Quantum of Space of the Universe—Correction of Previous Mistakes

A large number of scientific works, from ancient times to the present, have been dedicated to the search for “bricks” that make up the foundations of the material world. Justification of quantum of space parameters of the Universe is a complicated scientific problem, as its reliable information is unknown. Therefore, errors may appear in it, which must be corrected in a timely manner. In the latest works from this sphere, the quanta of the space of the Universe are replaced by hexahedral prisms instead of balls, which solves the problem of their dense packing. However, the mistake was the deformation of these prisms. The purpose of this work is to eliminate this deficiency. Its scientific novelty is the substantiation of the specified of refined parameters of the quantum of the space of the Universe on the basis of strict scientific provisions and the physical laws of nature. The solution to this problem is an urgent and important scientific and applied task, since it develops knowledge about the quantum foundations of the material world and the Universe as a whole. Research methods which used in this work: The performed work is based on the methods of deduction and induction in the research of the material world based on the application of the well-known reliable laws of physics and the general principles of the development of the theory of knowledge. Other research methods are still unknown, since the work performed is associated with new scientific discoveries, the search for which is difficult to formalize by known technique methods. Results and their discussion: The work is based on the hypothesis that was put forward that at the quantum-mechanical level of the material world, a longitudinal quantum shift by the wavelength λG and a transverse quantum shift by λG of the quantum of the Universe space is carried out in the time interval TG, which can be found on the basis of the Heisenberg uncertainty principle. The parameters obtained made it possible to clarify the length and shape of quanta of the space of the Universe, as well as the conditions for its rotation. It was also taken into account that the hexagonal prism of the circular quantum of the space of the Universe is composed of 6 trihedral prisms of elementary quanta of space. So she can be formed by 3 elements of real quark with a common top in the center of the prism, with the formation of 3 elements of virtual quark between them. In this case, a transverse shift by λG and a rotation of quarks by an angle of 2π/6 radians is performed without energy loss, only due to transformations of their real and virtual states. The totality of all the above transformations of quanta of the space of the Universe does not contradict previously known physical laws and regularities, which serves as the basis for confirming the scientific hypothesis put forward.

Characterizations of Universal Finite Representability and B-convexity of Banach Spaces via Ball Coverings

By a ball-covering B of a Banach space X, we mean that B is a collection of open （or closed） balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.

ON QK(p)-TEICHMüLLER SPACES

The QK(p)-Teichmüller space is introduced and studied in this paper.Various characterizations of the QK(p)-Teichmüller space and the QK,0(p)-Teichmüller space are given.Their Schwarzian derivative model and pre-logarithmic derivative model are also discussed.

SOME GEOMETRIC PROPERTIES ON A MODEL OF UNIVERSAL TEICHMLLER SPACES

The model of the universal Teichmller space by the derivatives of logarithm is the union of infinite disconnected components. In this paper, the fact that each component is not starlike with respect to its center is proved, and the outer radius of the space with respect to each center is obtained.

THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

The model of the universal Teichmuller union of infinite disconnected components. between different components is 0, and the every other component is 2. space by the derivatives of logarithm is the In this paper, it is proved that the distance distance from the center of a component to

Kobayashi＇s and Teichmiiller＇s Metrics on the Teichmiiller Space of Symmetric Circle Homeomorphisms

We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi＇s metric and Teichmuller＇s metric coincide with each other on the Teichmfiller space of symmetric circle homeomorphisms.

Integrable Teichmüller spaces

A new kind of subspaces of the universal Teichmüller space is introduced. Some characterizations of the subspaces are given in terms of univalent functions, Beltrami coefficients and quasisymmetric homeomorphisms of the boundary of the unit disc.

Besov Functions and Tangent Space to the Integrable Teichmüller Space

The authors identify the function space which is the tangent space to the integrable Teichmfiller space. By means of quasiconformal deformation and an operator induced by a Zygmund function, several characterizations of this function space are obtained.

From Nowhere Pioneer a New Path and Be of One Mind to Ascend the High——Profile of the Space Materials Research at Northwestern Polytechnical University

At the end of 2001 National Natural Science Foundation of China (NSFC) organized a laboratory evaluation for Creative Research Groups, a pilot program launched in 2000, in the northwestern area of China and the evaluating team was deeply impressed by a young group, around 30 of average age, with their work and achievements, with their effort in pursuit of scientific truth and with their teamwork spirits. They all acknowl-

Inequalities on the Inner Radius of Univalency and the Norm of Pre-Schwarzian Derivative

In this paper, we get a lower bound of inner radius of univalency of Schwarzian derivative by means of the norm of pre-Schwarzian derivative. Furthermore, we apply the theory of Universal Teichmuller Space to explain its geometric meaning which shows the relationship between the inner radius in Universal Teichmuller Space embedded by Schwarzian derivative and the norm defined in Universal Teichmuller Space embedded by pre-Schwarzian derivative.

On the inner radius of univalency by pre-Schwarzian derivative

In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the lower bounds of inner radiuses for angular domains and strongly starlike domains are obtained.

The cross-ratio distortion of integrably asymptotic affine homeomorphism of unit circle

Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary condition for a quasisymmetric homeomorphism to belong to QS *(S 1) from the aspect of cross-ratio distortion.

On the Compactness of Grunsky Differential Operators

Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces.The Grunsky map is known to be holomorphic on the universal Teichmüller space.In this paper the authors deal with the compactness of a Grunsky differential operator.They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.