Variance or spectral density in sampled data filtering?

Most physical systems operate in continuous time. However, to interact with such systems one needs to take samples. This raises the question of the relationship between the sampled response and the response of the underlying continuous-time system. In this paper we review several aspects of the sampling process. In particular, we examine the role played by variance and spectral density in describing discrete random processes. We argue that spectral density has several advantages over variance. We illustrate the ideas by reference to the problem of state estimation using the discrete-time Kalman filter.     

Mn(I) in an extended oxide: the synthesis and characterization of La(1-x)Ca(x)MnO(2+δ) (0.6 ≤ x ≤ 1)

Reduction of La(1-x)Ca(x)MnO(3) (0.6 ≤ x ≤ 1) perovskite phases with sodium hydride yields materials of composition La(1-x)Ca(x)MnO(2+δ). The calcium-rich phases (x = 0.9, 1) adopt (La(0.9)Ca(0.1))(0.5)Mn(0.5)O disordered rocksalt structures. However local structure analysis using reverse Monte Carlo refinement of models against pair distribution functions obtained from neutron total scattering data reveals lanthanum-rich La(1-x)Ca(x)MnO(2+δ) (x = 0.6, 0.67, 0.7) phases adopt disordered structures consisting of an intergrowth of sheets of MnO(6) octahedra and sheets of MnO(4) tetrahedra. X-ray absorption data confirm the presence of Mn(I) centers in La(1-x)Ca(x)MnO(2+δ) phases with x < 1. Low-temperature neutron diffraction data reveal La(1-x)Ca(x)MnO(2+δ) (x = 0.6, 0.67, 0.7) phases become antiferromagnetically ordered at low temperature.     

New intraband magneto-optical studies on n-InSb

A highly sensitive photoconductive technique has been used to provide the first direct evidence of emission of five optical phonons during the energy relaxation process of the photoexcited electrons induced by a CO₂ laser in n-InSb. The CO₂ laser-induced magnetophotoconductivity exhibits a number of very sharp resonances whose positions depend strongly upon photon energy. All observed transitions can be described with one single set of band parameters.     

Thermal formation of mixed-metal inorganic complexes at atmospheric pressure

Atmospheric-pressure thermal desorption ionization (APTDI), a new variant on older ionization methods, is employed to generate gas-phase ions from inorganic and organometallic compounds. The method is compared to conventional electrospray ionization (ESI) of these compounds and found in most cases examined to yield simpler mass spectra which are useful in the characterization of the pure compounds. Cluster formation, however, is prominent in these spectra and mixtures of V(IV)O(salen), Ni(II)(salen) and Co(II)(salen) show mixed-metal cluster ions. This makes APTDI a way to prepare gas-phase ions which contain multiple selected metal atoms and ligands. Such mixed-metal complexes can be mass-selected and structurally characterized by tandem mass spectrometry. Strong contrasts are evident in the dissociation behavior of homonuclear and heteronuclear metal clusters, the latter showing accompanying redox processes. The chemical reactivity accompanying collision-induced dissociation (CID) of some of the mixed-metal clusters is typified by the protonated species H+[NiVO(salen)], which undergoes a formal oxidation process (hydrogen atom loss) to give the molecular radical cation of Ni(salen). This ionization method may provide a new route to unique inorganic compounds on surfaces through soft landing of appropriate cluster ions. The contrasting behavior of the ESI and APTDI processes is evident in the salens where ESI shows simple Bronsted acid/base chemistry, no mixed-metal clusters and no redox chemistry.     

Direct synthesis of six-coordinate nitro complexes of cobalt meso-tetraphenylporphyrinate with trans-O-donor ligands

The formation of a series of six-coordinate complexes (B)Co(TPP)(NO₂) (B is ketone, aldehyde, ether or epoxide; TPP is meso-tetraphenylporphyrin dianion) on exposure of thin films of five-coordinate Co(TPP)(NO₂) to vapors of the O-donor ligands was established by IR and UV/Vis spectroscopy (resorting to the data on isotope-substituted ¹⁵NO₂). The complex formation is accompanied by shifts of the vibration frequencies of the trans-NO₂ ligand and gives rise to new IR bands corresponding to the O-donors in the ν(C=O) or ν(C-O) region shifted with respect to these bands of free ligands. The complexes are rather stable in the solid phase but eliminate the O-donor ligand upon dissolution in an inert solvent (or upon maintenance in a vacuum for some complexes) being converted into the initial five-coordinate nitro complex. Using the IR spectra of CCl₄ solutions of the complexes containing a large excess of O-donor molecules, the equilibrium constants and the formation enthalpies of some (B)Co(TPP)(NO₂) complexes were determined, indicating weak coordination of these ligands.     

Richardson Elements for Parabolic Subgroups of Classical Groups in Positive Characteristic

Let G be a simple algebraic group of classical type over an algebraically closed field k. Let P be a parabolic subgroup of G and let be the Lie algebra of P with Levi decomposition , where is the Lie algebra of the unipotent radical of P and ł is a Levi complement. Thanks to a fundamental theorem of Richardson (Bull. London Math. Soc. 6:21–24, 1974), P acts on with an open dense orbit; this orbit is called the Richardson orbit and its elements are called Richardson elements. Recently Baur (J. Algebra 297(1):168–185, 2006), the first author gave constructions of Richardson elements in the case for many parabolic subgroups P of G. In this note, we observe that these constructions remain valid for any algebraically closed field k of characteristic not equal to 2 and we give constructions of Richardson elements for the remaining parabolic subgroups. Presented by Peter Littelmann.     

Catalytic dioxygen activation by (nitro)(meso-tetrakis(2-n-methylpyridyl)porphyrinato)cobalt(III) cation derivatives electrostatically immobilized in nafion films: an experimental and DFT investigation

Complexes of the (nitro)( meso-tetrakis(2- N-methylpyridyl)porphyinato)cobalt(III) cation, [LCoTMpyP(2)(NO 2)] (4+), in which L = water or ethanol have been immobilized through ionic attraction within Nafion films (Naf). These immobilized six-coordinate species, [LCoTMPyP(2)(NO 2)/Naf], have been found to catalyze the oxidation of triphenylphosphine in ethanol solution by dioxygen, therefore retaining the capacity to activate dioxygen catalytically without an additional reducing agent as was previously observed in nonaqueous solution for the non-ionic (nitro)cobalt porphyrin analogs. Heating these immobilized six-coordinate species under vacuum conditions results in the formation of the five-coordinate nitro derivatives, [CoTMPyP(2)(NO 2)/Naf] at 85 degrees C and [CoTMPyP(2)/Naf] at 110 degrees C. The catalytic oxidation of gas-phase cyclohexene with O 2 is supported only by the resulting immobilized five-coordinate nitro complex as was previously seen with the corresponding solution-phase catalyst in dichloromethane solution. The simultaneous catalytic oxidation of triphenylphosphine and cyclohexene with O 2 in the presence of the Nafion-bound six-coordinate ethanol nitro complex is also observed; however, this process is not seen for the CoTPP derivative in dichloromethane solution. The oxidation reactions do not occur with unmodified Nafion film or with Nafion-supported [BrCo(III)TmpyP]/Naf or [Co(II)TmpyP]/Naf, indicating the necessity for the nitro/nitrosyl ligand in the oxidation mechanism. The existence of a second reactive intermediate is indicated because the two simultaneous oxidation reactions depend on two distinct oxygen atom-transfer steps having different reactivity. The absence of homogeneous cyclohexene oxidation by the six-coordinate (H 2O)CoTPP(NO 2) derivatives in the presence of Ph 3P and O 2 in dichloromethane solution indicates that the second reactive intermediate is lost by an unidentified route only in solution, implying that the immobilization of it in Nafion allows it to react with cyclohexene. Although direct observation of this species has not been achieved, a comparitive DFT study of likely intermediates in several catalytic oxidation mechanisms at the BP 6-31G* level supports the possibility that this intermediate is a peroxynitro species on the basis of relative thermodynamic accessibility. The alternate intermediates evaluated include the reduced cobalt(II) porphyrin, the dioxygen adduct cobalt(III)-O 2 (-), the oxidized cobalt(II) pi-cation radical, and the nitrito complex, cobalt(III)-ONO.