New quasi-one-dimensional tetracyanidoplatinate,Cs4[Pt(CN)4](CF3SO3)2: Synthesis,structure, and physical characterization

The synthesis and some physical properties of a new quasi-one-dimensional tetracyanidoplatinate, Cs₄[Pt(CN)₄](CF₃SO₃)₂ (CsCP(OTf)) are reported and described in comparison to the well-known K₂[Pt(CN)₄]Br_0.30·3.2H₂O (KCP). Single-crystal X-ray diffraction reveals Pt–Pt spacings to be greater than those of KCP by 5% longitudinal and 38% transverse, but much shorter than comparable spacings in other non-partially oxidized platinates. Anomalies are observed between temperatures 100 K and 200 K: (1) Longitudinal DC conductivity is two orders of magnitude higher and is non-monotonic with temperature, showing a minimum at around 170 K. (2) Nuclear magnetic resonance (NMR) longitudinal relaxation time T₁ is at least three orders of magnitude higher than that of KCP, and is also non-monotonic with temperature, showing a sharp peak at around 120 K. Since X-ray diffraction reveals no structural transition at 120 K, these suggest a possible lattice freezing or stiffening at around 120 K.     

On the uniform bound of the index of reducibility of parameter ideals of a module whose polynomial type is at most one

Let ${(R, \mathfrak{m})}$ be a Noetherian local ring, M a finitely generated R-module. The aim of this paper is to prove a uniform formula for the index of reducibility of parameter ideals of M provided the polynomial type of M is at most one.     

𝒟-Stability Radius of Linear Discrete Time Systems

We study robustness of 𝒟-stability of linear difference equations under multiperturbation and affine perturbation of coefficient matrices via the concept of 𝒟-stability radius. Some explicit formulae are derived for these 𝒟-stability radii. The obtained results include the corresponding ones established earlier in Hinrichsen and Son and Ngoc and Son as particular cases.     

Representations of finite special linear groups in non-defining characteristic

We classify irreducible modules over the finite special linear group SLn(q) in the non-defining characteristic ?, describe restrictions of irreducible modules from GLn(q) to SLn(q), classify complex irreducible characters of SLn(q) irreducible modulo l, and discuss unitriangularity of the l-decomposition matrix for SLn(q).     

Organotin reagents supported on ionic liquid: highly efficient catalytic free radical reduction of alkyl halides

Ionic liquid-supported organotin reagents were prepared in good yield and demonstrated a convenient catalytic free radical reduction of alkyl halides. A variety of alkyl and aryl halides could be reduced in high to excellent yields and selectively to afford the desired products with simple work-up procedure.     

On the boundedness of the Hardy operator in the weighted space BMO

The result of Golubov [5, Theorem 2] on the boundedness of the Hardy-Littlewood operator $$ \mathcal{B}f(x): = \frac{1} {x}\int_0^x {f(t)} dt $$ in the space BMO(?) is well known. The author of the present paper solves the analogous problem in the weighted space BMO on the semi-axis ?₊ for the operator $$ T_w f(x): = \frac{1} {{W(x)}}\int_0^x {f(t)w(t)} dt $$ and also in the classical space BMO(?₊) for a class of integral operators involving, for example, the Riemann-Liouville fractional integral.     

Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA

In this paper, we consider the case of downside risk measures with cardinality and bounding constraints in portfolio selection. These constraints limit the amount of capital to be invested in each asset as well as the number of assets composing the portfolio. While the standard Markowitz’s model is a convex quadratic program, this new model is a NP-hard mixed integer quadratic program. Realizing the computational intractability for this class of problems, especially large-scale problems, we first reformulate it as a DC program with the help of exact penalty techniques in Difference of Convex functions (DC) programming and then solve it by DC Algorithms (DCA). To check globality of computed solutions, a global method combining the local algorithm DCA with a Branch-and-Bound algorithm is investigated. Numerical simulations show that DCA is an efficient and promising approach for the considered problem.      

DC programming and DCA for globally solving the value-at-risk

The value-at-risk is an important risk measure that has been used extensively in recent years in portfolio selection and in risk analysis. This problem, with its known bilevel linear program, is reformulated as a polyhedral DC program with the help of exact penalty techniques in DC programming and solved by DCA. To check globality of computed solutions, a global method combining the local algorithm DCA with a well adapted branch-and-bound algorithm is investigated. An illustrative example and numerical simulations are reported, which show the robustness, the globality and the efficiency of DCA.     

2-Methylarsino-ethanol

2-Methylarsino-ethanol Synthesis and reactions of 2-methylarsino-ethanol MeAs(H)? CH₂CH₂? OH are described. These reactions result in the formation of bifunctional arsanes of the general formula MeAs(CH₂CH₂? X)₂ and MeAs(CH₂CH₂? X)CH₂CH₂? Y, respectively, with different groups X and Y.