—The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equati...
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The k -tuple domination problem, for a fixed positive integer k , is to find a minimum size vertex subset such that every vertex in the graph is dominated by at least k vertices in this set. The case when k = 2 is cal...
The k -tuple domination problem, for a fixed positive integer k , is to find a minimum size vertex subset such that every vertex in the graph is dominated by at least k vertices in this set. The case when k = 2 is called 2-tuple domination problem or double domination problem. In this paper, the 2-tuple domination problem is studied on interval graphs from an algorithmic point of view, which takes O ( n 2 ) time, n is the total number of vertices of the interval graph.
Let G = ( V , E ) be a simple connected undirected graph. Each vertex v ∈ V has a cost c ( v ) and provides a positive coverage radius R ( v ). A distance d uv is associated with each edge { u , v } ∈ E, and d ( u ,...
Let G = ( V , E ) be a simple connected undirected graph. Each vertex v ∈ V has a cost c ( v ) and provides a positive coverage radius R ( v ). A distance d uv is associated with each edge { u , v } ∈ E, and d ( u , v ) is the shortest distance between every pair of vertices u , v ∈ V . A vertex v can cover all vertices that lie within the distance R ( v ), except the vertex itself. The conditional covering problem is to minimize the sum of the costs required to cover all the vertices in G . This problem is NP-complete for general graphs, even it remains NP-complete for chordal graphs. In this paper, an O ( n 2 ) time algorithm to solve a special case of the problem in a trapezoid graph is proposed, where n is the number of vertices of the graph. In this special
case, d uv = 1 for every edge { u , v } ∈ E , c ( v ) = c for every v ∈ V ( G ), and R ( v ) = R , an integer >1, for every v ∈ V ( G ). A new data structure on trapezoid graphs is used to solve the problem.
When some suppliers offer trade credit periods and price discounts to retailers in order to increase the demand of their products, retailers have to face different types of discount offers and credits within which the...
When some suppliers offer trade credit periods and price discounts to retailers in order to increase the demand of their products, retailers have to face different types of discount offers and credits within which they have to take a decision which is the best offer for them to make more profit. The retailers try to buy perfect-quality items at a reasonable price, and also they try to invest returns obtained by selling those items in such a manner that their business is not hampered. In this point of view, we consider an economic order quantity (EOQ) model for various types of time-dependent demand when delay in payment and price discount are permitted by suppliers to retailers. The models of various demand patterns are discussed analytically. Some numerical examples and graphical representations are considered to illustrate the model.
The bipolar fuzzy set and interval-valued bipolar fuzzy set efficiently analyse real-world problems where for each input of an object, there has counter information. This study's main objective is to lay a foundat...
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A mathematical model of injection of liquid sulfur dioxide into a porous medium saturated with water and methane, accompanied by the formation of SO2 gas hydrate on the frontal surface is presented. The dependences of...
A mathematical model of injection of liquid sulfur dioxide into a porous medium saturated with water and methane, accompanied by the formation of SO2 gas hydrate on the frontal surface is presented. The dependences of the temperature and the coordinates for the formation front of sulfur dioxide gas hydrate on the pressure of the injection and the initial pressure of the layer are explored. It is established that at sufficiently high injection pressure values and the initial temperature of the layer, as well as the low values of the layer’s initial pressure, the temperature of the porous medium on the boundary of gas hydrate formation of sulfur dioxide may rise above the decomposition’s equilibrium temperature of the gas hydrate of sulfur dioxide. This corresponds to the appearance of a zone in a porous medium saturated with a mixture of water, sulfur dioxide and its gas hydrate, being in a state of phase equilibrium.
Japanese encephalitis (JE), a public health problem for the entire world, is caused by a virus called Japanese encephalitis virus (JEV) which is spread by mosquitoes. According to WHO’s report, nearly 68000 clinical ...
Japanese encephalitis (JE), a public health problem for the entire world, is caused by a virus called Japanese encephalitis virus (JEV) which is spread by mosquitoes. According to WHO’s report, nearly 68000 clinical cases of JE are reported globally each year and approximately 13600 to 20400 are deaths. Here, a mathematical model of JE is formulated considering different control measures such as vaccination, treatment, insecticide and efforts to reduce environmental discharges. An explicit expression of basic reproduction number is formulated and the stability of disease-free and endemic equilibrium of the system is analyzed. In this paper, we have formulated an optimal control problem and analyzed different strategies considering the minimum cost for applying such strategies. We have investigated the results of fixed control for endemic equilibrium both numerically and graphically. We have solved the optimal problem numerically when control parameters are time-dependent by applying Runge-Kutta 4th order forward and backward method and presented graphically. In our present work, we discussed the best cost-effective control strategy to prevent Japanese encephalitis when we consider environmental discharges have a positive impact on the breeding of mosquitoes and the growth of the pig population.
We consider the canonical ensemble of N-vertex Erdős-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity μ for each closed triple of bonds. We claim complete defragmentation of la...
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We consider the canonical ensemble of N-vertex Erdős-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity μ for each closed triple of bonds. We claim complete defragmentation of large-N graphs into the collection of [p−1] almost full subgraphs (cliques) above critical fugacity, μc, where p is the ER bond formation probability. Evolution of the spectral density, ρ(λ), of the adjacency matrix with increasing μ leads to the formation of a multizonal support for μ>μc. Eigenvalue tunneling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a block-diagonal form, where the number of vertices in blocks fluctuates around the mean value Np. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.
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