algebra

摘要： In two instances,the author unfortunately confused the weak^(*) separability and the separability of the predual for a von Neumann algebra.Therefore the Remark 1.3 and the proof of Proposition 7.1 must be replaced by what follows.

摘要： In this paper, we consider an integral basis for affine vertex algebra Vk (sl2) when the level k is integral by a direct calculation, then use the similar way to analyze an integral basis for Virasoro vertex algebra Vvir (2k,0). Finally, we take the combination of affine algebras and Virasoro Lie algebras into consideration. By analogy with the construction of Lie algebras over Z using Chevalley bases, we utilize the Z-basis of Lav whose structure constants are integral to find an integral basis for the universal enveloping algebra of it.

摘要： Let G be a discrete group with a weight w on it. For p>1, we define a class of generalized Figà-Talamanca-Herz algebras Ap(G, w,α,θ) and obtain their (w,α,θ)-Dual spaces. Moreover, we show that the generalized Figà-Talamanca-Herz algebras have an approximation property when G is a proper discrete group and satisfies the p-RD property.

摘要： In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differential equations. In 1970, D.C. Spencer and coworkers studied the formal theory of such systems, using methods of homological algebra that were giving rise to “differential homological algebra”, replacing unmixed polynomial ideals by “pure differential modules”. The use of “differential extension modules” and “differential double duality” is essential for such a purpose. In particular, 0-pure differential modules are torsion-free and admit an “absolute parametrization” by means of arbitrary potential like functions. In 2012, we have been able to extend this result to arbitrary pure differential modules, introducing a “relative parametrization” where the potentials should satisfy compatible “differential constraints”. We recently noticed that General Relativity is just a way to parametrize the Cauchy stress equations by means of the formal adjoint of the Ricci operator in order to obtain a “minimum parametrization” by adding sufficiently many compatible differential constraints, exactly like the Lorenz condition in electromagnetism. In order to make this difficult paper rather self-contained, these unusual purely mathematical results are illustrated by many explicit examples, two of them dealing with contact transformations, and even strengthening the comments we recently provided on the mathematical foundations of General Relativity and Gauge Theory. They also bring additional doubts on the origin and existence of gravitational waves.

摘要： This paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times from computer-based activities related to quadratic functions. We also measured brain response through event related potentials (ERP). Results demonstrate that students with higher mathematics anxiety (HMA) took more time than students with lower mathematics anxiety (LMA), both in translating equations to graphs and in translating graphs to equations. Moreover, based on analysis of ERP, brain waves of the HMA group recorded higher amplitude. In specific, both groups showed higher amplitude in translation from graphs to equation than vice versa. Higher amplitudes indicate greater demands on working memory, which we discuss in the concluding section, especially with regard to MA.

摘要： The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,which is a finite set consisting of two nontrivial elements.Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras.Moreover,associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,we charaterized twisted Heisenberg-Virasoro vertex operator algebras.This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets.

摘要： In this paper we consider properties of the four-dimensional space-time manifold M caused by the proposition that, according to the scheme theory, the manifold M is locally isomorphic to the spectrum of the algebra A, M ≅Spec (A), where A is the commutative algebra of distributions of quantum-field densities. Points of the manifold M are defined as maximal ideals of density distributions. In order to determine the algebra A, it is necessary to define multiplication on densities and to eliminate those densities, which cannot be multiplied. This leads to essential restrictions imposed on densities and on space-time properties. It is found that the only possible case, when the commutative algebra A exists, is the case, when the quantum fields are in the space-time manifold M with the structure group SO (3, 1) (Lorentz group). The algebra A consists of distributions of densities with singularities in the closed future light cone subset. On account of the local isomorphism M ≅Spec (A) , the quantum fields exist only in the space-time manifold with the one-dimensional arrow of time. In the fermion sector the restrictions caused by the possibility to define the multiplication on the densities of spinor fields can explain the chirality violation. It is found that for bosons in the Higgs sector the charge conjugation symmetry violation on the densities of states can be observed. This symmetry violation can explain the matter-antimatter imbalance. It is found that in theoretical models with non-abelian gauge fields instanton distributions are impossible and tunneling effects between different topological vacua | n> do not occur. Diagram expansion with respect to the -algebra variables is considered.

摘要： We study some properties of first order differential operators from an algebraic viewpoint. We show this last can be decomposed in sum of an element of a module and a derivation. From a geometric viewpoint, we give some properties on the algebra of smooth functions. The Dirac mass at a point is the best example of first order differential operators at this point. This allows to construct a basis of this set and its dual basis.

摘要： Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method together with regularization is investigated to study the electricity output related to vacuum level and temperature in the turbine. Ninety percent of the data was used to train the regression parameters while the remaining ten percent was used for validation. Final results showed that 99% accuracy could be obtained with this method. This opens a new window for electricity output prediction for power plants.

摘要： Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.

摘要： For processing backward reasoning and resolving the discrepancy between logic and probabihtv insequential decision problem with high order conditionals, we propose a backward Bavesian probabilistic logicreasoning approach.We propose a second-order backward Bavesian probabihstic logic reasoning approach, which combines CEAand Gibbs sampler to evaluate the quantitative value of second-order conditional probabihty.rnInprocessing backward reasoning in a decision probe usepartly change casual relations at first. And thenconditional event to denote casual relations forresolving the discrepancy between probabihtv and classiclogic, and transform higher-order conditional event tonormal events and corresponding joint events. By usingGibbs sampler, we obtain the normal events and jointevents in a stationary state. The quantitative value ofhigher-order conditional event is estimated, and we finish the backward reasoning.

摘要： For processing backward reasoning and resolving the discrepancy between logic and probabihtv insequential decision problem with high order conditionals, we propose a backward Bavesian probabilistic logicreasoning approach.We propose a second-order backward Bavesian probabihstic logic reasoning approach, which combines CEAand Gibbs sampler to evaluate the quantitative value of second-order conditional probabihty.rnInprocessing backward reasoning in a decision probe usepartly change casual relations at first. And thenconditional event to denote casual relations forresolving the discrepancy between probabihtv and classiclogic, and transform higher-order conditional event tonormal events and corresponding joint events. By usingGibbs sampler, we obtain the normal events and jointevents in a stationary state. The quantitative value ofhigher-order conditional event is estimated, and we finish the backward reasoning.

摘要： For processing backward reasoning and resolving the discrepancy between logic and probabihtv insequential decision problem with high order conditionals, we propose a backward Bavesian probabilistic logicreasoning approach.We propose a second-order backward Bavesian probabihstic logic reasoning approach, which combines CEAand Gibbs sampler to evaluate the quantitative value of second-order conditional probabihty.rnInprocessing backward reasoning in a decision probe usepartly change casual relations at first. And thenconditional event to denote casual relations forresolving the discrepancy between probabihtv and classiclogic, and transform higher-order conditional event tonormal events and corresponding joint events. By usingGibbs sampler, we obtain the normal events and jointevents in a stationary state. The quantitative value ofhigher-order conditional event is estimated, and we finish the backward reasoning.

摘要： For processing backward reasoning and resolving the discrepancy between logic and probabihtv insequential decision problem with high order conditionals, we propose a backward Bavesian probabilistic logicreasoning approach.We propose a second-order backward Bavesian probabihstic logic reasoning approach, which combines CEAand Gibbs sampler to evaluate the quantitative value of second-order conditional probabihty.rnInprocessing backward reasoning in a decision probe usepartly change casual relations at first. And thenconditional event to denote casual relations forresolving the discrepancy between probabihtv and classiclogic, and transform higher-order conditional event tonormal events and corresponding joint events. By usingGibbs sampler, we obtain the normal events and jointevents in a stationary state. The quantitative value ofhigher-order conditional event is estimated, and we finish the backward reasoning.