On the uniqueness of symmetric bases in finite dimensional Banach spaces

Suppose{e _i} _i=1 ⁿ and{f _i} _i=1 ⁿ are symmetric bases of the Banach spacesE andF. Letd(E,F)≦C andd(E,l _n ² )≧n' for somer>0. Then there is a constantC _r=C_r(C)>0 such that for alla _i∈Ri=1,...,n $$C_r^{ - 1} \left\| {\sum\limits_{i = 1}^n {a_i e_i } } \right\| \leqq \left\| {\sum\limits_{i = 1}^n {a_i f_i } } \right\| \leqq C_r \left\| {\sum\limits_{i = 1}^n {a_i e_i } } \right\|$$ We also give a partial uniqueness of unconditional bases under more restrictive conditions.     

Synthesis and Cellular Labeling of Caged Phosphatidylinositol Derivatives

Phosphatidylinositol (PI) is the biosynthetic precursor for seven phosphoinositides, important signaling lipids in cells. A membrane-permeant caged PI derivative featuring a photo-removable coumarinyl group masking the negative charge of the phosphate, as well as two enzymatically removable butyrate esters for increased lipophilicity and for preventing phosphate migration, were synthesized. Rapid cell entry and cellular labeling in fixed cells was demonstrated by a photo-cross-linkable diazirine followed by attachment of a fluorophore through click chemistry. Using this technique, we found that the multifunctional caged PI derivative resided predominantly at internal membranes but rapidly changed to the plasma membrane after uncaging. Accordingly, a preliminary proteomic analysis of the lipid–protein conjugates revealed that the two major PI transport proteins PITPα and β were prime targets of the photo-cross-linked PI derivative.     

Electronic Transitions in Different Redox States of Trinuclear 5,6,11,12,17,18-Hexaazatrinaphthylene-Bridged Titanium Complexes: Spectroelectrochemistry and Quantum Chemistry

Multinuclear transition metal complexes bridged by ligands with extended π-electronic systems show a variety of complex electronic transitions and electron transfer reactions. While a systematic understanding of the photochemistry and electrochemistry has been attained for binuclear complexes, much less is known about trinuclear complexes such as hexaphenyl-5,6,11,12,17,18-hexaazatrinaphthylene-tristitanocene [(Cp₂Ti)₃HATN(Ph)₆]. The voltammogram of [(Cp₂Ti)₃HATN(Ph)₆] shows six oxidation and three reduction waves. Solution spectra of [(Cp₂Ti)₃HATN(Ph)₆] and of the electrochemically formed oxidation products show electronic transitions in the UV, visible and the NIR ranges. Density functional theory (DFT) and linear response time-dependent DFT show that the three formally titanium(II) centers transfer an electron to the HATN ligand in the ground state. The optically excited transitions occur exclusively between ligand-centered orbitals. The charged titanium centers only provide an electrostatic frame to the extended π-electronic system. Complete active self-consistent field (CASSCF) calculation on a structurally simplified model compound, which considers the multi-reference character imposed by the three titanium centers, can provide an interpretation of the experimentally observed temperature-dependent magnetic behavior of the different redox states of the title compound in full consistency with the interpretation of the electronic spectra.     

An Interface Problem in Solid Mechanics with a Linear Elastic and a Hyperelastic Material

The three dimensional interface problem is considered with the homogeneous Lamé system in an unbounded exterior domain and some quasistatic nonlinear elastic material behavior in a bounded interior Lipschitz domain. The nonlinear material is of the Mooney-Rivlin type of polyconvex materials. We give a weak formulation of the interface problem based on minimizing the energy, and rewrite it in terms of boundary integral operators. Then, we prove existence of solutions.     

An experimental survey of a posteriori Courant finite element error control for the Poisson equation

This comparison of some a posteriori error estimators aims at empirical evidence for a ranking of their performance for a Poisson model problem with conforming lowest order finite element discretizations. Modified residual-based error estimates compete with averaging techniques and two estimators based on local problem solving. Multiplicative constants are involved to achieve guaranteed upper and lower energy error bounds up to higher order terms. The optimal strategy combines various estimators.     

A short proof of w1n (Hom(C2r+1, Kn+2)) = 0 for all n and A graph colouring theorem by Babson and Kozlov

We show that the n-th power of the first Stiefel-Whitney class of the ℤ₂-action on the graph complex Hom(C _2r+1, K _n+2) is zero, confirming a conjecture by Babson and Kozlov. This yields a considerably simplified proof of their graph colouring theorem, which is also known as the Lovsz conjecture. This research was supported by the Deutsche Forschungsgemeinschaft within the European graduate program “ Combinatorics, Geometry, and Computation” (No. GRK 588/2)     

Phytotherapy in Integrative Oncology—An Update of Promising Treatment Options

Modern phytotherapy is part of today’s conventional evidence-based medicine and the use of phytopharmaceuticals in integrative oncology is becoming increasingly popular. Approximately 40% of users of such phytopharmaceuticals are tumour patients. The present review provides an overview of the most important plants and nature-based compounds used in integrative oncology and illustrates their pharmacological potential in preclinical and clinical settings. A selection of promising anti-tumour plants and ingredients was made on the basis of scientific evidence and therapeutic practical relevance and included Boswellia, gingko, ginseng, ginger, and curcumin. In addition to these nominees, there is a large number of other interesting plants and plant ingredients that can be considered for the treatment of cancer diseases or for the treatment of tumour or tumour therapy-associated symptoms. Side effects and interactions are included in the discussion. However, with the regular and intended use of phytopharmaceuticals, the occurrence of adverse side effects is rather rare. Overall, the use of defined phytopharmaceuticals is recommended in the context of a rational integrative oncology approach.     

Characterization of Atropa belladonna L. compounds by capillary electrophoresis-electrospray ionization-time of flight-mass spectrometry and capillary electrophoresis-electrospray ionization-ion trap-mass spectrometry

This short communication describes the characterization of seven tropane alkaloid compounds in Atropa belladonna L. Thus a rapid and easy CE-electrospray interface (ESI)-TOF-MS procedure is developed to analyze these compounds in a pharmaceutical preparations of A. belladonna L. leaf extract. Optimum electrophoretic separation is obtained using an alkaline solution of 60 mM ammonium acetate at pH 8.5 containing 5% isopropanol. Under the optimum CE-ESI-TOF-MS conditions several important compounds such as tropine, belladonnine, norhyoscyamine, apoatropine, hyoscyamine, 6beta-hydroxyhyoscyamine, and scopolamine have been simultaneously identified from A. belladonna L. CE-ESI-IT-MS has been used to discriminate the putative presence of littorine. The sensitivity, together with mass accuracy and true isotopic pattern of the TOF-MS, allowed the identification of a broad series of tropane alkaloid compounds present in pharmaceutical preparations of A. belladonna L. leaf extract.     

Electrophoresis of soft particles at high electrolyte concentrations: an interpretation by the Henry theory

The existence of electrophoretic mobility at high electrolyte concentrations defines a remarkable peculiarity in the electrosurface characteristics of soft particles. According to Ohshima [H. Ohshima, Colloids Surf. 103 (1995) 249], this effect is caused by the electroosmotic flow within the soft particle shell. An explanation supporting Ohshima's conclusion can be derived from classic electrokinetic theories. Based on the Henry theory [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106], we demonstrate that the electrophoretic mobility of soft particles does not disappear at decinormal concentration.