MATHEMATICAL JUSTIFICATION OF STABILITY OF STEERING BRIDGE OF WHEELED TRACTOR

The article deals with the influence of wheel oscillation and the micro-profile of the road surface on the stability of the wheel tractor axle movement. The reasons for the oscillations of the steered wheels, the design diagram of the controlled axle of the tractor and the sequence for determining the oscillation frequency of the axle of the tractor are presented. The reasons for the oscillation of the steered wheels are collisions with bumps, imbalance of the wheels and a double connection with the tractor frame through the steering system and the fastening of the steering axle beam. The most common functions for describing road irregularities that affect the movement of a tractor are the mathematical expectation and the average value of the ordinates of the micro-profile, the variance or standard deviation of the ordinates, the correlation function characterizing the relationship of various implementations of the micro-profile functions along the length of the road section and spectral density. Oscillations of the steered wheels have a side effect on the stability of the tractor, which leads to oscillations of the steered axle due to the presence of an additional degree of freedom (turning around the pivot) in comparison with uncontrolled ones. In addition, the steered wheels are interconnected by a steering linkage, which is damped due to clearances. Oscillations of the wheels can also occur due to the fact that the radial (normal) stiffness of the tires around the circumference is not the same. When such a tire rolls, the wheel begins to oscillate in a vertical plane. Such oscillations, performed due to changes in the parameters of the oscillatory system, are called parametric. Self-oscillations of the steered wheels cause significant dynamic loads on the steering parts, intense tire wear and lead to a loss of tractor controllability and driving stability. One of the main reasons for the occurrence of oscillations of the steered wheels is the presence of a gyroscopic relationship between the angular oscillations of the beam of the steered bridge in the transverse plane and the rotation of the wheels of this bridge relative to the pins. The article also discusses the physical essence of the processes occurring during self-oscillations of the tractor's controlled wheels.

Computer Vision in Analyzing the Propagation of a Gas–Gunpowder Jet

A method of mathematically processing the digital images of targets is developed. The theoretical and mathematical justification and the experimental validation of the possibility of estimating the amount of gunshot residue (GSR) and determining the GSR distribution over the target on the basis of its digital image is provided. The analysis of the optical density in selected concentric rings in the images reveals the radial dependence of soot distribution in the cross section of a gas–gunpowder jet. The analysis of the optical density in selected sectors of the circle reveals the angular dependence of the soot distribution in the gas–gunpowder jet cross section. It is shown that the integral optical density averaged over a selected area in the target image characterizes the mass of GSP deposited on it. It is possible to quantify the differences in the radial and angular distributions of the thickness of the GSR layer on various targets obtained both with the help of weapons of different types at the same distances and with the help of weapons of the same type at different distances, by calculating the distribution of optical density on their digital images.

Theoretical Solutions to The Problem of Seepage and Consolidation in Saturated Clay Based on The Spatial Axisymmetric Model

The series solutions to the problem of spatial axisymmetric consolidation are deduced under non-homogeneous boundary conditions. Firstly, differentiable step function is introduced to construct the homogeneous operation function. Secondly, the operation function is used to superimpose the non-homogeneous boundaries to obtain homogeneous boundaries, non-homogeneous fundamental equation and new initial condition. Finally, the method of variables separation is used to construct the eigenfunction, and due to the mathematical justification of complete orthogonality of the eigenfunction, the series expansions of the fundamental equation and initial condition are carried out to obtain solutions for the seepage and consolidation in saturated clay with a borehole boundary. The correctness of the theoretical solutions are verified by the strict mathematical and mechanics derivation and the law of space-time variation in seepage flow.

A mathematical justification for metronomic chemotherapy in oncology

We mathematically justify metronomic chemotherapy as the best strategy to apply most cytotoxic drugs in oncology for both curative and palliative approaches, assuming the classical pharmacokinetic model together with the Emax pharmacodynamic and the Norton-Simon hypothesis.From the mathematical point of view, we will consider two mixed-integer nonlinear optimization problems, where the unknowns are the number of the doses and the quantity of each one, adjusting the administration times a posteriori.Mathematics Subject Classification: 93C15, 92C50, 90C30

A Short Note Regarding the Number of Bound Molecules of Oxygen to Hemoglobin

Oxygen, a molecule essential to many biological functions in the human body, binds coop?eratively to a protein known as hemoglobin. This cooperative binding of oxygen to hemoglobin can be described by a binding polynomial of degree n = 4. In this paper, I theoretically prove that a molecule of hemoglobin must have at least one molecule of oxygen bound to its subunits at any given point in time. I remove a condition for the equilibrium constants K_R and K_T in the binding polynomial for the binding of oxygen to hemoglobin. Removing the condition partially proves the proposed statement in this paper. I then make use of the cubic formula to derive the concentration of oxygen for which the number of bound oxygen molecules tohemoglobin is zero, thus completing a comprehensive mathematical justification of the proposed theoretical statement. Through this paper, I hope to provide a further insight into the mechanisms of oxygen and hemoglobin with regards to the respiratory system.

EXPERIMENTAL AND MATHEMATICAL JUSTIFICATION OF THE APPLICATION DIGITAL TECHNOLOGIES FOR RECORDING THE POSITION OF THE LOWER JAW DURING TOTAL PROSTHETICS USING DENTAL IMPLANTS

Subject. When prosthetics of toothless jaws are performed, the physiological position of the lower jaw must be determined before the final structures are made. In some cases, the use of temporary prostheses for several weeks may be useful to check for a new occlusion in a centric relationship. When the correct ratio is achieved, it is difficult to transfer them from the preliminary prostheses to the final ones. This article presents a case and a technique used to communicate information about the position of the lower jaw using a digital workflow. To determine the optimal position of the lower jaw, a computer tomogram of the temporomandibular joint was used to mathematically measure the correct position of the head of the lower jaw. Purpose. To describe a technique designed to transfer the inter-occlusal relations of the upper and lower jaws, using digital technologies in the prosthetics of full adentia using dental implants. Methodology. On the example of a clinical case of rehabilitation of a patient, total removal of failed teeth was performed, followed by prosthetics of complete adentia with the installation of six implants on the upper and lower jaws. After the completion of the integration period, a cone-beam computed tomography was performed with the capture of the temporomandibular joint, and a scan of plaster models with installed gum shapers was performed. The obtained data were compared in a specialized program for mathematical calculation of the optimal position of the lower jaw. This information was used to produce registration templates for the manufacture of fixed structures supported by implants in the resulting central jaw ratio. Results. A digital protocol for determining the central ratio of the jaws allowed us to transfer the information obtained in a virtual model of the temporomandibular joint to a permanent restoration based on implants. Conclusion. The approach described in this article predictably conveys information about the optimal position of the lower jaw during prosthetics and allows you to perform the final restoration on implants with optimal occlusal ratios, based on a mathematical calculation performed in specialized programs.

Factorization method with one plane wave: from model-driven and data-driven perspectives

The factorization method provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic plane waves at a fixed frequency (which are also called the multistatic data response matrix). This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source. Its one-wave version relies on the absence of analytical continuation of the scattered/radiated wave-fields in corner domains. It can be regarded as a domain-defined sampling method and does not require forward solvers. In this paper we provide a rigorous mathematical justification of the one-wave factorization method and present some preliminary numerical examples. In particular, the proposed method can be interpreted as a model-driven and data-driven imaging scheme, and it shows how to incorporate a priori knowledge about the unknown target into the test scatterers for the purpose of detecting obstacles/sources with specific features.

An Evolutionary Justification of the Emergence of Leadership Using Mathematical Models

The value and importance of leadership is evident by its prevalence throughout human societies and organizations. Based on an evolutionary argument, models are presented here that provide a mathematical justification as to how and why leadership arose in the first place and then persisted. In this setting, by a leader is meant a person whose overall actions are ultimately responsible for the well-being and survival of the group. The proposed models contain parameters whose values reflect group size, harshness of the environment, diversity of actions taken by individuals, and the amount of group cohesion. Mathematical analysis and computer simulations are used to identify conditions on these parameters under which leadership results in an increased survival probability for the community.

PROOF OF THE IMPOSSIBILITY OF THE PERFECT CUBOID EXISTENCE

The problem of finding, among the Euler parallelepipeds, one with an integer spatial diagonal, called the perfect cuboid problem, is one of the unsolved mathematical problems from the section of number theory. This article provides mathematical proof of the impossibility of the existence of the perfect cuboide among all possible Euler parallelepipeds. A mathematical justification for an equivalence of the problem of doubling a cube and the problem of constructing a perfect cuboid is also given.

Image Encryption Using RK-RSA Algorithm in Aadhaar Card

Cryptography is used for secretly sending information. The information or given data is protected by cryptographic technique. The technique is used in Text and images. The technique is supported by a lot of algorithms. RSA is a better encryption technique for smart cards. In this paper, an image in the Aadhaar card is encrypted using the RK-RSA algorithm for better protection and confidentiality. The proposed RK-RSA algorithm is very secure for smart cards and Aadhaar cards. The better performance of the RK-RSA is evaluated based on the Avalanche Effect, Speed, Throughput, and Power Consumption. The improved performance of the RK-RSA algorithm’s experimental results is reported. The mathematical justification supporting the RK-RSA algorithm is also detailed.