Representation of hysteresis operators for vector-valued inputs by functions on strings

In 1996, Brokate and Sprekels have shown that scalar-valued hysteresis operators for scalar-valued continuous input functions being piecewise monotone can be uniquely represented by functionals defined on the set of all finite alternating strings of real numbers.In this work, it is shown that a similar result can also be derived for hysteresis operators dealing with inputs in a general normed vector space. Considering hysteresis operators defined for continuous inputs that are piecewise monotaffine, it will be shown that these operators can be uniquely represented by functionals acting on an appropriate set of finite strings of elements of this space.     

Universality for bounded degree spanning trees in randomly perturbed graphs

We solve a problem of Krivelevich, Kwan and Sudakov concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph G_α on n vertices with δ(G_α) ≥ αn for α > 0 and we add to it the binomial random graph G(n,C/n), then with high probability the graph G_α∪G(n,C/n) contains copies of all spanning trees with maximum degree at most Δ simultaneously, where C depends only on α and Δ.     

A new tetracyclic saponin from Astragalus glycyphyllos L. and its neuroprotective and hMAO-B inhibiting activity

Abstract

A new tetracyclic saponin, 17(R),20(R)-3β,6α,16β-trihydroxycycloartanyl-23-carboxylic acid 16-lactone 3-O-β-D-glucopyranoside (1) together with one known flavonoid, camelliaside A (2) were isolated from the aerial parts of Astragalus glycyphyllos L. Their structures were determined by chemical, HRESIMS and NMR methods. On 6-hydroxydopamine in vitro model on isolated rat brain synaptosomes, compounds 1–2 had statistically significant neuroprotective activity similar to that of Silibinin, tested at 100?μM. Saponin 1 possessed the most prominent neuroprotective and antioxidant effects in this in vitro model. On human recombinant monoamine oxidase type B enzyme compound 1 displayed strong inhibiting activity, compared to Selegiline (1?μM). It could be concluded that the new epoxycycloartane saponin 1 could be a promising leading structure in respect of neurodegenerative diseases.     

Oxidative Addition of Dihydrogen to Divanadium in Solid Ne: Multiple-Bonded Triplet HVVH and Singlet V2(μ-H)2

Dinuclear compounds of early transition metals with a high metal–metal bond order are of fundamental interest due to their intriguing bonding situation and of practical interest because of their potential involvement in catalytic processes. In this work, two isomers of V₂H₂ have been generated in solid Ne by the reaction between V₂ and H₂ and detected by infrared spectroscopy: the linear HVVH molecule (³Σ_g⁻ ground state), which is the product of the spin-allowed reaction between V₂ (³Σ_g⁻ ground state) and H₂, and a lower-energy, folded V₂(μ-H)₂ isomer (¹A₁ ground state) with two bridging hydrogen atoms. Both isomers are characterized by metal–metal bonding with a high bond order; the orbital occupations point to quadruple bonding. Irradiation with ultraviolet light induces the transformation of linear HVVH to folded V₂(μ-H)₂, whereas irradiation with visible light initiates the reverse reaction.     

Reducing the effect of thermal noise in optical cavities

Thermal noise in optical cavities imposes a severe limitation in the stability of the most advanced frequency standards at a level of a few $10^{-16}\sqrt{\hbox{s}/\tau}$ for long averaging times τ. In this paper, we describe two schemes for reducing the effect of thermal noise in a reference cavity. In the first approach, we investigate the potential and limitations of operating the cavity close to instability, where the beam diameter on the mirrors becomes large. Our analysis shows that even a 10-cm short cavity can achieve a thermal-noise-limited fractional frequency instability in the low 10^?16 regime. In the second approach, we increase the length of the optical cavity. We show that a 39.5-cm long cavity has the potential for a fractional frequency instability even below 10^?16, while it seems feasible to achieve a reduced sensitivity of <10^?10/g for vibration-induced fractional length changes in all three directions.     

Novel Steroidal Glycosides from two Indian Caralluma species,C. stalagmifera and C. indica

New steroidal glycosides, stalagmosides I–V ( 1 – 5 ) and indicosides I and II ( 7 and 8 ), together with the known compounds carumbelloside III, lasianthoside A, and lasianthoside B, were isolated from whole plants of Caralluma stalagmifera and Caralluma indica, respectively. Their structures were elucidated by extensive NMR spectroscopic studies.     

Parabolic Differential Equations with Unbounded Coefficients – A Generalization of the Parametrix Method

We consider uniformly parabolic differential equations with unbounded first- and zero-order coefficients. A fundamental solution is constructed based on the classical parametrix method of E. Levi. From this the existence and uniqueness of the corresponding Cauchy problem is derived. Our approach does not require differentiable coefficients, as is usually assumed in the unbounded case. It only requires Hölder continuous coefficients. In this respect, our new proof also extends known results. We briefly discuss applications which make essential use of this extension.     

Solid‐Phase Synthesis and Characterization of N‐Terminally Elongated Aβ−3–x‐Peptides

In addition to the prototypic amyloid‐β (Aβ) peptides Aβ_1–40 and Aβ_1–42, several Aβ variants differing in their amino and carboxy termini have been described. Synthetic availability of an Aβ variant is often the key to study its role under physiological or pathological conditions. Herein, we report a protocol for the efficient solid‐phase peptide synthesis of the N‐terminally elongated Aβ‐peptides Aβ_?3–38, Aβ_?3–40, and Aβ_?3–42. Biophysical characterization by NMR spectroscopy, CD spectroscopy, an aggregation assay, and electron microscopy revealed that all three peptides were prone to aggregation into amyloid fibrils. Immunoprecipitation, followed by mass spectrometry, indicated that Aβ_?3–38 and Aβ_?3–40 are generated by transfected cells even in the presence of a tripartite β‐site amyloid precursor protein cleaving enzyme 1 (BACE1) inhibitor. The elongated Aβ peptides starting at Val(?3) can be separated from N‐terminally‐truncated Aβ forms by high‐resolution isoelectric‐focusing techniques, despite virtually identical isoelectric points. The synthetic Aβ variants and the methods presented here are providing tools to advance our understanding of the potential roles of N‐terminally elongated Aβ variants in Alzheimer's disease.     

A stability result for the relativistic Vlasov-Maxwell system

We consider a space-periodic version of the relativistic Vlasov-Maxwell system describing a collisionless plasma consisting of electrons and positively charged ions. As our main result, we prove that certain spacially homogeneous stationary solutions are nonlinearly stable. To this end we also establish global existence of weak solutions to the corresponding initial value problem. Our investigation is motivated by a corresponding result for the Vlasov-Poisson system, cf. [1, 14].