A mathematical model for the in-plane non-linear earthquake behaviour of unreinforced masonry walls. Part 1: Experiments and proposed model

Study of dynamic behavior of pipeline is required to access fatigue life of pipeline welds. Semi-empirical mathematical model is thus proposed to calculate responses of free-span pipelines under vortex induced vibrations. A two equation model interacted through velocity coupling with a non-linear stiffness term for pipeline model and a non-linear damping term for wake is considered. The proposed model is found to represent the real situation of responses to a greater extent.

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Imprecision of Laboratory Determinations and Diagnostic Accuracy: Theoretical Considerations

Methods of Information in Medicine ◽

10.1055/s-0038-1636147 ◽

1974 ◽

Vol 13 (03) ◽

pp. 151-158 ◽

Cited By ~ 5

Author(s):

D. A. B. Lindbebo ◽

Fr. R. Watson

Keyword(s):

Mathematical Model ◽

Diagnostic Accuracy ◽

Diagnostic Process ◽

Clinical Laboratories ◽

Non Linear ◽

Theoretical Considerations ◽

Made In

Recent studies suggest the determinations of clinical laboratories must be made more precise than at present. This paper presents a means of examining benefits of improvement in precision. To do this we use a mathematical model of the effect upon the diagnostic process of imprecision in measurements and the influence upon these two of Importance of Diagnosis and Prevalence of Disease. The interaction of these effects is grossly non-linear. There is therefore no proper intuitive answer to questions involving these matters. The effects can always, however, be calculated.Including a great many assumptions the modeling suggests that improvements in precision of any determination ought probably to be made in hospital rather than screening laboratories, unless Importance of Diagnosis is extremely high.

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Glycemia monitoring

Nonlinear Analysis Modelling and Control ◽

10.15388/na.1998.2.0.15282 ◽

1998 ◽

Vol 2 ◽

pp. 23-30

Author(s):

Igor Basov ◽

Donatas Švitra

Keyword(s):

Diabetes Mellitus ◽

Mathematical Model ◽

Numerical Methods ◽

Differential Equations ◽

Blood Sugar ◽

Self Regulation ◽

Physiological System ◽

Non Linear ◽

The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY SERIES MANAGEMENT COMPUTER SCIENCE AND INFORMATICS ◽

10.24143/2072-9502-2017-2-27-38 ◽

2017 ◽

pp. 27-38

Author(s):

Olga Mikhaylovna Tikhonova ◽

Alexander Fedorovich Rezchikov ◽

Vladimir Andreevich Ivashchenko ◽

Vadim Alekseevich Kushnikov

Keyword(s):

Mathematical Model ◽

System Dynamics ◽

Regression Model ◽

Oriented Graph ◽

Real Data ◽

Educational Process ◽

Proposed Model ◽

Linear Differential ◽

The University ◽

The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

Water Science & Technology ◽

10.2166/wst.1986.0295 ◽

1986 ◽

Vol 18 (7-8) ◽

pp. 239-248 ◽

Cited By ~ 2

Author(s):

Sung Ryong Ha ◽

Dwang Ho Lee ◽

Sang Eun Lee

Keyword(s):

Mathematical Model ◽

Anaerobic Digestion ◽

Biomass Concentration ◽

Gas Production ◽

Septic Tank ◽

Volatile Acid ◽

Hydraulic Residence Time ◽

Anaerobic Digestion Process ◽

Digestion Process ◽

Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

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On the Dragging Trajectory of Anchors in Clay for Merchant Ships

Journal of Marine Science and Engineering ◽

10.3390/jmse9020118 ◽

2021 ◽

Vol 9 (2) ◽

pp. 118

Author(s):

Xinqing Zhuang ◽

Keliang Yan ◽

Pan Gao ◽

Yihua Liu

Keyword(s):

Mathematical Model ◽

Structural Integrity ◽

Indirect Measurement ◽

Test System ◽

Flow Rule ◽

Burial Depth ◽

Proposed Model ◽

Depth Increase ◽

Two Parameters ◽

The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

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Content Dependent Representation Selection Model for Systems Based on MPEG DASH

Electronics ◽

10.3390/electronics10151843 ◽

2021 ◽

Vol 10 (15) ◽

pp. 1843

Author(s):

Jelena Vlaović ◽

Snježana Rimac-Drlje ◽

Drago Žagar

Keyword(s):

Mathematical Model ◽

Spatial Information ◽

Relevant Literature ◽

Video Quality ◽

Similarity Index ◽

Video Encoding ◽

Adaptation Algorithm ◽

Subjective Testing ◽

Proposed Model ◽

The Mathematical Model

A standard called MPEG Dynamic Adaptive Streaming over HTTP (MPEG DASH) ensures the interoperability between different streaming services and the highest possible video quality in changing network conditions. The solutions described in the available literature that focus on video segmentation are mostly proprietary, use a high amount of computational power, lack the methodology, model notation, information needed for reproduction, or do not consider the spatial and temporal activity of video sequences. This paper presents a new model for selecting optimal parameters and number of representations for video encoding and segmentation, based on a measure of the spatial and temporal activity of the video content. The model was developed for the H.264 encoder, using Structural Similarity Index Measure (SSIM) objective metrics as well as Spatial Information (SI) and Temporal Information (TI) as measures of video spatial and temporal activity. The methodology that we used to develop the mathematical model is also presented in detail so that it can be applied to adapt the mathematical model to another type of an encoder or a set of encoding parameters. The efficiency of the segmentation made by the proposed model was tested using the Basic Adaptation algorithm (BAA) and Segment Aware Rate Adaptation (SARA) algorithm as well as two different network scenarios. In comparison to the segmentation available in the relevant literature, the segmentation based on the proposed model obtains better SSIM values in 92% of cases and subjective testing showed that it achieves better results in 83.3% of cases.

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MODELING AND PRODUCTIVITY PREDICTION OF THE COMPANIES-INTERNAL CROWDSOURCING-BASED IDEATION

Proceedings of the Design Society ◽

10.1017/pds.2021.476 ◽

2021 ◽

Vol 1 ◽

pp. 2147-2156

Author(s):

Pavel Livotov

Keyword(s):

Mathematical Model ◽

Finite Number ◽

Research Question ◽

Performance Function ◽

Non Linear ◽

Series Of Experiments ◽

Productivity Prediction ◽

A Company

AbstractThe internal crowdsourcing-based ideation within a company can be defined as an involvement of its staff, specialists, managers, and other employees, to propose solution ideas for a pre-defined problem. This paper addresses a question, how many participants of the company-internal ideation process are required to nearly reach the ideation limit for the problems with a finite number of workable solutions. To answer the research question, the author proposes a set of metrics and a non-linear ideation performance function with a positive decreasing slope and ideation limit for the closed-ended problems. Three series of experiments helped to explore relationships between the metric attributes and resulted in a mathematical model which allows companies to predict the productivity metrics of their crowdsourcing ideation activities such as quantity of different ideas and ideation limit as a function of the number of contributors, their average personal creativity and ideation efficiency of a contributors’ group.

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