Abstract:
We discuss the problem of R-separability (separability of variables with a factor R) in the stationary Schr dinger equation on n-dimensional Riemann space. We follow the approach of Gaston Darboux who was the first to give the first general treatment of R-separability in PDE (Laplace equation on E^3). According to Darboux R-separability amounts to two conditions: metric is isothermic (all its parametric surfaces are isothermic in the sense of both classical differential geometry and modern theory of solitons) and moreover when an isothermic metric is given their Lamé coefficients satisfy a single constraint which is either functional (when R is harmonic) or differential (in the opposite case). These two conditions are generalized to n-dimensional case. In particular we define n-dimensional isothermic metrics and distinguish an important subclass of isothermic metrics which we call binary metrics. The approach is illustrated by two standard examples and two less standard examples. In all cases the approach offers alternative and much simplified proofs or derivations. We formulate a systematic procedure to isolate R-separable metrics. This procedure is implemented in the case of 3-dimensional Laplace equation. Finally we discuss the class of Dupin-cyclidic metrics which are non-regularly R-separable in the Laplace equation on E^3.

Abstract:
We discuss the problem of $R$-separability (separability of variables with a factor $R$) in the stationary Schr\"odinger equation on $n$-dimensional Riemann space. We follow the approach of Gaston Darboux who was the first to give the first general treatment of $R$-separability in PDE (Laplace equation on ${\mathbb E}^3$). According to Darboux $R$-separability amounts to two conditions: metric is isothermic (all its parametric surfaces are isothermic in the sense of both classical differential geometry and modern theory of solitons) and moreover when an isothermic metric is given their Lam\'e coefficients satisfy a single constraint which is either functional (when $R$ is harmonic) or differential (in the opposite case). These two conditions are generalized to $n$-dimensional case. In particular we define $n$-dimensional isothermic metrics and distinguish an important subclass of isothermic metrics which we call binary metrics. The approach is illustrated by two standard examples and two less standard examples. In all cases the approach offers alternative and much simplified proofs or derivations. We formulate a systematic procedure to isolate $R$-separable metrics. This procedure is implemented in the case of 3-dimensional Laplace equation. Finally we discuss the class of Dupin-cyclidic metrics which are non-regularly $R$-separable in the Laplace equation on ${\mathbb E}^3$.

Abstract:
We discuss integrability of normal field equations of arbitrary parametrised Bianchi surfaces. A novel geometric definition of Bianchi surfaces is presented as well as B\"acklund transformation for the normal field equations in arbitrary chosen surface parametrization.

Abstract:
According to [8] if the stationary Schroedinger equation on n-dim. Riemann space admits R-separation of variables (i.e. separation of variables with a factor R), then the underlying metric is necessarily isothermic. An important sub-class of isothermic metrics are the so called binary metrics. In this paper we study conditions for vanishing of components C_ijkl of Weyl tensor of arbitrary 4-binary metrics. In particular all 4-binary metrics for which C_ijij are the only non-vanishing components are classified into four classes. Finally, conformally flat metrics of the last class are isolated.

Abstract:
We show that the theory of isothermic surfaces in $\E^3$ -- one of the oldest branches of differential geometry -- can be reformulated within the modern theory of completely integrable (soliton) systems. This enables one to study the geometry of isothermic surfaces in $\E^3$ by means of powerful spectral methods available in the soliton theory. Also the associated non-linear system is interesting in itself since it displays some unconventional soliton features and, physically, could be applied in the theory of infinitesimal deformations of membranes.

Abstract:
The right of States, for a variety of reasons, to expel aliens hasnever been disputed by the European Court of Human Rights insofar as aState party to the European Convention on Human Rights continues, quite naturally, to exercise its sovereignty over its territory. However, this right has to be reconciled with the obligation of States parties to the European Convention on Human Rights not to expose aliens and, more generally, persons under their jurisdictionto a risk of violation of the provisions of the Convention. Yet, guaranteeing that no human right recognized as such by the Convention be violated in case of expulsion is too heavy a task for States to assume. Imposing such an obligation would end up in invalidatingthe sovereign right of States to expel aliens. The Court ofStrasbourg retains primarily the risk of Article 3 of the Convention being violated in expulsion cases, a provision according to which inhuman or degrading punishments or treatments and, of course, acts of torture are strictly prohibited. The Court’s case-law, abundant aswell as rich in nuances, results in rather a thorough examination of the human rights situation in any country towards which a alien will be (or has already been) expelled.

Abstract:
We present a class of orthogonal non-regular in a sense of Kalnins and Miller (hence non-St\"ackel) coordinates which are R-separable in 3-dim. Helmholtz equation. One family of parametric surfaces consists of parallel Dupin cyclides, the other two consist of circular cones. This coordinate system is used to simplify derivation of Friedlander's formulae for a general "simple progressive solution of the wave equation" (modulated soliton of wave equation) in $E^3$ and to correct some errors of his paper. The extended version of the paper will be published soon.

Abstract:
Reinforced concrete structures in marine environment are subjected to chloride penetration, which significantly degrades the structural performance due to the occurrence of corrosion in the steel reinforcement. The performance degradation of the structures would reduce the intended service life and caused higher maintenance and repair cost. Therefore, system to monitor chloride penetration into reinforced concrete before the starting corrosion of reinforcement is indispensable. An embedded probe system to detect chloride penetration into concrete was developed in Japan. This probe consists of a cementitious material body and some number of wires as sensors, which are set in the shallow ditches around the probe body. The system detect the chloride penetration by monitoring the initiation time of wire corrosion, it also has the advantages of continuous monitoring and early warning on the onset of corrosion in the reinforcement. However, the probe had not yet had high sensitivity for detecting critical chloride content in concrete. Therefore to increase its sensitivity, four types of improvements, namely partial coating of the wires, waterproofing on the probe body, filling the ditches with porous material and supplying small current on the wires were evaluated in this study. From the experimental result, it was observed that supplying small current and partial coating of the wires could improve the sensitivity of the probe significantly, while waterproofing treatment on the probe body and filling the ditches did not have significant contribution.

Abstract:
The effect of loading on the chloride penetration into plain concrete (PC) and fiber reinforced concrete (FRC) was studied experimentally by using modified NT Build 492 – Non-steady state chloride migration test that include the application of loading on the specimen during the test. Three types of polypropylene fibers with different lengths and shapes were used. The concretes were tested for chloride penetration at different stress ratios under static and cyclic loading. The results of the static loading showed that there was a slight reduction in the chloride penetration under low level of compressive stress while an increase in the chloride penetration was found at higher stress level. There are significance difference in chloride penetration behavior of the plain concrete, long fiber FRC and short fiber FRC. Chloride penetration increased even more at cyclic loading conditions showing difference behavior of FRC and PC at difference number of cycle and load level.