Representations of tensor rotations and the geometry of spin 1/2

Making use of the real sl(2,R) Lie group algebra generating a spin 1/2 Lie group allows to create an explicitly given Lorentz invariant fermion wave. As the generators are real valued they can be interpreted as a deformation tensor in particular as a deformation tensor of space. Therefore, it is possible to model a heuristic purely geometric representation of spin 1/2 in Minkowski space. However the bigger surprise is that this wave has the space-time structure of gravitational waves, which are understood to be spin 2 waves. Given that the uniqueness of angular momentum representations still holds, the examination of tensor rotations reveals the existence of different representations of tensor rotations with a different angular parameter due to an unaccounted basic symmetry of symmetric tensors, where the spin 1/2 representation is a specific representation of tensor rotations corresponding to the quantum theoretical approach. The seeming contradiction is fully resolved and allows in addition to understand the notion of different representations of spin in tensors, again related to different representations of the tensor.Comment: 5 pages,1 figur

Structural organization, expression, and functional characterization of the murine cytomegalovirus immediate-early gene 3.

We have previously defined ie3 as a coding region located downstream of the ie1 gene which gives rise to a 2.75-kb immediate-early (IE) transcript. Here we describe the structural organization of the ie3 gene, the amino acid sequence of the gene product, and some of the functional properties of the protein. The 2.75-kb ie3 mRNA is generated by splicing and is composed of four exons. The first three exons, of 300, 111, and 191 nucleotides (nt), are shared with the ie1 mRNA and are spliced to exon 5, which is located downstream of the fourth exon used by the ie1 mRNA. Exon 5 starts 28 nt downstream of the 3' end of the ie1 mRNA and has a length of 1,701 nt. The IE3 protein contains 611 amino acids, the first 99 of which are shared with the ie1 product pp89. The IE3 protein expressed at IE times has a relative mobility of 88 kDa in gels, and a mobility shift to 90 kDa during the early phase is indicative of posttranslational modification. Sequence comparison reveals significant homology of the exon 5-encoded amino acid sequence with the respective sequence of UL 122, a component of the IE1-IE2 complex of human cytomegalovirus (HCMV). This homology is also apparent at the functional level. The IE3 protein is a strong transcriptional activator of the murine cytomegalovirus (MCMV) e1 promoter and shows an autoregulatory function by repression of the MCMV ie1/ie3 promoter. The high degree of conservation between the MCMV ie3 and HCMV IE2 genes and their products with regard to gene structure, amino acid sequence, and protein functions suggests that these genes play a comparable role in the transcriptional control of the two cytomegaloviruses

Characterization of the murine cytomegalovirus early transcription unit e1 that is induced by immediate-early proteins

The regulation of murine cytomegalovirus early (E) gene expression was studied in the cell line B25, which is stably transfected with the immediate-early ie1/ie3 gene complex. Infection of B25 cells in the presence of the protein synthesis inhibitor cycloheximide resulted in the expression of some E genes, whereas for the expression of other E genes prior protein synthesis was still mandatory, thus showing differences in the expression requirements of individual E genes. Transcription unit e1, a member of the E genes induced by immediate-early products of the ie1/ie3 gene complex, was characterized. It is located between map units 0.709 and 0.721 of the genome of murine cytomegalovirus strain Smith. A 2.6-kilobase RNA specified in this region is spliced from three exons of 912, 177, and 1,007 or 1,020 nucleotides, which are separated by introns of 93 and 326 nucleotides. The second AUG located in the first exon 119 nucleotides downstream of the 5' cap site is followed by an open reading frame of 990 nucleotides. The predicted polypeptide of 330 amino acids has a calculated molecular mass of 36.4 kilodaltons. Transfection with e1 revealed three antigenically related proteins of 36, 37, and 38 kilodaltons; these proteins probably represent differently modified forms of the predicted protein. These three proteins are phosphorylated and are associated with intranuclear inclusion bodies. A 33-kilodalton protein also derived from e1 was identified as a product of nonspliced transcripts. Comparison of amino acid sequences revealed homology between the murine cytomegalovirus transcription unit e1 and a human cytomegalovirus E transcription unit

Controlling the stability transfer between oppositely traveling waves and standing waves by inversion-symmetry-breaking perturbations

The effect of an externally applied flow on symmetry degenerated waves propagating into opposite directions and standing waves that exchange stability with the traveling waves via mixed states is analyzed. Wave structures that consist of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and explained quantitatively by amplitude equations containing quintic coupling terms. The latter are appropriate to describe the influence of inversion symmetry breaking perturbations on many oscillatory instabilities with O(2) symmetry.Comment: 4 pages, 4 figure

Mass-based depth and velocity scales for gravity currents and related flows

Gravity driven flows on inclines can be caused by cold, saline or turbid inflows into water bodies. Another example are cold downslope winds, which are caused by cooling of the atmosphere at the lower boundary. In a well-known contribution, Ellison and Turner (ET) investigated such flows by making use of earlier work on free shear flows by Morton, Taylor and Turner (MTT). Their entrainment relation is compared here with a spread relation based on a diffusion model for jets by Prandtl. This diffusion approach is suitable for forced plumes on an incline, but only when the channel topography is uniform, and the flow remains supercritical. A second aspect considered here is that the structure of ET's entrainment relation, and their shallow water equations, agrees with the one for open channel flows, but their depth and velocity scales are those for free shear flows, and derived from the velocity field. Conversely, the depth of an open channel flow is the vertical extent of the excess mass of the liquid phase, and the average velocity is the (known) discharge divided by the depth. As an alternative to ET's parameterization, two sets of flow scales similar to those of open channel flows are outlined for gravity currents in unstratified environments. The common feature of the two sets is that the velocity scale is derived by dividing the buoyancy flux by the excess pressure at the bottom. The difference between them is the way the volume flux is accounted for, which—unlike in open channel flows—generally increases in the streamwise direction. The relations between the three sets of scales are established here for gravity currents by allowing for a constant co-flow in the upper layer. The actual ratios of the three width, velocity, and buoyancy scales are evaluated from available experimental data on gravity currents, and from field data on katabatic winds. A corresponding study for free shear flows is referred to. Finally, a comparison of mass-based scales with a number of other flow scales is carried out for available data on a two-layer flow over an obstacle. Mass-based flow scales can also be used for other types of flows, such as self-aerated flows on spillways, water jets in air, or bubble plume

Efficient production of the Nylon 12 monomer ω-aminododecanoic acid methyl ester from renewable dodecanoic acid methyl ester with engineered Escherichia coli

The expansion of microbial substrate and product scopes will be an important brick promoting future bioeconomy. In this study, an orthogonal pathway running in parallel to native metabolism and converting renewable dodecanoic acid methyl ester (DAME) via terminal alcohol and aldehyde to 12-aminododecanoic acid methyl ester (ADAME), a building block for the high-performance polymer Nylon 12, was engineered in Escherichia coli and optimized regarding substrate uptake, substrate requirements, host strain choice, flux, and product yield. Efficient DAME uptake was achieved by means of the hydrophobic outer membrane porin AlkL increasing maximum oxygenation and transamination activities 8.3 and 7.6-fold, respectively. An optimized coupling to the pyruvate node via a heterologous alanine dehydrogenase enabled efficient intracellular L-alanine supply, a prerequisite for self-sufficient whole-cell transaminase catalysis. Finally, the introduction of a respiratory chain-linked alcohol dehydrogenase enabled an increase in pathway flux, the minimization of undesired overoxidation to the respective carboxylic acid, and thus the efficient formation of ADAME as main product. The completely synthetic orthogonal pathway presented in this study sets the stage for Nylon 12 production from renewables. Its effective operation achieved via fine tuning the connectivity to native cell functionalities emphasizes the potential of this concept to expand microbial substrate and product scopes

Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain

Recently a new integral equation describing the thermodynamics of the 1D Heisenberg model was discovered by Takahashi. Using the integral equation we have succeeded in obtaining the high temperature expansion of the specific heat and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than those obtained so far by the standard methods such as the linked-cluster algorithm. Our results will be useful to examine various approximation methods to extrapolate the high temperature expansion to the low temperature region.Comment: 5 pages, 4 figures, 2 table

Effects of Orthogonal Rotating Electric Fields on Electrospinning Process

Electrospinning is a nanotechnology process whereby an external electric field is used to accelerate and stretch a charged polymer jet, so as to produce fibers with nanoscale diameters. In quest of a further reduction in the cross section of electrified jets hence of a better control on the morphology of the resulting electrospun fibers, we explore the effects of an external rotating electric field orthogonal to the jet direction. Through extensive particle simulations, it is shown that by a proper tuning of the electric field amplitude and frequency, a reduction of up to a $30 \%$ in the aforementioned radius can be obtained, thereby opening new perspectives in the design of future ultra-thin electrospun fibres. Applications can be envisaged in the fields of nanophotonic components as well as for designing new and improved filtration materials.Comment: 22 pages, 8 figure