On Diophantine sets over polynomial rings

We prove that the recursively enumerable relations over a polynomial ring , where is the ring of integers in a totally real number field, are exactly the Diophantine relations over .

     

Almost f-maps and almost f-rings

In the beginning of the eighties, Buskes and Holland proved that any archimedean almost f-ring is commutative. One decade later, Steinberg showed that if G and H are ? with H archimedean, then any positive bilinear map G × G ${{\begin{array}{ll} B \\ \rightarrow \end{array}}}$ H such that ${x \wedge y = 0}$ implies B(x, y) = 0 is symmetric. At first sight, the Steinberg Theorem might seem to be a considerable generalization of the Buskes and Holland result. It turns out, surprisingly enough, that these two results are equivalent. The main purpose of this paper is to establish this equivalence. A second objective is to apply the aforementioned Steinberg Theorem to prove that if R is an f-ring with a unit element e and S is an archimedean f-ring, then an ?-homomorphism R ${{{\begin{array}{ll} h \\\rightarrow \end{array}}}}$ S is a ring homomorphism if and only if h(e) is idempotent in S. This extends a well-known result by Huijsmans and de Pagter, who obtained the same conclusion for semiprime f-algebras.     

Fast local searches and updates in bounded universes

Given a bounded universe $\{0,1,\dots ,U?1\}$, we show how to perform predecessor searches in $O(\log \log \mathrm{\Delta })$ expected time, where Δ is the difference between the element being searched for and its predecessor in the structure, while supporting updates in $O(\log \log \mathrm{\Delta })$ expected amortized time, as well. This unifies the results of traditional bounded universe structures (which support predecessor searches in $O(\log \log U)$ time) and hashing (which supports membership queries in $O(1)$ time). We also show how these results can be applied to approximate nearest neighbour queries and range searching.     

Using cross correlations of turbulent flow-induced ambient vibrations to estimate the structural impulse response. Application to structural health monitoring

It has been demonstrated theoretically and experimentally that an estimate of the impulse response (or Green's function) between two receivers can be obtained from the cross correlation of diffuse wave fields at these two receivers in various environments and frequency ranges: ultrasonics, civil engineering, underwater acoustics, and seismology. This result provides a means for structural monitoring using ambient structure-borne noise only, without the use of active sources. This paper presents experimental results obtained from flow-induced random vibration data recorded by pairs of accelerometers mounted within a flat plate or hydrofoil in the test section of the U.S. Navy's William B. Morgan Large Cavitation Channel. The experiments were conducted at high Reynolds number (Re > 50 million) with the primary excitation source being turbulent boundary layer pressure fluctuations on the upper and lower surfaces of the plate or foil. Identical deterministic time signatures emerge from the noise cross-correlation function computed via robust and simple processing of noise measured on different days by a pair of passive sensors. These time signatures are used to determine and/or monitor the structural response of the test models from a few hundred to a few thousand Hertz.     

A new synthetic route to Mg(2)Na(2)NiH(6) where a [NiH(4)] complex is for the first time stabilized by alkali metal counterions

Mg2Na2NiH6 was synthesized by reacting NaH and Mg2NiH4 at 310 degrees C under hydrogen pressure. The novel structure type was refined from neutron-diffraction data in the orthorhombic space group Pnma (No. 62), with unit cell dimensions of a = 11.428(2), b = 8.442(2), and c = 5.4165(9) Angstrom and a unit cell volume = 523 Angstrom(3) (Z = 4). The structure can be described by (Mg2H2)(2+) layers intersected by (Na2NiH4)(2-) layers. The [NiH4](4-) complex is approximately tetrahedral, indicating formal zerovalent nickel. This is the first example of a solid-state hydride where a [NiH4](4-) complex is directly stabilized by alkali metal ions instead of the more polarizing Mg(2+) ions. A rather long nickel-hydrogen bond distance of 1.65 Angstrom indicates a weaker Ni-H bond as a result of the weaker support from the less polarizing alkali metal counterions.     

Using tolerance intervals in pre-study validation of analytical methods to predict in-study results. The fit-for-future-purpose concept

It is recognized that the purpose of validation of analytical methods is to demonstrate that the method is suited for its intended purpose. Validation is not only required by regulatory authorities, but is also a decisive phase before the routine use of the method. For a quantitative analytical method the objective is to quantify the target analytes with a known and suitable accuracy. For that purpose, first, a decision about the validity of the method based on prediction is proposed: a method is declared proper for routine application if it is considered that most of the future results generated will be accurate enough. This can be achieved by using the "beta-expectation tolerance interval" (accuracy profile) as the decision tool to assess the validity of the analytical method. Moreover, the concept of "fit-for-purpose" is also proposed here to select the most relevant response function as calibration curve, i.e. choosing a response function based solely on the predicted results this model will allow to obtain. This paper reports four case studies where the results obtained with quality control samples in routine were compared to predictions made in the validation phase. Predictions made using the "beta-expectation tolerance interval" are shown to be accurate and trustful for decision making. It is therefore suggested that an adequate way to conciliate both the objectives of the analytical method in routine analysis and those of the validation step consists in taking the decision about the validity of the analytical method based on prediction of the future results using the most appropriate response function curve, i.e. the fit-for-future-purpose concept.     

The role of water H-bond imbalances in B-DNA substate transitions and peptide recognition revealed by time-resolved FTIR spectroscopy

The conformational substates B(I) and B(II) of the phosphodiester backbone in B-DNA are thought to contribute to DNA flexibility and protein recognition. We have studied by rapid scan FTIR spectroscopy the isothermal B(I)-B(II) transition on its intrinsic time scale. Correlation analysis of IR absorption changes occurring within seconds after a reversible incremental growth of the DNA hydration shell identifies water populations w(1) (PO(2)(-)-bound) and w(2) (non-PO(2)(-)-bound) exhibiting weaker and stronger H-bonds, respectively, than those dominating in bulk water. The B(II) substate is stabilized by w(2). The water H-bond imbalance of 3-4 kJ mol(-1) is equalized at little enthalpic cost upon formation of a contiguous water network (at 12-14 H(2)O molecules per DNA phosphate) of reduced ν(OH) bandwidth. In this state, hydration water cooperatively stabilizes the B(I) conformer via the entropically favored replacement of w(2)-DNA interactions by additional w(2)-water contacts, rather than binding to B(I)-specific hydration sites. Such water rearrangements contribute to the recognition of DNA by indolicidin, an antimicrobial 13-mer peptide from bovine neutrophils which, despite little intrinsic structure, preferentially binds to the B(I) conformer in a water-mediated induced fit. The FTIR spectra resolve sequential steps leading from PO(2)(-)-solvation to substate transition and eventually to base stacking changes in the complex. In combination with CD-spectral titrations, the data indicate that, in the absence of a bulk aqueous phase, as in molecular crowded environments, water relocation within the DNA hydration shell allows for entropic contributions similar to those assigned to water upon DNA ligand recognition in solution.     

Temperature dependence of coarse-grained potentials for liquid hexane

The present molecular dynamics study is an investigation of the temperature (T) dependence of liquid hexane coarse-grained potentials optimized with the Iterative Boltzmann Inversion method. An approach for the derivation of coarse-grained potentials at temperatures T different from the optimization temperature T(0) has recently been proposed for ethylbenzene. This method is based on the use of a T-dependent scaling factor f(T) to generate ethylbenzene potentials at T≠T(0). The approach is here extended to hexane, considering different reference temperatures T(0) and functional forms for f(T). From our simulations, it appears that the accuracy of the temperature transferability depends simultaneously on the T(0) chosen and the analytic form of f(T). Such a behavior is suppressed by the use of a new 2-point interpolation formula to generate coarse-grained potentials as a function of T. This scheme employs a linear interpolation based on the optimization of coarse-grained potentials at two reference temperatures, T(L) and T(U), with T(L)≤T≤T(U). Accurate coarse-grained simulations of liquid hexane can be performed using the new interpolation scheme. The results are encouraging for the use of potential interpolations as a practical means for devising coarse-grained potentials within a wider temperature range.     

Self-assembling dicopper(II) complexes of di-2-pyridyl ketone Schiff base ligands derived from S-alkyldithiocarbazates

Condensation of di-2-pyridyl ketone with S-methyldithiocarbazate or S-benzyldithiocarbazate yields potentially bridging ligands of the form Py₂CNNHC(S)SR; Hdpksme (R = Me; the di-2-pyridyl ketone Schiff base of S-methyldithiocarbazate) and Hdpksbz (R = Bz; the di-2-pyridyl ketone Schiff base of S-benzyldithiocarbazate). Complexation of these ligands with Cu(II) in a 1:1 M ratio leads to the formation of dinuclear complexes of the general formula [Cu(NNNS)X]₂ (X = Cl⁻, NO₃⁻, H₂O). X-ray crystallographic structure determinations show that each ligand provides three donor atoms (NNS) in a meridional configuration to one metal, viz. one of the pyridine nitrogen atoms, the azomethine nitrogen atom and the thiolate sulfur, while the nitrogen atom of the second pyridyl group forms a bridge to another copper(II) ion within the dimer. The coordination geometry around each copper(II) ion is approximately square pyramidal, the basal plane of which is composed of one of the pyridine nitrogen atoms, the azomethine nitrogen atom and a chlorido, nitrato or aqua ligand. The apical position of the square pyramid is always occupied by the pyridine nitrogen atom of the second ligand.     

Time-dependent radiolytic yield of OH• radical studied by picosecond pulse radiolysis

Picosecond pulse radiolysis measurements using a pulse-probe method are performed to measure directly the time-dependent radiolytic yield of the OH(?) radical in pure water. The time-dependent absorbance of OH(?) radical at 263 nm is deduced from the observed signal by subtracting the contribution of the hydrated electron and that of the irradiated empty fused silica cell which presents also a transient absoption. The time-dependent radiolytic yield of OH(?) is obtained by assuming the yield of the hydrated electron at 20 ps equal to 4.2 × 10(-7) mol J(-1) and by assuming the values of the extinction coefficients of e(aq)(-) and OH(?) at 782 nm (ε(λ=782 nm) = 17025 M(-1) cm(-1)) and at 263 nm (ε(λ=263 nm) = 460 M(-1) cm(-1)), respectively. The value of the yield of OH(?) radical at 10 ps is found to be (4.80 ± 0.12) × 10(-7) mol J(-1).