On resolvable Golomb rulers,symmetric configurations and progressive dinner parties

Journal of Algebraic Combinatorics - We define a new type of Golomb ruler, which we term a resolvable Golomb ruler. These are Golomb rulers that satisfy an additional “resolvability”...     

Statistical properties of shocks in Burgers turbulence

We consider the statistical properties of solutions of Burgers' equation in the limit of vanishing viscosity, , with Gaussian whitenoise initial data. This system was originally proposed by Burgers^[1] as a crude model of hydrodynamic turbulence, and more recently by Zel'dovichet al..^[12] to describe the evolution of gravitational matter at large spatio-temporal scales, with shocks playing the role of mass clusters. We present here a rigorous proof of the scaling relationP(s)s ^1/2,s1 whereP(s) is the cumulative probability distribution of shock strengths. We also show that the set of spatial locations of shocks is discrete, i.e. has no accumulation points; and establish an upper bound on the tails of the shock-strength distribution, namely 1–P(s)exp{–Cs ³} fors1. Our method draws on a remarkable connection existing between the structure of Burgers turbulence and classical probabilistic work on the convex envelope of Brownian motion and related diffusion processes.Inadvertently the sequel to this article, Statistical Properties of Shocks in Burgers Turbulence, II. Tail Probabilities for Velocities, Shock-Strengths and Rarefaction Intervals has already appeared in an earlier issue of Commun. Math. Phys. (Commun. Math. Phys.169, 45–59 (1995).     

Practical aspects of Mössbauer spectroscopy instrumentation

The setting up and updating of a Mössbauer laboratory imply the acquisition and assembling of different units. Guidelines concerning either the construction or the acquisition of the various parts which compose a Mössbauer spectrometer are given in this paper.     

Iron-57 Mössbauer spectroscopic studies of materials of composition Fe x NbTiP3O12: materials with low concentrations of iron and the effects of treatment in air

The⁵⁷Fe Mössbauer spectrum recorded from the material of composition Fe_0.25NbTiP₃O₁₂ shows the presence of Fe²⁺ in a distribution of approximately octahedral type I sites within the channels of the NbTiP₃O₁₂ structure. A comparison of the results with those recorded from the material Fe_0.33NbTiP₃O₁₂ demonstrates the existence of an upper limit to the occupation by the Fe²⁺ species of the type I sites. Lattice parameter measurements and⁵⁷Fe Mössbauer spectroscopy show that treatment of Fe_0.25NbTiP₃O₁₂ in air induces the migration of the incorporated iron from the channels to form macroscopic -Fe₂O₃.     

The rate difference between the weak decays of t and in supersymmetry

We find that the CP-violating asymmetry

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at the one-loop order within the minimal supersymmetric extension of the standard model is of the order of few percent for maximal CP violation. It could be measured by considering the rate difference in the one-lepton events.     

Bioinspired Intervertebral Disc with Multidirectional Stiffness Prepared via Multimaterial Additive Manufacturing

Degenerative disc disease (DDD) has become a significant public health issue worldwide. This can result in loss of spinal function affecting patient health and quality of life. Artificial total disc replacement (A-TDR) is an effective approach for treating symptomatic DDD that compensates for lost functionality and helps patients perform daily activities. However, because current A-TDR devices lack the unique structure and material characteristics of natural intervertebral discs (IVDs), they fail to replicate the multidirectional stiffness needed to match physiological motions and characterize anisotropic behavior. It is still unclear how the multidirectional stiffness of the disc is affected by structural parameters and material characteristics. Herein, a bioinspired intervertebral disc (BIVD-L) based on a representative human lumbar segment is developed. The proposed BIVD-L reproduces the multidirectional stiffness needed for the most common physiological kinematic behaviors. The results demonstrate that the multidirectional stiffness of the BIVD-L can be regulated by structural and material parameters. The results of this research deepen knowledge of the biomechanical behavior of the human lumbar disc and may provide new inspirations for the design and fabrication of A-TDR devices for both engineering and functional applications.     

Recent Advances on High-Speed and Holographic Two-Photon Direct Laser Writing

Two-Photon Lithography, thanks to its very high sub-diffraction resolution, has become the lithographic technique par excellence in applications requiring small feature sizes and complex 3D pattering. Despite this, the fabrication times required for extended structures remain much longer than those of other competing techniques (UV mask lithography, nanoimprinting, etc.). Its low throughput prevents its wide adoption in industrial applications. To increase it, over the years different solutions have been proposed, although their usage is difficult to generalize and may be limited depending on the specific application. A promising strategy to further increase the throughput of Two-Photon Lithography, opening a concrete window for its adoption in industry, lies in its combination with holography approaches: in this way it is possible to generate dozens of foci from a single laser beam, thus parallelizing the fabrication of periodic structures, or to engineer the intensity distribution on the writing plane in a complex way, obtaining 3D microstructures with a single exposure. Here, the fundamental concepts behind high-speed Two-Photon Lithography and its combination with holography are discussed, and the literary production of recent years that exploits such techniques is reviewed, and contextualized according to the topic covered.     

WKB-type approximations for second-order differential equations in -algebras

Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to in the framework of -algebras. Both cases and are included, thus generalizing the classical theory for scalar equations developed by F.W.J. Olver to matrix as well as to infinite-dimensional equations.

     

Reactions of Substituted Boryl Radicals with Nitroalkanes. EPR, Kinetic, and Product Studies

The radical-initiated reaction of amine-boranes and phosphine-boranes, LBH(3) (L = R(3)N, R(3)P) with aliphatic nitro compounds has been investigated in order to explore the possibility of reducing tertiary nitroalkanes to the corresponding hydrocarbons. In all the examined cases boroxy nitroxides, RN(O(*))OBLH(2), resulting from the addition of ligated boryl radicals, LBH(2)(*), to an oxygen atom of the nitro group were detected and characterized by EPR spectroscopy. This reaction occurs at room temperature with a rate constant of 1.5 x 10(7) M(-)(1) s(-)(1) for LBH(2)(*) = Me(3)NBH(2)(*) and RNO(2) = Me(3)CNO(2). The boroxy nitroxides from tertiary nitroalkanes decay by a fragmentation reaction occurring with cleavage of the nitrogen-oxygen bond, rather than of the carbon-nitrogen bond as would be required for the reduction to the corresponding alkane to take place. The Arrhenius parameters for this fragmentation have been determined in few cases.     

Formation of ferrocyanides-IV Th(IV), Nd(III), UO(2)(II) and Hg(II)

The stoichiometry of the reaction between ferrocyanide and thorium, neodymium, uranyl ion and mercury(II) has been investigated. The first three give single products irrespective of the order of addition of the reagents, but the last does not. If mercury(II) is added to ferrocyanide Hg(2)Fe(CN)(6) is obtained, but if ferrocyanide is added to mercury(II) various cyanide complexes of mercury are formed. The K(sp) values for the precipitates are reported.