Synthesis Of Mathematical Models Research Articles

Spatial motions transformers for incorporation into robot systems – review of the Bulgarian experience

This work is a review of research carried out by the author on the synthesis and design of the spatial gear mechanisms, oriented for incorporation in various technical devices, especially in robotic systems. It contains also a description of the innovative and inventive activities of the author over the years. The study illustrates the elaborated through the years, basic algorithms for the synthesis of spatial motions transformers (in particular Spiroid and Helicon gear sets), which are based on the mathematical model for synthesis upon a pitch contact point. The content of the solution of the two main tasks of the synthesis - synthesis of the pitch configurations and synthesis of the active tooth surfaces configures the mentioned above algorithm. Through it, real models of Spiroid and Helicon gear transmissions are synthesized and elaborated by 3D printing subsequently, which are designed for incorporation into robots of various purposes

Mathemathical Simulation of the Combustion of a Mechanically Activated 3Ni + Al Mixture

A mathematical model of synthesis in a mechanically activated 3Ni–Al system is constructed in a macroscopic approximation. Different combustions as the functions of duration of mechanical activation and the duration of isothermal exposure of the mechanical mixture are determined. Experimental data are used to calculate kinetic constants that characterize the conversion of the substance during mechanical treatment.

SYNTHESIS OF DOUBLE-LOBED CAM MECHANISMS WITH TRANSLATING DOUBLE - ROLLER FOLLOWER

Two rational mathematical models for synthesis of mechanisms with conjugate disk cams translating with offset roller follower are derived from the equivalent four-bar linkage theory. They are linear and comparable in their relative simplicity, applicability and principle accuracy. The re-sults obtained from one model are verified by another, so any errors are excluded. The conditions for the same profile of the double-lobed cam are obtained. The models are demonstrating by means of example for the cam profile synthesis.

Математическая модель синтеза интегрированной системы безопасности на основе теории игр и применения квалиметрической оценки качества

Математическая модель синтеза интегрированной системы безопасности на основе теории игр и применения квалиметрической оценки качества

Regular Mechanical Transformation of Rotations Into Translations: Part 1. Kinematic Analysis and Definition of the Basic Characteristics

Abstract The science that study the processes of motions transformation upon a preliminary defined law between non-coplanar axes (in general case) axes of rotations or axis of rotation and direction of rectilinear translation by three-link mechanisms, equipped with high kinematic joints, can be treated as an independent branch of Applied Mechanics. It deals with mechanical behaviour of these multibody systems in relation to the kinematic and geometric characteristics of the elements of the high kinematic joints, which form them. The object of study here is the process of regular transformation of rotation into translation. The developed mathematical model is subjected to the defined task for studying the sliding velocity vector function at the contact point from the surfaces elements of arbitrary high kinematic joints. The main kinematic characteristics of the studied type motions transformation (kinematic cylinders on level, kinematic relative helices (helical conoids) and kinematic pitch configurations) are defined on the bases of the realized analysis. These features expand the theoretical knowledge, which is the objective of the gearing theory. They also complement the system of kinematic and geometric primitives, that form the mathematical model for synthesis of spatial rack mechanisms.

Mathematical modeling of the thermal explosion in mechanically activated SiO2 + Al mixtures

A mathematical model of synthesis in a mechanically activated SiO2 + Al mixture is constructed in the macroscopic approximation. It is demonstrated that preliminary mechanical activation makes it possible to obtain solid-phase ignition and to ensure synthesis of Al2O3 and Si products in the thermal explosion regime. Based on experimental data, thermophysical and thermokinetic constants of the process are determined.

Synthesis of radiological models and radiological constants. Part 4: Synthesis of population-phenomenological models and the Lyman model

The goal of this work was to synthesize Lyman mathematical models (MM), which describe the probability of post-radiation complications (PRC) in tissue subjected to radiation therapy with given scheme of dose fractionating (DF), and population-phenomenological (PP) MMs PP3 and PP4, which describe equivalent DF schemes for a fixed PRC value. Construction of synthesized MMs (SMMs) becomes possible only on the basis of several assumptions requiring further clinical validation. Synthesized MMs can be used for determination of the optimal dynamic conditions of irradiation of malignant tumors. These conditions include the optimal physical plan of irradiation and the optimal time scheme of its implementation. Synthesis of MMs leads to determination of radiological invariants (constants), which can become a basis for a new branch of medical science, quantitative radiology.

Synthesis of radiological models and radiological invariants (constants). Part 3: Synthesis of population-phenomenological models and Klepper model

The goal of this work was to synthesize Klepper mathematical models (MM), which describes the probability of post-radiation complications (PRC) in tissue subjected to radiation therapy with given scheme of dose fractionating (DF), and population-phenomenological (PP) MMs PP3 and PP4, which describe equivalent DF schemes for a fixed PRC value. Construction of synthesized MMs (SMMs) becomes possible only on the basis of several assumptions requiring further clinical validation. Synthesized MMs can be used for determination of the optimal dynamic conditions of irradiation of malignant tumors. These conditions include the optimal physical plan of irradiation and the optimal time scheme of its implementation. Synthesis of MMs leads to determination of radiological invariants (constants), which can become a basis for a new branch of medical science, quantitative radiology.

Synthesis of radiological models and radiological invariants (Constants). Part 2

The goal of this work was to synthesize a mathematical model (MM) on the basis of Klepper and Lyman MMs, which describe the probability of post-radiation complications (PRC) in tissue subjected to radiation therapy with given scheme of dose fractionating (DF), and the LQ-model, which describes equivalent DF schemes for a fixed PRC value. Construction of synthesized MMs (SMMs) becomes possible only on the basis of several assumptions requiring further clinical validation. Synthesized MMs can be used for determination of the optimal dynamic conditions of irradiation of malignant tumors. These conditions include the optimal physical plan of irradiation and the optimal time scheme of its implementation. Synthesis of MMs leads to determination of radiological invariants (constants), which can become a basis for a new branch of medical science, quantitative radiology.

Synthesis of Radiological Models and Radiological Invariants (Constants). Part 1

Work is devoted to synthesis of mathematical models (MM) which describe probability of appearance of radiation complication (ARC) in a tissue at the Klepper's fixed scheme of dose fractionation (FD) and Ellis's MM, which describes equivalent schemes FD for fixed value ARC. Creation of synthesized mathematical models(S) appears possible at some assumptions which require a check on the basis of the clinical information are necessary for definition of optimum dynamic conditions of an radiation of cancerous growths which include the optimum physical radiation plan and the optimum scheme its realization in time. The synthesis of MM leads to natural appearance of radiological invariants (constants) which can become a basis for construction of a new scientific direction of quantitative radiology.

Mathematical model of goethite synthesis by oxyprecipitation of steel pickling liquors

The aim of this paper is to study the synthesis of goethite by means of oxyprecipitation of sulphuric steel pickling liquors. The selected variables are pH, stirring velocity and flow of oxygen as oxidizer agent, a mathematical model of this synthesis being proposed from the experimental design. The model has validity in the variables' intervals. An analysis of residuals, a plot of predicted vs. observed values and an analysis of variance of the model are carried out as diagnostic probes. Posteriorly, the influence of the variables and their optimum values are determined for obtaining high quality goethite.