Physicochemical Analysis of the System Zr(SO<Subscript>4</Subscript>)<Subscript>2</Subscript>–Na<Subscript>2</Subscript>SO<Subscript>4</Subscript>–H<Subscript>2</Subscript>SO<Subscript>4</Subscript>–H<Subscript>2</Subscript>O at 25°С

The solubility in the quaternary water–salt system Zr(SO₄)₂ · 4Н₂О–Na₂SO₄–H₂SO₄–H₂O at 25°C was studied. It was found that, in the system, there is crystallization of not only Na₂SO₄ and Zr(SO₄)₄ · 4H₂O, but also sodium sulfate zirconates Na₂Zr(SO₄)₂(OH)₂ · 0.3H₂O, Na₄Zr(SO₄)₄ · 3H₂O, and Na₂Zr(SO₄)₂ · 3H₂O and two new compounds, S₁ and S₂, which are presumably Na₂ZrO(SO₄)₂ · 2H₂O and Na₂Zr₂O₂(SO₄)₃ · 6H₂O.     

The NaCl–AlCl<Subscript>3</Subscript>–HCl–H<Subscript>2</Subscript>O system at 25°С

Solubility was studied in the system NaCl–AlCl₃–HCl–H₂O at 25°C in the section 28 wt % HCl. The system is of the eutonic type and has an extensive sodium chloride crystallization region. The composition of the eutonic solution is the following, wt %: NaCl, 0.47; AlCl₃ ? 6H₂O, 8.88; HCl, 25.38; and H₂O, 65.27. The lines of saturated solutions were approximated by polynomial equations.     

On P𝔉-Supplemented subgroups of finite groups

Let 𝔉 be a class of groups and G a finite group. A maximal subgroup M of G is called 𝔉-abnormal provided G∕M_G?𝔉. Let K<H be subgroup of G. Then we say that (K,H) is an 𝔉-abnormal pair of G provided K is a maximal 𝔉-abnormal subgroup of H. Let A be a subgroup of G. Then we say that A is 𝔉-quasipermutable in G provided A either covers or avoids every 𝔉-abnormal pair of G. In this paper, we consider some applications of 𝔉-quasipermutable subgroups.     

Solubility in the LaCl<Subscript>3</Subscript>-LnCl<Subscript>3</Subscript>-HCl-H<Subscript>2</Subscript>O (Ln = Pr,Nd) Systems at 25°C

The solubility in the quaternary water-salt systems LaCl₃-NdCl₃-HCl-H₂O (1) and LaCl₃-PrCl₃-HCl-H₂O (2) at 25°C was studied in the section of 40 wt % hydrochloric acid, a system with a eutonic discontinuity. The composition at the point of discontinuity for the eutonic solution is the following. In system 1: 4.67 wt % LaCl₃ · 7H₂O, 0.37 wt % PrCl₃ · 7H₂O, 37.98 wt % HCl, and 56.98 wt % H₂O; in system 2: 4.37 wt % LaCl₃ · 7H₂O, 0.93 wt % NdCl₃ · 6H₂O, 37.88 wt % HCl, and 56.82 wt % H₂O.     

A two-sided Arnoldi algorithm with stopping criterion and MIMO selection procedure

In this paper we introduce a two-sided Arnoldi method for the reduction of high order linear systems and we propose useful extensions, first of all a stopping criterion to find a suitable order for the reduced model and secondly, a selection procedure to significantly improve the performance in the multi-input multi-output (MIMO) case. One application is in micro-electro-mechanical systems (MEMS). We consider a thermo-electric micro thruster model, and a comparison between the commonly used Arnoldi algorithm and the two-sided Arnoldi is performed.     

Finite groups with subnormal second or third maximal subgroups

In the paper, the precise structure of finite groups all of whose second (or all of whose third) maximal subgroups are subnormal is established.     

On an efficient splitting‐based method for solving the diffusion equation on a sphere

A novel numerical approach for solving the diffusion problem on a sphere is suggested. By using operator splitting, we develop a new method that allows constructing finite difference schemes of the second and fourth approximation orders in the spatial variables. Both schemes properly ensure the balance of mass and the energy dissipation in the L₂ ‐norm. The schemes are very cheap from the computational standpoint. Numerical results demonstrate the skillfulness of the approach in describing the diffusion dynamics on a sphere. It is shown the method can directly be extended to nonlinear diffusion problems.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 331–352, 2012     

Finite groups in which every 3-Maximal subgroup commutes with all maximal subgroups

The structure of finite groups in which every 3-maximal subgroup commutes with all maximal subgroups is described.     

Structure of finite groups with <Emphasis Type="Italic">S</Emphasis>-quasinormal third maximal subgroups

We study finite groups whose 3-maximal subgroups are permutable with all Sylow subgroups.