**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2433

# Search results for: mathematical model

##### 2433 All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model

**Authors:**
S. A. Sadegh Zadeh,
C. Kambhampati

**Abstract:**

Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

**Keywords:**
All-or-none,
computational modelling,
mathematical model,
transmembrane voltage,
action potential.

##### 2432 Mathematical Model for the Transmission of Two Plasmodium Malaria

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
Dynamical analysis,
Malaria,
mathematical model,
threshold condition.

##### 2431 Development of Mathematical Model for Overall Oxygen Transfer Coefficient of an Aerator and Comparison with CFD Modeling

**Authors:**
Shashank.B. Thakre,
L.B. Bhuyar,
Samir.J. Deshmukh

**Abstract:**

**Keywords:**
CFD Model,
Overall oxygen transfer coefficient,
Power,
Mathematical Model,
Validation.

##### 2430 Numerical Analysis of Oil-Water Transport in Horizontal Pipes Using 1D Transient Mathematical Model of Thermal Two-Phase Flows

**Authors:**
Evgeniy Burlutskiy

**Abstract:**

**Keywords:**
Mathematical model,
Oil-Water,
Pipe flows.

##### 2429 Analysis of a Mathematical Model for Dengue Disease in Pregnant Cases

**Authors:**
Rujira Kongnuy,
Puntani Pongsumpun,
I-Ming Tang

**Abstract:**

Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.

**Keywords:**
Dengue disease,
local stability,
mathematical model,
pregnancy.

##### 2428 Nonlinear Mathematical Model of the Rotor Motion in a Thin Hydrodynamic Gap

**Authors:**
Jaroslav Krutil,
František Pochylý,
Simona Fialová

**Abstract:**

**Keywords:**
CFD modeling,
hydrodynamic gap,
matrices of
mass,
stiffness and damping,
nonlinear mathematical model.

##### 2427 Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
Adult human,
juvenile human,
leptospirosis,
mathematical model.

##### 2426 Mathematical Model of Depletion of Forestry Resource: Effect of Synthetic Based Industries

**Authors:**
Manisha Chaudhary,
Joydip Dhar,
Govind Prasad Sahu

**Abstract:**

A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1: forest biomass free and wood industries free equilibrium; E2: wood industries free equilibrium and two coexisting equilibria E∗1 , E∗2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopf-bifurcation about the non-trivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.

**Keywords:**
A mathematical model,
Competition between wood based and synthetic industries,
Hopf-bifurcation,
Stability analysis.

##### 2425 Mathematical Modeling of SISO based Timoshenko Structures – A Case Study

**Authors:**
T.C. Manjunath,
Student Member,
B. Bandyopadhyay

**Abstract:**

This paper features the mathematical modeling of a single input single output based Timoshenko smart beam. Further, this mathematical model is used to design a multirate output feedback based discrete sliding mode controller using Bartoszewicz law to suppress the flexural vibrations. The first 2 dominant vibratory modes is retained. Here, an application of the discrete sliding mode control in smart systems is presented. The algorithm uses a fast output sampling based sliding mode control strategy that would avoid the use of switching in the control input and hence avoids chattering. This method does not need the measurement of the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement.

**Keywords:**
Smart structure,
Timoshenko beam theory,
Discretesliding mode control,
Bartoszewicz law,
Finite Element Method,
State space model,
Vibration control,
Mathematical model,
SISO.

##### 2424 A New Fuzzy Mathematical Model in Recycling Collection Networks: A Possibilistic Approach

**Authors:**
B. Vahdani,
R. Tavakkoli-Moghaddam,
A. Baboli,
S. M. Mousavi

**Abstract:**

Focusing on the environmental issues, including the reduction of scrap and consumer residuals, along with the benefiting from the economic value during the life cycle of goods/products leads the companies to have an important competitive approach. The aim of this paper is to present a new mixed nonlinear facility locationallocation model in recycling collection networks by considering multi-echelon, multi-suppliers, multi-collection centers and multifacilities in the recycling network. To make an appropriate decision in reality, demands, returns, capacities, costs and distances, are regarded uncertain in our model. For this purpose, a fuzzy mathematical programming-based possibilistic approach is introduced as a solution methodology from the recent literature to solve the proposed mixed-nonlinear programming model (MNLP). The computational experiments are provided to illustrate the applicability of the designed model in a supply chain environment and to help the decision makers to facilitate their analysis.

**Keywords:**
Location-allocation model,
recycling collection networks,
fuzzy mathematical programming.

##### 2423 Formulation of Extended-Release Gliclazide Tablet Using a Mathematical Model for Estimation of Hypromellose

**Authors:**
Farzad Khajavi,
Farzaneh Jalilfar,
Faranak Jafari,
Leila Shokrani

**Abstract:**

Formulation of gliclazide in the form of extended-release tablet in 30 and 60 mg dosage forms was performed using hypromellose (HPMC K4M) as a retarding agent. Drug-release profiles were investigated in comparison with references Diamicron MR 30 and 60 mg tablets. The effect of size of powder particles, the amount of hypromellose in formulation, hardness of tablets, and also the effect of halving the tablets were investigated on drug release profile. A mathematical model which describes hypromellose behavior in initial times of drug release was proposed for the estimation of hypromellose content in modified-release gliclazide 60 mg tablet. This model is based on erosion of hypromellose in dissolution media. The model is applicable to describe release profiles of insoluble drugs. Therefore, by using dissolved amount of drug in initial times of dissolution and the model, the amount of hypromellose in formulation can be predictable. The model was used to predict the HPMC K4M content in modified-release gliclazide 30 mg and extended-release quetiapine 200 mg tablets.

**Keywords:**
Hypromellose,
gliclazide,
drug release,
modified-release tablet,
mathematical model.

##### 2422 Evaluation of Low-Reducible Sinter in Blast Furnace Technology by Mathematical Model Developed at Centre ENET, VSB – Technical University of Ostrava

**Authors:**
S. Jursová,
P. Pustějovská,
S. Brožová,
J. Bilík

**Abstract:**

The paper deals with possibilities of interpretation of iron ore reducibility tests. It presents a mathematical model developed at Centre ENET, VŠB – Technical University of Ostrava, Czech Republic for an evaluation of metallurgical material of blast furnace feedstock such as iron ore, sinter or pellets. According to the data from the test, the model predicts its usage in blast furnace technology and its effects on production parameters of shaft aggregate. At the beginning, the paper sums up the general concept and experience in mathematical modelling of iron ore reduction. It presents basic equation for the calculation and the main parts of the developed model. In the experimental part, there is an example of usage of the mathematical model. The paper describes the usage of data for some predictive calculation. There are presented material, method of carried test of iron ore reducibility. Then there are graphically interpreted effects of used material on carbon consumption, rate of direct reduction and the whole reduction process.

**Keywords:**
Blast furnace technology,
iron ore reduction,
mathematical model,
prediction of iron ore reduction.

##### 2421 Mathematical Modeling for Dengue Transmission with the Effect of Season

**Authors:**
R. Kongnuy.,
P. Pongsumpun

**Abstract:**

**Keywords:**
Dengue disease,
mathematical model,
season,
threshold parameters.

##### 2420 Numerical Analysis on Rapid Decompression in Conventional Dry Gases using One- Dimensional Mathematical Modeling

**Authors:**
Evgeniy Burlutskiy

**Abstract:**

**Keywords:**
Mathematical model,
Rapid Gas Decompression

##### 2419 Numerical Analysis of Rapid Gas Decompression in Pure Nitrogen using 1D and 3D Transient Mathematical Models of Gas Flow in Pipes

**Authors:**
Evgeniy Burlutskiy

**Abstract:**

**Keywords:**
Mathematical model,
Rapid Gas Decompression

##### 2418 Generalized Mathematical Description and Simulation of Grid-Tied Thyristor Converters

**Authors:**
V. S. Klimash,
Ye Min Thu

**Abstract:**

**Keywords:**
Direct current,
alternating current,
rectifier,
AC voltage regulator,
generalized mathematical model.

##### 2417 Mathematical Modeling of Elastically Creeping State of Arbitrarily Orientated Cavities in the Transversally Isotropic Massif

**Authors:**
N. Azhikhanov,
T. Turimbetov,
Zh. Masanov,
N. Zhunisov

**Abstract:**

It can be determined in preference between representative mechanical and mathematical model of elasticcreeping deformation of transversally isotropic array with doubly periodic system of tilted slots, and offer of the finite elements calculation scheme, and inspection of the states of two diagonal arbitrary profile cavities of deep inception, and in setting up the tense and dislocation fields distribution nature in computing processes.

**Keywords:**
Mathematical model,
tunnel,
transversally isotropic,
finite elements.

##### 2416 Mathematical Modelling of Different Types of Body Support Surface for Pressure Ulcer Prevention

**Authors:**
Mahbub C. Mishu,
Venketesh N. Dubey,
Tamas Hickish,
Jonathan Cole

**Abstract:**

Pressure ulcer is a common problem for today’s healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body, blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

**Keywords:**
Pressure ulcer,
viscoelastic material,
mathematical
model,
experimental validation.

##### 2415 Mathematical Model and Control Strategy on DQ Frame for Shunt Active Power Filters

**Authors:**
P. Santiprapan,
K-L. Areerak,
K-N. Areerak

**Abstract:**

**Keywords:**
shunt active power filter,
mathematical model,
DQ
control strategy,
DQ axis with Fourier,
pulse width modulation
control.

##### 2414 On the Mathematical Model of Vascular Endothelial Growth Connected with a Tumor Proliferation

**Authors:**
N. Khatiashvili,
Ch. Pirumova,
V. Akhobadze

**Abstract:**

**Keywords:**
Differential Equations,
Mathematical Models,
Vascular Endothelial,
Tumor

##### 2413 Integrated Evaluation of Green Design and Green Manufacturing Processes Using a Mathematical Model

**Authors:**
Yuan-Jye Tseng,
Shin-Han Lin

**Abstract:**

In this research, a mathematical model for integrated evaluation of green design and green manufacturing processes is presented. To design a product, there can be alternative options to design the detailed components to fulfill the same product requirement. In the design alternative cases, the components of the product can be designed with different materials and detailed specifications. If several design alternative cases are proposed, the different materials and specifications can affect the manufacturing processes. In this paper, a new concept for integrating green design and green manufacturing processes is presented. A green design can be determined based the manufacturing processes of the designed product by evaluating the green criteria including energy usage and environmental impact, in addition to the traditional criteria of manufacturing cost. With this concept, a mathematical model is developed to find the green design and the associated green manufacturing processes. In the mathematical model, the cost items include material cost, manufacturing cost, and green related cost. The green related cost items include energy cost and environmental cost. The objective is to find the decisions of green design and green manufacturing processes to achieve the minimized total cost. In practical applications, the decision-making can be made to select a good green design case and its green manufacturing processes. In this presentation, an example product is illustrated. It shows that the model is practical and useful for integrated evaluation of green design and green manufacturing processes.

**Keywords:**
Supply chain management,
green supply chain,
green design,
green manufacturing,
mathematical model.

##### 2412 A Sustainable Design Model by Integrated Evaluation of Closed-loop Design and Supply Chain Using a Mathematical Model

**Authors:**
Yuan-Jye Tseng,
Yi-Shiuan Chen

**Abstract:**

**Keywords:**
Closed-loop design,
closed-loop supply chain,
design evaluation,
mathematical model,
supply chain management,
sustainable design model.

##### 2411 A Mathematical Representation for Mechanical Model Assessment: Numerical Model Qualification Method

**Authors:**
Keny Ordaz-Hernandez,
Xavier Fischer,
Fouad Bennis

**Abstract:**

This article illustrates a model selection management approach for virtual prototypes in interactive simulations. In those numerical simulations, the virtual prototype and its environment are modelled as a multiagent system, where every entity (prototype,human, etc.) is modelled as an agent. In particular, virtual prototyp ingagents that provide mathematical models of mechanical behaviour inform of computational methods are considered. This work argues that selection of an appropriate model in a changing environment,supported by models? characteristics, can be managed by the deter-mination a priori of specific exploitation and performance measures of virtual prototype models. As different models exist to represent a single phenomenon, it is not always possible to select the best one under all possible circumstances of the environment. Instead the most appropriate shall be selecting according to the use case. The proposed approach consists in identifying relevant metrics or indicators for each group of models (e.g. entity models, global model), formulate their qualification, analyse the performance, and apply the qualification criteria. Then, a model can be selected based on the performance prediction obtained from its qualification. The authors hope that this approach will not only help to inform engineers and researchers about another approach for selecting virtual prototype models, but also assist virtual prototype engineers in the systematic or automatic model selection.

**Keywords:**
Virtual prototype models,
domain,
qualification criterion,
model qualification,
model assessment,
environmental modelling.

##### 2410 Mathematical Modelling and Numerical Simulation of Maisotsenko Cycle

**Authors:**
Rasikh Tariq,
Fatima Z. Benarab

**Abstract:**

Evaporative coolers has a minimum potential to reach the wet-bulb temperature of intake air which is not enough to handle a large cooling load; therefore, it is not a feasible option to overcome cooling requirement of a building. The invention of Maisotsenko (M) cycle has led evaporative cooling technology to reach the sub-wet-bulb temperature of the intake air; therefore, it brings an innovation in evaporative cooling techniques. In this work, we developed a mathematical model of the Maisotsenko based air cooler by applying energy and mass balance laws on different air channels. The governing ordinary differential equations are discretized and simulated on MATLAB. The temperature and the humidity plots are shown in the simulation results. A parametric study is conducted by varying working air inlet conditions (temperature and humidity), inlet air velocity, geometric parameters and water temperature. The influence of these aforementioned parameters on the cooling effectiveness of the HMX is reported. Results have shown that the effectiveness of the M-Cycle is increased by increasing the ambient temperature and decreasing absolute humidity. An air velocity of 0.5 m/sec and a channel height of 6-8mm is recommended.

**Keywords:**
Renewable energy,
indirect evaporative cooling,
Maisotsenko cycle,
HMX,
mathematical model,
numerical simulation.

##### 2409 Mathematical Models for Overall Gas Transfer Coefficient Using Different Theories and Evaluating Their Measurement Accuracy

**Authors:**
Shashank.B. Thakre,
Lalit.B. Bhuyar,
Samir.J. Deshmukh

**Abstract:**

**Keywords:**
Theories,
Dissolved oxygen,
Mathematical model,
Gas Transfer coefficient,
Accuracy.

##### 2408 Parameters Identification of Mathematical Model of the Fission Yeast Cell Cycle Control Using Evolutionary Strategy

**Authors:**
A. Ghaffari,
A. S. Mostafavi

**Abstract:**

**Keywords:**
Cell cycle,
Cyclin-dependent kinase,
Fission yeast,
Genetic algorithms,
Mathematical modeling,
Wiring diagram

##### 2407 Mathematical Model for Progressive Phase Distribution of Ku-band Reflectarray Antennas

**Authors:**
M. Y. Ismail,
M. Inam,
A. F. M. Zain,
N. Misran

**Abstract:**

Progressive phase distribution is an important consideration in reflectarray antenna design which is required to form a planar wave in front of the reflectarray aperture. This paper presents a detailed mathematical model in order to determine the required reflection phase values from individual element of a reflectarray designed in Ku-band frequency range. The proposed technique of obtaining reflection phase can be applied for any geometrical design of elements and is independent of number of array elements. Moreover the model also deals with the solution of reflectarray antenna design with both centre and off-set feed configurations. The theoretical modeling has also been implemented for reflectarrays constructed on 0.508mm thickness of different dielectric substrates. The results show an increase in the slope of the phase curve from 4.61°/mm to 22.35°/mm by varying the material properties.

**Keywords:**
Mathematical modeling,
Progressive phase distribution,
Reflectarray antenna,
Reflection phase.

##### 2406 Mathematical Modeling of Non-Isothermal Multi-Component Fluid Flow in Pipes Applying to Rapid Gas Decompression in Rich and Base Gases

**Authors:**
Evgeniy Burlutskiy

**Abstract:**

**Keywords:**
Mathematical model,
Multi-Component gas mixture
flow,
Rapid Gas Decompression

##### 2405 Suspended Matter Model on Alsat-1 Image by MLP Network and Mathematical Morphology: Prototypes by K-Means

**Authors:**
S. Loumi,
H. Merrad,
F. Alilat,
B. Sansal

**Abstract:**

**Keywords:**
Classification K-means,
mathematical morphology,
neural network MLP,
remote sensing,
suspended particulate matter

##### 2404 A Fuzzy Mathematical Model for Order Acceptance and Scheduling Problem

**Authors:**
E. Koyuncu

**Abstract:**

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

**Keywords:**
Fuzzy mathematical programming,
fuzzy ranking,
order acceptance,
single machine scheduling.