Design Of Mathematical Model Research Articles

Application of Mathematical Models in Graphic Design

The article shares the practical experience in creating graphic design in the implementation of projects in the field of applied information technology. The creation of digital art is largely based on mathematical models and concepts that give a good perception of graphics, and it is scientifically justified. The STEAM approach is considered with the idea of the transdisciplinary level of integration between mathematics, graphic design and production practice in student education. For the development of projects like logo design, magazine cover and others, we use software specialized in the field of graphic design and computer graphics. For the realization of the considered projects, among which there are also awarded ones, we use CorelDRAW, Adobe InDesign and Desmos.

Mechanical design and friction modelling of a cable-driven upper-limb exoskeleton

This paper presents a lightweight and low-inertia cable-driven upper-limb exoskeleton powerful enough to meet the requirements for activities of daily living. It presents the mechanical design, kinematic structure,the underlying actuation system, sensors, other electronic components as well as the controller of the exoskeleton.The extensive effect of friction on cable-driven designs, such as the one presented in this paper, requires proper mathematical modelling for controller design. Thus, we propose a current actuator model that describes the relationship between the motor current, velocity, and external load. The model relies on an underlying Stribeck+Coulomb friction representation and an additional parameter that modifies its Coulomb friction representation with an offset to represent adhesion between a cable and sheath.The model has been validated based on experimental data collected with the exoskeleton. The results show that the proposed model better captures the non-linear behaviour of the exoskeleton’s actuation system, increasing overall descriptive performance by 15%. However, adding the adhesion offset to extend the relation of static friction, does not improve the model.

Burden Imposed by Heterologous Protein Production in Two Major Industrial Yeast Cell Factories: Identifying Sources and Mitigation Strategies.

Production of heterologous proteins, especially biopharmaceuticals and industrial enzymes, in living cell factories consumes cellular resources. Such resources are reallocated from normal cellular processes toward production of the heterologous protein that is often of no benefit to the host cell. This competition for resources is a burden to host cells, has a negative impact on cell fitness, and may consequently trigger stress responses. Importantly, this often causes a reduction in final protein titers. Engineering strategies to generate more burden resilient production strains offer sustainable opportunities to increase production and profitability for this growing billion-dollar global industry. We review recently reported impacts of burden derived from resource competition in two commonly used protein-producing yeast cell factories: Saccharomyces cerevisiae and Komagataella phaffii (syn. Pichia pastoris). We dissect possible sources of burden in these organisms, from aspects related to genetic engineering to protein translation and export of soluble protein. We also summarize advances as well as challenges for cell factory design to mitigate burden and increase overall heterologous protein production from metabolic engineering, systems biology, and synthetic biology perspectives. Lastly, future profiling and engineering strategies are highlighted that may lead to constructing robust burden-resistant cell factories. This includes incorporation of systems-level data into mathematical models for rational design and engineering dynamical regulation circuits in production strains.

A Developed Mathematical Model for Designing a Multilevel Sustainable Supply Chain Network Taking into Account Environmental Decisions

In this research, a novel mathematical model for sustainable supply chain network design is proposed. The main contribution and novelty of this research are considering environmentally friendly facilities and several thresholds for emitted pollution, which bring this research closer to real‐world conditions. Since the amount of pollution produced by different supply chain facilities is not the same, it is better to make different decisions regarding each repair and renovation measure, i.e., environmental decisions should be considered step‐by‐step. In addition, the proposed model was optimized by the whale optimization algorithm (WOA) to find the best solution in large‐scale instances in a short and reasonable time. Finally, the performance of the proposed model and the reduction of environmental impacts to improve the stability of logistics systems are reviewed in a case study. The results of the computational analysis show the efficiency of the proposed model.

A Novel Mathematical Model for Tillage Production Planning and Facility Layout Design

Cell formation and layout design are important steps in the implementation of production systems. Existing models focus mainly on the problem of cell formation and machine layout design and cell location in a dynamic environment, with the exception of a few recent studies. Also, in many existing articles, binary information has been used for cell formation and other information such as production volume, operation sequence and lower production costs have played a role in the structure of existing models. In this paper, a nonlinear programming model under possible dynamic conditions is presented. The objectives of the model include minimizing the total costs of intracellular and intercellular movements of parts, the existence of exceptional parts, intercellular layout of machines, operating costs, fixed costs of machines and the cost of the difference in demand estimated by the model from its expected value. A genetic algorithm is used to solve and the results are compared with the optimal solution.

AN OPTIMIZATION MODEL FOR PRELIMINARY STABILITY AND CONFIGURATION ANALYSES OF SEMI-SUBMERSIBLES

In the modern era of design governed by economics and efficiency, the preliminary design of a semi-submersible is critically important because in an evolutionary design environment new designs evolve from the basic preliminary designs and the basic dimensions and configurations affect almost all the parameters related to the economics and efficiency (e.g. hydrodynamic response, stability, deck load and structural steel weight of the structure, etc.). The present paper is focused on exploring an optimum design method that aims not only at optimum motion characteristics but also optimum stability, manufacturing and operational efficiency. Our proposed method determines the most preferable optimum principal dimensions of a semi-submersible that satisfies the desired requirements for motion performance and stability at the preliminary stage of design. Our proposed design approach interlinks the mathematical design model with the global optimization techniques and this paper presents the preliminary design approach, the mathematical model of optimization. Finally, a real world design example of a semi-submersible is presented to show the applicability and efficiency of the proposed design optimization model at the preliminary stage of design.

Computational modeling of schedule-specific chemotherapy outcomes in mouse tumor model

Despite the rapid development of new innovative strategies in cancer treatment like immunotherapy, chemotherapy still remains a common choice in many cases. Standard protocols of chemotherapeutic administration rely on a maximal tolerated dose paradigm, however there is growing evidence that this approach is not always optimal. Alternative scheduling, like metronomic - low dose continuous drug administration - were recently proved their efficacy. The space of available variants of drug administration protocols is prohibitively large to be explored empirically, and there is an urgent need of predictive mathematical models for rational chemotherapeutic scheduling design. In this work we tested the ability of the minimal pharmacokinetic-pharmacodynamics model to describe schedule-specific tumor volume time evolution in different mouse tumor models.

Geometric forming and mechanical performance of reciprocal frame structures assembled using fibre reinforced composites

Reciprocal frame (RF) structures were developed in this work using pultruded glass fibre reinforced polymer (GFRP) members and the formulation of mathematical model for geometric forming and capacity design of such structures were presented. Firstly, governing geometric relationships are identified for the height, span and slope of the RF structure and its overall geometry can be formed accordingly. Once the geometry is determined, the structure can be analysed to calculate the internal forces of each component and connections under given loads. GFRP pultruded members were used to assemble the RF structure due to their high strength and lightweight. Considering the closed shape of the tubular section and the anisotropy of the materials, an innovative connection configuration was developed to facilitate the assembly and minimise the requirement of tools in the construction. Both the conceptual design and modelling analysis are supported with experimental results at connection and structural levels. The load-drift relationships of the connections were experimentally examined. Subsequently, A GFRP reciprocal frame structure was then assembled with a span of 4.5 m and subjected to multi-point bending to verify the proposed evaluation method and to study its mechanical performance. Verified by experimental results, a two-dimensional numerical model of the RF structure was developed and analysed using the finite element (FE) approach where different structural boundary conditions and connection stiffnesses were discussed. Finally, the geometrical nonlinear analysis was also studied for the structure through FE modelling.

A New Design Model of an MR Shock Absorber for Aircraft Landing Gear Systems Considering Major and Minor Pressure Losses: Experimental Validation

This work presents a novel design model of a magnetorheological (MR) fluid-based shock absorber (MR shock absorber in short) that can be applied to an aircraft landing gear system. When an external force acts on an MR shock absorber, pressure loss occurs at the flow path while resisting the fluid flow. During the flow motion, two pressure losses occur: the major loss, which is proportional to the flow rate, and the minor loss, which is proportional to the square of the flow rate. In general, when an MR shock absorber is designed for low stroke velocity systems such as an automotive suspension system, the consideration of the major loss only for the design model is well satisfied by experimental results. However, when an MR shock absorber is applied to dynamic systems that require high stroke velocity, such as aircraft landing gear systems, the minor loss effect becomes significant to the pressure drop. In this work, a new design model for an MR shock absorber, considering both the major and minor pressure losses, is proposed. After formulating a mathematical design model, a prototype of an MR shock absorber is manufactured based on the design parameters of a lightweight aircraft landing gear system. After establishing a drop test for the MR shock absorber, the results of the pressure drop versus stroke/stroke velocity are investigated at different impact energies. It is shown from comparative evaluation that the proposed design model agrees with the experiment much better than the model that considers only the major pressure loss.

A new multi-objective mathematical model for a Citrus supply chain network design: Metaheuristic algorithms

Nowadays, the citrus supply chain has been motivated by both industrial practitioners and researchers due to several real-world applications. This study considers a four-echelon citrus supply chain, consisting of gardeners, distribution centers, citrus storage, and fruit market. A Mixed Integer Non-Linear Programming (MINLP) model is formulated, which seeks to minimize the total cost and maximize the profit of the Citrus supply chain network. Due to the complexity of the model when considering large-scale samples, two well-known meta-heuristic algorithms such as Ant Colony Optimization (ACO) and Simulated Annealing (SA) algorithms have been utilized. Additionally, a new multi-objective ACO algorithm based on a set of non-dominated solutions form the Pareto frontier developed to solve the mathematical model. An extensive comparison based on different measurements analyzed to find a performance solution for the developed problem in the three sizes (small, medium, and large-scale). Finally, the various outcomes of numerical experiments indicate that the MOACO algorithm is more reliable than other algorithms.

Forward osmosis system design and optimization using a commercial cellulose triacetate hollow fibre membrane module for energy efficient desalination

This study is aimed at developing system mathematical design models to simulate and optimize a full scale forward osmosis (FO) for a hollow fibre membrane module for energy efficient desalination. Experimental data from a commercial outer selective CTA hollow fibre FO membrane module was used for validation. Less than 10% difference between the simulation and experimental results were observed which validated the reliability of the models. Simulation and design were performed for a 1000 m3/day FO plant using 0.6 M NaCl as draw solution (DS) (~seawater) and 0.02 M NaCl feed solution (FS) (~MBR effluent) to produce 0.25, 0.2 and 0.15 M NaCl diluted seawater to reduce the energy consumption of downstream pressure driven desalination process. A single element parallel module arrangement was found more suitable for this commercial hollow fibre membrane element. Finally, the numerical simulations revealed that to achieve 0.25, 0.20 and 0.15 M final DS concentrations, the optimum number of modules required were 370, 435 and 555 respectively considering membrane cost and energy consumption. The FO system using the commercial CTA hollow fibre module was found more energy efficient than a commercial TFC spiral wound membrane module.

Curriculum spaces and mathematical models for curriculum design

The area of mathematical psychology concerning knowledge spaces is complemented by the theoretical notion of a “curriculum space,” which is developed as a mathematical model for curriculum design in order to illuminate the interplay between learners and the curricula in which they enroll. The analysis is carried out in terms of concepts from graph theory and order theory, yielding a precise language in which to communicate aspects of curricular influences on student-achievement. Emphasis is placed on the structure of tasks that are addressed in a curriculum, the structure of prerequisite-course assignments within the curriculum, and the compatibility between these structures. Among the main results, conditions are given under which the tasks in a curriculum induce a partially ordered set, curricula that admit “compatible” prerequisite-structures are completely characterized, and a greedy algorithm is presented for categorizing courses into “curriculum maps” that respect the compatibility condition.

LCTC Ships Concept Design in the North Europe- Mediterranean Transport Scenario Focusing on Intact Stability Issues

In late years, the size of RoRo cargo ships has continuously increased, leading to the so-called Large Car Truck Carriers (LCTC). The design of these vessels introduced new challenges that shall be considered during the ship design since the conceptual stage, which has a very strong impact on the technical and economic performances of the vessel during all its life-cycle. In this work, the concept design of an LCTC is presented based on Multi-Attribute Decision Making (MADM). A large set of design alternatives have been generated and compared in order to find out the most promising feasible designs. The proposed approach is based on a Mathematical Design Model (MDM) capable to assess all the main technical and economic characteristics for each design. Among the others, here focus has been done on the ship stability to assure the compliance with statutory rules within the MDM. A new stability metamodel has been developed capable to define the cross curves of stability at the concept design stage. The proposed MADM methodology has been applied to North Europe-Mediterranean transport scenario highlighting the impact of main particulars describing hull geometry on the technical and economic performances of an LCTC ship.

Measuring the spatial quality of bedrooms in nursing homes with visual environmental performance

The elderly's perception of their environment largely depends on acquired visual information. This study provides a quantitative analytical method for designing bedrooms in nursing homes by developing a computational model that uses viewing distance, viewing angle, and viewing field as variables. The model is utilized to measure a range of visual environmental properties, including privacy, accessibility, permeability, and visibility, which reflect the quality of bedrooms in nursing homes. The suitability levels of bedroom planes for the elderly and their main living functions as well as the fitting degree of the functional layout are calculated based on these data. After validating the computational model's feasibility, this study optimizes the typical schemes of single and double rooms in nursing homes. Results reveal certain advantages of the arrangement where bathroom doors are set toward the inside of the bedroom and double rooms have a large width. The computational model can be used in measuring the spatial quality of bedrooms in nursing homes and as a mathematical model for related algorithm design and software programming to assist in the design and optimization of bedrooms for the elderly.

Mathematical model of a journal bearing with low-melting and porous coating in its structure on different contacting surfaces with incomplete filling of operating clearance

The authors consider the development of a mathematical design model of an infinite journal bearing lubricated with a lubricant with Newtonian rheological properties and a melt of a low-melting metal alloy covering the surface of the bearing bush, as well as a porous coating on the surface of the shaft, taking into consideration the dependence of the viscosity characteristics of the lubricant, the melt and the permeability of the porous coatings on the pressure with incomplete filling of the operating clearance. The authors found asymptotic solution of the system of differential equations with respect to the parameter K due to the melt and the rate of dissipation of mechanical energy and the exact self-similar solution for the zero approximation without regard for the melt and the first approximation taking into consideration the melt. This solution was found according to the equation of motion of a viscous incompressible fluid for a thin layer, the equations of continuity, Darcy equation and the equation determining, taking into account the expression for the rate of dissipation of mechanical energy, the profile of the molten contour of the bearing bush with regard to the dependence of the permeability of the porous coating, the viscosity of the lubricant depending on pressure. As a result, the fields of velocities and pressures in the lubricating and porous layers were determined taking into consideration the dependence of the lubricant viscosity and the permeability of the porous coating on pressure, as well as the function Φ1(θ), reasoned by the melt of the bearing bush surface. In addition, the main performance characteristics were determined: load-bearing capacity and friction force.

Effects of nitrogen application rate and hill density on rice yield and nitrogen utilization in sodic saline–alkaline paddy fields

Soil salinity and alkalinity can inhibit crop growth and reduce yield, and this has become a global environmental concern. Combined changes in nitrogen (N) application and hill density can improve rice yields in sodic saline–alkaline paddy fields and protect the environment. We investigated the interactive effects of N application rate and hill density on rice yield and N accumulation, translocation and utilization in two field experiments during 2018 and 2019 in sodic saline–alkaline paddy fields. Five N application rates (0 (control), 90, 120, 150, and 180 kg N ha–1 (N0–N4), respectively) and three hill densities (achieved by altering the distance between hills, in rows spaced 30 cm apart: 16.5 cm (D1), 13.3 cm (D2) and 10 cm (D3)) were utilized in a split-plot design with three replicates. Nitrogen application rate and hill density significantly affected grain yield. The mathematical model of quadratic saturated D-optimal design showed that with an N application rate in the range of 0–180 kg N ha–1, the highest yield was obtained at 142.61 kg N ha–1 which matched with a planting density of 33.3×104 ha–1. Higher grain yield was mainly attributed to the increase in panicles m–2. Nitrogen application rate and hill density significantly affected N accumulation in the aboveground parts of rice plants and showed a highly significant positive correlation with grain yield at maturity. From full heading to maturity, the average N loss rate of the aboveground parts of rice plants in N4 was 70.21% higher than that of N3. This is one of the reasons why the yield of N4 treatment is lower than that of the N3 treatment. Nitrogen accumulation rates in the aboveground parts under treatment N3 (150 kg N ha–1) were 81.68 and 106.07% higher in 2018 and 2019, respectively, than those in the control. The N translocation and N translocation contribution rates increased with the increase in the N application rate and hill density, whereas N productivity of dry matter and grain first increased and then decreased with the increase in N application rate and hill density. Agronomic N-use efficiency decreased with an increase in N application rate, whereas hill density did not significantly affect it. Nitrogen productivity of dry matter and grain, and agronomic N-use efficiency, were negatively correlated with grain yield. Thus, rice yield in sodic saline–alkaline paddy fields can be improved by combined changes in the N application rate and hill density to promote aboveground N accumulation. Our study provides novel evidence regarding optimal N application rates and hill densities for sodic saline–alkaline rice paddies.

A Robust Mathematical Model for Sustainable and Resilient Supply Chain Network Design: Preparing a Supply Chain to Deal with Disruptions

Supply chains suffer from serious vulnerabilities and disruptions with increasing global crises, including pandemics and natural disasters. Dynamic and complex supply chain environments have constantly led companies to modern management approaches such as resilience to address disruptions. Besides, the sustainability approach enhances the strength of the supply chain in disruptions by considering economic, social, and environmental aspects. This paper develops a mathematical model for designing a supply chain network considering resilience and sustainability. In this model, suppliers were exposed to disruption with different probabilities. The model has three objectives: minimizing total costs and maximizing suppliers’ social and environmental scores. A robust scenario‐based stochastic programming approach has been used for potential disruption scenarios. The multiobjective model is solved by theε‐constraint method in GAMS software. The numerical results show the performance of the model in a different situation. Also, the robust scenario‐based stochastic programming approach allows the average performance of the supply chain in each objective to improve.

A Mathematical Model for Integrated Green Healthcare Supply Network Design

This research presents a novel integrated mathematical programming model for green healthcare supply network design. A multi-graph integrated supply network was designed to meet real-world situations. Minimizing total cost and minimizing delivery time are considered as the objective functions. Since the considered problem is np-hard and the presented mathematical model is very complex and highly constrained, an innovative non-dominated ranked genetic algorithm (NRGA) called M-NRGA is developed to solve the real word problems. Three different selection procedures were implemented to improve the quality and diversity of solutions in the Pareto-front resulted from M-NRGA. Several numerical examples and a case study are solved to validate the model and performance evaluation of the solution algorithm. Four different performance metrics are implemented for performance evaluation of the solution algorithm. The quality of resulted solutions, the diversity of the solutions in the Pareto front are calculated for evaluation. The results are compared with two other meta-heuristic algorithms.

Mathematical Model for Gaussian-Like Pulse Design for a UWB System Based on the Generalized Bessel Polynomials

Mathematical Model for Gaussian-Like Pulse Design for a UWB System Based on the Generalized Bessel Polynomials

Возможность оценки безопасности судна на начальных стадиях проектирования

This paper presents safety assessments incorporated to the mathematical design model of a container ship, implemented and investigated in procedural documents. From the theoretical standpoint, these results enrich ship design theory. From the practical standpoint, they could become an additional justification in the selection of optimal ship design with respect to RS Register Rules, so that the customer could estimate the safety of his novel ship already at early design stages.