On the problem of algebraic completeness for the invariants of the Riemann Tensor: I

We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space-times into two distinct, invariantly characterized, classes: a general class M_G+, and a special, singular class M_S For each class, we provide an independent set of invariants (I_G+) ⊂ CZ and I_S ⊂ CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete.

On the problem of algebraic completeness for the invariants of the Riemann tensor. III.

We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.

Using fractal geometry to make rapid field measurements of riverbed topography at ecologically useful spatial scales

A method is described for making rapid in situ field measurements of riverbed topography over spatial scales of ≅1–10 m. This method uses rolling balls to make quick, accurate measurements of river-bed roughness at several spatial scales. Random sampling and replication generate multiple estimates of the fractal dimension (d) that can be used to test for significant differences in the complexity of riverbed architecture between habitat types and spatial scales.

Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.

The relationship between muscle size and bone geometry during growth and in response to exercise

As muscles become larger and stronger during growth and in response to increased loading, bones should adapt by adding mass, size, and strength. In this unilateral model, we tested the hypothesis that (1) the relationship between muscle size and bone mass and geometry (nonplaying arm) would not change during different stages of puberty and (2) exercise would not alter the relationship between muscle and bone, that is, additional loading would result in a similar unit increment in both muscle and bone mass, bone size, and bending strength during growth. We studied 47 competitive female tennis players aged 8–17 years. Total, cortical, and medullary cross-sectional areas, muscle area, and the polar second moment of area (Ip) were calculated in the playing and nonplaying arms using magnetic resonance imaging (MRI); BMC was assessed by DXA. Growth effects: In the nonplaying arm in pre-, peri- and post-pubertal players, muscle area was linearly associated BMC, total and cortical area, and Ip (r = 0.56–0.81, P < 0.09 to < 0.001), independent of age. No detectable differences were found between pubertal groups for the slope of the relationship between muscle and bone traits. Post-pubertal players, however, had a higher BMC and cortical area relative to muscle area (i.e., higher intercept) than pre- and peri-pubertal players (P < 0.05 to < 0.01), independent of age; pre- and peri-pubertal players had a greater medullary area relative to muscle area than post-pubertal players (P < 0.05 to < 0.01). Exercise effects: Comparison of the side-to-side differences revealed that muscle and bone traits were 6–13% greater in the playing arm in pre-pubertal players, and did not increase with advancing maturation. In all players, the percent (and absolute) side-to-side differences in muscle area were positively correlated with the percent (and absolute) differences in BMC, total and cortical area, and Ip (r = 0.36–0.40, P < 0.05 to < 0.001). However, the side-to-side differences in muscle area only accounted for 11.8–15.9% of the variance of the differences in bone mass, bone size, and bending strength. This suggests that other factors associated with loading distinct from muscle size itself contributed to the bones adaptive response during growth. Therefore, the unifying hypothesis that larger muscles induced by exercise led to a proportional increase in bone mass, bone size, and bending strength appears to be simplistic and denies the influence of other factors in the development of bone mass and bone shape.

Algebraic attacks over GF(q)

Recent algebraic attacks on LFSR-based stream ciphers and S-boxes have generated much interest as they appear to be extremely powerful. Theoretical work has been developed focusing around the Boo- lean function case. In this paper, we generalize this theory to arbitrary finite fields and extend the theory of annihilators and ideals introduced at Eurocrypt 2004 by Meier, Pasalic and Carlet. In particular, we prove that for any function f in the multivariate polynomial ring over GF(q), f has a low degree multiple precisely when two low degree functions appear in the same coset of the annihilator of f ^{q – 1} – 1. In this case, many such low degree multiples exist.

Influence of the geometry of an immersed steel workpiece on mass transfer coefficient in a chemical heat treatment fluidised bed

The mass transfer during carburising in a fluidised bed and in a steel workpiece has been studied experimentally in this work. This involved carburising experiment in an electrically heated fluidised bed at 900–970°C with natural gas and air as the atmosphere. A steel workpiece was designed to provide a range of carbon transfer surfaces of different geometries in the fluidised bed, and the carbon transfer coefficient was measured at these surfaces. The carbon transfer coefficient was determined from the carbon distribution within the diffusion layer of the sample. An empirical relationship of the carbon potential as a function of carburising atmosphere, bed temperature and fluidising velocity was determined, based on the understanding of the mass transfer mechanism and analysis of the experimental results.

A computational approach to the reconstruction of surface geometry from early temple superstructures

Recovering the control or implicit geometry underlying temple architecture requires bringing together fragments of evidence from field measurements, relating these to mathematical and geometric descriptions in canonical texts and proposing "best-fit" constructive models. While scholars in the field have traditionally used manual methods, the innovative application of niche computational techniques can help extend the study of artefact geometry. This paper demonstrates the application of a hybrid computational approach to the problem of recovering the surface geometry of early temple superstructures. The approach combines field measurements of temples, close-range architectural photogrammetry, rule-based generation and parametric modelling. The computing of surface geometry comprises a rule-based global model governing the overall form of the superstructure, several local models for individual motifs using photogrammetry and an intermediate geometry model that combines the two. To explain the technique and the different models, the paper examines an illustrative example of surface geometry reconstruction based on studies undertaken on a tenth century stone superstructure from western India. The example demonstrates that a combination of computational methods yields sophisticated models of the constructive geometry underlying temple form and that these digital artefacts can form the basis for in depth comparative analysis of temples, arising out of similar techniques, spread over geography, culture and time.

Long-term effects of calcium-vitamin-D3-fortified milk on bone geometry and strength in older men

The long-term effects of calcium and vitamin D supplementation on bone material and structural properties in older men are not known. The aim of this study was to examine the effects of high calcium (1000 mg/day)- and vitamin-D3 (800 IU/day)-fortified milk on cortical and trabecular volumetric BMD (vBMD) and bone geometry at the axial and appendicular skeleton in men aged over 50 years. One hundred and eleven men who were part of a larger 2-year randomized controlled trial had QCT scans of the mid-femur and lumbar spine (L1–L3) to assess vBMD, bone geometry and indices of bone strength [polar moment of inertia (Ipolar)]. After 2 years, there were no significant differences between the milk supplementation and control group for the change in any mid-femur or L1–L3 bone parameters for all men aged over 50 years. However, the mid-femur skeletal responses to the fortified milk varied according to age, with a split of ≤62 versus >62 years being the most significant for discriminating the changes between the two groups. Subsequent analysis revealed that, in the older men (>62 years), the expansion in mid-femur medullary area was 2.8% (P < 0.01) less in the milk supplementation compared to control group, which helped to preserve cortical area in the milk supplementation group (between group difference 1.1%, P < 0.01). Similarly, for mid-femur cortical vBMD and Ipolar, the net loss was 2.3 and 2.8% less in the milk supplementation compared to control group (P < 0.01 and <0.001, respectively). In conclusion, calcium–vitamin-D3-fortified milk may represent an effective strategy to maintain bone strength by preventing endocortical bone loss and slowing the loss in cortical vBMD in elderly men.

Algebraic attacks on clock-controlled stream ciphers

We present an algebraic attack approach to a family of irregularly clock-controlled bit-based linear feedback shift register systems. In the general set-up, we assume that the output bit of one shift register controls the clocking of other registers in the system and produces a family of equations relating the output bits to the internal state bits. We then apply this general theory to four specific stream ciphers: the (strengthened) stop-and-go generator, the alternating step generator, the self-decimated generator and the step1/step2 generator. In the case of the strengthened stop-and-go generator and of the self-decimated generator, we obtain the initial state of the registers in a significantly faster time than any other known attack. In the other two situations, we do better than or as well as all attacks but the correlation attack. In all cases, we demonstrate that the degree of a functional relationship between the registers can be bounded by two. Finally, we determine the effective key length of all four systems.

Algebraic attacks on clock-controlled cascade ciphers

In this paper, we mount the first algebraic attacks against clock controlled cascade stream ciphers. We first show how to obtain relations between the internal state bits and the output bits of the Gollmann clock controlled cascade stream ciphers. We demonstrate that the initial states of the last two shift registers can be determined by the initial states of the others. An alternative attack on the Gollmann cascade is also described, which requires solving quadratic equations. We then present an algebraic analysis of Pomaranch, one of the phase two proposals to eSTREAM. A system of equations of maximum degree four that describes the full cipher is derived. We also present weaknesses in the filter functions of Pomaranch by successfully computing annihilators and low degree multiples of the functions.

1-Naphthyl- and mesityltellurium(IV,II) derivatives of small bite chelating organic ligands: effect of steric bulk and intramolecular secondary bonding interaction on molecular geometry and supramolecular association

The synthesis and characterization of unsymmetric diorganotellurium compounds containing a sterically demanding I-naphthyl or
mesitylligand and a small bite chelating organic ligand capable of 1,4-Te···N(O) intramolecular interaction is described. The reaction
of ArTeCl₃ (Ar = I-C_lOH₇, Np; 2,4,6-Me₃C₆H_2' Mes) with (SB)HgCI [SB = the Schiff base, 2-(4,4'-N0₂C₆H₄CH=NC₆H₃-Me)] or a methyl ketone (RCOCH₃) afforded the corresponding dichlorides (SB)ArTeCI₂ (Ar = Np, 1Aa; Mes, 1Ba) or (RCOCH₂)ArTeCl₂ (Ar = Np; R = Ph (2Aa), Me (3Aa), Np (4Aa); Ar = Mes, R = Ph (2Ba)). Reduction of 1Aa and 1Ba by Na₂S₂0₅ readily gave the tellurides (SB)ArTe (Ar = Np (1A), Mes, (1B) but that of dichlorides derived from methylketones was complicated due to partial decomposition to tellurium powder and diarylditelluride (Ar₂Te₂), resulting in poor yields of the corresponding tellurides 2A, 2B and 3A. Oxidation of the isolated tellurides with S0₂Cl₂, Br₂ and I₂ yielded the corresponding dihalides. All the synthesized compounds have been characterized with the help of IR, ¹H, ^l3C, and ¹²⁵Te NMR and in the case of 2Aa, and 2Ba by X-ray crystallography. Appearance of only one ¹²⁵Te signal indicated that the unsymmetric derivatives were stable to disproportionation to symmetric species. Intramolecular 1,4-Te· . ·0 secondary bonding interactions (SBIs) are exhibited in the crystal structures of both the tellurium(IV) dichlorides, 2Aa, and 2Ba. Steric repulsion of the mesityl group in the latter dominates over lone pair-bond pair repulsion, resulting in significant widening of the equatorial C-Te-C angle. This appears to be responsible for the lack of Te· . ·CI involved supramolecular associations in the crystal structure of 2Ba.

Design of experiments and springback prediction for AHSS automotive components with complex geometry

With the drive towards implementing Advanced High Strength Steels (AHSS) in the automotive industry; stamping engineers need to quickly answer questions about forming these strong materials into elaborate shapes.
Commercially available codes have been successfully used to accurately predict formability, thickness and strains in complex parts. However, springback and twisting are still challenging subjects in numerical simulations of AHSS components. Design of Experiments (DOE) has been used in this paper to study the sensitivity of the implicit and explicit numerical results with respect to certain arrays ofuser input parameters in the forming ofan AHSS component. Numerical results were compared to experimental measurements of the parts stamped in an industrial production line. The forming predictions of the implicit and explicit codes were in good agreement with the experimental measurements for the conventional steel grade, while lower accuracies were observed for the springback predictions. The forming
predictions of the complex component with an AHSS material were also in good correlation with the respective experimental measurements. However, much lower accuracies were observed in its springback predictions. The number of integration points through the thickness and tool offset were found to be of significant importance, while coefficient of friction and Young's modulus (modeling input parameters) have no significant effect on the accuracy of the predictions for the complex geometry.