Claiming Land, Claiming Water shares what historians and geographers wish readers knew about maps and borders before, during, and after the founding of the United States. The essays collected in this volume model how people can learn to interpret maps as arguments, rather than as historical facts, and to read maps for evidence of people and places that were elided, renamed, or destroyed. Contributors travel through the sixteenth, seventeenth, eighteenth, and nineteenth centuries in the place known by many names: the Atlantic World; the North American continent; borderlands; and homelands. Onto this place where people exercised power over space by forging relationships, colonizers came and imagined borders onto maps. Featuring reproductions of twenty historical maps, the book takes readers through this era of immense disruption to teach them strategies for reading and interpreting these maps critically. Essays attend carefully to water alongside land and land alongside water in search of new interpretive avenues that reframe what we know about space, control, and sovereignty. By using historical examples of people--farmers, fishers, hunters, religious leaders, colonial projectors, traders, sailors, soldiers, diplomats, and cartographers, it becomes possible to resist the temptation to impose modern geographical constructs backwards onto the histories we read, teach, and write. Claiming Land, Claiming Water investigates why some of these people imagined and made claims to bounded space, and how and why other people confounded and challenged those claims. Contributors: Sarah Chute, Edward G. Gray, Kim M. Gruenwald, Rachel B. Herrmann, Christian J. Koot, Chad McCutchen, Jennifer Monroe McCutchen, John Morton, Paul Musselwhite, Charles Prior, Karen Rann, Jessica Choppin Roney, Samuel Truett, Harvey Amani Whitfield, Alex Zukas.
Polyhedra are used in several fields by mathematicians and other scientists. It is easy to think of examples from architecture. Polyhedra have been used to scientifically explain the world around us. In the early days of study, polyhedra included only convex polyhedra. Since the ancient Greeks, many thinkers have worked on convex polyhedra. There are only five regular convex polyhedra known as Platonic solids, thirteen semi-regular convex polyhedra known as Archimedean solids, and thirteen irregular convex polyhedra which are duals of the Archimedean solids and known as Catalan solids. In this study, we show that the isometry group of the threedimensional analytic space formed by the metrics of the Tetrakis hexahedron and the Disdyakis dodecahedron is the semi-direct product of Oh and T(3), where the octahedral group Oh is the (Euclidean) symmetry group of the octahedron and T(3) is the group of all translations of the three-dimensional space.
The Lane-Emden equations have been used to model some phenomena in astrophysics, such as mathematical physics and stellar structure theory. In addition, the Lane-Emden equation is a central equation in the theory of stellar structures. In this paper, we introduce the Lane-Emden differential equations. A special second order Lane-Emden differential equation is solved by He’s variational iteration, adomian decomposition method, homotopy analysis method, homotopy perturbation method, and finite difference method respectively. The results obtained are compared with each other and it is analyzed which method gives more reliable results and is more useful than the others.
Many generalizations of the traditional metric space have been introduced in the literature, such as 2−, D−, G−, S− and b−metric spaces. When the studies on these generalized metric spaces are examined, it is seen that the main motivation of the researchers is to develop and generalize the famous Banach fixed point theorem. Although introduced with a similar motivation, its ability to measure the distance between n points simultaneously distinguishes the n th order G−metric space from other generalized metric spaces. In this study, we will give new and original fixed point theorems that reveal the importance of G−metric techniques since they cannot be reduced to the framework of quasi and conventional metric spaces.
Minkowski geometry is a non-Euclidean geometry in a finite number of dimensions. In a Minkowski geometry the unit ball is a symmetric, convex closed set instead of the usual sphere in Euclidean space. In [14], it is shown that there are some geometries which unit spheres are cuboctahedron and truncated octahedron-which are Archimedean solids-, they are also Minkowski geometries. In geometry determining the group of isometries of a space with a metric is a fundamental problem. In this article we show that the group of isometries of the 3−dimensional spaces covered by CO − metric and TO − metric are the semi-direct product of Oh and T(3), where octahedral group Oh is the (Euclidean) symmetry group of the octahedron and T(3) is the group of all translations of the 3−dimensional space.
In this paper, we have obtained new Hermite Hadamard Fejer type inequality different from the classical fej ´ er inequality. ´ Thanks to this new inequality, new types of fractional integral inequalities obtained in recent years can be obtained in special cases.
The application of artificial neural networks (ANN) is a new and important trend in experimental particle physics. In this study a novel approach of using an ANN for constraining masses in particle decays is described and the performance compared to a traditional method. The ANN approach is found to perform slightly better than the traditional method and, importantly, is significantly faster. Reducing the CPU footprint of algorithms is critical for “big data” environments such as experimental particle physics experiments on the Large Hadron Collider.
This study explores the soliton solutions for the perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation which includes M-truncated derivative. Initially, a wave transformation technique is employed for the RKL equation, yielding a nonlinear ordinary differential equation (NODE). Then, the NODE is solved using the new Kudryashov method. A candidate solution and its related derivatives are incorporated into the NODE, resulting in a polynomial expression. A system of algebraic equations emerges by equating coefficients of terms with similar degrees to zero. Solving this system provides the identification of unknown variables in the candidate solution, thereby yielding the solutions to the RKL equation. Diverse illustrations of the obtained solutions are presented via contour, two-dimensional, and three-dimensional plots. The findings of this research may present potential implications for future studies in nonlinear optics.
We first obtain a new auxiliary identity by utilizing twice differentiable functions on α−type sets. Afterwards, two generalized Ostrowski type estimations for mappings whose second local fractional derivatives are bounded are derived, and special cases of these comprehensive inequalities are observed. Finally, some related applications such as inequalities including special means and generalized quadrature rules are presented.
In the present study, we focus on obtaining the optical soliton solutions of the Drinfeld-Sokolov-Satsuma-Hirota (DSSH) equation using Kudryhashov methods. First, a wave transformation is applied to the DSSH equation, resulting in a nonlinear ordinary differential equation (NLODE). A balance number is deduced through the balancing of this NLODE. Subsequently, candidate solutions, inclusive of their respective derivatives and the wave transformation, are inserted into the DSSH equation. This results in an equation in polynomial form. Terms with equal power are grouped together in the new equation, and their coefficients are set to zero, leading to a system of algebraic equations. Solving this algebraic system facilitates the identification of undetermined parameters within the candidate solutions, thus yielding the solutions for the DSSH equation. Visualization of these solutions is executed through contour plots as well as two- and three-dimensional graphical representations. The contributions of this study are of substantial relevance for subsequent research in nonlinear science.
We firstly establish an identity of Simpson type involving local fractional integral. By using the obtained result, some new Simpson type integral inequalities for mappings whose certain powers of the local fractional derivatives in modulus are generalized strongly convex are derived. Finally, some error estimations for local fractional integrals and inequalities involving generalized special means are given.
In this paper we present some new products on undirected graphs, explain them by examples and introduce some properties of these products. Moreover, we define the neighborhood set of vertices in these products and examine their sizes.
In this study, an effort has been made to obtain optical soliton solutions of the (1+1)-dimensional Biswas-Milovic equation which was introduced by Biswas and Milovic in 2010, having Kerr law and parabolic-law with weak non-local nonlinearity in the presence of spatio-temporal dispersion, which is one of the important models for nonlinear optics. Although, the model is an equation that has been studied by many researchers, the fact that the form to be examined has not been studied before. As a general algorithm, first converting the model to nonlinear ordinary differential form with a complex wave transformation, then obtaining candidate optical soliton solutions by utilizing the new Kudryashov technique, determining the ones that satisfy the main equation from these solutions as the exact solution, and in order to better understand the obtained solutions by making graphical presentation and providing the necessary comments constitute the main framework of the article.
This study presents a method for reaching user equilibrium in network traffic assignment problems with capacity constraints. The presented approach minimizes each user’s own travel time using a gradient-based algorithm based on the Taylor series. The algorithm is shown to converge efficiently to user equilibrium after a limited number of iterations. A numerical example is provided to demonstrate the effectiveness of the presented approach, and comparisons are made with other algorithms available in the literature. The obtained results show that the presented method is capable of reaching user equilibrium for capacity network traffic assignment problems.
In this study, an attempt to obtain optical soliton solutions of stochastic perturbed (1+1)-dimensional nonlinear Schrödinger equation having the Kerr law nonlinearity is presented. With the help of complex wave transform, the investigated nonlinear partial differential equation was converted into the nonlinear ordinary differential form. Analytical stochastic optical soliton solutions of the ordinary differential form were derived by applying the Kudryashov auxiliary equation method. By replacing the wave transformation and the appropriate solution set parameters, the main equation is provided. Graphic presentations were made for better interpretation of the results.
This aim of this paper is revealing the optical soliton solutions of the perturbed quintic Gerdjikov-Ivanov equation, which models optical soliton transmission in the photonic crystal fibers and optical fibers. With the aid of the new Kudryashov scheme, we successful achieved the bright and dark solitons and we simulated their graphical presentation.
This paper proves an equality for the case of twice-differentiable convex mappings with respect to the conformable fractional integrals. With the help of this equality, several trapezoid-type inequalities are established by convex functions involving conformable fractional integrals. Sundry significant inequalities are acquired with taking advantage of the convexity, the Holder inequality, and the ¨ power mean inequality. Furthermore, we present several new results connected with trapezoid-type inequalities by using the special choices of obtained results.
The aim of this study is to obtain the lower and upper bounds for the distance-based Wiener index, Hyper-Wiener index and Harary index of the Fibonacci-sum graph. Firstly, the shortest distance of the vertices in the Fibonacci-sum graph is characterized. Afterwards, the numbers of decision vertices and leaves are obtained by applying the BFS algorithm to the Fibonacci-sum graph.
