proved that nearly pseudocompact spaces are ideal spaces. For the converse, we introduced a property called “RCC” property and showed that an ideal space X is nearly pseudocompact if and only if X satisfies ”RCC” property. We further discussed some topological properties of ideal spaces.Mitra, B.; Chowdhury, D. (2021). Ideal spaces. Applied General Topology. 22(1):79-89. https://doi.org/10.4995/agt.2021.13608OJS7989221F. Azarpanah, M. Ghirati and A. Taherifar, Closed ideals in C(X) with different representations, Houst. J. Math. 44, no. 1 (2018), 363-383.F. Azarpanah and T. Soundarajan, When the family of functions vanishing at infinity is an ideal of C(X), Rocky Mountain J. Math. 31, no. 4 (2001), 1-8. https://doi.org/10.1216/rmjm/1021249434R. L. Blair and M. A. Swardson, Spaces with an Oz Stone-Cech compactification, Topology Appl. 36 (1990), 73-92. https://doi.org/10.1016/0166-8641(90)90037-3W. W. Comfort, On the Hewitt realcompactification of a product space, Trans. Amer. Math. Soc. 131 (1968), 107-118. https://doi.org/10.1090/S0002-9947-1968-0222846-1J. M. Domínguez, J. Gómez and M. A. Mulero , Intermediate algebras between C*(X) and C(X) as rings of fractions of C*(X), Topology Appl. 77 (1997), 115-130. https://doi.org/10.1016/S0166-8641(96)00136-8R. Engelking, General Topology, Heldermann Verlag, Berlin , 1989L. Gillman and M. Jerison, Rings of Continuous Functions, University Series in Higher Math, Van Nostrand, Princeton, New Jersey,1960. https://doi.org/10.1007/978-1-4615-7819-2I. Glicksberg, Stone-Cech compactifications of products, Trans. Amer. Math. Soc. 90 (1959), 369-382. https://doi.org/10.2307/1993177M. Henriksen, B. Mitra, C(X) can sometimes determine X without X being realcompact, Comment. Math. Univ. Carolina 46, no. 4 (2005), 711-720.M. Henriksen and M. Rayburn, On nearly pseudocompact spaces, Topology Appl. 11 (1980),161-172. https://doi.org/10.1016/0166-8641(80)90005-XT. Isiwata, On locally Q-complete spaces, II, Proc. Japan Acad. 35, no. 6 (1956), 263-267. https://doi.org/10.3792/pja/1195524322B. Mitra and S. K. Acharyya, Characterizations of nearly pseudocompact spaces and spaces alike, Topology Proceedings 29, no. 2 (2005), 577-594.M. C. Rayburn, On hard sets, General Topology and its Applications 6 (1976), 21-26. https://doi.org/10.1016/0016-660X(76)90004-0A. Rezaei Aliabad, F. Azarpanah and M. Namdari, Rings of continuous functions vanishing at infinity, Comm. Math. Univ. Carolinae 45, no. 3 (2004), 519-533.A. H. Stone, Hereditarily compact spaces, Amer. J. Math. 82 (1960), 900-914. https://doi.org/10.2307/2372948A. Wood Hager, On the tensor product of function rings, Doctoral dissertation, Pennsylvania State Univ., University Park, 1965

C(X) determines X -- an inherent theory

One of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y . The development started back from Tychono? who first pointed out inevitability of Tychono? space in this category of problem. Later S.Banach and M. Stone proved independently with slight variance, that if X is compact Hausdor? space, C(X) also determine X. Their works were maximally extended by E. Hewitt by introducing realcompact spaces and later Melvin Henriksen and Biswajit Mitra solved the problem for locally compact and nearly realcompact spaces. In this paper we tried to develop an inherent theory of this problem to cover up all the works in the literature introducing a notion so called P-compact spaces

Supercritical gas cooling and condensation of refrigerant R410A at near-critical pressures

A comprehensive study of heat transfer and pressure drop of refrigerant R410A during condensation and supercritical cooling at near-critical pressures was conducted. Investigations were carried out at five nominal pressures: 0.8, 0.9, 1.0, 1.1 and 1.2xpcrit. The refrigerant was tested in commercially available horizontal smooth tubes of 6.2 and 9.4 mm I.D. Heat transfer coefficients were measured using a thermal amplification technique that measures heat duty accurately while also providing refrigerant heat transfer coefficients with low uncertainties. For condensation tests, local heat transfer coefficients and pressure drops were measured for the mass flux range 200 G 800 kg/m2-s in small quality increments over entire vapor-liquid region. For supercritical tests, local heat transfer coefficients and pressure drops were measured for the same mass flux range as in the condensation tests for temperatures ranging from 30 110oC. Condensation heat transfer coefficients and pressure drops increased with quality and mass flux. The effect of reduced pressure on heat transfer is not very significant, while this effect is more pronounced on the pressure gradient. The flow regime transition criteria of Coleman and Garimella (2003) were used to initially designate the prevailing flow regimes for a given combination of mass flux and quality. The condensation data collected in the present study were primarily in the wavy and annular flow regimes. During supercritical cooling, the sharp variations in thermophysical properties in the vicinity of the critical temperature resulted in sharp peaks in the heat transfer coefficients and sudden jumps in the pressure drop. Based on the characteristics of the specific work of thermal expansion (contraction), the data from the supercritical tests were grouped into three regimes: liquid-like, pseudo-critical transition and gas-like regimes. Flow regime-based heat transfer and pressure drop models were developed for both condensation and supercritical cooling. For condensation, the overall heat transfer model predicts 98% of the data within 15% while the overall pressure drop model predicts 87% of the data within 15%. For supercritical cooling, the heat transfer model predicted 88% of the data within 25% while the pressure gradient model predicts 84% of the data within 25%.Ph.D.Committee Chair: Garimella, Srinivas; Committee Member: Ghiaasiaan, S. Mostafa; Committee Member: Breedveld, Victor; Committee Member: Fuller,Tom; Committee Member: Graham, Samue

Amino Acid Compositions of 27 Food Fishes and Their Importance in Clinical Nutrition

Proteins and amino acids are important biomolecules which regulate key metabolic pathways and serve as precursors for synthesis of biologically important substances; moreover, amino acids are building blocks of proteins. Fish is an important dietary source of quality animal proteins and amino acids and play important role in human nutrition. In the present investigation, crude protein content and amino acid compositions of important food fishes from different habitats have been studied. Crude protein content was determined by Kjeldahl method and amino acid composition was analyzed by high performance liquid chromatography and information on 27 food fishes was generated. The analysis showed that the cold water species are rich in lysine and aspartic acid, marine fishes in leucine, small indigenous fishes in histidine, and the carps and catfishes in glutamic acid and glycine. The enriched nutrition knowledge base would enhance the utility of fish as a source of quality animal proteins and amino acids and aid in their inclusion in dietary counseling and patient guidance for specific nutritional needs

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects