“…The aim of this book is to develop a contraction method for classical orthogonal and unitary groups (algebras), and apply it to the investigation of physical structures, offering a new and unique interpretation to the high-energy limit of the Standard Model. …”
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“…Each step along the way is elementary and requires only algebraic manipulation. This frames the wonder of mathematics and highlights the complex world that lies behind a series of simple, mathematical, deductions. …”
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“…The ambitious program for the birational classification of higher-dimensional complex algebraic varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program. …”
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“…These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980. …”
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“…The primary goal of these lectures is to introduce a beginner to the finite­ dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. …”
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“…This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of k-Poincare Hopf algebras, two frameworks which are often confused with each other in the literature.…”
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“…Modern ab initio treatments of H-Hbar systems are inconsistent with the logic behind algebraic Hamiltonians H(+-)=H(0)+/-deltaH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H(2) and HHbar. …”
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“…A novel quantitative structure-activity (property) relationship model, namely Spectral-SAR, is presented in an exclusive algebraic way replacing the old-fashioned multi-regression one. …”
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“…To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. …”
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“…The content addresses a wide range of historical and contemporary invariants of knots and links, as well as related topics including: three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology, hyperbolic knots and geometric structures of three-dimensional manifolds, the mechanism of topological surgery in physical processes, knots in nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. …”
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“…We derive for the first time a Fourier space version of the streaming model, which yields an algebraic relation between the real- and redshift-space power spectra which can be compared to earlier, phenomenological models. …”
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“…The Aczel-Alsina t-norms ware proposed by Aczel and Alsina in 1982, which are a very effective and dominant technique used in the construction of any kind of aggregation operators. Moreover, the Algebraic t-norms are a special case of the Aczel-Alsina t-norms because of the parameter [Formula: see text] . …”
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“…Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). …”
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“…Life history theory reveals how reproductive values can be determined via the estimation of life-history parameters, but this requires an adequate life-history model and intricate algebraic calculations. Recently, an alternative pedigree-based method has become popular, which estimates the expected genetic contribution of individuals to future generations by tracking their descendants down the pedigree. …”
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“…We investigate the performance of different methods for calculating XES of liquid water, focusing on the ability of time-dependent density functional theory (TDDFT) to reproduce reference spectra obtained by high-level coupled cluster and algebraic-diagrammatic construction scheme calculations. …”
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“…Owing to their shared algebraic structure with two-qubit gate operators, Gamma matrices allow for enhanced analysis and manipulation of these operators. …”
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“…In the first and direct technique, the clique coefficients are determined in an accurate way through solving an algebraic system of nonlinear equations. To get rid of the nonlinearity of the models and in order to gain efficacy, the quasilinearization method (QLM) is utilized in the second approach. …”
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“…We consider the α-FDK algorithm, the shift-variant FBP method derived from the T-FDK, an FBP method based on the Grangeat formula, and an iterative algebraic method (SART). The results show that the low contrast artifacts can be efficiently corrected by the shift-variant method and the SART method to achieve good quality images at the expense of increased computation time, but the geometrical deformations are still not compensated for by these techniques.…”
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“…The CI analytical formula is derived assuming a Gaussian sampling distribution and recurring to the algebraic relationship between W and the Simpson's index of diversity. …”
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“…The method employed is a variant of the so-called “Segmentation by Weighted Aggregation” technique, which itself is based on Algebraic Multigrid methods. The variant of the method used is described in detail, and it is explained how it is tailored to the application at hand. …”
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