A Novel INDI based Guidance Law for Fixed Wing Aircrafts: Derivation and Application

In this paper, we comprehensively present and derive two INDI principle based guidance laws for fixed wing aircrafts. More specifically, two control methods are mathematically derived in detail, where the first decouples the lateral and the longitudinal channels while the second takes the interactions into account. The cumbersome mathematical operations involved in the derivation process aim at reaching a more concise control method and also at providing the community with clearer physical concepts behind this formula. The reason for manipulating transformation matrices is to find a univariate function and to isolate the variable as a virtual input. Efficient and modular guidance control law is then permitted. Lastly, the proposed guidance methods are applied to a 6 dof nonlinear platform under various flight modes to demonstrate the feasibility and advantages.

A Novel INDI based Guidance Law for Fixed Wing Aircrafts: Derivation and Application

In this paper, we comprehensively present and derive two INDI principle based guidance laws for fixed wing aircrafts. More specifically, two control methods are mathematically derived in detail, where the first decouples the lateral and the longitudinal channels while the second takes the interactions into account. The cumbersome mathematical operations involved in the derivation process aim at reaching a more concise control method and also at providing the community with clearer physical concepts behind this formula. The reason for manipulating transformation matrices is to find a univariate function and to isolate the variable as a virtual input. Efficient and modular guidance control law is then permitted. Lastly, the proposed guidance methods are applied to a 6 dof nonlinear platform under various flight modes to demonstrate the feasibility and advantages.

Compositional Closure—Its Origin Lies Not in Mathematics but Rather in Nature Itself

Compositional closure, spurious negative correlations in data sets of a fixed sum (e.g., fractions and percent), is often encountered in geostatistical analyses, particularly in mineralogy, petrology, and geochemistry. Techniques to minimize the effects of closure (e.g., log-ratio transformations) can provide consistent geostatistical results. However, such approaches do not remove these effects because closure does not result from mathematical operations but is an inherent property of the physical systems under study. The natural world causes physical closure; mathematics simply describes that closure and cannot alter it by manipulations. Here, we examine the distinct types of geologic systems and samples to determine in which situations closure (physical and mathematical) does or does not ensue and the reasons therefor. We parse compositional systems based on (1) types of components under study, immutable (e.g., elements) or reactive (minerals), and (2) whether the system is open or closed to component transfer. Further, open systems can be (1) displacive in which addition of a component physically crowds out others, or (2) accommodative in which addition or subtraction of components does not affect the others. Only displacive systems are subject to compositional closure. Accommodative systems, even with components expressed as percent or fractions, are not closed physically or, therefore, mathematically.

Educational Games Design

Video games are widely and increasingly adopted in the educational field thanks to their inherent engaging, immersive, and adaptive capacities. Yet, one of the greatest problematic in educational games design remains how to create ludic and adaptive experiences without going astray from the targeted learning objectives. In creating adaptive educational games, modeling the learner/player is a prerequisite. This chapter highlights the importance of educational standards in learning content design and proposes an adaptive mechanism “AMEG” based on IMS learning design and artificial intelligence that model learners using game metrics and adapt the gameplay as well as the learning content. As a practical experimentation of the mechanism, MathQuests, an educational game that helps in teaching mathematical operations for first year middle school students was created.

Predicting Logarithm of Real Numbers to any Real Number Base

This paper aims to propose an algorithm that can predict the values of logarithmic function for any domain and for any bases with minimum possible error using basic mathematical operations. It talks about a univariate quadratic function that overlaps with the graph of the common logarithmic function to some extent, and using this resemblance to fullest advantage. It proposes a formula and certain algorithms based on the same formula.

Совершенствование методов планирования ремонтных работ на основе анализа надежности нефтепроводной системы

The author presents the methodology for identifying risks in operation of main oil pipelines, which can be based upon in improvement of methods for planning overhauls of the main pipelines. A method for calculating reliability indicators of the system is reviewed, including analysis of the type distributions of the system elements failures pattern. The reliability of the system is determined by purely mathematical operations on the obtained distributions. Such an approach is typical for the system (structural, mathematical) theory of reliability, the key task thereof being the transition from the elements reliability indicators to the system reliability indicators. It is advisable to resolve the problems of calculating the actual reliability of a complex technical system taking for consideration the dependencies of its elements, based on the approach assuming that reliability of the elements and the system shall be calculated in the general multi-level simulation process wherein both physical and structural models are used. Physical models of elements reliability are used at lower levels, while structural models are used at higher ones. Установлена своевременность и актуальность идентификации и формализации структурно-логических связей показателей эксплуатации линейной части магистральных нефтепроводов. Представлена методология идентификации рисков при эксплуатации магистральных нефтепроводов, которая может быть положена в основу совершенствования методов планирования их капитальных ремонтов. Рассмотрен метод для расчета показателей надежности технической системы, предусматривающий анализ типовых распределений отказов ее элементов. Надежность системы находится чисто математическими операциями над полученными распределениями. Подобный подход характерен для системной (структурной, математической) теории надежности, основной задачей которой является переход от показателей надежности элементов к показателям надежности системы. Задачи расчета реальной надежности сложной технической системы с учетом зависимостей ее элементов целесообразно решать на основе подхода, который состоит в том, что расчет надежности элементов и системы проводится в общем многоуровневом имитационном моделирующем процессе с применением физических и структурных моделей. Физические модели надежности элементов используются на низших уровнях, а структурные модели – на высших.

25 Meter Rifle Shooting Training Kit

The goal of this project is to obtain all of the details about the shotgun so that we can correct any mistakes made during practice. With so many undetectable errors made by operators at work, this device aids in locating and adjusting the timing of adjustments in accordance with their errors. This procedure is carried out by detecting deviations from the shooters while shooting from a distance. Following each session, all data is verified, and steps are taken to improve the shooters game and correct their mistakes. This device improves the quality of the archer while also assisting in the improvement of the game. It also appears to be a list of minor blunders that one may deal with. The arduino IDE, which does all mathematical and mathematical operations, is in charge of this device. The light attached to this device indicates the start and stop positions of the shooter, allowing the shooter to be trained to start and stop fire.

The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

Generalized deep iterative reconstruction for sparse-view CT imaging

Sparse-view CT is a promising approach in reducing the X-ray radiation dose in clinical CT imaging. However, the CT images reconstructed from the conventional filtered backprojection (FBP) algorithm suffer from severe streaking artifacts. Iterative reconstruction (IR) algorithms have been widely adopted to mitigate these streaking artifacts, but they may prolong the CT imaging time due to the intense data-specific computations. Recently, model-driven deep learning (DL) CT image reconstruction method, which unrolls the iterative optimization procedures into the deep neural network, has shown exciting prospect in improving the image quality and shortening the reconstruction time. In this work, we explore the generalized unrolling scheme for such iterative model to further enhance its performance on sparse-view CT imaging. By using it, the iteration parameters, regularizer term, data-fidelity term and even the mathematical operations are all assumed to be learned and optimized via the network training. Results from the numerical and experimental sparse-view CT imaging demonstrate that the newly proposed network with the maximum generalization provides the best reconstruction performance.

Alternative Methods of the Largest Lyapunov Exponent Estimation with Applications to the Stability Analyses Based on the Dynamical Maps—Introduction to the Method

Controlling stability of dynamical systems is one of the most important challenges in science and engineering. Hence, there appears to be continuous need to study and develop numerical algorithms of control methods. One of the most frequently applied invariants characterizing systems’ stability are Lyapunov exponents (LE). When information about the stability of a system is demanded, it can be determined based on the value of the largest Lyapunov exponent (LLE). Recently, we have shown that LLE can be estimated from the vector field properties by means of the most basic mathematical operations. The present article introduces new methods of LLE estimation for continuous systems and maps. We have shown that application of our approaches will introduce significant improvement of the efficiency. We have also proved that our approach is simpler and more efficient than commonly applied algorithms. Moreover, as our approach works in the case of dynamical maps, it also enables an easy application of this method in noncontinuous systems. We show comparisons of efficiencies of algorithms based our approach. In the last paragraph, we discuss a possibility of the estimation of LLE from maps and for noncontinuous systems and present results of our initial investigations.