A Mathematical Model of Consumer Behavior

1965 ◽  
Vol 2 (3) ◽  
pp. 259-265 ◽  
Author(s):  
Benjamin Lipstein
Keyword(s):  
Mathematical Model ◽  
Consumer Behavior ◽  
Markov Process ◽  
Analytical Method ◽  
Stochastic Matrices ◽  
Market Conditions ◽  
Numerical Examples ◽  
Advertising Effort ◽  
Attitude Changes

A mathematical model is presented of consumer behavior in the marketplace under advertising stimulation. The model relates advertising effort to attitude changes and consumer purchases, using a nonstationary Markov process. A new analytical method of handling nonstationary stochastic matrices is developed. The behavior of brand shares under different market conditions is considered along with numerical examples of how the model operates.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

scholarly journals A Mathematical Model and Numerical Solution of a Boundary Value Problem for a Multi-Structure Plate

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Transmission Conditions ◽  
Numerical Examples ◽  
Deformation Problem ◽  
The Common ◽  
Plate System ◽  
Structure Plate ◽  
Numerical Approaches

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

scholarly journals Mathematical model for reliability indicators calculation of tethered UAV hybrid navigation system

2021 ◽  
Vol 2091 (1) ◽  
pp. 012033
Author(s):  
V M Vishnevsky ◽  
K A Vytovtov ◽  
E A Barabanova ◽  
V E Buzdin
Keyword(s):  
Mathematical Model ◽  
Navigation System ◽  
Analytical Method ◽  
Mathematical Expression ◽  
Equation System ◽  
Kolmogorov Equation ◽  
Reliability Indicators ◽  
Technical Vision ◽  
The Mathematical Model ◽  
First Time

Abstract The mathematical model for reliability indicators calculation of the hybrid navigation system containing microwave and technical vision subsystems is proposed in this paper for the first time. The proposed method is based on the translation matrix concept of solutions to the Kolmogorov equation system and it allows us to obtain the mathematical expression of availability factor, downtime ratio, and other reliability indicators. Also the presented approach allows finding the reliability indicators for the cases of jump change of transition intensities caused by external influences. Besides the analytical method can be used for investigation of hybrid navigation system transient mode functioning. The results of the numerical calculations clearly demonstrated correctness of the proposed approach.

Coupling Effects on Synchronizability of Two-Layer Network's Projective Outer Synchronization

2017 ◽  
Vol 873 ◽  
pp. 353-357
Author(s):  
Bo Yu Feng ◽  
Zhi Hao Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Complex Network ◽  
Simulation Experiment ◽  
Small World ◽  
Experimental Results ◽  
Coupling Effects ◽  
Network Synchronization ◽  
Numerical Examples ◽  
Outer Synchronization

Based on nonlinear dynamics theory and knowledge of complex network, this paper expanded the range of two-layer network synchronization to projective outers synchronization. A mathematical model was constructed and feasibility of synchronization was demonstrated. Then we improved the model in order to study the function of different couplings [1]. Numerical examples are examined to compare the synchronizability of projective outer synchronization with different couplings. A rule called "outer small-world effect" was found due to simulation experiment. Finally, some instances were used to explain experimental results.

scholarly journals Research on Two-stage Order Picking Sequencing for Intensive Shelf

2019 ◽  
Vol 296 ◽  
pp. 02003
Author(s):  
Xue Tian ◽  
Li Zhou ◽  
Jianglong Yang
Keyword(s):  
Mathematical Model ◽  
Global Optimum ◽  
Order Picking ◽  
Storage Space ◽  
Time Cost ◽  
Two Stage ◽  
Numerical Examples ◽  
Stage Order ◽  
Waiting Cost ◽  
The Law

The increasingly usage of Intensive shelves, greatly increase the utilization of storage space, but also is more demanding on order picking time . Based on the storage layout of intensive mobile shelves, this paper combines the time cost of shelf movement with the moving distance under the guidance of seeking global optimum. Transform the single order picking process into TSP problem, while considering the picking process. The waiting cost of the order, and the minimum of the picking cost and the waiting cost of the whole batch of orders requiring shelf movement, to establish a two-stage mathematical model of the order picking order. Then, the algorithm for solving the model is designed, and the simulation is carried out by numerical examples to illustrate the law and characteristics of the problem more vividly, in order to provide reference and reference for the order picking activities of intensive mobile shelves.

Analysis of Half-Pipe Heating Channels on Pressure Vessel Shells

1986 ◽  
Vol 108 (4) ◽  
pp. 526-529
Author(s):  
A. E. Blach
Keyword(s):  
Pressure Vessel ◽  
Analytical Method ◽  
External Pressure ◽  
Pressure Vessels ◽  
Numerical Examples ◽  
Asme Code

Half-pipe heating channels are used on the outside of pressure vessels such as agitators, mixers, reactors, etc., to avoid the high external pressure associated with heating jackets. No applicable method of analysis is contained in the ASME Code and proof tests are normally required for registration with governing authorities. An analytical method is presented which permits the evaluation of stresses in shell and half pipe; numerical examples are included.

A Mathematical Model of Consumer Behavior

1965 ◽  
Vol 2 (3) ◽  
pp. 259 ◽  
Author(s):  
Benjamin Lipstein
Keyword(s):  
Mathematical Model ◽  
Consumer Behavior

Mobile Robots Characterized by Kinematic and Dynamic Equations: Motion Planning, Trajectory Tracking, and Group Control

2008 ◽  
Author(s):  
Amit Ailon
Keyword(s):  
Mathematical Model ◽  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Equations ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
Reference Trajectory ◽  
Numerical Examples ◽  
Group Control ◽  
The Mathematical Model

The paper solves some control problems of mobile robots as both kinematics and dynamics are intertwined in the mathematical model. The problems of driving the vehicle to a desired configuration in a specified time and tracking a reference trajectory are considered. The control problems associated with motion in convoy and rigid formations of a group of vehicles are studied and some results are demonstrated by numerical examples.

Role of extravascular protein in capillary-tissue fluid exchange

1978 ◽  
Vol 234 (1) ◽  
pp. H52-H58
Author(s):  
E. P. Salathe ◽  
R. Venkataraman
Keyword(s):  
Mathematical Model ◽  
Perturbation Theory ◽  
Osmotic Pressure ◽  
Analytic Solutions ◽  
Tissue Fluid ◽  
Fluid Exchange ◽  
Numerical Examples ◽  
Pathological Conditions ◽  
And Diffusion

A mathematical model of capillary-tissue fluid exchange is presented. The effect of variation in plasma and interstitial osmotic pressure that occurs as a result of convection and diffusion of protein is examined. Analytic solutions to the resulting equations are obtained by using the methods of perturbation theory. It is found that fluid exchange can significantly alter the pericapillary interstitial osmotic pressure, reducing both filtration and reabsorption. Variation in plasma osmotic pressure is important only for certain pathological conditions in which excessive filtration occurs. Specific numerical examples are presented which show quantitatively the extent of these effects for various normal and pathological conditions of physiological interest.

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