The study examined the effectiveness of Gully Erosion Control Measures in Edo State, Nigeria. The objectives are to investigate erosion prone areas in Edo State; the measure(s) were adopted to control gully erosion in the area and the effectiveness of the adopted measures across the study area. The research adopted questionnaire administration and direct field observation as methodo-logical approach. It was observed that control measures put in place in the study area include mechanical methods of back filling, sand bagging, construc-tion of channels and construction of speed breakers. The biological control methods in use are trees and crop planting. These control measures as observed during the fieldwork are partly successful as pointed out by respondents in their respective zones. Therefore, there is an urgent need to address this emerging looming disaster in the State.

Abstract:
The ubiquitin/proteasome pathway plays a crucial role in many biological processes. Here we report a novel role for the Arabidopsis 19S proteasome subunit RPT2a in regulating gene activity at the transcriptional level via DNA methylation. Knockout mutation of the RPT2a gene did not alter global protein levels; however, the transcriptional activities of reporter transgenes were severely reduced compared to those in the wild type. This transcriptional gene silencing (TGS) was observed for transgenes under control of either the constitutive CaMV 35S promoter or the cold-inducible RD29A promoter. Bisulfite sequencing analysis revealed that both the transgene and endogenous RD29A promoter regions were hypermethylated at CG and non-CG contexts in the rpt2a mutant. Moreover, the TGS of transgenes driven by the CaMV 35S promoters was released by treatment with the DNA methylation inhibitor 5-aza-2′-deoxycytidine, but not by application of the inhibitor of histone deacetylase Trichostatin A. Genetic crosses with the DNA methyltransferase met1 single or drm1drm2cmt3 triple mutants also resulted in a release of CaMV 35S transgene TGS in the rpt2a mutant background. Increased methylation was also found at transposon sequences, suggesting that the 19S proteasome containing AtRPT2a negatively regulates TGS at transgenes and at specific endogenous genes through DNA methylation.

Abstract:
We review recent developments in noncommutative deformations of instantons in . In the operator formalism, we study how to make noncommutative instantons by using the ADHM method, and we review the relation between topological charges and noncommutativity. In the ADHM methods, there exist instantons whose commutative limits are singular. We review smooth noncommutative deformations of instantons, spinor zero-modes, the Green's functions, and the ADHM constructions from commutative ones that have no singularities. It is found that the instanton charges of these noncommutative instanton solutions coincide with the instanton charges of commutative instantons before noncommutative deformation. These smooth deformations are the latest developments in noncommutative gauge theories, and we can extend the procedure to other types of solitons. As an example, vortex deformations are studied. 1. Introduction Instantons in commutative space are one of the most important objects for nonperturbative analysis. We can overview them for example in [1] from the physicist's view points or in [2] from mathematical view points. See for example [3] for recent developments of them. Noncommutative (NC for short) instantons were discovered by Nekrasov and Schwarz [4]. After [4], NC instantons have been investigated by many physicists and mathematicians. However, many enigmas are left until now. Let us focus into instantons of gauge theories in NC and understand what is clarified and what is unknown. Instanton connections in the 4-dim Yang-Mills theory are defined by where is a curvature 2-form and is the Hodge star operator. This condition says that curvature is anti-self-dual. In this paper, we call anti-self-dual connections instantons. The choice of anti-self-dual connection or self-dual connection to define instantons is not important to mathematics but just a habit. NC instanton solutions were discovered by Nekrasov and Schwartz by using the ADHM method [4]. (See also [5] for the original ADHM method.) The ADHM construction which generates the instanton gauge field requires a pair of the two complex vector spaces and . Here is an integer called instanton number. Introduce , , and which are called ADHM data that satisfy the ADHM equations that we will see soon. In other words, and are complex-valued matrices, and and are complex-valued matrices that satisfy (2.13) and (2.14) in Section 2.2. Using these ADHM data, we can construct instanton [6–17]. We call it NC ADHM instanton in the following. The NC ADHM construction is a strong method. A lot of instanton solutions are

Abstract:
It is known that if gauge conditions have Gribov zero modes, then topological symmetry is broken. In this paper we apply it to topological gravity in dimension $n \geq 3$. Our choice of the gauge condition for conformal invariance is $R+{\alpha}=0$ , where $R$ is the Ricci scalar curvature. We find when $\alpha \neq 0$, topological symmetry is not broken, but when $\alpha =0$ and solutions of the Einstein equations exist then topological symmetry is broken. This conditions connect to the Yamabe conjecture. Namely negative constant scalar curvature exist on manifolds of any topology, but existence of nonnegative constant scalar curvature is restricted by topology. This fact is easily seen in this theory. Topological symmetry breaking means that BRS symmetry breaking in cohomological field theory. But it is found that another BRS symmetry can be defined and physical states are redefined. The divergence due to the Gribov zero modes is regularized, and the theory after topological symmetry breaking become semiclassical Einstein gravitational theory under a special definition of observables.

Abstract:
We study topological aspects of matrix models and noncommutative cohomological field theories (N.C.CohFT). N.C.CohFT have symmetry under the arbitrary infinitesimal noncommutative parameter $\theta$ deformation. This fact implies that N.C.CohFT possess a less sensitive topological property than K-theory, but the classification of manifolds by N.C.CohFT has a possibility to give a new view point of global characterization of noncommutative manifolds. To investigate properties of N.C.CohFT, we construct some models whose fixed point loci are given by sets of projection operators. Particularly, the partition function on the Moyal plane is calculated by using a matrix model. The moduli space of the matrix model is a union of Grassman manifolds. The partition function of the matrix model is calculated using the Euler number of the Grassman manifold. Identifying the N.C.CohFT with the matrix model, we get the partition function of the N.C.CohFT. To check the independence of the noncommutative parameters, we also study the moduli space in the large $\theta$ limit and the finite $\theta$, for the Moyal plane case. If the partition function of N.C.CohFT is topological in the sense of the noncommutative geometry, then it should have some relation with K-theory. Therefore we investigate certain models of CohFT and N.C.CohFT from the point of view of K-theory. These observations give us an analogy between CohFT and N.C.CohFT in connection with K-theory. Furthermore, we verify it for the Moyal plane and noncommutative torus cases that our partition functions are invariant under the those deformations which do not change the K-theory. Finally, we discuss the noncommutative cohomological Yang-Mills theory.

Abstract:
Measurements of HBT correlations and event-by-event fluctuations of mean pT and the net charge in Pb-Au collisions at 40, 80, and 158 AGeV/c are presented. From comparisons of HBT radii measured from AGS to RHIC energies, a universal mean free path of pions at the thermal freeze-out of about 1 fm is derived. Non-statistical mean pT fluctuations of about 0.7 % are measured, which are somewhat smaller than fluctuations at RHIC. No indication for the QCD critical point is observed. Fluctuations of the net charge are reproduced by RQMD and URQMD models, but significantly larger than prediction in equilibrated QGP.

Abstract:
Radiative transfer effects due to overlapping X-ray lines in a high-temperature, optically-thick, highly-ionized medium are investigated. One particular example, where the O VIII Ly-alpha doublet coincide in frequency with the N VII Ly-zeta lines is studied in detail to illustrate the effects on the properties of the emergent line spectrum. We solve the radiative transfer equation to study the energy transport of resonance line radiation in a static, infinite, plane-parallel geometry, which is used to compute the destruction/escape probabilities for each of the lines for various total optical thicknesses of the medium, as well as destruction probabilities by sources of underlying photoelectric opacity. It is found that a large fraction of the O VIII Ly-alpha line radiation can be destroyed by N VII, which can result in an reversal of the O VIII Ly-alpha/N VII Ly-alpha line intensity ratio similar to what may be seen under non-solar abundances. Photoelectric absorption by ionized carbon and nitrogen can also subsequently increase the emission line intensities of these ions. We show that line ratios, which are directly proportional to the abundance ratios in optically thin plasmas, are not good indicators of the true CNO abundances. Conversely, global spectral modeling that assumes optically thin conditions may yield incorrect abundance estimates when compared to observations, especially if the optical depth is large. Other potentially important overlapping lines and continua in the X-ray band are also identified and their possible relevance to recent high resolution spectroscopic observations with Chandra and XMM-Newton are briefly discussed.

Abstract:
We get three types of results on measure equivalence rigidity; direct product groups of Ozawa's class $\mathcal{S}$ groups, wreath product groups and amalgamated free products. We prove measure equivalence factorization results on direct product groups of Ozawa's class $\mathcal{S}$ groups. As consequences, Monod--Shalom type orbit equivalence rigidity theorems follow. We prove that if two wreath product groups $A \wr G$, $B \wr \Gamma$ of non-amenable exact direct product groups $G$, $\Gamma$ with amenable bases $A$, $B$ are measure equivalent, then $G$ and $\Gamma$ are measure equivalent. We get Bass--Serre rigidity results on amalgamated free products of non-amenable exact direct product groups.

Abstract:
We introduce a generalization of expander graphs, which is called a weak expander sequence. It is proved that a uniform Roe algebra of a weak expander sequence is not locally reflexive. It follows that uniform Roe algebras of expander graphs are not exact. We introduce the notion of a generalized box space to discuss box spaces and expander sequences in a unified framework. Key tools for the proof are amenable traces and measured groupoids associated to generalized box spaces.