Stability of bars made of linear elastic materials with voids

Summary Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.     

Difference in micellar properties of sodium dodecyl sulfonate from sodium 4-decyl naphthalene sulfonate in D2O solution studied by 1H NMR relaxation and 2D NOESY

¹H chemical shift changes of sodium 4-decyl naphthalene sulfonate (SDNS) at 313 K show that its critical micellar concentration lies between 0.82 and 0.92 mmol/dm³, which is in the same range as that of the previous study at 298 K. The spin–lattice relaxation time, spin–spin relaxation time and two-dimensional nuclear Overhauser enhancement spectroscopy experiments give information about the structure of the SDNS micelle and the dynamics of the molecules in the micelle. The size of the SDNS micelle remains almost unchanged in the temperature range from 298 to 313 K as deduced by analyzing the self-diffusion coefficient. Special arrangement of the naphthyl rings of SDNS in the micelles affects the packing of these hydrophobic chains. The methylene groups of the alkyl chain nearest the naphthalene groups penetrate into the aromatic region, which results in a more tightly packed hydrophobic micellar core than that of sodium dodecyl sulfonate.     

Regular Approximations of Singular Sturm-Liouville Problems with Limit-Circle Endpoints

For any self-adjoint realization S of a singular Sturm-Liouville equation on an interval (a,b) with limit-circle endpoints, we construct a family of self-adjoint realizations S _r ,r ∈ (0,∞), of this equation on subintervals (a _r ,b _r ) of (a,b) such that every eigenvalue of S is the limit of a continuous eigenvalue branch of this family. Of particular interest are the cases when at least one endpoint is oscillatory or the leading coefficient function changes sign. In these cases, we show that the index determining each continuous eigenvalue branch has an infinite number of jump discontinuities and give an explicit characterization of these discontinuities.     

Power scaling of printed-circuit-board preionized TEA CO2 laser up to 3.6 kW

A high average power, high-repetition-rate TEA CO₂ laser employing printed-circuit-board preionizer is described. The power scaling of this preionization configuration has been demonstrated. The average output power reaches 3.6 kW at pulse repetition rate of 180 pps. Furthermore, the scaling-up ability of the rotating spark gap as high-voltage switch for high-average-power gas laser has been validated.     

Medicinal Organometallic Chemistry: Designing Metal Arene Complexes as Anticancer Agents

The field of medicinal inorganic chemistry is rapidly advancing. In particular organometallic complexes have much potential as therapeutic and diagnostic agents. The carbon‐bound and other ligands allow the thermodynamic and kinetic reactivity of the metal ion to be controlled and also provide a scaffold for functionalization. The establishment of structure–activity relationships and elucidation of the speciation of complexes under conditions relevant to drug testing and formulation are crucial for the further development of promising medicinal applications of organometallic complexes. Specific examples involving the design of ruthenium and osmium arene complexes as anticancer agents are discussed.     

Genetically Encoded Bioluminescent Indicator for ERK2 Dimer in Living Cells

In this study, a genetically encoded bioluminescent indicator for ERK2 dimer was developed with the split Renilla luciferase complementation method, in which the formation of ERK2 dimer induces a spontaneous emission of bioluminescence in living cells. In response to extracellular stimuli, such as epidermal growth factor (EGF) or 17β‐estradiol (E2), extracellular signal‐regulated kinase 2 (ERK2) is phosphorylated by its upstream kinase MEK, and also phosphorylates its substrates in various regions of the cell, including the nucleus. Phosphorylated ERK2 is led to form its dimer, thereby transporting itself into the nucleus. We demonstrated with the indicator that stimulation with EGF or E2 induces the formation of ERK2 dimer in living MCF‐7 cells. The dynamics of this dimer formation was examined and discussed.     

Synthesis and luminescence properties of lanthanide(III) chelates with polyacid derivatives of thienyl-substituted terpyridine analogues

Two new polyacid derivative ligands of thienyl-substituted terpyridine analogues, N,N,N¹,N¹-[4′-(2?-thienyl)-2,2′:6′,2″-terpyridine-6,6″-diyl]bis(methylenenitrilo) tetrakis(acetic acid) (TTTA) and N,N,N¹,N¹-[2,6-bis(3′-aminomethyl-1′-pyrazolyl)-4-(2″-thienyl)pyridine] tetrakis(acetic acid) (BTTA), were synthesized, and the luminescence properties of their Eu³⁺ and Tb³⁺ chelates were investigated. The Eu³⁺chelates of the two ligands are strongly luminescent having luminescence quantum yields of 0.150 (TTTA-Eu³⁺) and 0.114 (BTTA-Eu³⁺), and lifetimes of 1.284 ms (TTTA-Eu³⁺) and 1.352 ms (BTTA-Eu³⁺), whereas their Tb³⁺ chelates are weakly luminescent. The TTTA-Eu³⁺ chelate was used for streptavidin (SA) labeling, and the labeled SA was used for time-resolved fluoroimmunoassay of insulin in human sera. The method gives the detection limits of 33 pg ml⁻¹.     

Prädikatives und funktionales Denken in der Wahrscheinlichkeitsrechnung

In order to emphasize functional thinking in mathematical education, arguments are brought forward for an early and frequent use of tree diagrams in teaching stochastics. Since set and tree diagrams can be regarded as two sides of the same matter, Bayes’ theorem, which is strongly associated with predicative set diagrams, need not be dealt with explicitly any longer. Set diagrams are replaced by tree diagrams that are labelled in detail and by tree inversion as a functional instrument of dealing with conditioned probabilities. This technique is demonstrated by three typical problems in the context of conditioned probability. Finally, two letters by Pascal to Fermat are analysed in order to illustrate that predicative and functional approaches were already pursued in the early stages of probability calculus in the 17^th century.