A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS

For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.

Groups Analysis and Localized Solutions of the(2+1)-Dimensional Ito Equation

By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the （2-t-1）-dimensional Ito equation better.

MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.

A Dark Matter Theory by Quantum Gravitation for Galaxies and Clusters

This paper develops an original theory of dark matter in the current ΛCDM framework, whose main hypothesis is that DM is generated by the own gravitational field, according to an unknown quantum gravitational phenomenon. This work is the best version of the theory, which I have been developing and publishing since 2014. The hypothesis of DM by quantum gravitation, DMbQG hereafter, has two main consequences: the first one is that the law of DM generation has to be the same, in the halo region, for all the galaxies and the second one is that the haloes are unbounded, so the total DM goes up without limit as the gravitational field is unbounded as well. The first one consequence is backed by the fact that M31 and MW has a fitted function with the same power exponent for the rotation curve at the halo region and both giant galaxies are the only ones whose rotation curves at the halo region may be studied with accuracy. This paper is firstly developed all the theory with M31 rotation curve data up to Chapter 9. The most important formula of the theory is the called Direct mass, which calculates the total mass at a specific radius into the halo region. Chapter 10 is dedicated to apply the theory to Milky Way, it is calculated its total mass at different radius into the halo and such results have been validated successfully using the data of masses at different radius published by two researcher teams. In Chapter 11, it is calculated the direct mass for the Local Group, and it is shown how the DMbQG theory is able to calculate the total mass at 770 kpc, that the dynamical methods estimate to be 5×1012MΘ. In Chapter 12, it is shown a method to estimate the Direct mass formula for a cluster of galaxies, using only its virial mass and virial radius. By this method, it is estimated the parameter a2 of the Local Group, which match with the one calculated in previous chapter by a different method. Also are calculated the parameters a2 associated to Virgo and Coma clusters. In Chapter 13, it is demonstrated how the DE is able to counterbalance the DM at cluster scale, as the Direct mass grows up with the square root of radius whereas the DE grows up with the cubic power. The chapter is an introduction to the DMbQG theory for cluster of galaxies, which has been developed fully by the author in other works. This theory aims to be a powerful method to study DM in the halo region of galaxies and cluster of galaxies and conversely the measures in galaxies and clusters offer the possibility to validate the theory.

On Semilocal Group Rings

Let R be an associative ring with identity. R is said to be semilocal if R/J（R） is （semisimple） Artinian, where J（R） denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.

Probing satellite galaxies in the Local Group by using FAST

The abundance of neutral hydrogen（HI）in satellite galaxies in the local group is important for studying the formation history of our local group.In this work,we generated mock HI satellite galaxies in the Local Group using the high mass-resolution hydrodynamic APOSTLE simulation.The simulated HI mass function agrees with the ALFALFA survey very well above 10~6M_⊙,although there is a discrepancy below this scale because of the observed flux limit.After carefully checking various systematic elements in the observations,including fitting of line width,sky coverage,integration time and frequency drift due to uncertainty in a galaxy’s distance,we predicted the abundance of HI in galaxies in a future survey that will be conducted by FAST.FAST has a larger aperture and higher sensitivity than the Arecibo telescope.We found that the HI mass function could be estimated well around 10~5M_⊙ if the integration time is 40 minutes.Our results indicate that there are 61 HI satellites in the Local Group and 36 in the FAST field above 10~5M_⊙.This estimation is one order of magnitude better than the current data,and will put a strong constraint on the formation history of the Local Group.Also more high resolution simulated samples are needed to achieve this target.

Screening Breakdown for Finite-Range Gravitational Field and the Motion of Galaxies in the Local Group

The lack of Birkhoff theorem in finite-range gravitation reveals nonzero acceleration of the test body inside the massive spherical shell, as well as breakdown of screening inside the charged conductor gives rise to acceleration of the test charge. An application of this effect to the motion of galaxies in Local Group allows to constraint quintessence parameter in some massive gravitational theories.

SAR image de-noising via grouping-based PCA and guided filter

A novel synthetic aperture radar(SAR)image de-noising method based on the local pixel grouping(LPG)principal component analysis(PCA)and guided filter is proposed.This method contains two steps.In the first step,we process the noisy image by coarse filters,which can suppress the speckle effectively.The original SAR image is transformed into the additive noise model by logarithmic transform with deviation correction.Then,we use the pixel and its nearest neighbors as a vector to select training samples from the local window by LPG based on the block similar matching.The LPG method ensures that only the similar sample patches are used in the local statistical calculation of PCA transform estimation,so that the local features of the image can be well preserved after coefficients shrinkage in the PCA domain.In the second step,we do the guided filtering which can effectively eliminate small artifacts left over from the coarse filtering.Experimental results of simulated and real SAR images show that the proposed method outstrips the state-of-the-art image de-noising methods in the peak signalto-noise ratio(PSNR),the structural similarity(SSIM)index and the equivalent number of looks(ENLs),and is of perceived image quality.

A novel secure multicast scheme in mobile Internet

A novel multicast communication model using a RingNet hierarchy is proposed. The RingNet hierarchy consists of 4 tiers: border router tier, access gateway tier, access proxy tier and mobile host tier. Within the hierarchy, the upper 2 tiers are dynamically organized into logical rings with network entities. A novel hierarchical secure access control scheme on key management is proposed based on the RingNet model. Network entities within the multicast hierarchy belong to different privileged local groups. Network entities of the higher-privileged local groups have the right to derive the keys held by network entities of the lower-privileged local groups, and the reverse operation is not allowed. With the key management approach, any insertion and changing of local group key will not affect other local groups. The analytical result shows that the scheme has higher security than Lin’s.

Transversality on locally pseudocompact groups

Two non-discrete Hausdorff group topologiesτandδon a group G are called transversal if the least upper boundτ⋁δofτandδis the discrete topology.In this paper,we discuss the existence of transversal group topologies on locally pseudocompact,locally precompact,or locally compact groups.We prove that each locally pseudocompact,connected topological group satisfies central subgroup paradigm,which gives an affirmative answer to a problem posed by Dikranjan,Tkachenko,and Yaschenko[Topology Appl.,2006,153:3338–3354].For a compact normal subgroup K of a locally compact totally disconnected group G,if G admits a transversal group topology,then G/K admits a transversal group topology,which gives a partial answer again to a problem posed by Dikranjan,Tkachenko,and Yaschenko in 2006.Moreover,we characterize some classes of locally compact groups that admit transversal group topologies.

Subhalo Abundance and Satellite Spatial Distribution in Milky Way-Andromeda-like Paired Haloes

We study the subhalo and satellite populations in haloes similar to the Milky Way(MW)-Andromeda paired configuration in the Millennium II and P-Millennium simulations.We find subhaloes are 5%–15%more abundant in paired haloes than their isolated counterparts that have the same halo mass and large-scale environmental density.Paired haloes tend to reside in a more isotropic environment than isolated haloes,the shear tensor of their large-scale tidal field is possibly responsible for this difference.We also study the thickness of the spatial distribution of the top 11 most massive satellite galaxies obtained in the semi-analytic galaxy sample constructed from the Millennium II simulation.Moreover,satellites that have lost their host subhaloes due to the resolution limit of the simulation have been taken into account.As a result,we find that the difference in the distribution of the satellite thickness between isolated and paired haloes is indistinguishable,which suggests that the paired configuration is not responsible for the observed plane of satellites in the MW.The results in this study indicate the paired configuration could bring some nonnegligible effect on the subhalo abundance in the investigation of the MW's satellite problems.

CONTINUOUS FRAME WAVELETS

Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜〈π（G）ψ,Ф｜2dg≤B｜｜Ф｜｜2（Ф∈H）,in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.

Γ-amenability of Locally Compact Groups

Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.

On Local Nilpotency of the Normal Subgroups of a Group

A group G is said to have property μ whenever N is a non-locally nitpotent normal subgroup of G, there is a finite non-nilpotent G-quotient of N. FC-groups and groups with property v satisfy property μ, where a group G is said to have property v if every non-nilpotent normal subgroup of G has a finite non-nilpotent G-quotient. HP（G） is the Hirsch-Plotkin radical of G, and φf （G） is the intersection of all the maximal subgroups of finite index in G （here φf（G） = G if no such maximal subgroups exist）. It is shown that a group G has property μ if and only if HP（G/φf（G）） = HP（G）/φf（G） and that the class of groups with property v is a proper subclass of that of groups with property it. Also, the structure of the normal subgroups of a group： nilpotency with the minimal condition, is investigated.

SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON'S EQUATION

In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.

Locally Graded n-Bell Groups

Let n ≠ 0, 1 be an integer and Bn be the variety of n-Bell groups defined by the law [ xn, y] [ x, yn ] ^-1= 1. Let Bn be the class of groups in which for any infinite subsets X and Y there exist x ∈ X and y ∈ Y such that [xn,y][x,yn]-1 = 1. In this paper we prove Bn ∩ L： = （Bn U F） M ∩L：, where F and L are the classes of all finite groups and all locally graded groups, respectively.

The LAMOST spectroscopic survey of globular clusters in M31and M33.I.catalog and new identifications

We present a catalog of 908 objects observed with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope（LAMOST） in fields in the vicinity of M31 and M33, targeted as globular clusters（GCs） and candidates. The targets include known GCs and candidates selected from the literature, as well as new candidates selected from the Sloan Digital Sky Survey（SDSS）. Analysis shows that 356 of them are likely GCs with various confidence levels, while the remaining ones turn out to be background galaxies and quasars, stars and H II regions in M31 or foreground Galactic stars. The 356 likely GCs include 298 bona fide GCs and 26 candidates known in the literature. Three candidates, selected from the Revised Bologna Catalog of M31 GCs and candidates（RBC） and one possible cluster from Johnson et al., are confirmed to be bona fide clusters. We search for new GCs in the halo of the M31 among the new candidates selected from the SDSS photometry. Based on radial velocities yielded by LAMOST spectra and visual examination of the SDSS images, we find 28 objects, 5bona fide and 23 likely GCs. Among the five bona fide GCs, three have been recently discovered independently by others, and the remaining 25 are our new identifications,including two bona fide ones. The newly identified objects fall at projected distances ranging from 13 to 265 kpc from M31. Of the two newly discovered bona fide GCs,one is located near M33, probably a GC belonging to M33. The other bona fide GC falls on the Giant Stream with a projected distance of 78 kpc from M31. Of the 23 newly identified likely GCs, one has a projected distance of about 265 kpc from M31 and could be an intergalactic cluster.

Sustainability and Entrepreneurship in the Biofuels Supply Chain： A Proposal for a Survey

Investments in bio-energies require deep and accurate analysis to evaluate their economical feasibility both by the investors＇ and the policy makers＇ perspectives. The chance to attain locally organized supply chains is presumably higher where there is a higher concentration of human, natural and financial capitals. After a literature review about social capital and energy supply chain （prg. 1）, we investigate the instruments for public direct financial incentive （prg. 2） and the development of the public intervention plans in the agro-energy sector within the Local Development Plans （LDP） by Local Action Groups （LAG）. Then, we present the case study of the Apulia Region （prg. 3） based upon a unique dataset, specifically built that collects LDP data relative to social capital. We finally propose a new methodological approach that makes use of social network analysis investigating the net of relationships underneath the territorial organization of the LAGs and the local supply chains. Results seem to show that site specificities affect the sustainability of biofuels supply chains, and that effect seems to be reciprocally bounded, thus calling for the inclusion of such measures when planning new policies, and for analytical approaches encompassing historical perspectives. Finally, we draw the conclusions.

The Isomorphisms of Orthogonal Groups over Local Rings

1. Introduction Since O’Meara worked out the automorphisms of orthogonal groups Ωn(V) over fields in [4] by using well-known residual space method, many results about the isomorphisms and automorphisms of orthogonal groups over integral domains have been achieved. Refer to O’Meara, Hahn for example. B. R. McDonald, in [12], determined the automorphisms of O(V) over local rings with 2 a unit by using involutions.

The Nonvelocity Cosmological Spectral Shift

Beginning from the premise that the universe is static, and that the cosmological redshift is due to a nonconservative tired light effect, the following examines evidence supporting the prediction that photons will progressively blueshift when transiting through the gravity wells of galaxies, galaxy clusters, and superclusters. The presence of such a nonvelocity blueshift effect is seen to make a substantial contribution to Virgo cluster galaxy spectra, sufficient to dramatically decrease the cluster’s velocity dispersion and assessed virial mass and eliminate the need to assume the presence of large quantities of dark matter. The effect is also shown to account for the Fingers-of-God effect and Kaiser pancaking effect seen when the spectra of cluster galaxies are plotted in redshift space. The opposite effect, excessive redshifting of photons passing through cosmic voids is able to explain void elongation in redshift space, and also the subnormal luminosity of void galaxies. The proposed cosmological blueshifting phenomenon also explains the downturn of the slope of the Hubble Flow in the vicinity of the Local Group which projects a negative apparent velocity for photons propagating near the Milky Way. It also offers an explanation for the blueshift of the Andromeda galaxy spectra and for Arp’s findings that the spectra of primary galaxies in a cluster tend to be blueshifted relative to their companion galaxies. These photon energy phenomena are anticipated by the physics of subquantum kinetics which predicts that photons traversing long distances through intergalactic space should undergo nonconservative tired-light redshifting, and that photons passing through gravity potential wells should undergo progressive blueshifting. The latter effect may be visualized as a negative nonvelocity Hubble constant.