Rapid extension of a crack

Summary For a body which is initially in a state of uniform anti-plane shear, the wave motion generated by a rapidly extending crack is analyzed in this paper. It is shown that extension with constant speeds of the crack tips is not consistent with the criterion for brittle fracture, but it is consistent with a fracture criterion related to postulated zones of cohesive tractions near the crack tips.

---

Zusammenfassung Anbringen eines Lochs in einem gespannten Körper kann die Entstchung eines rasch sich ausbreitenden Risses veranlassen. In dieser Arbeit wird für einen Körper, der sich ursprünglich in einem Zustand gleichförmiger Schubspannung befand, die durch einen in schneller Ausbreitung begriffenen Riß verursachte Wellenbewegung untersucht. Es wird gezeigt, daß eine Ausbreitung mit konstanten Geschwindigkeiten der Rißenden nicht verträglich ist mit dem Kriterium für Sprödbruch, wohl aber mit einem Bruchkriterium, das mit postulierten Zonen kohäsiver Zugspannungen in der Nähe der Rißenden zusammenhängt.

     

Aziridine-mediated ligation and site-specific modification of unprotected peptides

A synthesis of aziridine-containing peptides via the Cu(II)-promoted coupling of unprotected peptide thioacids and N-H aziridine-2-carbonyl peptides is reported. The unique reactivity of the resulting N-acylated aziridine-2-carbonyl peptides facilitates their subsequent regioselective and stereoselective nucleophilic ring-opening to give unprotected peptides that are specifically modified at the ligation site. The aziridine-mediated peptide ligation concept is exemplified using H(2)O as the nucleophile, producing a Xaa-Thr linkage (where Xaa can be an epimerizable and hindered amino acid). The overall process is compatible with a variety of unprotected amino acid functionality, most notably the N-terminal and Lys side chain amines.     

Parameter dependence for a class of ordinary differential equations with measurable right‐hand side

The paper studies differential equations of the form u′(x) = f(x, u(x), λ(x)), u(x₀) = u₀, where the right‐hand side is merely measurable in x. In particular sufficient conditions for the continuous and the differentiable dependence of solution u on the data and on the parameter λ are stated. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Magnetische Ladungen

Zusammenfassung Es kann in der Praxis sinnvoll sein, für physikalische Vorg?nge mathematische Modelle zu betrachten, die mehr enthalten als die Realit?t. Dies gilt insbesondere dann, wenn das Modell für Computersimulationen verwendet wird. Als Beispiel werden elektromagnetische Wellen gezeigt, deren Simulation tats?chlich besser gelingt, wenn man magnetische Ladungen ins mathematische Modell einführt.     

7,8‐(Dichloromethano)homo[70]fullerene,an Unusual,but Unexceptional,Methanoannulene

The crystal structure of 7,8‐(dichloromethano)homo[70]fullerene shows that addition of the dichlorocarbene (:CCl₂) to C₇₀ gives a surprisingly normal methano‐bridged [9]annulene. The structural changes caused by the addition are highly localized; the C(7)? C(8) distance lengthens by 0.705(2) Å but no other distance changes by more than 0.022(3) Å. Bond angles within the [9]annulene increase by as much as 7.8(1)°, but changes outside the C₉ ring are much smaller. The nearly ellipsoidal molecules form hexagonally close‐packed layers that interact in pairs through short Cl???C, and possibly short Cl???Cl and C???C, interactions.     

Some monotonicity properties of Schur powers of matrices and related inequalities

A series of inequalities are developed relating the spectral radius ?(A ° B) of the Schur product A ° B of two nonnegative matrices A and B with those of ?(A ° A) and ?(B ° B) yielding $\text{?(A ° B) ? [?(A ° A)?(B ° B)]}\text{1}\text{2}$. As a corollary it is proved that the spectral radius of the Schur powers ?_r = ?(A^[r]), A^[r] = A ° A °?°A (r factors) satisfies $\text{(}\text{1}\text{r}\text{)}\text{log}\text{?}{}_{\mathrm{r}}$ is decreasing while $\text{(}\text{1}\text{r?1}\text{)}\text{log}\text{?}{}_{\mathrm{r}}$ is increasing, the latter provided A is a stochastic matrix. The entropy of a finite stationary Markov chain is identified with $\text{d?}{}_{\mathrm{r}}\text{dr|}{}_{\mathrm{r=1}}$. A number of majorization comparisons for the spectral radius of Schur powers is given.     

Direct measurement of the quantum yield for the creation of mobile excitons from localized states using optically detected electron spin coherence

Optically detected spin locking and adiabatic demagnetization in the rotating frame are used to directly measure the rate constants for trap-to-band promotion and trap-to-trap energy migration in 1,2,4,5-tetrachlorobenzene. Comparison of these rate constants at a given temperature gives the quantum yield for the decay of a promoted localized state into a mobile exciton state. Its dependence on temperature is also determined.     

Diamond a sorting method for vector machines

A method for parallel sorting in vector machines is described. It is shown that it has complexityO(N(logN)²).     

Analysing power for neutron-proton scattering at 14.1 MeV

The analysing power A_γ(θ) for neutron-proton scattering has been measured at 14.1 MeV for c.m. angles between 50° and 157°. A polarized neutron beam was produced by the reaction ${}^3\text{H}\text{(}\text{d}\text{, n}\text{)}{}^4\text{He}$ at 110 keV, using polarized deuterons from an atomic beam polarized ion source. Liquid and plastic scintillators were used for proton targets and the scattered particles were detected in an array of plastic scintillators. Use of the associated alpha technique, multi-parameter recording of events and off-line computer treatment led to very low backgrounds. The results differ significantly from the predictions of the phase-shift analyses of Yale IV, Livermore X and Arndt et al. We find, however, excellent agreement with the predictions of the “Paris potential” of Lacombe et al. Existing n-p analysing power results up to 30 MeV are surveyed and found to be consistent. An attempt was made to look for an isospin splitting of the triplet P-wave phase shifts.     

Spatial photorelease of oligonucleotides, using a safety-catch photolabile linker

[reaction: see text] We report the development of a safety-catch photolabile linker that allows the light-directed synthesis and spatially selective photorelease of oligonucleotides from microarrays. The linker remains stable to light during DNA synthesis, and is activated for photorelease after acidic hydrolysis. We demonstrate that the photoreleased oligonucleotides can be amplified by PCR to produce double stranded DNA. The advantages offered by this linker could aid the development of an automated gene synthesis platform.