Synchrotron XANES and ED‐XRF analyses of fine‐paste ware from 13th to 14th century maritime Southeast Asia

The combination of energy dispersive X‐ray fluorescence (ED‐XRF) and synchrotron X‐ray absorption near‐edge structure (XANES) provides the detailed composition of fine‐paste ware (FPW) kendis, dated back to 13th–14th century maritime Southeast Asia. Sources of clay and production sites were classified according to Al₂O₃, SiO₂, α‐Fe₂O₃ and γ‐Fe₂O₃ as well as trace elements. The similarities based on these components provided another evidence of a trade route between Kota Cina in North Sumatra of Indonesia and Kok Moh on Satingphra Peninsula, a well‐known production area in present‐day Thailand. In additions, the uniquely large contribution of α‐Fe₂O₃ in XANES spectra suggests that Nakhon Si Thammarat province of Thailand could also be one of FPW production areas in maritime Southeast Asia. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamic contact problem for a bridge modeled by a viscoelastic full von Kármán system

The existence of solutions is proved for a full system of dynamic von Kármán equations expressing vibrations of geometrically nonlinear viscoelastic plate, the viscosity of which has the character of a short memory. The system models the behaviour of a bridge. The in-plane acceleration terms are taken into account. The boundary contact conditions for plane displacements and possibly the contact with the rigid support are considered.     

On a Test Statistic for Linear Trend

Let {W(s)} _s 0 be a standard Wiener process. The supremum of the squared Euclidian norm Y (t)², of the R²-valued process Y(t)=(1/t W(t), {12/t ³ int_{0 t} s dW (s)– {3/t} W(t)), t [, 1], is the asymptotic, large sample distribution, of a test statistic for a change point detection problem, of appearance of linear trend. We determine the asymptotic behavior P {sup _t [, 1] Y(t)² > u as u , of this statistic, for a fixed (0,1), and for a moving = (u) 0 at a suitable rate as u . The statistical interest of our results lie in their use as approximate test levels.     

Indentation of an Elastic Half-space by a Rigid Flat Punch as a Model Problem for Analysing Contact Problems with Coulomb Friction

One important problem which still remains to be solved today is the uniqueness of the solution of contact problems in linearized elastostatics with small Coulomb friction. This difficult question is addressed here in the case of the indentation of a two-dimensional elastic half-space by a rigid flat punch of finite width, which has been previously studied by Spence in Proc. Camb. Philos. Soc. 73, 249–268 (1973). It is proved that all the solutions have the same simple structure, involving active contact everywhere below the punch and a sticking interval surrounded by two inward slipping intervals. All these solutions show the same local asymptotics for surface traction and displacement at a border between a sticking and a slipping zone. These asymptotics describe (soft) singularities, which are universal (they hold with any geometry) and are explicitly given. It is also proved that in cases where the friction coefficient is small enough, the sticking intervals present in two distinct solutions, if two distinct solutions exist, cannot overlap.     

Normal Compliance Contact Models with Finite Interpenetration

We study contact problems with contact models of normal compliance type, where the compliance function tends to infinity for a given finite interpenetration. Such models are physically more realistic than standard normal compliance models, where the interpenetration is not restricted, because the interpenetration is typically justified by deformations of microscopic asperities of the surface; therefore it should not exceed a certain value that corresponds to a complete flattening of the asperities. The model can be interpreted as intermediate between the usual normal compliance models and the unilateral contact condition of Signorini type. For the static problem without friction, we prove the existence and uniqueness of solutions and establish the equivalence to an optimization problem. For the static problem with Coulomb friction, we show the existence of a solution. The analysis is based on an approximation of the problems by standard normal compliance models, the derivation of regularity results for these auxiliary problems in Sobolev spaces of fractional order by a special translation technique, and suitable limit procedures.     

On Optimality Conditions in Control of Elliptic Variational Inequalities

In the paper we consider optimal control of a class of strongly monotone variational inequalities, whose solution map is directionally differentiable in the control variable. This property is used to derive sharp pointwise necessary optimality conditions provided we do not impose any control or state constraints. In presence of such constraints we make use of the generalized differential calculus and derive, under a mild constraint qualification, optimality conditions in a “fuzzy” form. For strings, these conditions may serve as an intermediate step toward pointwise conditions of limiting (Mordukhovich) type and in the case of membranes they lead to a variant of Clarke stationarity conditions.     

DNA-, RNA- and self-pairing properties of a pyrrolidinyl peptide nucleic acid with a (2′R,4′S)-prolyl-(1S,2S)-2-aminocyclopentanecarboxylic acid backbone

A new pyrrolidinyl peptide nucleic acid (PNA) comprising of an alternate sequence of 4′-nucleobase-modified proline with (2′R,4′S) configuration and a (1S,2S)-2-aminocyclopentanecarboxylic acid [(2′R,4′S)-acpcPNA] backbone was synthesized and its DNA-, RNA- and self-pairing properties studied. T_m and CD studies suggested that the (2′R,4′S)-acpcPNA forms antiparallel hybrids to DNA and RNA with high sequence and direction specificity. The stability of these hybrids is comparable to those of the (2′R,4′R)-acpcPNA hybrids previously reported by our group. On the other hand, experiments with a self-complementary sequence indicated that the new (2′R,4′S)-acpcPNA forms a more stable antiparallel self-hybrid than (2′R,4′R)-acpcPNA.     

Testing Appearance of Polynomial Trend

For deciding whether a gradual polynomial trend appears in mean of a sequence of independent random variables a trimmed maximum-type statistic may be used. As the number of observations tends to infinity the suggested statistic converges in distribution to a maximum of a differentiable ²-process. The method for asymptotic critical values approximation based on high level exceedence probability was developed.     

Solvability of Static Contact Problems with Coulomb Friction for Orthotropic Material

We calculate an exact upper bound for the magnitude of the coefficient of friction that ensures the existence of a solution to a static contact problem with Coulomb friction. The approach is based on a general existence result that is valid under the assumption that the coefficient of friction is bounded by a certain constant depending on the constants in two special trace type estimates for a half space domain. We calculate these constants for orthotropic material and two space dimensions with the help of a representation for a partial Fourier transform of the solution to the corresponding system of elasticity equations. The result is compared to the formula for general anisotropic material. The new bound for orthotropic material is significantly larger than the old one for general material, if the material is close to an isotropic material with Poisson ration greater than zero. For some cases the new bound can be even larger than one.      

Testing for multiple change points

In this paper we concentrate on testing for multiple changes in the mean of a series of independent random variables. Suggested method applies a maximum type test statistic. Our primary focus is on an effective calculation of critical values for very large sample sizes comprising (tens of) thousands of observations and a moderate to large number of segments. To that end, Monte Carlo simulations and a modified Bellman’s principle of optimality are used. It is shown that, indisputably, computer memory becomes a critical bottleneck in solving a problem of such a size. Thus, minimization of the memory requirements and appropriate order of calculations appear to be the keys to success. In addition, the formula that can be used to get approximate asymptotic critical values using the theory of exceedance probability of Gaussian fields over a high level is presented.