88 research outputs found
Trust based routing protocol in MANET
Traditional network routing protocols find the shortest path by minimizing a cost over the paths. Number of hops is the most common metric to measure this cost of forwarding. However, this administrative cost metric is not guaranteed to have the same level of quality in mobile ad hoc networks (MANET). In addition malicious nature of nodes augments the problem even further. There is a need for generic cost metric to find the most reliable path for forwarding the packets. We propose a trust-based metric for routing in MANETs. This metric works as a reliability measure of nodes and the ad hoc routing protocol tries to find the most reliable path. We propose a quantitative measure of trustworthiness of a node based on node's properties like signal strength, stability, node's performance to forward packets and its rating by other nodes. To our knowledge, our approach is the first attempt to use a generic trust metric for reliable routing in MANETs
Fabrication and Characterisation of Polyaniline/Laponite based Semiconducting Organic/Inorganic Hybrid Material
Novel organic-inorganic semiconducting hybrid material is developed by chemically grafting polyaniline (PANI) onto an inorganic template, Laponite. The surface active silanol groups of the Laponite sheets were silylated with an aniline functionalised 3-phenylaminopropyltrimethoxysilane (PAPTMOS) coupling agent followed by deposition of PANI onto the silylated surface. The method includes the reaction of Laponite with PAPTMOS dissolved in a very small amount of methanol at 110 °C for 44 h in a vacuum oven, interaction of the silylated product with PANI via in situ polymerisation of aniline and one-step isolation process by means of the removal of the non-connected PANI with N-methylpyrrolidinone-diethylamine binary solvent. After isolation and re-doping with methane sulfonic acid the Laponite-PAPTMOS-PANI hybrid becomes electrically conductive. The chemical attachment of PANI with silylated Laponite in the hybrids were characterised by Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, elemental analysis, and scanning electron microscopy.Defence Science Journal, Vol. 64, No. 3, May 2014, pp. 193-197, DOI:http://dx.doi.org/10.14429/dsj.64.718
Zero-divisor graph of the rings and
In this article we introduce the zero-divisor graphs
and of the two rings and
; here is an ideal of closed sets in
and is the aggregate of those functions in , whose
support lie on . is the
analogue of the ring . We find out conditions on the topology on
, under-which (respectively,
) becomes triangulated/ hypertriangulated. We
realize that (respectively,
) is a complemented graph if and only if the
space of minimal prime ideals in (respectively
) is compact. This places a special case of this
result with the choice the ideals of closed sets in ,
obtained by Azarpanah and Motamedi in \cite{Azarpanah} on a wider setting. We
also give an example of a non-locally finite graph having finite chromatic
number. Finally it is established with some special choices of the ideals
and on and respectively that the rings
and are isomorphic if and only if
and are isomorphic
Intrinsic characterizations of C-realcompact spaces
[EN] c-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41, no. 8 (2018), 1135-1167. We offer a characterization of these spaces X via c-stable family of closed sets in X by showing that X is c-realcompact if and only if each c-stable family of closed sets in X with finite intersection property has nonempty intersection. This last condition which makes sense for an arbitrary topological space can be taken as an alternative definition of a c-realcompact space. We show that each topological space can be extended as a dense subspace to a c-realcompact space with some desired extension properties. An allied class of spaces viz CP-compact spaces akin to that of c-realcompact spaces are introduced. The paper ends after examining how far a known class of c-realcompact spaces could be realized as CP-compact for appropriately chosen ideal P of closed sets in X.University Grand Commission, New Delhi, research fellowship (F. No. 16-9 (June 2018)/2019 (NET/CSIR))Acharyya, SK.; Bharati, R.; Deb Ray, A. (2021). Intrinsic characterizations of C-realcompact spaces. Applied General Topology. 22(2):295-302. https://doi.org/10.4995/agt.2021.13696OJS295302222S. K. Acharyya and S. K. Ghosh, A note on functions in C(X) with support lying on an ideal of closed subsets of X, Topology Proc. 40 (2012), 297-301.S. K. Acharyya and S. K. Ghosh, Functions in C(X) with support lying on a class of subsets of X, Topology Proc. 35 (2010), 127-148.S. K. Acharyya, R. Bharati and A. Deb Ray, Rings and subrings of continuous functions with countable range, Queast. Math., to appear. https://doi.org/10.2989/16073606.2020.1752322F. Azarpanah, O. A. S. Karamzadeh, Z. Keshtkar and A. R. Olfati, On maximal ideals of and the uniformity of its localizations, Rocky Mountain J. Math. 48, no. 2 (2018), 345-384. https://doi.org/10.1216/RMJ-2018-48-2-345P. Bhattacherjee, M. L. Knox and W. W. Mcgovern, The classical ring of quotients of , Appl. Gen. Topol. 15, no. 2 (2014), 147-154. https://doi.org/10.4995/agt.2014.3181L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand Reinhold co., New York, 1960. https://doi.org/10.1007/978-1-4615-7819-2M. Ghadermazi, O. A. S. Karamzadeh and M. Namdari, On the functionally countable subalgebras of C(X), Rend. Sem. Mat. Univ. Padova. 129 (2013), 47-69. https://doi.org/10.4171/RSMUP/129-4O. A. S. Karamzadeh and Z. Keshtkar, On c-realcompact spaces, Queast. Math. 41, no. 8 (2018), 1135-1167. https://doi.org/10.2989/16073606.2018.1441919M. Mandelkar, Supports of continuous functions, Trans. Amer. Math. Soc. 156 (1971), 73-83. https://doi.org/10.1090/S0002-9947-1971-0275367-4R. M. Stephenson Jr, Initially k-compact and related spaces, in: Handbook of Set-Theoretic Topology, ed. Kenneth Kunen and Jerry E. Vaughan. Amsterdam, North-Holland, (1984) 603-632. https://doi.org/10.1016/B978-0-444-86580-9.50016-1A. Veisi, -filters and -ideals in the functionally countable subalgebra of , Appl. Gen. Topol. 20, no. 2 (2019), 395-405. https://doi.org/10.4995/agt.2019.1152
-topology and -topology on the ring of Measurable Functions, generalized and revisited
Let be the ring of all real valued measurable
functions defined over the measurable space . Given an ideal
in and a measure
, we introduce the -topology and the
-topology on as generalized versions of
the topology of uniform convergence or the -topology and the -topology on
respectively. With ,
these two topologies reduce to the -topology and the -topology on
respectively, already considered before. If is
a countably generated ideal in , then the
-topology and the -topology coincide if and only if
is a -bounded subset of . The components of
in in the -topology and the
-topology are realized as and
respectively. Here
is the set of all functions in
which are essentially -bounded over and
. It is
established that an ideal in is dense in the
-topology if and only if it is dense in the -topology and this
happens when and only when there exists such that .
Furthermore, it is proved that is closed in in
the -topology if and only if it is a -ideal in the sense that if
almost everywhere on with and
, then
A Generalization of -topology and -topology on rings of measurable functions
For a measurable space (), let be
the corresponding ring of all real valued measurable functions and let be
a measure on (). In this paper, we generalize the so-called
and topologies on via an ideal
in the ring . The generalized versions will be
referred to as the and topology, respectively,
throughout the paper. stands for the subring
of consisting of all functions that are
essentially -bounded (over the measure space ()). Also
let -. Then is
an ideal in containing and contained in
. It is also shown that and are the components of
in the spaces and , respectively. Additionally,
we obtain a chain of necessary and sufficient conditions as to when these two
topologies coincide
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