On an Extremal Problem concerning Bernstein Operators

* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

The Lower Estimate for Bernstein Operator

MSC 2010: 41A10, 41A15, 41A25, 41A36

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.

Paläobiogeographische Aspekte am Beispiel der Inklusen des Baltischen Bernsteins unter besonderer Berücksichtigung der Steinfliegen (Insecta: Plecoptera) und ein Unterrichtsentwurf zum Thema Baltischer Bernstein und seine Inklusen für den Biologieunterricht verschiedener Schulstufen

Der erste Teil der Dissertation befasst sich mit einem Forschungsprojekt zum Thema Paläobiogeographie der Steinfliegen des Baltischen Bernsteins. Nach einer Untersuchung von über 200 Steinfliegeninklusen des 40-50 Millionen Jahre alten Baltischen Bernsteins konnten vier Neubeschreibungen zu den bisher existierenden 14 hinzugefügt werden. Bei einem Vergleich der Verbreitungshistorie rezenter Gattungen wurden auf der Basis des Aktualitätsprinzips mögliche Verbreitungsrouten der Steinfliegengattungen des Baltischen Bernsteins über die kreidezeitliche Bering Landbrücke aufgestellt. Ausgewählte Aspekte des Forschungsprojekts stellten im zweiten, didaktischen Teil der Dissertation die Basis eines für die Mittelstufe entwickelten Projektes zum Thema Bernstein und seine Inklusen dar. Das Bernsteinprojekt wurde am zdi-Schülerlabor der Universität zu Köln mit mehrern Schulklassen durchgeführt und auf der Basis der im Vorfeld formulierten Forschungsfragen formativ evaluiert.

Clozapine Promotes Glycolysis And Myelin Lipid Synthesis In Cultured Oligodendrocytes.

Clozapine displays stronger systemic metabolic side effects than haloperidol and it has been hypothesized that therapeutic antipsychotic and adverse metabolic effects of these drugs are related. Considering that cerebral disconnectivity through oligodendrocyte dysfunction has been implicated in schizophrenia, it is important to determine the effect of these drugs on oligodendrocyte energy metabolism and myelin lipid production. Effects of clozapine and haloperidol on glucose and myelin lipid metabolism were evaluated and compared in cultured OLN-93 oligodendrocytes. First, glycolytic activity was assessed by measurement of extra- and intracellular glucose and lactate levels. Next, the expression of glucose (GLUT) and monocarboxylate (MCT) transporters was determined after 6 and 24 h. And finally mitochondrial respiration, acetyl-CoA carboxylase, free fatty acids, and expression of the myelin lipid galactocerebroside were analyzed. Both drugs altered oligodendrocyte glucose metabolism, but in opposite directions. Clozapine improved the glucose uptake, production and release of lactate, without altering GLUT and MCT. In contrast, haloperidol led to higher extracellular levels of glucose and lower levels of lactate, suggesting reduced glycolysis. Antipsychotics did not alter significantly the number of functionally intact mitochondria, but clozapine enhanced the efficacy of oxidative phosphorylation and expression of galactocerebroside. Our findings support the superior impact of clozapine on white matter integrity in schizophrenia as previously observed, suggesting that this drug improves the energy supply and myelin lipid synthesis in oligodendrocytes. Characterizing the underlying signal transduction pathways may pave the way for novel oligodendrocyte-directed schizophrenia therapies.

New constraints on muon-neutrino to electron-neutrino transitions in MINOS

This paper reports results from a search for nu(mu) -> nu(e) transitions by the MINOS experiment based on a 7 x 10(20) protons-on-target exposure. Our observation of 54 candidate nu(e) events in the far detector with a background of 49.1 +/- 7.0(stat) +/- 2.7(syst) events predicted by the measurements in the near detector requires 2sin(2)(2 theta(13))sin(2)theta(23) < 0.12(0.20) at the 90% C.L. for the normal (inverted) mass hierarchy at delta(CP) = 0. The experiment sets the tightest limits to date on the value of theta(13) for nearly all values of delta(CP) for the normal neutrino mass hierarchy and maximal sin(2)(2 theta(23)).

Search for Muon-Neutrino to Electron-Neutrino Transitions in MINOS

This Letter reports on a search for nu(mu)->nu(e) transitions by the MINOS experiment based on a 3.14x10(20) protons-on-target exposure in the Fermilab NuMI beam. We observe 35 events in the Far Detector with a background of 27 +/- 5(stat)+/- 2(syst) events predicted by the measurements in the Near Detector. If interpreted in terms of nu(mu)->nu(e) oscillations, this 1.5 sigma excess of events is consistent with sin(2)(2 theta(13)) comparable to the CHOOZ limit when |Delta m(2)|=2.43x10(-3) eV(2) and sin(2)(2 theta(23))=1.0 are assumed.

Search for Active Neutrino Disappearance Using Neutral-Current Interactions in the MINOS Long-Baseline Experiment

We report the first detailed comparisons of the rates and spectra of neutral-current neutrino interactions at two widely separated locations. A depletion in the rate at the far site would indicate mixing between nu(mu) and a sterile particle. No anomalous depletion in the reconstructed energy spectrum is observed. Assuming oscillations occur at a single mass-squared splitting, a fit to the neutral- and charged-current energy spectra limits the fraction of nu(mu) oscillating to a sterile neutrino to be below 0.68 at 90% confidence level. A less stringent limit due to a possible contribution to the measured neutral-current event rate at the far site from nu(e) appearance at the current experimental limit is also presented.

Testing Lorentz Invariance and CPT Conservation with NuMI Neutrinos in the MINOS Near Detector

A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).

Measurement of neutrino oscillations with the MINOS detectors in the NuMI beam

This Letter reports new results from the MINOS experiment based on a two-year exposure to muon neutrinos from the Fermilab NuMI beam. Our data are consistent with quantum-mechanical oscillations of neutrino flavor with mass splitting vertical bar Delta m(2)vertical bar = (2.43 +/- 0.13) x 10(-3) eV(2) (68% C.L.) and mixing angle sin(2)(2 theta) > 0.90 (90% C.L.). Our data disfavor two alternative explanations for the disappearance of neutrinos in flight: namely, neutrino decays into lighter particles and quantum decoherence of neutrinos, at the 3.7 and 5.7 standard-deviation levels, respectively.

New Measurement of the pi(0) Radiative Decay Width

High precision measurements of the differential cross sections for pi(0) photoproduction at forward angles for two nuclei, (12)C and (208)Pb, have been performed for incident photon energies of 4.9-5.5 GeV to extract the pi(0) -> gamma gamma decay width. The experiment was done at Jefferson Lab using the Hall B photon tagger and a high-resolution multichannel calorimeter. The pi(0) -> gamma gamma decay width was extracted by fitting the measured cross sections using recently updated theoretical models for the process. The resulting value for the decay width is Gamma(pi(0) -> gamma gamma) = 7.82 +/- 0.14(stat) +/- 0.17(syst) eV. With the 2.8% total uncertainty, this result is a factor of 2.5 more precise than the current Particle Data Group average of this fundamental quantity, and it is consistent with current theoretical predictions.

Stereologic investigation of the posterior part of the hippocampus in schizophrenia

Structural magnetic resonance imaging and postmortem studies showed volume loss in the hippocampus in schizophrenia. The noted tissue reduction in the posterior section suggests that some cellular subfractions within this structure might be reduced in schizophrenia. To address this, we investigated numbers and densities of neurons, oligodendrocytes and astrocytes in the posterior hippocampal subregions in postmortem brains from ten patients with schizophrenia and ten matched controls using design-based stereology performed on Nissl-stained sections. Compared to the controls, the patients with schizophrenia showed a significant decrease in the mean number of oligodendrocytes in the left and right CA4. This is the first finding of reduced numbers of oligodendrocytes in CA4 of the posterior part of the hippocampus in schizophrenia. Our results are in line with earlier findings in the literature concerning decreased numbers of oligodendrocytes in the prefrontal cortex in schizophrenia. Our results may indicate disturbed connectivity of the CA4 of the posterior part of the hippocampus in schizophrenia and, thus, contribute to the growing number of studies showing the involvement of posterior hippocampal pathology in the pathophysiology of schizophrenia.