On a conjecture of V.V. Shchigolev

AbstractV.V. Shchigolev has proven that over any infinite field k of characteristic p>2, the T-space generated by G={x1p,x1px2p,…} is finitely based, which answered a question raised by A.V. Grishin. Shchigolev went on to conjecture that every infinite subset of G generates a finitely based T-space. In this paper, we prove that Shchigolev's conjecture was correct by showing that for any field of characteristic p>2, the T-space generated by any subset {x1px2p⋯xi1p,x1px2p⋯xi2p,…}, i1<i2<i3<⋯ , of G has a T-space generating set of size at most i2−i1+1

A maximal T-space of F₃[x]₀

In earlier work, we have established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]₀, has infinitely many maximal T-spaces, but exactly two maximal T-ideals (each of which is a maximal T-space). However, aside from these two T-ideals, no specific examples of maximal T-spaces of k[x]₀ were determined at that time. In a subsequent work, we proposed that for a finite field k of characteristic p > 2 and order q, for each positive integer n which is a power of 2, the T-space Wn, generated by {x + xqⁿ, xqⁿ⁺¹}, is maximal, and we proved that W₁ is maximal. In this note, we prove that for q = p = 3, W₂ is maximal

Photoelectron diffraction: from phenomenological demonstration to practical tool

The potential of photoelectron diffraction—exploiting the coherent interference of directly-emitted and elastically scattered components of the photoelectron wavefield emitted from a core level of a surface atom to obtain structural information—was first appreciated in the 1970s. The first demonstrations of the effect were published towards the end of that decade, but the method has now entered the mainstream armoury of surface structure determination. This short review has two objectives: First, to outline the way that the idea emerged and the way this evolved in my own collaboration with Neville Smith and his colleagues at Bell Labs in the early years: Second, to provide some insight into the current state-of-the art in application of (scanned-energy mode) photoelectron diffraction to address two key issue in quantitative surface structure determination, namely, complexity and precision. In this regard a particularly powerful aspect of photoelectron diffraction is its elemental and chemical-state specificity

Apparently synonymous substitutions in FGFR2 affect splicing and result in mild Crouzon syndrome

Background: Mutations of fibroblast growth factor receptor 2 (FGFR2) account for a higher proportion of genetic cases of craniosynostosis than any other gene, and are associated with a wide spectrum of severity of clinical problems. Many of these mutations are highly recurrent and their associated features well documented. Crouzon syndrome is typically caused by heterozygous missense mutations in the third immunoglobulin domain of FGFR2.Case presentation: Here we describe two families, each segregating a different, previously unreported FGFR2 mutation of the same nucleotide, c.1083A>G and c.1083A>T, both of which encode an apparently synonymous change at the Pro361 codon. We provide experimental evidence that these mutations affect normal FGFR2 splicing and document the clinical consequences, which include a mild Crouzon syndrome phenotype and reduced penetrance of craniosynostosis.Conclusions: These observations add to a growing list of FGFR2 mutations that affect splicing and provide important clinical information for genetic counselling of families affected by these specific mutations

Pulsars as Fantastic Objects and Probes

Pulsars are fantastic objects, which show the extreme states of matters and plasma physics not understood yet. Pulsars can be used as probes for the detection of interstellar medium and even the gravitational waves. Here I review the basic facts of pulsars which should attract students to choose pulsar studies as their future projects.Comment: Invited Lecture on the "First Kodai-Trieste Workshop on Plasma Astrophysics", Kodaikanal Obs, India. Aug.27-Sept.7th, 2007. In: "Turbulence, Dynamos, Accretion Disks, Pulsars and Collective Plasma Processes". Get a copy from: http://www.springerlink.com/content/978-1-4020-8867-

Propagation phase-contrast micro-computed tomography allows laboratory-based three-dimensional imaging of articular cartilage down to the cellular level

High-resolution non-invasive three-dimensional (3D) imaging of chondrocytes in articular cartilage remains elusive. The aim of this study was to explore whether laboratory micro-computed tomography (micro-CT) permits imaging cells within articular cartilage

Evolutionarily conserved Tbx5-Wnt2/2b pathway orchestrates cardiopulmonary development

Codevelopment of the lungs and heart underlies key evolutionary innovations in the transition to terrestrial life. Cardiac specializations that support pulmonary circulation, including the atrial septum, are generated by second heart field (SHF) cardiopulmonary progenitors (CPPs). It has been presumed that transcription factors required in the SHF for cardiac septation, e.g., Tbx5, directly drive a cardiac morphogenesis gene-regulatory network. Here, we report instead that TBX5 directly drives Wnt ligands to initiate a bidirectional signaling loop between cardiopulmonary mesoderm and the foregut endoderm for endodermal pulmonary specification and, subsequently, atrial septation. We show that Tbx5 is required for pulmonary specification in mice and amphibians but not for swim bladder development in zebrafish. TBX5 is non-cell-autonomously required for pulmonary endoderm specification by directly driving Wnt2 and Wnt2b expression in cardiopulmonary mesoderm. TBX5 ChIP-sequencing identified cis-regulatory elements at Wnt2 sufficient for endogenous Wnt2 expression domains in vivo and required for Wnt2 expression in precardiac mesoderm in vitro. Tbx5 cooperated with Shh signaling to drive Wnt2b expression for lung morphogenesis. Tbx5 haploinsufficiency in mice, a model of Holt-Oram syndrome, caused a quantitative decrement of mesodermal-to-endodermal Wnt signaling and subsequent endodermal-to-mesodermal Shh signaling required for cardiac morphogenesis. Thus, Tbx5 initiates a mesoderm-endoderm-mesoderm signaling loop in lunged vertebrates that provides a molecular basis for the coevolution of pulmonary and cardiac structures required for terrestrial life

Mechanical stability of the CMS strip tracker measured with a laser alignment system

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