Abstract:
This paper is concerned with strictly cyclic functionals of operator algebras on Banach spaces. It is shown that if X is a reflexive Banach space and is a norm-closed semisimple abelian subalgebra of B(X) with a strictly cyclic functional ∈？, then is reflexive and hereditarily reflexive. Moreover, we construct a semisimple abelian operator algebra having a strictly cyclic functional but having no strictly cyclic vectors. The hereditary reflexivity of an algbra of this type can follow from theorems in this paper, but does not follow directly from the known theorems that, if a strictly cyclic operator algebra on Banach spaces is semisimple and abelian, then it is a hereditarily reflexive algebra.

Abstract:
Suppose that is a transitive subalgebra of and its norm closure contains a nonzero minimal left ideal . It is shown that if is a bounded reflexive transitive derivation from into , then is spatial and implemented uniquely; that is, there exists such that for each , and the implementation of is unique only up to an additive constant. This extends a result of E. Kissin that “if contains the ideal of all compact operators in , then a bounded reflexive transitive derivation from into is spatial and implemented uniquely.” in an algebraic direction and provides an alternative proof of it. It is also shown that a bounded reflexive transitive derivation from into is spatial and implemented uniquely, if is a reflexive Banach space and contains a nonzero minimal right ideal . 1. Introduction Throughout this paper, is a Banach space (and will be replaced by if it is a Hilbert space) and is a subalgebra of , the Banach algebra of all bounded operators on . Suppose that and is an -bimodule. A linear map from into is called a derivation if Then is called the domain of and denoted by . The derivation is called inner (resp., spatial) if there exists an operator (resp., ) such that If the operator is not bounded, then is said to be quasispatial. More precisely, if there exists a densely defined, closed operator such that then the derivation is called quasispatial, and the operator is an implementation of . Compared to the spatiality, the quasispatiality is a slightly weaker notion. Given a bounded derivation on an operator algebra, the natural question is whether the derivation is inner (or spatial). The spatiality of derivations is a classical problem when formulated for self-adjoint algebras and non-self-adjoint reflexive operator algebras. And it has been extensively studied in the literature in a large variety of situations, and some interesting results have been obtained [1–13]. For example, every derivation of a -algebra is spatial [12], every derivation of a von Neumann algebra is inner [13], and so is the derivation of a nest algebra [14]. Every derivation from an atom Boolean subspace lattice algebra into its ideal is quasispatial [7]. A necessary and sufficient condition is given for a derivation on CDC algebras to be quasispatial [6]. In [10], the quasispatiality of derivations on CSL algebras is studied. As to general operator algebras, it is well known that every derivation of is inner [9] and that every derivation of a standard operator subalgebra on a normed space is spatial [4]. Since these operator algebras are transitive, the above question for a

Abstract:
The true meaning of the constant in the Robertson-Walker metric is discussed when the scalar factor s the function of time. By strict calculation based on the Riemannian geometry, it is proved that the spatial curvature of the R-W metric is K=(κ-R^{2})/R^{2} . The result indicates that the R-W metric has no constant curvature when R(t)≠0 and κ is not spatial curvature factor. We can only consider κ as an adjustable parameter with κ≠0 in general situations. The result is completely different from the current understanding which is based on the precondition that the scalar factor R(t) is fixed. Due to this result, many conclusions in the current cosmology such as the densities of dark material and dark energy should be re-estimated. In this way, we may overcome the current puzzling situation of cosmology thoroughly.

Abstract:
According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high order perturbation normalizations. It is proved in the paper that when the renormalization effect of third order vertex angles process is taken into account, the symmetry of time reversal will be violated in electromagnetic interaction process. Because the magnitude order of symmetry violation is about 10–5, but the precision of current experiments on time reversal in particle physics is about 10–3, this kind of symmetry violation can not be found. The result reveals the micro-origin of asymmetry of time reversal and can be used to solve the famous irreversibility paradox in the evolution processes of macro- material systems.

In the classical Newtonian mechanics, the gravity fields of static
thin loop and double spheres are two simple but foundational problems. However,
in the Einstein’s theory of gravity, they are not simple. In fact, we do not
know their solutions up to now. Based on the coordinate transformations of the
Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field
with axial symmetry, the gravity fields of static thin loop and double spheres
are obtained. The results indicate that, no matter how much the mass and density
are, there are singularities at the central point of thin loop and the contact
point of double spheres. What is more, the singularities are completely exposed
in vacuum. Space near the surfaces of thin loop and spheres are highly curved,
although the gravity fields are very weak. These results are inconsistent with
practical experience and completely impossible. By reasonable analogy, black
holes with singularity in cosmology and astrophysics are something illusive. Caused
by the mathematical description of curved space-time, they do not exist in real
world actually. If there are black
holes in the universe, they can only be the types of the Newtonian black holes
without singularities, rather than the Einstein’s singularity black holes.
In order to escape the puzzle of singularity thoroughly, the description of gravity
should return to the traditional form of dynamics in flat space. The renormalization
of gravity and the unified description of four basic interactions may be possible
only based on the frame of flat space-time. Otherwise, theses problems can not
be solved forever. Physicists should have a clear understanding about this
problem.

It is
proved in this paper that there are at least five situations in the interaction
theories of microparticle physics that the Lorentz transformations have no
invariabilities. 1) In the formula to calculate transition probabilities in
particle physics, the so-called invariability factor of phase space d^{3}p/E is not invariable actually
under the Lorentz transformations. Only in one-dimensional motion with u_{y} = u_{z} = 0, it is invariable. 2) The propagation function of
spinor field in quantum theory of field has no invariability of Lorentz
Transformation actually. What appears in the transformation is the sum of
Lorentz factors a_{μν}a_{λμ}≠δ_{νλ} when ν, λ = 1, 4, rather than a_{μν}a_{λμ}=δ_{νλ}. But in the current

Abstract:
Based on
general relativity, J. R. Oppenheimer proved that massive celestial bodies may
collapse into singular black holes with infinite densities. By analyzing the
original paper of Oppenheimer, this paper reveals that the calculations had a
series and serious of mistakes. The basic problem is that the calculation
supposes that the density of celestial body does not change with space-time coordinates.
The density is firstly assumed invariable with space coordinates and then it is
assumed invariable with time. But at last, the conclusion that the density of a
celestial body becomes infinity is deduced. The premise contradicts with conclusion.
In fact, there is no restriction on the initial density and radius for celestial
body in the calculation. According to the calculation results of Oppenheimer, a
cloud of thin gas may also collapse into singular black hole under the action
of gravity. The calculations neglect great rotating speeds of massive and high density
celestial bodies which would make them falling apart rather than collapsing
into singularities. Because we do not know the function relations that material
densities depend on space-time coordinates in advance, there exists the
rationality problem of procedure using the Einstein’s equation of gravity field
to calculate material collapse. Besides these physical problems, the
calculation of Oppenheimer also has some obvious mistakes in mathematics.
Another improved method to calculate massive celestial body’s collapse also has
similar problems. The results are also unreliable. The conclusion of this paper
is that up to now general relativity actually has not proved that massive
celestial bodies may collapse into singularity black holes.

Abstract:
The new coordination polymer formulated as [Zn(bim)2]·(H2O)1.67 (Hbim = benzimidazole, bim = benzimi-dazolate) has been synthesized and shown by single-crystal structural analysis to be a three-dimensional network with the 4264 sodalite topology, constructed by tetrahedral building blocks, [Zn(bim)4]2 . Each sodalite cage defined by the 24 zinc atoms at the apexes centers hosts 10 water molecules (ca. 18% occupancy).

Abstract:
With the rapid speed of development for information technology in China, Chinese middle-aged and older adults benefit from various of mobile applications and services. However, most of them have difficulty to learn to use these mobile technologies. Thus, the goal of research is to design an interactive tutorial for middle-aged and older adults, which can adapt to existing applications. By conducting a survey to investigate their requirements for smartphone mobile applications tutorials and doing empirical analysis of the survey, we designed “Help Center”, which solves the problems we found from the survey study: 1) by implementing a fixed FAB (Floating Action Button) button as the access of help feature, the problem that users “can’t find the help features in a mobile application” is solved; 2) by implementing a PIP (picture in picture) tutorial, which allows users to do operations while watching the instructions, the problem that users “can remember nothing but easy instructions of on-boarding tutorials” is solved; 3) “learning center” feature solves the problem that users “don’t know how to express the problems that they are facing with”; 4) “icons and features” feature solves the recurrent problem of users “feeling confused with the meanings of icons and features”.