On the Relation between the Scalar Moment Problem and the Matrix Moment Problem on *-Semigroups

There is a countable cancellative commutative *-semigroup S withzero (in fact, a *-subsemigroup of G × N₀ for some abelian group G carrying the inverse involution) such that the answer to the question “if f is a function on S , with values in M_d(C) (the square matrices of order d) and such that $\sum^{n}_{j,k=1} \lbrak f(s^*_k s_j)\xi_j, \xi_k \rbrak \ge 0$ for all n in N, s₁, . . . , s_n in S , and $\xi_1$, . . . , $\xi_n$ in C^d, does it follow that $f(s) = \int_{S^*}\sigma (s) d\mu(\sigma) (s \memb S)$ for some measure $\mu$ (with values in M_d(C)₊ , the positive semidenite matrices) on the space S of hermitian multiplicative functions on S?” is “yes” if d = 1 but “no” if d = 2 (hence also for d > 2).     

Nonadiabatic alignment of asymmetric top molecules: rotational revivals

The rotational revival structure of asymmetric top molecules, following irradiation by an intense picosecond laser pulse, is explored theoretically and experimentally. Numerically we solve nonperturbatively for the rotational dynamics of a general asymmetric top subject to a linearly polarized intense pulse, and analyze the dependence of the dynamical alignment on the field and system parameters. Experimentally we use time-resolved photofragment imaging to measure the alignment of two molecules with different asymmetry, iodobenzene, and iodopentafluorobenzene. Our numerical results explain the experimental observations and generalize them to other molecules. The rotational revival structure of asymmetric tops differs qualitatively from the intensively studied linear top case. Potentially it provides valuable structural information about molecules.     

Metallextraktion mit N-thiobenzoyl-N-phenylhydroxylamin: Extraction of metal ions with N-thiobenzoyl-N-phenylhydroxylamine

The extraction parameters pH_{$\text{1}\text{2}$} and K_ex for Mn, Fe, Co, Ni, Cu, Zn, Cd, and Pb with N-thiobenzoyl-N-phenylhydroxylamine are reported. N-Thiobenzoyl-N-phenylhydroxylamine extracts metals from more strongly acidic solutions than does N-benzoyl-N-phenylhydroxylamine. Iron(III) is extracted as a 1:2 chelate with the extracant, whereas iron(II) forms the expected tris chelate by oxidation. The other bivalent ions are extracted as their bis chelates.     

Two-dimensional electrophoretic analysis of transformation-sensitive polypeptides during chemically, spontaneously, and oncogene-induced transformation of rat liver epithelial cells.

Recently, we described the establishment of a computerized database of rat liver epithelial (RLE) cellular polypeptides (Wirth et al., Electrophoresis, 1991, 12, 931-954). This database has now been expanded to include the analysis of cellular polypeptide alterations during chemically (aflatoxin B1; AFB), spontaneously, and oncogene (v-Ha-ras, v-raf, and v-myc/v-raf)-induced transformation of RLE cells. Two-dimensional mapping of [35S]methionine-labeled whole cell lysate, cell-free in vitro translation products and [32P]orthophosphate-labeled polypeptides revealed subsets of polypeptides specific for each transformation modality. A search of the RLE protein database indicated the specific subcellular location for the majority of these transformation-sensitive proteins. Significant alterations in the expression of the extracellular matrix protein, fibronectin, as well as tropomyosin- and intermediate filament-related polypeptides (vimentin, beta-tubulin, the cytokeratins, and actin) were observed among the various transformant cell lines. Immunoprecipitation and Western immunoblot analysis of tropomyosin expression in four individual AFB-, as well as four spontaneously induced, and each of the oncogene-transformed cell lines indicated that five major tropomyosin (Tm 1-5) isoforms were variably expressed in the various cell lines, including one polypeptide tentatively identified as Tm6. Whereas alterations in tropomyosin expression appeared to be transformation-specific, alterations in the individual intermediate filament polypeptides were related more to the differentiation state of the individual cell lines rather than to the transformation phenotype. These studies extend our earlier efforts toward the establishment of a comprehensive computerized database of RLE cellular proteins and demonstrates how such a database may serve as a useful source for studies concerning the regulation of growth and differentiation as well as transformation of RLE cells.     

On the positive definiteness of n ↦ epnα for α close to 2

For >2, let Q ⁺() be the infimum of those q>0 for which the function n e^pn is positive definite on N ₀ for every pq. We shall prove that Q ⁺()0 as 2.     

On the Stieltjes moment problem on semigroups

We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).     

On the Growth of Positive Definite Double Sequences Which Are not Moment Sequences

For every a > 1, there is a function f : N²₀ → R, which is positive semidefinite but not a moment sequence, such that |f(m, n)| ≥ m+ n^a(m+n) for all (m, n). The constant 1 is the best possible.