Necessary optimality conditions for differential-difference inclusions with state constraints

We consider the Mayer optimal control problem with dynamics given by a nonconvex differential-difference inclusion, whose trajectories are constrained to a closed set. Necessary optimality conditions in the form of the maximum principle are obtained.     

Mössbauer spectroscopy monitoring the spin transition of a FeII 1D chain with a fluorinated 4-R-1,2,4-triazole

The spin transition properties of [Fe(fletrz)₃](BF₄)₂?2H₂O are described. Fletrz (4-(2’-fluoroethyl)-4H-1,2,4-triazole) is a novel fluorine substituted 1,2,4-triazole ligand which forms 1D chain upon self-assembly with Fe^II ions. This coordination polymer exhibits reversible abrupt thermochromic spin transition that has been probed by SQUID magnetometry, variable temperature ⁵⁷Fe Mossbauer spectroscopy (77–300 K) and differential scanning calorimetry (100–300 K).     

Heterometallic Cr2/Ag2 1D polymer: Synthesis,structure and properties

A 1D heterometallic Cr₂/Ag₂ polymer formulated as {[Ag(μ-H₂O)Ag(nta)Cr(μ-OH)(μ-AcO,O′)Cr(nta)]·H₂O}_n (1) (H₃nta = nitrilotriacetic acid) has been prepared and structurally characterized. {Cr(μ-OH)(μ-OAc)Cr} dimeric units containing two different bridging ligands, hydroxo and acetate groups are coordinated to six Ag atoms forming the 1D network. The temperature dependence of magnetic susceptibility for 1 which was fitted with an isotropic Hamiltonian including biquadratic exchange parameters, yielded antiferromagnetic interaction parameters (J = −8.5(1), j = −0.50(7) cm⁻¹ g = 2.0).     

Two‐Step Spin Transition in a 1D FeII 1,2,4‐Triazole Chain Compound

A thermochromic 1D spin crossover coordination (SCO) polymer [Fe(βAlatrz)₃](BF₄)₂ ? 2 H₂O ( 1? 2 H₂O), whose precursor βAlatrz, (1,2,4‐triazol‐4‐yl‐propionate) has been tailored from a β‐amino acid ester is investigated in detail by a set of superconducting quantum interference device (SQUID), ⁵⁷Fe Mössbauer, differential scanning calorimetry, infrared, and Raman measurements. An hysteretic abrupt two‐step spin crossover (T_1/2^↓=230 K and T_1/2^↑=235 K, and T_1/2^↓=172 K and T_1/2^↑=188 K, respectively) is registered for the first time for a 1,2,4‐triazole‐based Fe^II 1D coordination polymer. The two‐step SCO configuration is observed in a 1:2 ratio of low‐spin/high‐spin in the intermediate phase for a 1D chain. The origin of the stepwise transition was attributed to a distribution of chains of different lengths in 1? 2 H₂O after First Order Reversal Curves (FORC) analyses. A detailed DFT analysis allowed us to propose the normal mode assignment of the Raman peaks in the low‐spin and high‐spin states of 1? 2 H₂O. Vibrational spectra of 1? 2 H₂O reveal that the BF₄^? anions and water molecules play no significant role on the vibrational properties of the [Fe(βAlatrz)₃]²⁺ polymeric chains, although non‐coordinated water molecules have a dramatic influence on the emergence of a step in the spin transition curve. The dehydrated material [Fe(βAlatrz)₃](BF₄)₂ ( 1 ) reveals indeed a significantly different magnetic behavior with a one‐step SCO which was also investigated.     

Maximal approximation order for a box-spline semi-cardinal interpolation scheme on the three-direction mesh

Let M be the centred 3-direction box-spline whose direction matrix has every multiplicity 2. A new scheme is proposed for interpolation at the vertices of a semi-plane lattice from a subspace of the cardinal box-spline space generated by M. The elements of this semi-cardinal box-spline subspace satisfy certain boundary conditions extending the not-a-knot end-conditions of univariate cubic spline interpolation. It is proved that the new semi-cardinal interpolation scheme attains the maximal approximation order 4. AMS subject classification 41A15, 41A05, 41A25, 41A63, 39A70, 47B35     

Sequential product of quantum effects

Unsharp quantum measurements can be modelled by means of the class of positive contractions on a Hilbert space , in brief, quantum effects. For the operation of sequential product was proposed as a model for sequential quantum measurements. We continue these investigations on sequential product and answer positively the following question: the assumption implies .

Then we propose a geometric approach of quantum effects and their sequential product by means of contractively contained Hilbert spaces and operator ranges. This framework leads us naturally to consider lattice properties of quantum effects, sums and intersections, and to prove that the sequential product is left distributive with respect to the intersection.

     

Index formulae for subspaces of Kreîn spaces

For a subspaceS of a Kreîn spaceK and an arbitrary fundamental decompositionK=K ^?[+]K ⁺ ofK, we prove the index formula $$\kappa ^ - \left( \mathcal{S} \right) + \dim \left( {\mathcal{S}^ \bot \cap \mathcal{K}^ + } \right) = \kappa ^ + \left( {\mathcal{S}^ \bot } \right) + \dim \left( {\mathcal{S} \cap \mathcal{K}^ - } \right)$$ where κ^±(S) stands for the positive/negative signature ofS. The difference dim(S∩K ^?)?dim(S ^⊥∩K ⁺), provided it is well defined, is called the index ofS. The formula turns out to unify other known index formulac for operators or subspaces in a Kreîn space.     

A note on the viable solutions for a class of nonconvex differential inclusions

We prove the existence of viable solutions to the Cauchy problemx′ ∈F(x),x(0)=x ₀, whereF is a multifunction defined on a convex locally compact setM of a Hilbert space that satisfiesF(x) ∩K _xM ∩ ?_F V (x) ≠ Ø, whereK _xM is the contingent cone toM atx and ?_F V is the Fréchet subdifferential of theφ-convex function of order twoV.     

Cation deficient layered Ruddlesden-Popper-related oxysulfides La2LnMS2O5 (Ln=La, Y; M=Nb, Ta)

The structures of the new oxysulfide Ruddlesden-Popper phases La2LnMS2O5 (Ln=La, Y; M=Nb, Ta) are reported together with an iodide-containing variant: La3-xNb1+xS2O5I2x (0相似文献