Statistical experiments and their conical measures

Summary In the theory of functional analytic comparison of statistical experiments (started by L. LeCam) one can characterize equivalence classes of experiments by conical measures (in the sense of G. Choquet). We begin with a short proof of the (known) fact that any conical measure with normed resultant belongs to an experiment class. Then we are concerned with the special case of dominated experiments which are characterized by the extendability of their conical measures to finite concrete measures. These results are in close connection with a paper of E.N. Torgersen (Mixtures and products of dominated experiments. Ann. Statist. 5, 44–64 (1977)).After this we study class properties of experiments which are expressible in terms of their conical measures. Simple examples are domination, existence of bounded densities and compactness. It follows the investigation of a more profound class property which we call extremality and which generalizes the concept of an experiment with a sufficient and boundedly complete subalgebra. Finally we prove that the extreme points of the compact convex set of conical measures with normed resultant are just the conical measures of the extremal experiments.     

The generalized Wiener Theorem for groups with finite dimensional irreducible representations

It is shown that the generalized Wiener Theorem for ideals in group algebras of locally compact Abelian groups extends to group algebras of locally compact groups with finite-dimensional irreducible representations (Moore groups).     

Weak spectral synthesis for the projective tensor product of commutative Banach algebras

Let and be regular commutative Banach algebras and their projective tensor product, and suppose that is semisimple. We investigate the relation between weak spectral synthesis properties of and those of and .

     

A study of tilt-stable optimality and sufficient conditions

Recent results by Eberhard et al. (2006) [4] and Eberhard and Wenczel (2009) [3] on the interaction of single- and double-envelope operations of nonsmooth functions and their interaction with second-order derivations have been used to study tilt-stability of local minima. This continues the study begun by Poliquin and Rockafellar (1998) [1] but now, armed with new tools we are able to make some new observations. We observe that tilt-stability entails a local density within the graph of the proximal subderivative of strict local minima order two of the tilted function. Indeed, it also entails the strict local minimality (order two) of the tilt-stable local minimum itself. For prox-regular, subdifferentially continuous functions this density property characterises tilt stability.     

On 1-isometries of affine quadrics over finite fields

Letq be a regular quadratic form on a vector space (V, $\mathbb{F}$ ) and assume $4 \leqslant dim V \leqslant \infty \wedge |\mathbb{F}| \in \mathbb{N}$ . A 1-isometry of the central quadric $\mathcal{F}: = \{ x \in V|q(x) = 1\}$ is a permutation ? of $\mathcal{F}$ such that (*) $$q(x - y) = \nu \Leftrightarrow q(x^\varphi - y^\varphi ) = \nu \forall x,y \in \mathcal{F}$$ holds true for a fixed element ν of $\mathbb{F}$ . For arbitraryν ∈ $\mathbb{F}$ we prove that? is induced (in a certain sense) by a semi-linear bijection $(\sigma ,\varrho ):(V,\mathbb{F}) \to (V,\mathbb{F})$ such thatq oσ =? oq, provided $\mathcal{F}$ contains lines and the exceptional case $(\nu = 2 \Lambda |\mathbb{F}| = 3 \Lambda \dim V = 4 \Lambda |\mathcal{F}| = 24)$ is excluded. In the exceptional case and as well in case of dim V = 3 there are counterexamples. The casesν ≠ 2 and v=2 require different techniques.     

Tandem cyclopropanation with dibromomethane under Grignard conditions

Tertiary Grignard reagents and dibromomethane efficiently cyclopropanate allylic (and certain homoallylic) magnesium and lithium alcoholates at ambient temperature in ether solvents. Lithium (homo)allyl alcoholates are directly cyclopropanated with magnesium and CH2Br2 under Barbier conditions at higher temperatures. The reaction rates depend on the substitution pattern of the (homo)allylic alcoholates and on the counterion with lithium giving best results. Good to excellent syn-selectivities are obtained from alpha-substituted substrates, which are in accord with a staggered Houk model. In tandem reactions, cyclopropyl carbinols are obtained from allyloxylithium or -magnesium intermediates, generated in situ by alkylation of conjugated aldehydes, ketones, and esters as well as from allyl carboxylates or vinyloxiranes. Using this methodology, numerous fragrance ingredients and their precursors were efficiently converted to the corresponding cyclopropyl carbinols.     

Cationic P-S-X cages (X=Br, I)

The first condensed-phase preparation of ternary P-Ch-X cations (Ch=O-Te, X=F-I) is reported: [P5S3X2]+, [P5S2X2]+, and [P4S4X]+ (X=Br, I). [P5S3X2]+ is formed from the reaction of the Ag+/PX3 reagent with P4S3. The [P5S3X2]+ ions have a structure that is related to P4S5 by replacing P=S by P+--X and S in the four-membered ring by P(X). We provide evidence that the active ingredient of the Ag+/PX3 reagent is the (H2CCl2)Ag-X-PX2+ cation. The latter likely reacts with the HOMO of P4S3 in a concerted HOMO-LUMO addition to give the P5S3X2+ ion as the first species visible in situ in the low-temperature 31P NMR spectrum. The [P5S3X2]+ ions are metastable at -78 degrees C and disproportionate at slightly higher temperatures to give [P5S2X2]+ and [P4S4X]+, probably with the extrusion of 1/n (PX)n (X=Br, I). All six new cage compounds have been characterized by multinuclear NMR spectroscopy and, in part, by IR or Raman spectroscopy. The [P5S2X2]+ salts have a nortricyclane skeleton and were also characterized by X-ray crystallography. The structure of the [P4S4X]+ ion is related to that of P4S5 in that the exo-cage P=S bond is replaced by an isoelectronic P+--X moiety.     

Nonlinear current-voltage relationship of the plasma membrane of single CHO cells

The application of electric field pulses to Chinese Hamster Ovary (CHO) cells causes membrane electroporation (MEP). If a voltage or current ramp is applied to the cellular membrane of a single CHO cell, the membrane conductance increases nonlinearly with field strength reaching saturation. In particular, the kinetics of the induced conductance changes represents the data basis for the interpretation in terms of underlying structural changes. The current/voltage characteristic is found to be continuous, but displays occasionally a sharp increase in the conductance. The step-like increases are interpreted to reflect the formation of one (or more) larger pore(s). The analysis of current clamp data yields pores of radius (r(p)) in the range of 2.5< or =r(p)/nm< or =20; the pores of the voltage clamp data are in the range of 2.5< or =r(p)/nm< or =55. The larger pores occur predominantly during hyperpolarising and less frequently during depolarising conditions, respectively. The different kinetics of pore formation in the hyperpolarising condition, where the inward field increases, and the depolarising condition, where the inward field first decreases and then increases in the opposite direction, suggests structural asymmetry with respect to the direction of the electric membrane field. At the required higher voltage, the effect of the resting potential is negligibly small.     

Free-flow isoelectric focusing of proteins remaining in cell fragments following sonication of thyroid carcinoma cells

The method of preparing protein mixtures for electrophoretic analysis of membrane-associated cell proteins was improved. By sonication, about one-half of the proteins of thyroid cells were released into the supernatant, while the other half preferentially comprising membrane proteins still remained in cell fragments, which could be sedimented by centrifugation. After sonication, even those proteins which remained in cell fragments, could completely be dissolved by free-flow isoelectric focusing media. They migrated through the free-flow electrophoresis chamber without forming precipitates. Because of these improvements, it was possible to show that the two thyroid cancer cell lines ML-1 and ONCO-DG1 express cytokeratin 8 at similar rates, but cytokeratins 7 and 18 differently. In addition, the presence of inorganic pyrophosphatase, tubulin-beta-5, and tubulin-beta-1 chains in human thyroid cells was proved for the first time.