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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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 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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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.
The purpose of the experimental study presented in the paper is to generate new knowledge about the possibility of using unmanned aerial vehicles to survey buildings and structures for subsequent extraction of informa...
The purpose of the experimental study presented in the paper is to generate new knowledge about the possibility of using unmanned aerial vehicles to survey buildings and structures for subsequent extraction of information about their condition in hard-to-reach or remote places. As objects for the pilot experiment, the following were selected: a residential building in an urban environment that has been destroyed during operation; an object of unfinished construction; a roadway on the carriageway. An unmanned aerial vehicle of the model: DJI Mavic Air was used to survey the objects. The results of the study of objects are recorded in the form of photo and video streams for each object. Comparison of the results of the inspection of objects by experts and unmanned aerial vehicles showed the possibility and necessity of using new means to collect information about the condition of buildings and structures. The primary processing of the obtained images revealed their features: the effect of illumination on the color characteristics of the object of study; the presence of a textural component that complicates the process of separating the defect from the background; the presence of objects in the image that are not related to the elements of surface destruction; the change in the initial size of the object over time. The detected features of the images allow the use of standard algorithms and processing and require the synthesis of unique trajectories of their application.
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