We study relations between properties of the Miura map r 7→ q = B(r) = r′ + r2 and Schrödinger operators Lq = −d2/dx2 + q where r and q are real-valued functions or distributions (possibly not decaying at infinity) from various classes. In particular, we study B as a map from Lloc(R) to the local Sobolev space H−1 loc (R) and the restriction of B to the Sobolev spaces Hβ(R) with β ≥ 0. For exam...

machine of AMINE Here, we review the definition of the abstract machine formally: 42 Definition 3.3.2 (Notations for maps) • We use [ ] as an empty map. • Let ψ be a map. We use the following notation: ψ[x 7→ a](z) def =  a (z is x) ψ(z) (otherwise). When ψ(x) is undefined, we use the following notation: ψ[x 7→ ⊥](z) def =  undefined (z = x) ψ(z) (otherwise). We may also write ψ(x) = ⊥ when...

An indicator-based evolutionary multiobjective optimization algorithm (EMOA) is introduced which incorporates the contribution to the unary R2-indicator as the secondary selection criterion. First experiments indicate that the R2-EMOA accurately approximates the Pareto front of the considered continuous multiobjective optimization problems. Furthermore, decision makers’ preferences can be inclu...

This study attempts to estimate spatial soil moisture in South Korea (99,000 km2) from January 2013 to December 2015 using a multiple linear regression (MLR) model and the Terra moderate-resolution imaging spectroradiometer (MODIS) land surface temperature (LST) and normalized distribution vegetation index (NDVI) data. The MODIS NDVI was used to reflect vegetation variations. Observed precipita...

In this paper we prove some results on the computational complexity of standard quantifierfree spatial logics with the connectedness predicate interpreted over the Euclidean spaces R and R. Topological logics with connectedness. A topological logic is a formal language whose variables range over subsets of topological spaces, and whose non-logical primitives denote fixed topological properties ...

Saline lakes can increase the soil and water salinity of the coastal areas. The main aim of this study is to distinguish the characteristics of the spectral reflectance of saline soil, analyze the statistical relationship between soil EC and characteristics of the spectral reflectance of saline soil, and to map soil salinity east of the Maharloo Lake. The correlation between field measurements ...