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Maximal Concurent Limited Cost Flow Problems on Extended Multi-commodity Multi-cost Network
Ho Van Hung,
Tran Quoc Chien
Issue:
Volume 8, Issue 3, June 2020
Pages:
74-82
Received:
1 April 2020
Accepted:
20 April 2020
Published:
29 April 2020
Abstract: Graphs are excellent mathematical tools applied in many fields such as transportation, communication, informatics, economy,…. A network and a flow network is a useful device to solve many problems in many fields in reality. However, most of the network applications in traditional graphs have only considered the weights of edges and vertexes independently, in which the length of a path is the sum of weights of the edges and the vertexes on the path. However, in many practical problems, weights at a vertex are not the same for all paths passing the vertex, but depend on the edges coming to and leaving the vertex. For example, the transit time on the transport network depends on the direction of transportation: turn right, turn left or go straight, even some directions are forbidden. Furthermore, on a network, there are many types of commodities, each of which are at different costs. Types of commodities share the capacity of edges and vertexes. Therefore, it is necessary to study a network with multiple commodities at multiple costs. The article builds a model of extended multi-commodity multi-cost network in order to modelise practical problems more exactly and effectively. The maximal concurent multi-commodity multi-cost flow limited cost problems, that are modelized by implicit linear programming problems. On the basis of duality theory in linear programming, an effective polynomial approximation algorithm is developed.
Abstract: Graphs are excellent mathematical tools applied in many fields such as transportation, communication, informatics, economy,…. A network and a flow network is a useful device to solve many problems in many fields in reality. However, most of the network applications in traditional graphs have only considered the weights of edges and vertexes indepen...
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The D-, A-, E- and T-optimal Values of a Second Order Rotatable Design in Four Dimension Constructed Using Balanced Incomplete Block Designs
Kabue Timothy Gichuki,
Koske Joseph,
Mutiso John
Issue:
Volume 8, Issue 3, June 2020
Pages:
83-88
Received:
5 March 2020
Accepted:
10 April 2020
Published:
14 May 2020
Abstract: In response surface methodology, optimal designs are experimental designs generated based on a particular optimality criterion and are optimal only for a specific statistical model. Optimality criterion are single number criteria sometimes called alphabetical optimality criteria where each one intends to capture an aspect of the ‘goodness’ of a design. Most studies on optimization of process variables have concentrated on Central Composite Designs (CCD) yet second order rotatable deigns with any number of factors with reasonably small number of points constructed using properties of balanced incomplete block designs exist. A class of experimental designs that are optimal with respect to some statistical criterion are said to be Optimal designs. These designs allow parameter estimation with increased precision using fewer experimental runs, without bias and with minimum variance thus reducing time and costs of experimentation as opposed to non-optimal designs. A measure of relative efficiency of one design over another according to an optimality criterion aids in discriminating between the two designs for the “best” design. The D-, E-, A- and T-Optimal values of the general second order rotatable design in four dimensions constructed using balanced incomplete block designs when the number of replications (r) are less than three the number of times (λ) pairs of treatments occur together in the design were found which may be used to determine the relative efficiency of the general design to the D-, E-, A- and T-Optimal designs.
Abstract: In response surface methodology, optimal designs are experimental designs generated based on a particular optimality criterion and are optimal only for a specific statistical model. Optimality criterion are single number criteria sometimes called alphabetical optimality criteria where each one intends to capture an aspect of the ‘goodness’ of a des...
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Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process
Mohammed Hirpho Tobe,
Zerihun Kinfe Birhanu
Issue:
Volume 8, Issue 3, June 2020
Pages:
89-97
Received:
26 March 2020
Accepted:
12 May 2020
Published:
27 May 2020
Abstract: Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equations, which characterize the temperature distribution within the aquifer thermal energy storage system during the thermal injection process. The heat transfer equation is considered when the temperature difference between the solid and fluid phases is very small. We showed the solution to the model is positive and bounded. Simulations have been carried out for a constant Peclet number of 0.5, 500 and 100. Hot water is considered being injected throughout the depth of a single injection well into the aquifer at one end of the domain and the temperature of the hot water is assumed to be constant throughout the whole injection period. The finite element method has been utilized to solve the governing equations numerically. The results showed that the temperature front of injected hot water passes through the aquifer from left to right and the temperature of the aquifer increases gradually with the passage of injection time. Furthermore, if the Peclet number is very high the temperature of injected hot water makes a high change on the aquifer temperature, while if Peclet number is less than 1 there is a little change on the aquifer temperature as time t increases.
Abstract: Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equati...
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Differential Incremental Equilibrium Geometry-Effects of Cerebral Groove and Protein Granule Motion on Thinking Space and Mental Activity
Issue:
Volume 8, Issue 3, June 2020
Pages:
98-122
Received:
16 April 2020
Accepted:
3 May 2020
Published:
27 May 2020
Abstract: The research direction of this paper is to construct brain-like spatial structure and brain, nervous system and neurotransmitters from molecular cytobiology to construct mental acquisition from the influence of neuron and genome expression on brain, especially the material suspension caused by mental collapse to the neuron-like topological spatial structure and fluid topological structure of neurotransmitters. The spatial construction of acquired immunity and fluid morphology of neurotransmitters in the field of psychiatry (Carrying schizophrenia and other factors) also has brain-like mental activity traits. Stable traceability of neurotransmitter structure of series signal in schizophrenics with advanced intelligence. The high-end hyperspherical convex spherical fiber bundles with reduced dimension in 3+1 dimension system, special light field with radiation, and the collapse of mental force cause the suspension of substance in stationary state, the similar solution of solitary wavelet of petal-like micro-fibers in superimposed bundles. That is to say, the intelligent information particles carrying special image fragments in the form of mental energy in Psychological Acquired Immunity. Including primitive and innovative mathematical models of neuronal cell modification. Therefore, on the basis of original mathematical "differential incremental equilibrium geometry". The geometric models of spatial geometry and fluid structure of neurotransmitters of all neurons in life sciences are solved at the molecular level. Even using the nonlinearity of 4-dimensional super-high-end super-spherical convex fiber plexus "redundancy, petal-like micro-fibers" Sex-like solitary wavelet, which truly establishes the internal structure and law of molecular cell biology model. Reflects the new field of human brain research. It provides the basis and precondition of theory and application for the establishment of hybrid artificial intelligence of life and machine. and has far-reaching influence and important development prospects for the development of artificial intelligence, especially in brain-like artificial intelligence.
Abstract: The research direction of this paper is to construct brain-like spatial structure and brain, nervous system and neurotransmitters from molecular cytobiology to construct mental acquisition from the influence of neuron and genome expression on brain, especially the material suspension caused by mental collapse to the neuron-like topological spatial ...
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Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis
Shimelis Bekele Zerefe,
Temesgen Tibebu Mekonnen
Issue:
Volume 8, Issue 3, June 2020
Pages:
123-144
Received:
22 April 2020
Accepted:
15 May 2020
Published:
29 May 2020
Abstract: In this work we considered nonlinear dynamical system to study the dynamics of two-strain Tuberculosis epidemic in Ethiopia. We proved that the solution of the considered dynamical system is positive and bounded. We found that the considered dynamical system has disease free and endemic equilibrium points. We proved that the local and global stability of disease free equilibrium point and endemic equilibrium point. We found the effective reproduction number of the dynamical system. Also, the effective reproduction number of the dynamical system which experience drug sensitive strain and the effective reproduction number of the dynamical system which experience multi drug resistance strain. Using real data collected from different health sectors from Ethiopia we found that the numerical value of the effective reproduction number of the drug sensitive tuberculosis is 1.03 and the effective reproduction number of the drug resistance tuberculosis is 4.78 and the effective reproduction number of the dynamical system max{1.03, 4.78}=4.78. So that MDR strain is spreads strongly than DS strain. Numerical simulation is also done to illustrate the influence of different parameters on the effective reproduction number. Using sensitive analysis we identify the most influential parameter to change the behavior of the solution of the considered dynamical system is the number of effective contacts of susceptible or vaccinated individuals make with an infectious individual.
Abstract: In this work we considered nonlinear dynamical system to study the dynamics of two-strain Tuberculosis epidemic in Ethiopia. We proved that the solution of the considered dynamical system is positive and bounded. We found that the considered dynamical system has disease free and endemic equilibrium points. We proved that the local and global stabil...
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A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia
Tibebu Tulu Guya,
Temesgen Tibebu Mekonnen
Issue:
Volume 8, Issue 3, June 2020
Pages:
145-157
Received:
22 April 2020
Accepted:
15 May 2020
Published:
29 May 2020
Abstract: In this work we considered a nonlinear deterministic dynamical system to study the dynamics of HIV/AIDS with age structure and different mode of transmissions in Ethiopia. We found that the diseases free equilibrium point and endemic equilibrium points exist and we perform their local stability and global stability analysis using nonlinear stability methods. We found that the basic reproduction number of the considered dynamical system depends on the considered parameters and using real data collected from different health sectors in Ethiopia we found the numerical value of the reproduction number is R_0=1.05>1. This shows that the considered disease spreads in the community. From the sensitivity index of the dynamical system we found that the most sensitive parameter is the transmission rate of unaware infective humans to aware infectiveθ. We also showed that the effect of all parameters on the basic reproduction number using numerical simulation.
Abstract: In this work we considered a nonlinear deterministic dynamical system to study the dynamics of HIV/AIDS with age structure and different mode of transmissions in Ethiopia. We found that the diseases free equilibrium point and endemic equilibrium points exist and we perform their local stability and global stability analysis using nonlinear stabilit...
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Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure
Dereje Gutema Edossa,
Alemu Geleta Wedajo,
Purnachandra Rao Koya
Issue:
Volume 8, Issue 3, June 2020
Pages:
158-170
Received:
27 December 2019
Accepted:
3 June 2020
Published:
17 June 2020
Abstract: Malaria is an infectious disease caused by Plasmodium parasite and is transmitted among humans through bites of female Anopheles mosquitoes. It is estimated 216 million people suffered from malaria in 2016, with over 400,000 deaths mainly in sub-Saharan Africa. A number of control measures have been put in place: most importantly the insecticide treated net (ITN) and indoor residual sprayings (IRS) of insecticide. Currently, the emergence and spread of resistance in mosquito populations against insecticides is the most common and widely spread .It is also poses a key obstacle to malaria control as well as jeopardizing the effects of the most efficient malaria control interventions. A mathematical model that incorporates the evolution of insecticide resistance and its impact on endemic malaria transmission i.e., effects of indoor residual sprayings (IRS) on the insecticide resistant and sensitive malaria vector strains as a control strategy is incorporated and analyzed. The object of the study is to understand qualitatively the factor that have more influence for the emergence and spread of resistance of malaria vectors against IRS and their impacts on the efficacy of IRS. Based on a Ross-Macdonald derivation of malaria model the effective reproduction number〖 R〗_e isused to assess the effects of IRS in the qualitative analysis of the model. The existence and stability of the disease-free and endemic equilibria of the model are studied. It is established that the malaria can be brought under control as long as R_(e )is kept below the threshold value. Numerical simulations studies are conducted so as to determine the role played by key parameters of the model. The public health implications of the results include: (i) every effort should be taken to minimize the evolution of insecticide resistance due to malaria control interventions failure and (ii) at least a combination of two types of different control measures and followed by rotation of intervention strategies could be more realistic to minimize the number of resistant malaria vector strains and essential in reducing the malaria burden in the community.
Abstract: Malaria is an infectious disease caused by Plasmodium parasite and is transmitted among humans through bites of female Anopheles mosquitoes. It is estimated 216 million people suffered from malaria in 2016, with over 400,000 deaths mainly in sub-Saharan Africa. A number of control measures have been put in place: most importantly the insecticide tr...
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