Thermal transformations in soils studied by Mössbauer spectroscopy and x-ray diffraction

Mossbauer spectroscopy and X-ray diffraction techniques were used to investigate the iron oxides and other mineral phase developments in calcareous and noncalcareous soil samples after firing at ≈ 1000°C. Well crystalline haematite with larger particle size was produced in the fired non-calcareous soil. On the other hand, while goethite in the strongly calcareous natural material was transformed into haematite at the oven drying temperature, non of the latter was detected after firing at 1050°C. This could be related to the reaction between CaO, quartz and aluminosilicates at 800°C to produce calcium aluminosilicates which may have hindered the growth of haematite above this temperature.     

Explicit block iterative method for the solution of the biharmonic equation

We develop an iterative algorithm for the solution of a finite difference approximation of the biharmonic equation over a rectangular region by using the explicit block iterative method, i.e., box over relaxation scheme. The 4- and 9-point explicit blocks were considered and performance results for the two algorithms are presented.© 1993 John Wiley & Sons, Inc.     

Highly efficient widely tunable subpicosecond double mode-locked laser

A high average power (≈150 mW) subpicosecond (0.5 ps) passively double mode-locked dye laser is described. Two synchronized cw pulse trains are generated which are independently tunable over broad wavelength ranges (≈600 Å).     

C4- and D4-Modules via perspective direct summands

In this article, we study the C4- and D4-modules in terms of perspective direct summands, providing new characterizations and results. Endomorphism rings of C4-modules and extensions of right C4-rings are also investigated. Decompositions of C4-modules with restricted ACC on direct summands and D4-modules with restricted DCC on direct summands are obtained.     

Singular spectrum analysis and Fisher–Shannon analysis of spring flow time series: An application to Anjar Spring,Lebanon

In this study, the time dynamics of water flow from Anjar Spring was investigated, which is one of the major issuing springs in the central part of Lebanon. Likewise, many water sources in Lebanon, this spring has no continuous records for the discharge, and this would prevent the application of standard time series analysis tools. Furthermore, the highly nonstationary character of the series implies that suited methodologies can be employed to get insight into its dynamical features. Therefore, the Singular Spectrum Analysis (SSA) and Fisher–Shannon (FS) method, which are useful methods to disclose dynamical features in noisy nonstationary time series with gaps, are jointly applied to analyze the Anjar Spring water flow series. The SSA revealed that the series can be considered as the superposition of meteo-climatic periodic components, low-frequency trend and noise-like high-frequency fluctuations. The FS method allowed to extract and to identify among all the SSA reconstructed components the long-term trend of the series. The long-term trend is characterized by higher Fisher Information Measure (FIM) and lower Shannon entropy, and thus, represents the main informative component of the whole series. Generally water discharge time series presents very complex time structure, therefore the joint application of the SSA and the FS method would be very useful in disclosing the main informative part of such kind of data series in the view of existing climatic variability and/or anthropogenic challenges.     

Extensions of simple-injective rings

A ring Ris called right simple-injective if every itMinear map with simple image from a right ideal to Rcan be extended to R. We characterize when matrix rings, upper triangular matrix rings and trivial extensions are right simple-injective. We also study split null extensions of simple-injective rings.     

On finitely embedded rings

A result of Ginn and Moss asserts that a left and right noetherian ring with essential right socle is left and right artinian. There are examples of right finitely embedded rings with ACC on left and right annihilators which are not artinian. Motivated by this, it was shown by Faith that a commutative, finitely embedded ring with ACC on annihilators (and square-free socle) is artinian (quasi-Frobenius). A ring R is called right minsymmetric if, whenever k R is a simple right ideal of R, then R k is also simple. In this paper we show that a right noetherian right minsymmetric ring with essential right socle is right artinian. As a consequence we show that a ring is quasi-Frobenius if and only if it is a right and left mininjective, right finitely embedded ring with ACC on right annihilators. This extends the known work in the artinian case, and also extends Faith's result to the non-commutative case.