Generalized solutions of a class of nuclear-space-valued stochastic evolution equations

Generalized solutions are defined for stochastic evolution equations of the formdY _t =A ^* Y _t dt + dZ _t on the nuclear triplel(R ^d ) L²(R ^d ) l(R ^d ), whereA does not mapl(R ^d ) into itself. One case which is treated in detail involvesA = –(–) ^/2 ,0 < < 2. This example arises as the Langevin equation for the fluctuation limit of a system of particles migrating according to a symmetric stable process and undergoing critical branching in a random medium.The research of D. A. Dawson was supported by the Natural Sciences and Engineering Research Council of Canada. L. G. Gorostiza's research was supported in part by CONACyT Grants PCEXCNA-040319 and 140102 G203-006, Mexico.     

Consistency of decision processes

If a statistical or a voting decision procedure is used by several subpopulations and if each reaches an identical conclusion, then one might expect this conclusion to be the outcome for the full group. It is shown that this property fails to hold for large classes of decision procedures. The geometric reasons why the consistency does not hold are described. A general theorem is given to characterize the procedures that satisfy this property of weak consistency.This research was supported in part by NSF Grant IRI-8803505 and a Guggenheim Fellowship. Also, the author thanks a referee for some comments that stimulated certain revisions.     

Inversion of the exponential X-ray transform. I: Analysis

The exponential X-ray transform arises in single photon emission computed tomography and is defined on functions on ?ⁿ by , where μ is a constant. Approximate inversion, and inversion formulae of filtered back-projection type are derived for this operator in all dimensions. In particular, explicit formulae are given for convolution kernels (filters) K corresponding to a general point spread function E that can be used to invert the exponential X-ray transform via a filtered back-projection algorithm. The results extend and refine work of Tretiak and Metz¹⁷.     

Quantum relativistic action at a distance

A well-known relativistic action at a distance interaction of two unequal masses is altered so as to yield purely Newtonian radial forces with fixed particle rest masses in the system center-of-momentum inertial frame. Although particle masses experience no kinematic mass increase in this frame, speeds are naturally restricted to less than the speed of light. We derive a relation between the center-of-momentum frame total Newtonian energy and the composite rest mass. In a new proper time quantum formalism, we obtain an L²(R⁴ R⁴, C) Hilbert space by varying individual particle rest masses. We propose the use of density operators, recognizing that the auxiliary proper time parameter is not an observable. The quantum formalism is applied to our altered version of the relativistic harmonic oscillator. Our generalized coherent states yield four-dimensional wave packets which follow the correct classical world lines. Appendices contain reviews of classical Hamiltonian reparametrization (incorporating our notion of manifest covariance), and a comparison of this work with the literature.     

Thermodynamic properties of transition metals in aqueous solution. 2. The enthalpies of mixing of aqueous solutions of CoCl2, CuCl2, and MnCl2 with NaCl at varying ionic strength at 25°C

Enthalpies of mixing (_m H) aqueous solutions of CoCl₂, CuCl₂, and MnCl₂ with NaCl solutions were measured at constant ionic strengths of 0.5, 1.0, and 3.0 molal at 25°C. The excess enthalpy equations of Pitzer were then fit to the resulting _m H data. The resulting parameters are the temperature derivatives of the activity coefficient mixing parameters in the Pitzer system. The heat of mixing data for CoCl₂ and CuCl₂ were in agreement with earlier isomolal results by other workers.     

Classification and identification of mass spectra of toxic compounds with an inductive rule-building expert system and information theory

An expert system for classifying and identifying low-resolution mass spectra of toxic and related compounds was developed with an expert shell program. The shell system used was an inexpensive, rule-building software package with an implementation of the ID3 algorithm. Seventy-eight target compounds were used to establish classes previously found by SIMCA class modeling. The six classes included nonhalobenzenes; chlorobenzenes; bromoalkanes and bromoalkenes; mono- and di-chloroalkanes and the analogous alkenes; tri-, tetra- and penta-chloroalkanes and the analogous alkenes; and unknowns. Identification modules for the target compounds were forward-chained to the classification modules. An expert system based on binary-encoded mass spectra, with 17 masses selected on the basis of information content, gave 97 and 86% classification accuracy for training and test spectra, respectively. Identification accuracy was 77 and 80%, respectively. An expert system was also developed which was based on ternary encoding of the mass spectra of 108 training compounds using 25 masses. Ternary encoding has many of the advantages of binary encoding, without the disadvantages. This latter system was tested with the spectra of thirty compounds found in field samples or potential air pollutants. The classification accuracy for training and test spectra was 99 and 97%, respectively. The identification accuracy was 96 and 93%, respectively. With proper precautions, the rule-building expert system can be very effective in spectral classification and identification problems.     

Interactions of dendrimers with selected amino acids and proteins studied by continuous wave EPR and Fourier transform EPR

Interactions of polyamidoamine dendrimers, termed Gn, where n indicates the generation (=number of amidoamine layers), at different protonation levels with selected amino acids and proteins have been investigated by means of continuous wave electron paramagnetic resonance (cw-EPR) and pulsed-EPR (electron spin-echo = ESE) analyses. A low-generation dendrimer (G2) and a high-generation one (G6) were labeled with nitroxides for the EPR measurements. Gly, Glu, Arg, and Leu were selected as representative of neutral(zwitterionic)-polar, acidic, basic, and low-polar amino acids, respectively. The water-soluble proteins alpha-chymotrypsin and albumin were selected on the basis of a basic and an acidic isoelectric point, respectively. The cw-EPR spectra were analyzed by computing the line shapes to extract information about the dendrimer-biomolecule interactions. In general, dendrimers at a high protonation level interact stronger with amino acids than those at a low level of protonation. However, even for highly protonated dendrimers, a synergistic effect between hydrophilic and hydrophobic interactions promoted the formation of stable Gn-amino acid adducts, as demonstrated by the enhanced interactions with Leu. As expected from acid-base interactions, stable adducts were formed between Arg and highly protonated dendrimers and between Glu and low level protonated dendrimers. The relatively strong dendrimer interactions with the protein chymotrypsin and the poor interactions of dendrimers with albumin demonstrated that the protonated amino groups of the dendrimers are predominantly involved in the interactions with these proteins and indicated a significant role in the interactions with the dendrimers of the hydrophobic external residues of chymotrypsin. Computer-aided analysis of the ESE experiments was consistent with the cw-EPR results and supported the conclusion of a partial complexation of the nitroxides of the dendrimer with Leu and alpha-chymotrypsin.     

Comparative preparations of homoleptic hydridic anions of iron and ruthenium using solution-based organometal hydrogenation techniques

A study of the preparations of the complex hydridic anions [MH(6)](4)(-) (M = Fe and Ru) reveals a number of distinctive features. Here a soluble homoleptic ruthenium hydride has been prepared for the first time. For example, both FeX(2) and [Ru(eta(4)-1,5-COD)X(2)], X = Cl and Br, react with PhMgBr solutions under hydrogen to produce the title compounds. The benzene liberated in these reactions is more readily hydrogenated in the case of a homogeneous room temperature ruthenium hydride preparation to both cyclohexane and cyclohexene. The (1)H NMR spectroscopic data show that the two complex anions have hydride absorptions in the low-frequency region, delta -20.3 and -14.7, respectively. Further, (1)H spin-lattice relaxation times (T(1)) for M-H are longer in the case of Ru vs Fe.