Betti numbers for p -stable ideals

Abstract

All Riemannian algebras of dimension ≤3 are classified in this paper.     

The motion equations of rotors,gyrostats and gyrodesics: application to powertrain-vehicle mechanical systems

The kinematics of wheels and rotors is described using a new auxiliary frame called gyrodesic frame or simply gyrodesic. By this, the absolute motion of the wheel becomes a serial composite of two motions: (1) the gyrodesic motion and (2) the wheels eigenmotion (or spin), i.e., the motion relative to the gyrodesic. The eigenmotion is described by an equation called rotor-equation. Gyrodesic coordinates turn out to be a particular useful tool in powertrain- and vehicle-dynamics as well as for general multibody systems. They allow a proper separation of the rotor- from the vehicle-equations and provide a rigorous method of coupling the powertrain-model into full spatial multibody-systems vehicle model. Some common misconceptions regarding this subject are identified and dispelled. The method is generalized to be applicable to the study of motion of general systems of rigid bodies with gyrostats or rotors as subsystems. The usefulness of the formalism is demonstrated by means of an illustrative example of non-trivial nature: the gyrostatic chain. Gyrodesic coordinates lead to a better grasp and deeper understanding of the structure of the dynamic equations of spatial vehicles in particular and of the motion of multibody-systems with rotors in general. The investigation reveals an interesting analogy to concept of parallel transport of vector fields in the sense of Levi-Civita. Dedicated to Prof. J. Wittenburg at the occasion of his 70th birthday.     

Biofunctional rapid prototyping for tissue-engineering applications: 3D bioplotting versus 3D printing

Two important rapid-prototyping technologies (3D Printing and 3D Bioplotting) were compared with respect to the computer-aided design and free-form fabrication of biodegradable polyurethane scaffolds meeting the demands of tissue-engineering applications. Aliphatic polyurethanes were based on lysine ethyl ester diisocyanate and isophorone diisocyanate. Layer-by-layer construction of the scaffolds was performed by 3D Printing, that is, bonding together starch particles followed by infiltration and partial crosslinking of starch with lysine ethyl ester diisocyanate. Alternatively, the 3D Bioplotting process permitted three-dimensional dispensing and reactive processing of oligoetherurethanes derived from isophorone diisocyanate, oligoethylene oxide, and glycerol. The scaffolds were characterized with X-ray microtomography, scanning electron microscopy, and mechanical testing. Osteoblast-like cells were seeded on such scaffolds to demonstrate their potential in tissue engineering. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 624–638, 2004     

Synthesis and Reactivity of Iridium(I) Fluorido Complexes: Oxidative Addition of SF4 at trans-[Ir(F)(CO)(PEt3)2]

The facile access to the Vaska type fluorido complexes trans-[Ir(F)(CO)(PR₃)₂] [ 6 : R = Et, 7 : R = Ph, 8 : R = iPr, 9 : R = Cy, 10 : R = tBu] was achieved by halide exchange at trans-[Ir(Cl)(CO)(PR₃)₂] ( 1 – 5 ) with Me₄NF. Furthermore, the reaction of complex 6 with SF₄ gave cis,trans-[Ir(F)₂(SF₃)(CO)(PEt₃)₂] ( 11 ), whereas 8 – 10 did not react. Reactivity studies revealed that 11 can selectively be manipulated at the sulfur atom by hydrolysis or fluoride abstraction to give cis,trans-[Ir(F)₂(SOF)(CO)(PEt₃)₂] ( 12 ) and cis,trans-[Ir(F)₂(SF₂)(CO)(PEt₃)₂][AsF₆] ( 13 ), respectively.     

Detection of catecholamines in single specimens of groundwater amphipods

Catecholamines play essential roles in several physiological processes in vertebrates as well as in invertebrates. While several studies have shown the presence of these substances in surface water invertebrates, their occurrence in groundwater fauna is unproven. In the present study, the presence of different catecholamines (i.e., noradrenaline, adrenaline, and dopamine) in individual specimens of groundwater amphipods of the genus Niphargus (mostly Niphargus inopinatus) was investigated via two independent analytical methods: HPLC/EcD and UPLC/TOF-MS. Mean values for catecholamine levels were 533 pg mg^?1 fresh weight for noradrenaline, 314 pg mg^?1 for adrenaline, and 16.4 ng mg^?1 for dopamine. The optimized protocol allowed the detection of CAs in single organisms of less than 1 mg fresh weight. Catecholamine concentration patterns in groundwater invertebrates are briefly discussed here with respect to their evolutionary adaptation to an environmentally stable, energy-poor habitat.

A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.     

A family of cohen-macaulay modules over singularities of type xt + y3

Let K be a field with char K ≠ 3 and it two positive integers such that 1 ≤i <t/2,t ≠ 3i. The classification problem for maximal Cohen-Macaulay modules over K[[X,Y]]/(X^t+Y³ ) is complicated if t≥ 6, because there exist parameter families of non-isomorphic maximal Cohen-Macaulay modules [Sc], or [GK], [Yo, Ch.9] and [DG]). Here we describe parameter families of such modules N, such that N/YN is a direct sum of copies of K[[X]]/(X ⁱ)K[[X]]/(X^t-i ).     

Strigolactones: Plant Hormones with Promising Features

Almost 80 years after the discovery of the first plant hormone, auxin, a few years ago a new class of plant hormones, the strigolactones, was discovered. These molecules have unprecedented biological activity in a number of highly important biological processes in plants but also outside the plant in the rhizosphere, the layer of soil surrounding the roots of plants and teeming with life. The exploitation of this amazing biological activity is not without challenges: the synthesis of strigolactones is complicated and designing the desired activity a difficult task. This minireview describes the current state of knowledge about the strigolactones and how synthetic analogs can be developed that can potentially contribute to the development of a sustainable agriculture.