**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**7775

# Search results for: Mathematical Model

##### 7775 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.

##### 7774 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.

##### 7773 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

##### 7772 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

##### 7771 Mathematical Modeling of Human Cardiovascular System: A Lumped Parameter Approach and Simulation

**Authors:**
Ketan Naik,
P. H. Bhathawala

**Abstract:**

**Keywords:**
Cardiovascular system,
lumped parameter method,
mathematical modeling,
simulation.

##### 7770 The Effects of a Thin Liquid Layer on the Hydrodynamic Machine Rotor

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

**Abstract:**

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

##### 7769 Mathematical Models of Flow Shop and Job Shop Scheduling Problems

**Authors:**
Miloš Šeda

**Abstract:**

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.

**Keywords:**
Flow shop,
job shop,
mixed integer model,
representation scheme.

##### 7768 Numerical Analysis on Rapid Decompression in Conventional Dry Gases using One- Dimensional Mathematical Modeling

**Authors:**
Evgeniy Burlutskiy

**Abstract:**

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

##### 7767 Model of Optimal Centroids Approach for Multivariate Data Classification

**Authors:**
Pham Van Nha,
Le Cam Binh

**Abstract:**

**Keywords:**
Analysis of optimization,
artificial intelligence-based
optimization,
optimization for learning and data analysis,
global
optimization.

##### 7766 Mathematical Modeling of Surface Roughness in Surface Grinding Operation

**Authors:**
M.A. Kamely,
S.M. Kamil,
C.W. Chong

**Abstract:**

**Keywords:**
Mathematical Modeling,
Response surfacemethodology,
Surface roughness,
Cylindrical Grinding.

##### 7765 Design of the Mathematical Model of the Respiratory System Using Electro-acoustic Analogy

**Authors:**
M. Rozanek,
K. Roubik

**Abstract:**

**Keywords:**
Model of the respiratory system,
total lung
impedance,
intrapulmonary parameters.

##### 7764 Simulating the Dynamics of Distribution of Hazardous Substances Emitted by Motor Engines in a Residential Quarter

**Authors:**
S. Grishin

**Abstract:**

**Keywords:**
Urban ecology,
time-dependent mathematical
model,
exhaust concentration,
turbulent and molecular diffusion,
airflow velocity.

##### 7763 Mathematical Modeling of Cell Volume Alterations under Different Osmotic Conditions

**Authors:**
Juliana A. Knocikova,
Yann Bouret,
Médéric Argentina,
Laurent Counillon

**Abstract:**

Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.

**Keywords:**
Eukaryotic cell,
mathematical modeling,
osmosis,
volume alterations.

##### 7762 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.

##### 7761 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.

##### 7760 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.

##### 7759 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.

##### 7758 Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations

**Authors:**
Gilbert Makanda,
Roelf Sypkens

**Abstract:**

**Keywords:**
Differential equations,
knowledge acquisition,
least
squares nonlinear,
dynamical systems.

##### 7757 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.

##### 7756 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.

##### 7755 Influence of IMV on Space Station

**Authors:**
Fu Shiming,
Pei Yifei

**Abstract:**

To study the impact of the inter-module ventilation (IMV) on the space station, the Computational Fluid Dynamic (CFD) model under the influence of IMV, the mathematical model, boundary conditions and calculation method are established and determined to analyze the influence of IMV on cabin air flow characteristics and velocity distribution firstly; and then an integrated overall thermal mathematical model of the space station is used to consider the impact of IMV on thermal management. The results show that: the IMV has a significant influence on the cabin air flow, the flowrate of IMV within a certain range can effectively improve the air velocity distribution in cabin, if too much may lead to its deterioration; IMV can affect the heat deployment of the different modules in space station, thus affecting its thermal management, the use of IMV can effectively maintain the temperature levels of the different modules and help the space station to dissipate the waste heat.

**Keywords:**
CFD,
Environment control and life support,
Space station,
Thermal management,
Thermal mathematical model.

##### 7754 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.

##### 7753 Mathematical Modeling of Storm Surge in Three Dimensional Primitive Equations

**Authors:**
Worachat Wannawong,
Usa W. HumphriesPrungchan Wongwises,
Suphat Vongvisessomjai

**Abstract:**

**Keywords:**
lateral boundary,
mathematical modeling,
numericalsimulations,
three dimensional primitive equations,
storm surge.

##### 7752 The Integrated Studies of Infectious Disease Using Mathematical Modeling and Computer Simulation

**Authors:**
R. Kongnuy,
E. Naowanich

**Abstract:**

**Keywords:**
Age Group,
Equilibrium State,
Leptospirosis,
Mathematical Modeling.

##### 7751 Drilling of Glass Sheets by Abrasive Jet Machining

**Authors:**
A. El-Domiaty,
H. M. Abd El-Hafez,
M. A. Shaker

**Abstract:**

**Keywords:**
Abrasive Jet Machining,
Erosion rate,
Glass,
Mathematical model.

##### 7750 Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans

**Authors:**
P. Pongsumpun

**Abstract:**

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

##### 7749 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.

##### 7748 Mathematical Model for the Transmission of Two Plasmodium Malaria

**Authors:**
P. Pongsumpun

**Abstract:**

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

##### 7747 Mathematical Rescheduling Models for Railway Services

**Authors:**
Zuraida Alwadood,
Adibah Shuib,
Norlida Abd Hamid

**Abstract:**

This paper presents the review of past studies concerning mathematical models for rescheduling passenger railway services, as part of delay management in the occurrence of railway disruption. Many past mathematical models highlighted were aimed at minimizing the service delays experienced by passengers during service disruptions. Integer programming (IP) and mixed-integer programming (MIP) models are critically discussed, focusing on the model approach, decision variables, sets and parameters. Some of them have been tested on real-life data of railway companies worldwide, while a few have been validated on fictive data. Based on selected literatures on train rescheduling, this paper is able to assist researchers in the model formulation by providing comprehensive analyses towards the model building. These analyses would be able to help in the development of new approaches in rescheduling strategies or perhaps to enhance the existing rescheduling models and make them more powerful or more applicable with shorter computing time.

**Keywords:**
Mathematical modelling,
Mixed-integer
programming,
Railway rescheduling,
Service delays.

##### 7746 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