On the torsion function with Robin or Dirichlet boundary conditions

For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set \Om \subset \R^m satisfies formally the equation $-\Delta_p =1$ in \Om and $|\nabla u|^{p-2} \frac{\partial u}{\partial n} + b|u|^{p-2} u =0$ on \partial \Om. We obtain bounds of the $L^\infty$ norm of $u$ {\it only} in terms of the bottom of the spectrum (of the Robin $p$-Laplacian), $b$ and the dimension of the space in the following two extremal cases: the linear framework (corresponding to $p=2$) and arbitrary $b>0$, and the non-linear framework (corresponding to arbitrary $p>1$) and Dirichlet boundary conditions ($b=+\infty$). In the general case, $p\not=2, p \in (1, +\infty)$ and $b>0$ our bounds involve also the Lebesgue measure of \Om.Comment: 19 page

High resolution angular sensor

Specifications for the pointing stabilization system of the large space telescope were used in an investigation of the feasibility of reducing ring laser gyro output quantization to the sub-arc-second level by the use of phase locked loops and associated electronics. Systems analysis procedures are discussed and a multioscillator laser gyro model is presented along with data on the oscillator noise. It is shown that a second order closed loop can meet the measurement noise requirements when the loop gain and time constant of the loop filter are appropriately chosen. The preliminary electrical design is discussed from the standpoint of circuit tradeoff considerations. Analog, digital, and hybrid designs are given and their applicability to the high resolution sensor is examined. the electrical design choice of a system configuration is detailed. The design and operation of the various modules is considered and system block diagrams are included. Phase 1 and 2 test results using the multioscillator laser gyro are included

Form-factors of exponential fields in the sine-Gordon model

An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.Comment: 8 pages, harvmac.tex, added the formula (25) for two soliton form-factors at the reflectionless point

Gene expression analysis of bovine embryonic disc, trophoblast and parietal hypoblast at the start of gastrulation

In cattle early gastrulation-stage embryos (Stage 5), four tissues can be discerned: (i) the top layer of the embryonic disc consisting of embryonic ectoderm (EmE); (ii) the bottom layer of the disc consisting of mesoderm, endoderm and visceral hypoblast (MEH); (iii) the trophoblast (TB); and (iv) the parietal hypoblast. We performed microsurgery followed by RNA-seq to analyse the transcriptome of these four tissues as well as a developmentally earlier pre-gastrulation embryonic disc. The cattle EmE transcriptome was similar at Stages 4 and 5, characterised by the OCT4/SOX2/NANOG pluripotency network. Expression of genes associated with primordial germ cells suggest their presence in the EmE tissue at these stages. Anterior visceral hypoblast genes were transcribed in the Stage 4 disc, but no longer by Stage 5. The Stage 5 MEH layer was equally similar to mouse embryonic and extraembryonic visceral endoderm. Our data suggest that the first mesoderm to invaginate in cattle embryos is fated to become extraembryonic. TGFβ, FGF, VEGF, PDGFA, IGF2, IHH and WNT signals and receptors were expressed, however the representative members of the FGF families differed from that seen in equivalent tissues of mouse embryos. The TB transcriptome was unique and differed significantly from that of mice. FGF signalling in the TB may be autocrine with both FGFR2 and FGF2 expressed. Our data revealed a range of potential inter-tissue interactions, highlighted significant differences in early development between mice and cattle and yielded insight into the developmental events occurring at the start of gastrulation

An ERTS-1 study of coastal features on the North Carolina coast

There are no author-identified significant results in this report

Higgs diphoton rate enhancement from supersymmetric physics beyond the MSSM

We show that supersymmetric "new physics" beyond the MSSM can naturally accommodate a Higgs mass near 126 GeV and enhance the signal rate in the Higgs to diphoton channel, while the signal rates in all the other Higgs decay channels coincide with Standard Model expectations, except possibly the Higgs to Z-photon channel. The "new physics" that corrects the relevant Higgs couplings can be captured by two supersymmetric effective operators. We provide a simple example of an underlying model in which these operators are simultaneously generated. The scale of "new physics" that generates these operators can be around 5 TeV or larger, and outside the reach of the LHC.Comment: 24 pages, 4 figure