Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.     

Syntheses and crystal structures of dinuclear complexes containing d-block and f-block luminophores. Sensitization of NIR luminescence from Yb(III), Nd(III), and Er(III) centers by energy transfer from Re(I)- and Pt(II)-bipyrimidine metal centers

Mononuclear complexes [Re(bpym)(CO)(3)Cl] and [Pt(bpym)(CC-C(6)H(4)CF(3))(2)] (bpym = 2,2'-bipyrimidine), in which one of the bipyrimidine sites is vacant, have been used as "complex ligands" to prepare heterodinuclear d-f complexes in which a lanthanide tris(1,3-diketonate) unit is attached to the secondary bipyrimidine site to evaluate the ability of d-block chromophores to act as antennae for causing sensitized near-infrared (NIR) luminescence from adjacent lanthanide(III) centers. The two sets of complexes so prepared are [Re(CO)(3)Cl(mu-bpym)Ln(fod)(3)] (abbreviated as Re-Ln; where Ln = Yb, Nd, Er) and [(F(3)C-C(6)H(4)-CC)(2)Pt(mu-bpym)Ln(hfac)(3)] (abbreviated as Pt-Ln; where Ln = Nd, Gd). Members of both series have been structurally characterized; the metal-metal separation across the bipyrimidine bridge is approximately 6.3 A in each case. In these complexes, the (3)MLCT (MLCT = metal to ligand charge-transfer) luminescences of the mononuclear [Re(bpym)(CO)(3)Cl] and [Pt(bpym)(CC-C(6)H(4)CF(3))(2)] complexes are quenched by energy transfer to those lanthanides (Ln = Yb, Nd, Er) that have low-lying f-f states capable of NIR luminescence; as a result, sensitized NIR luminescence is seen from the lanthanide center following excitation of the d-block unit. In the solid state, quenching of the luminescence from the d-block chromophore is complete, indicating efficient d --> f energy transfer, as a result of the short metal-metal separation across the bipyrimidine bridge. In a CH(2)Cl(2) solution, partial dissociation of the dinuclear complexes into the mononuclear units occurs, with the result that some (3)MLCT luminescence is observed from mononuclear [Re(bpym)(CO)(3)Cl] or [Pt(bpym)(CC-C(6)H(4)CF(3))(2)] present in the equilibrium mixture. Solution UV-vis and luminescence titrations, carried out by the addition of portions of Ln(fod)(3)(H(2)O)(2) or Ln(hfac)(3)(H(2)O)(2) to the d-block complex ligands, indicate that binding of the lanthanide tris(1,3-diketonate) unit at the secondary bipyrimidine site to give the d-f dinuclear complexes occurs with an association constant of ca. 10(5) M(-)(1).     

Crystal structure of 1H+,10H+-1,10-diazonia-18-crown-6 diethyldithiophosphate

An x-ray diffraction structural analysis was carried out on 1H⁺,10H⁺-1,10-diazonia-18-crown-6 diethyldithiophosphate, which exists in the crystal as isolated ionic hydrogen-bonded complexes [H₂DA18C6]²⁺·2(EtO)₂PS₂ ^– with strong inter-ion N-HS hydrogen bonds. The centrosymmetric DA18C6 dication has an unusual two-cornered conformation stabilized by a pair of weak intra-ring furcated OH(N)O hydrogen bonds.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 190–192, January, 1991.     

Acid-Basic and Complexing Properties of Compounds with a C(X)NHP(Y) Fragments

Abstract

N-(thio)carbonyl(thio)amidophosphates, their open-chain and crown-containing analogues with a C (X) NHP (Y) fragments are NH acids with pKa 8–11 and the effective complexing agents for “soft” ion metals.     

Local-in-time adjoint-based method for design optimization of unsteady flows

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickly become prohibitive for large-scale applications. The key idea of the local-in-time method is to divide the entire time interval into several subintervals and to approximate the solution of the unsteady adjoint equations and the sensitivity derivative as a combination of the corresponding local quantities computed on each time subinterval. Since each subinterval contains relatively few time levels, the storage cost of the local-in-time method is much lower than that of the global methods, thus making the time-dependent adjoint optimization feasible for practical applications. Another attractive feature of the new technique is that the converged solution obtained with the local-in-time method is a local extremum of the original optimization problem. The new method carries no computational overhead as compared with the global implementation of adjoint-based methods. The paper presents a detailed comparison of the global- and local-in-time adjoint-based methods for design optimization problems governed by the unsteady compressible 2-D Euler equations.     

REACTIONS OF TETRAPHOSPHORUS DECASULFIDE AND LAWESSON'S REAGENT WITH SILANES CONTAINING A FEW Si-O BONDS

Abstract

The reactions of tetraphosphorus decasulfide and Lawesson's reagent with tetra-, tri- and dialkoxysilanes were studied. On the basis of these reactions, new S-silyl esters of phosphorus(V) thioacids have been prepared. The prepared compounds were identified by IR, ¹H, and ³¹P NMR and mass spectra as well as elemental analyses.     

Crown-Containing N-(Thio)Phosphoryl-(Thio)Ureas,their Ligand Properties and Analytical Application

Abstract

Crown-containing N-(thio)phosphoryl(thio)ureas are related to a class of NH-acids due to the presence of two acceptor-groups: (thio)phosphorylic and (thio)acylic. In agreement with structure of lariat ether, it was observed a stage corresponding to the step ejection of two H* ion on the potentiometric titration curve of ligand by alkaline. Calculated step ionization constants demonstrate that these compounds are weak acids with relative values of pK₁ and pK₂.     

Polymer chain dynamics under nanoscopic confinements

It is shown that the confinement of polymer melts in nanopores leads to chain dynamics dramatically different from bulk behavior. This so-called corset effect occurs both above and below the critical molecular mass and induces the dynamic features predicted for reptation. A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands that are in turn embedded in a quasi-solid and impenetrable methacrylate matrix. Both the molecular weight of the PEO and the mean diameter of the strands were varied to a certain degree. The chain dynamics of the PEO in the molten state was examined with the aid of field-gradient NMR diffusometry (time scale, 10(-2)-10(0) s) and field-cycling NMR relaxometry (time scale, 10(-9)-10(-4) s). The dominating mechanism for translational displacements probed in the nanoscopic strands by either technique is shown to be reptation. On the time scale of spin-lattice relaxation time measurements, the frequency dependence signature of reptation (i.e., T1 approximately nu(3/4)) showed up in all samples. A "tube" diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. This corset effect is traced back to the lack of the local fluctuation capacity of the free volume in nanoscopic confinements. The confinement dimension is estimated at which the crossover from confined to bulk chain dynamics is expected.