“…This text covers equations such as linear equations, quadratic equations, and higher degree equations. The Cartesian coordinate system, graphing equations in two variables, and some special functio…”
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“…Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo…”
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“…<br><br>Comprised of 10 chapters, this book begins with exercises related to set theory and concepts such as the union and intersection of sets. Exercises on Cartesian coordinate…”
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“…This model applies the concept of the percent buried volume (%V(Bur)) to fluoride adducts of Lewis acids, as many fluoride adducts are crystallographically characterized and are frequently calculated to judge fluoride ion affinities (FIAs). Thus, data such as cartesian coordinates are often easily available. A list of 240 Lewis acids together with topographic steric maps and cartesian coordinates of an oriented molecule suitable for the SambVca 2.1 web application is provided, together with different FIA values taken from the literature. …”
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“…We previously described a Cartesian cine imaging technique, pseudo-projection motion tracking with golden-step phase encoding, capable of tracking both cardiac and respiratory motion at no cost to imaging data acquisition. …”
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“…METHODS: In contrast to other programs relying on local Metropolis moves in the space of dihedral angles, our sampler utilizes local crankshaft rotations of rigid peptide bonds in Cartesian space. RESULTS: The sampler allows fast simulation and analysis of secondary structure formation and conformational changes for proteins of average length.…”
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“…An MRF sequence based on a fast imaging with steady precession sequence and a numerical phantom were used for dictionary generation. Cartesian and spiral readout gradients were used for the Bloch image simulation. …”
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“…This paper proposes a method for the identification of kinematic parameters of multilink series industrial robots, which does not require the use of complex and expensive equipment for high-precision external measurements of the position and orientation of an end effector in a Cartesian coordinate system. This method, by means of simple and affordable tools, enables us to achieve a significantly increased accuracy of movement of end effectors in serial robots performing various technological operations. …”
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“…Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. …”
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“…Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB(R) introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. …”
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“…We conclude that both eccentricity scaling and polar rather than Cartesian stimulus configuration are important considerations for optimal experimental design in pRF mapping. …”
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“…When compared to the player load determined using the Cartesian formula, the Catapult reported PlayerLoad™ was consistently lower by approximately 15%. …”
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“…From starting in an upright sitting position, facing the Cartesian coordinate system, each participant performed five repetitions for each movement direction. …”
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“…We investigated two options to represent molecular structures within PathReducer: aligned Cartesian coordinates and matrices of interatomic distances. …”
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“…This precludes analysis of data acquired with nonspherical sampling schemes, for example, Cartesian sampling. Additionally, nonspherical sampling can also arise due to technical issues, for example, gradient nonlinearities, resulting in a spatially dependent bias of the apparent tissue densities and connectivity information. …”
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“…We also discuss the multivariate generalization of the Pearson correlation as the contraction between Cartesian polyad alignment tensors for the LRVVs and weighted average. …”
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“…We test the proposed model using simulated radially sampled data from a 2D phantom and 2D cartesian ex vivo measurements of a mouse kidney specimen. …”
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“…In addition, examples were provided in a variety of different application contexts (including brain MRI, vocal tract MRI, and cardiac MRI; accelerated Cartesian and non‐Cartesian imaging; and outer volume suppression) that demonstrate the strong potential of this kind of approach. …”
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“…Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjunction, symmetric difference of graphs and hence apply our results to find the F-coindex of different chemically interesting molecular graphs and nano-structures.…”
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“…Furthermore, the rotationally resolved electronic Stark spectrum of anisole in the molecular beam is presented. Finally, the Cartesian coordinates of the CC2/cc-pVTZ optimized structures of anisole are given in bohr units. …”
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