How To Use Topological In A Sentence
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A key ingredient of this proof was to represent the complex numbers geometrically, and then to use a topological argument.
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It is a small region of space, in which the field configuration is out of the vacuum manifold, but which remains metastably in that configuration because the topological properties of the vacua chosen by the field at infinity are nontrivial.
Embedded in Montreal
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The structure of preform is described, the processing parameters are predicted in theory and the designs of functional and structural composites are provided by the method of topological analysis.
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Topological feature based methods detect and code straight lines and the orientation of strokes.
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That result means that topologically, the manifold in question is a 3 - sphere .
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These two-dimensional examples give us an idea of how to build the more difficult three-dimensional, topologically compact spaces.
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The paper arrives at the fundamental domain and harmonic domain model by the analysis of topological structure of HVPQC. The detecting part is the premise of power quality control.
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The thesis contains a different proof of the fact just shown by Lefschetz that for any closed manifold the sum of the indices of a generic vector field is a topological invariant, namely the Euler characteristic.
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The author has succeeded in writing a book understandable to readers with very little knowledge of functional analysis and topological vector spaces.
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Apart from its effect on the molecular free energy, the topological constraint determines the total length and diameter of the superhelix, and hence, the volume excluded to another supercoil.
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The method herein used is of creativeness. The conclusion reached is also of real plenitude to the theoretical basis about topological space.
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He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups.
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In this paper, a topological optimization mathematical model of oil-gas gathering and transforming system is founded, and the computational complexity is discussed.
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Smoothly of us meritorious internet provider speed our topological sommelier for what we tritanopia our fissile, bodacious and silverish papaver to get fictitiously with.
Rational Review
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Here, we discuss the new methods as well as additional analysis tools we developed to analyze the inhomogeneous and topological properties of large DNA systems bound to proteins.
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In classical mathematics, he founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem.
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For the case of a finite-dimensional real linear space these are infinite systems whose adjoint cone is topologically closed.
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A novel topological map is proposed in this paper, and its nodes are represented with the visual scale-invariant features and the beam features of the laser range finder.
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The proposed methodology is applicable to a broad class of problems that require comparison of the topological properties of various dendrograms.
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We suggest that it was during R. L. Moore's tenure at Penn that he began to develop his method of teaching axiomatic systems, particularly topological spaces.
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It was not just to these areas that he contributed but, even more importantly, his work brought out fundamental relationships between the areas when he studied harmonic analysis on topological groups and characteristic classes.
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The physical interpretation and limitation of the topological criteria are also given.
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Graphical modelling is a new research field in applied statistics. It utilizes the intuitional form of topological graphs to make statistical inferences and causal analysis fur multiple variables.
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Spatial adjacency is a fundamental type of topological relations, a relationship crucial for discovering rules of geographical changes and distributions.
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Even a wormhole is not a “rip” in spacetime, it is just a topological feature in spacetime.
Objections to Kaku and Liu’s “How to Time Travel?”
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Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic.
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Three important papers on plane topology proved the topological invariance of the dimension of the square.
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In this lecture, we use topological dynamics methods to prove some other Ramsey-type theorems, and more specifically the polynomial van der Waerden theorem, the hypergraph Ramsey theo ...
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A key ingredient of this proof was to represent the complex numbers geometrically, and then to use a topological argument.
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In contrast, quantum theory depends on a more fundamental, non-local topological invariance which is well known to be free of metrical constraints.
The Birdcage
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High levels of refractory elements such as rhenium can make the alloys prone to the formation of what are known as deleterious topologically close packed
The Engineer - News
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The rate at which proteins fold decreases with increasing complexity of their folds, a ‘topological’ effect.
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The bison know a lot about Longfellow and wisteria and patrimony, the piscine nuance of the clouds, God's topological integument.
The Bison's Alimony
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Most of the features for surfaces appearing in this book are closely related to topological geometry.
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The key divergence from traditional modelling methods was to think of the form as a topological entity, with topology being the study of geometry unaffected by change in scale or shape.
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The thesis contains a proof of the fact that for any closed manifold the sum of the indices of a generic vector field is a topological invariant, namely the Euler characteristic.
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Using this system, geodata is topologically processed and the result saved in a three-dimensional database so that modeled objects can be continuously updated.
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A key ingredient of this proof was to represent the complex numbers geometrically, and then to use a topological argument.
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While we have understood and appreciated that there is a rich bounty of physical phenomena contained in the theory, this has mostly been uncovered in perturbation theory, occasionally sweetened by a glimpse into the non – perturbative realm afforded by special sectors of the theory such as soliton solutions (including branes of various sorts) or various topological reductions.
News From The Front, II
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The object of the course was to study the modular group and some of its subgroups, with help of algebraic rather than analytic or topological methods.
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The structure can be described using mereology and how about topological relation of the structure.
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The experiments showed that the model can work efficiently and practically, and keep the topological insistency of the vector spatial data.
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The topological optimization method was used to solve the lightweight design problems of components and parts in automatic weapons.
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The power - train mount bracket has been researched by topological optimization method.
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Here we ignore topological subtleties in the case of the cylinder by considering only paths that do not cross the cut.
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He showed that spaces of constant curvature could have several different topological structures.
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He worked on the theory of continuous mappings of topological spaces.
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Topological feature based methods detect and code straight lines and the orientation of strokes.
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This paper tells us the conceive plan about effective management according to thematic data. geometrical data and topological data which is based on the theory of Object Oriented Database.
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Using the method of topological optimization, by means of adjusting the axial crush stiffness of the component, a topological optimization model was built to perform the optimization analysis.
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I assure you, however, I have accurately mapped the topological surface density and transitional energy gradients of the timeline in question.
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A series of logical steps, originally discussed as postings and comments to two blogs, led to the outcome described here of a central hypervalent atom bound on one face by a small cyclic carbon ligand, with the other free face having an interaction to a helium atom with the topological properties of a charge-shift rather than a covalent bond.
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In addition to this expressive limitation, Euler's system also suffers other kinds of expressive limitations with respect to non-empty sets, due to topological restrictions on plane figures.
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However he continued to work on topological ideas, in particular embedding complexes in Euclidean space.
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This mirror is at the core of what he calls the Nawatl Topological Scheme, which is a wheel that is divided into four different dimensions, with a fifth at its center that is produced by the interrelation of the others.
The Obsidian Butterfly
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According to the extensive theory of topological degree for set-valued mapping , the authors derive the topological degree for upper semicontinuous set-valued 1-set-contractive mapping.
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The generation employs space filling curves to preserve the spatial and topological properties (see the Resources section for the H. Sagan book).
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In applications for statistical or topological modeling, for example, inputs could be frequencies, spatial locations, and so on.
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Topologically, then, a sphere and a torus are distinct entities.
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In the traditional chrono-topological sequence, short-necked forms follow the bell beakers, with the long-necked forms following still later.
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assume that the topological space is finite dimensional
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In general, these two closed chains are linked catenanes, and the type of linkage reflects a topological property of the original substrate.
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His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras.
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New paradigms of quantum algorithms have appeared, such as adiabatic algorithms, measurement-based algorithms, and topological-quantum-field-theory-based algorithms, as well as new physical models for realizing a large scale quantum computer with cold ion traps, quantum optics (using photons and optical cavity), condensed matter systems and solid state physics (meanwhile, the first NMR model had turned out to be a dead-end with respect to scaling; see DiVicenzo 2000).
Quantum Computing
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Isomorphism, in brief , means two graphs possess identical topological structures.
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They both fail for open set logic, which is to say intuitionism, just as they both fail for its topological dual, closed set logic.
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He discovered characterisations of topological mappings of the Cartesian plane and a number of fixed point theorems.
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The physical interpretation and limitation of the topological criteria are also given.
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He combined topological and metrical methods to attack problems of real analysis.
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Density contours are adopted to interpret the topological optimization result and continuous contour thus obtained.
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He also started work on elliptic curves and, with Baer, on topological fields.
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Perhaps they’re Hodge numbers (i.e. topological data) telling us the correct manifold on which to compactify to get our four dimensional world with all the observed physics.
Friday Random Ten: iPod Tells the Future of String Theory?
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In addition, the measurement results can be displayed dynamically, topologically, statistically, or in a tabular format on a monitor.
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; Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f (2), Re f (3), and Re f (4); and the positivity of the real part of a linear functional on a subspace of C (X).
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In contrast, the teleost POA is considered to be the functional and topological equivalent to the paraventricular and supraoptic nuclei of the hypothalamus, which do not express POMC in mammals.
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As such the annular drive conditions all specific drives, and outlines a space for history very different from the "electromagnetic orgasm" that is Martin Wallen's topological figure for the relation between expansive and contractive forces in Schelling's "cosmic history
'The Abyss of the Past': Psychoanalysis in Schelling's Ages of the World (1815)
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This paper considers network topological optimization with a reliability constraint.
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Sequence pseudo orbit tracing property is defined, and a sufficient condition on topological transitive is given.
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Topological feature based methods detect and code straight lines and the orientation of strokes.
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Middle school students would perceive the global-first topological invariance of the solid figure when they make the projection, and then the local property or components.
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Euclidean geometry studies Euclidean-space-structure, topology studies topological structures, and so on.
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By using a universal method a new existence theorem of solution for a generalized equilibrium problem in topological vector space is obtained.