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

Effect of Dravidian vernacular, English and Hindi during onscreen reading text: A physiological, subjective and objective evaluation study

Multilingualism has become an integral part of our present lifestyle. India has twenty two registered official languages with English and Hindi being most widely used for all official activities across the nation. As both these languages are introduced later in life, it was hypothesised that comprehensive reading will be better and faster if the native medium was used. Therefore present study aimed to evaluate the differences in performance while using one of the four Indian Dravidian vernaculars (Tamil, Telugu Kannada and Malayalam) and two non-vernacular (English and Hindi) languages for onscreen reading task. A multi-dimensional approach including physiological (Eye movement recording), subjective (Language Experience And Proficiency Questionnaire, LEAP-Q, Legibility rating) and Objective (Reading time and Word processing rate) measurements were used to quantify the effects. Forty-four Indian infantry soldiers from each of the Dravidian language groups participated in the study. Volunteers read aloud two simple story passages onscreen in their respective vernacular and non-vernacular languages using both time bound and self-paced reading mode. Reading time was lower and word processing rate was higher respectively in case of vernacular than non-vernacular. Consideration of fixation count in both the modes of reading indicated better performance with vernaculars. Legibility score was better in Dravidian languages than others. Results indicated that reading text was faster in vernacular media followed by English and Hindi. Use of vernaculars in onscreen text display of high density workstation may therefore be recommended for easier and faster comprehensio

Tidal disruption of white dwarfs in a modified gravity theory with SPH

Low energy imprints of modifications to general relativity are often found in pressure balance equations inside stars. These modifications are then amenable to tests via astrophysical phenomena, using observational effects in stellar astrophysics that crucially depend on such equations. One such effect is tidal disruption of stars in the vicinity of black holes. In this paper, using a numerical scheme modelled with smoothed particle hydrodynamics, we study real time tidal disruption of a class of white dwarfs by intermediate-mass black holes, in the low energy limit of a theory of modified gravity that alters the internal physics of white dwarfs, namely the Eddington inspired Born-Infeld theory. In this single parameter extension of general relativity, the mass-radius relation of white dwarfs as well as their tidal disruption radius depend on the modified gravity parameter, and these capture the effect of modifications to general relativity. Our numerical simulations incorporating these show that departure from general relativity in these scenarios might be observationally significant, and should therefore be contrasted with data. In particular, we study observationally relevant physical quantities, i.e., tidal kick velocity and trajectory deviation of the remnant core and fallback rates of the tidal debris in this theory and compare them to the Newtonian limit of general relativity. We also comment on the qualitative differences between the modified gravity theory and one with stellar rotation.Comment: 23 Page

Peptides on a rescue mission against the hazardous cidal chemicals used in Eastern Indian Agriculture: An in-silico approach based on field survey in 2020

Background: The use of poisonous agrochemicals is both necessary and menacing for a farmer. The long-term hazards of chemicals can even be life-threatening to many people. Recently, the adverse effects of such chemicals on the environment and human health received serious attention throughout the world. In an Indian context, the usage of the chemical sprays has costed many lives and influenced vital organs to the greatest extent. This serious situation advocates the search for ways to prevent the inhalation and absorption of these chemicals into the body. The present study was conducted to evaluate different types of chemical sprays, their impact, and explore remedial ways to neutralize their toxic effects. Methods: Alpha-cypermethrin, phorate, fenobucarb, buprofezin, and mancozeb were selected for binding based on the feedback of severity in actions reported by the respondents and statistical analysis of different physical and chemical parameters. Chemical similarity analysis of the 39 cidal chemicals was performed to predict the binding similarity with respect to the above-mentioned 5 seed molecules. These five chemicals were docked with three different proteins 121p GTPase HRas, Torpedo acetylcholinesterase, and trypanosoma phosphoglycerate kinase, selected based on the common target prediction. Results: Common target prediction revealed that these chemicals have an affinity to bind these proteins with a higher binding interaction towards the aromatic amino acid residues and those capable of H-bonding, escorted by a predilection towards acetylcholinesterase. Conclusion: The in-silico findings are the basis to propose that acetylcholinesterase can be considered as a potential binding agent to trap fatal agrochemicals. Keywords: Agrochemicals, Molecular docking analysis, Cypermethrin, Buprofezin, Fenobucarb, Acetylcholinesteras