International Journals
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Item A STRUCTURE OF OPEN SETS IN QUAD TOPOLOGICAL SPACES(The International journal of analytical and experimental modal analysis, 2019-11) Sasikala, D; Deepa, MThe main aim of this paper is to present a new set, namely quad j-open set in quad topological space. We discuss the basic properties of quad j-open sets using quad j-interior and quad j-closure. In Addition we study the relationships among quad j-closed, quad b- closed and quad j-regular open in quad topological space.Item SOFT ˆ - GENERALIZED CLOSED SETS AND SOFT ˆ - GENERALIZED OPEN SETS IN SOFT TOPOLOGICAL SPACES(International Journal of Innovative Research in Science, Engineering and Technology, 2015-11) Parvathy, C.R; Deepa, MIn this paper a new class of soft sets called Soft- generalized closed sets and Soft ˆ- generalized open sets in Soft Topological spaces are introduced and studied. This new class is defined over an initial universe and with a fixed set of parameters. Some basic properties of this new class of soft sets are investigated. This new class of Soft - generalized closed sets and Softˆ- generalized open sets widening the scope of Soft Topological spaces and its applications.Item A CONTEMPORARY POSTULATES ON RESOLVABLE SETS AND FUNCTIONS(University of New Mexico, 2023) Deepa, M; Sasikala, D; Said, BIn this article, a new class of sets namely neutrosophic resolvable sets in neutrosophic topological space have been introduced. We present the neutrosophic resolvable functions between neutrosophic topological spaces by neutrosophic resolvables sets. Also we examine the characteristics of neutrosophic resolvable sets and neutrosophic resolvable functions with the existing sets.Item STABILITY ANALYSIS OF SINGLE NEURON SYSTEM WITH LEVY NOISE(INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH, 2020-01) Ganesan, ArthiThis article addresses the asymptotic stability of single neuron system with neutral delay and Levy noise. Sufficient conditions are derived to ensure that the considered system with Levy noise is asymptotic stable by means of the linear matrix inequality (LMI) approach together with a Lyapunov-Krasovskii functional and stochastic analysis theory. This work provides two examples of application of stability analysis in numerical formulation about the impact of Levy noise on neutral type single neuron modelItem CONTROLLABILITY OF HIGHER-ORDER FRACTIONAL DAMPED STOCHASTIC SYSTEMS WITH DISTRIBUTED DELAY(Springer Open, 2021-10-28) Arthi G; Suganya K; Yong-Ki, MaIn this paper, the controllability analysis is proposed for both linear and nonlinear higher-order fractional damped stochastic dynamical systems with distributed delay in Hilbert spaces which involve fractional Caputo derivative of different orders. Based on the properties of fractional calculus, the fixed point technique, and the construction of controllability Gramian matrix, we establish the controllability results for the considered systems. Finally, examples are constructed to illustrate the applicability of obtained results.Item FINITE-TIME STABILITY OF MULTITERM FRACTIONAL NONLINEAR SYSTEMS WITH MULTISTATE TIME DELAY(Springer Open, 2021-02-06) Arthi G; Brindha N; Yong-Ki, MaThis work is mainly concentrated on finite-time stability of multiterm fractional system for 0<α2≤1<α1≤2 with multistate time delay. Considering the Caputo derivative and generalized Gronwall inequality, we formulate the novel sufficient conditions such that the multiterm nonlinear fractional system is finite time stable. Further, we extend the result of stability in the finite range of time to the multiterm fractional integro-differential system with multistate time delay for the same order by obtaining some inequality using the Gronwall approach. Finally, from the examples, the advantage of presented scheme can guarantee the stability in the finite range of time of considered systems.Item GENERALIZED 3 – COMPLEMENT OF SET DOMINATION(The International Journal of Science & Technoledge, 2015-10) Sumathi P; Brindha TLet G=(V,E) be a simple, undirected, finite nontrivial graph. A set S⊆V of vertices of a graph G = (V, E) is called a dominating set if every vertex v∈V is either an element of S or is adjacent to an element of S. A set S⊆V is a set dominating set if for every set T⊆V-S, there exists a non-empty set R⊆S such that the subgraph is connected. The minimum cardinality of a set dominating set is called set domination number and it is denoted by γs (G).Let P=(V1,V2,V3) be a partition of V of order 3. Remove the edges between Vi and Vj where i≠j (1≤i,j≤3) in G and join the edges between Vi and Vjwhich are not in G. The graph G3p thus obtained is called 3-complement of G with respect to ‘P’.Item SPLIT TOTAL DOMINATION NUMBER OF SOME SPECIAL GRAPHS(International Journal of Mathematics And its Applications, 2020-06-15) T, Brindha; R, SubikshaA dominating set for a graph is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number is the number of vertices in a smallest dominating set for G. In this paper a new parameter, Split Total Dominating Set and the Split Total Domination Number has been introduced. A dominating set is called split total dominating set if is disconnected and every vertex is adjacent to an element of D. The split total domination number is given by In this paper the split total domination number for some standard graphs like star, path, cycle, complete, ladder, wheel, bistar, tadpole, comb, barbell, butterfly and fan graphs are found. Also the complement of graphs are obtained.Item SET DOMINATION MAXSUBDIVISION NUMBER OF GRAPHS(International Journal of Software & Hardware Research in Engineering, 2016-01-01) Sumathi P; Brindha TLet G=(V,E) be a simple, undirected, finite nontrivial graph. A non empty set SV of vertices in a graph G is called a dominating set if every vertex in V-S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G.A dominating set S is a set dominating set of G if for every set TV-S , there exists a non-empty set RS such that the subgraph is connected. The set domination number of G is the minimum cardinality of a set dominating set of G and it is denoted by γs (G).The set domination maxsubdivision number of G is the maximum number of edges that must be subdivided (where each edge in G can be subdivided atmost once) in order to increase the set domination number and is denoted by msdγs(G). In this paper, we establish the properties and exact values of the set domination maxsubdivision number for some families of graphs.Item OBSERVER-BASED FAULT TOLERANT CONTROL DESIGN FOR PERIODIC PIECEWISE TIME-VARYING SYSTEMS: A FAULT ESTIMATION APPROACH(Taylor & Francis Online, 2023-02-22) Sakthivel R; Aravinth N; Thilagamani V; Sasirekha RThis study tackles the fault estimation issue for a continuous-time periodic piecewise time-varying systems (PPTVSs) with delays, fault signal and external disturbances. In particular, the PPTVSs are conjured up by segmenting the fundamental period of the periodic system into a finite number of subintervals. Moreover, fault estimator is designed in line with periodic piecewise observer systems to estimate the immeasurable states of the PPTVSs and the fault signal, simultaneously. Subsequently, in accordance with the estimated values of the fault signal and state dynamics, a fault-tolerant controller is devised. Moreover, by utilising Lyapunov stability theory and matrix polynomial lemma, sufficient criteria are procured in context of linear matrix inequalities to affirm the uniform boundedness of the undertaken system and error system. Further, relying on the acquired constraints, the precise configuration of the fault-tolerant control and observer gain matrices are proffered. Eventually, by offering two illustrative examples including mass-spring-damper system, the utility and potential of presented theoretical insights are validated.