Abstract:
Computer Automated Tomography has been shown to be a valuable tool in production research because it provides a non-destructive method to identify and evaluate the internal structural characteristics of reservoir rock. In CT scan, Hounsfield Unit (HU) is proportional to the degree of X-ray attenuation by the tissue. The aim of the present study was to introduce the method to estimate porosity which is one of physical parameters of reservoir rock though HU data. In this study, an Image J software was used to extract Hounsfield Unit data and calibrate by standard material’s density. This method provides the ability of using CT Scanner in advanced reservoir characterization and flow test experiments.

Abstract:
Using the Singwi-Tosi-Land-Sjolander theory we have studied the many-body effects in the two-dimensional electron gas with arbitrary polarization at finite temperatures. We have calculated the structure factors, pair correlation functions, local-field factors and the Helmholtz free energy for different values of spin polarization, temperature and density parameter. We have shown that the spin polarization and finite temperature effects are remarkable and in the low temperature or paramagnetic case our results match closely with those obtained in earlier papers .

Abstract:
In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates for gradients of solutions to the quasilinear parabolic equations: $$u_t-\operatorname{div}(A(x,t,\nabla u))=\operatorname{div}(F),$$ in a bounded domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$, under minimal regularity assumptions on the boundary of domain and on nonlinearity $A$. Then results yields existence of a solution to the Riccati type parabolic equations: $$u_t-\operatorname{div}(A(x,t,\nabla u))=|\nabla u|^q+\operatorname{div}(F)+\mu,$$ where $q>1$ and $\mu$ is a bounded Radon measure.

Abstract:
We prove the stable rationality of almost simple algebraic groups, the connected components of the Dynkin diagram of anisotropic kernel of which contain at most two vertices. The (stable) rationality of many isotropic almost simple groups with small anisotropic kernel and some related results over $p$-adic and arbitrary fields are discussed.

Abstract:
We extend an exact sequence of Colliot-Thelene and Sansuc which connects arithmetic and birational invariants of tori over a number field to one for arbitrary connected linear algebraic groups.

Abstract:
In this paper, we study the existence and regularity of the quasilinear parabolic equations: $$u_t-\text{div}(A(x,t,\nabla u))=B(u,\nabla u)+\mu$$ in $\mathbb{R}^{N+1}$, $\mathbb{R}^N\times(0,\infty)$ and a bounded domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$. Here $N\geq 2$, the nonlinearity $A$ fulfills standard growth conditions and $B$ term is a continuous function and $\mu$ is a radon measure. Our first task is to establish the existence results with $B(u,\nabla u)=\pm|u|^{q-1}u$, for $q>1$. We next obtain global weighted-Lorentz, Lorentz-Morrey and Capacitary estimates on gradient of solutions with $B\equiv 0$, under minimal conditions on the boundary of domain and on nonlinearity $A$. Finally, due to these estimates, we solve the existence problems with $B(u,\nabla u)=|\nabla u|^q$ for $q>1$.

Abstract:
We prove some new relations between weak approximation and some rational equivalence relations (Brauer and R-equivalence) in algebraic groups over arithmetical fields. By using weak approximation and local - global approach, we compute completely the group of Brauer equivalence classes of connected linear algebraic groups over number fields, and also completely compute the group of R-equivalence classes of connected linear algebraic groups $G$, which either are defined over a totally imaginary number field, or contains no anisotropic almost simple factors of exceptional type $^{3,6}\D_4$, nor $\E_6$. We discuss some consequences derived from these, e.g., by giving some new criteria for weak approximation in algebraic groups over number fields, by indicating a new way to give examples of non stably rational algebraic groups over local fields and application to norm principle.

Abstract:
This is a revision of a McMaster University preprint, with extension. In this paper we prove that over local or global fields of characteristic 0, the Corestriction Principle holds for kernel and image of all maps which are connecting maps in group cohomology and the groups of $R$-equivalences. Some related questions over arbitrary fields of characteristic 0 are also discussed. AMS Mathematics Subject Classification (1991): Primary 11E72, Secondary 18G50, 20G10

Abstract:
We propose in this paper the construction of non-commutative Chern characters of the C*-algebras of spheres and quantum spheres. The final computation gives us a clear relation with the ordinary Z/(2)-graded Chern characters of tori or their normalizers.

Abstract:
The nano-gold layer formed on the platinum rotating disk electrode (nano-Au/Pt-RD) inherited the catalytic property for Cr(VI) reduction from platinum surface and owned the good features of nano-gold such as insensitivity with hydrogen ion, high surface area, augmenting diffusion of Cr(VI) and ability for self-assembling with 4-pyridine-ethanethiol (PET) through Au←S linkages, to form PET/nano-Au/Pt-RD electrode capable of accumulating Cr(VI) from sample. The obtained PET/ nano-Au/Pt-RD electrode showed an extreme sensitivity to Cr(VI). By using this electrode, 1.09 ng·L^{﹣1} was the detection limit of differential pulse adsorptive cathodic stripping voltammetry for Cr(VI) with the accumulation time of only 2 min. Moreover, this electrode was reproducible with 3.5% RSD for 30 times of Cr(VI) accumulating and stripping. In addition, this electrode was also selective for Cr(VI) determination, which was not almost interfered by other inorganic ions.