Characteristics of Conservation Laws for Difference Equations

Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not derivations and do not obey the chain rule for derivatives. We show how these problems may be resolved and illustrate various uses of the characteristic. In particular, we establish the converse of Noether's Theorem for difference equations, we show (without taking a continuum limit) that the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and we obtain all five-point conservation laws for the potential Lotka-Volterra equation

Receptor tyrosine kinase activation of RhoA is mediated by AKT phosphorylation of DLC1

We report several receptor tyrosine kinase (RTK) ligands increase RhoA-guanosine triphosphate (GTP) in untransformed and transformed cell lines and determine this phenomenon depends on the RTKs activating the AKT serine/threonine kinase. The increased RhoA-GTP results from AKT phosphorylating three serines (S298, S329, and S567) in the DLC1 tumor suppressor, a Rho GTPase-activating protein (RhoGAP) associated with focal adhesions. Phosphorylation of the serines, located N-terminal to the DLC1 RhoGAP domain, induces strong binding of that N-terminal region to the RhoGAP domain, converting DLC1 from an open, active dimer to a closed, inactive monomer. That binding, which interferes with the interaction of RhoA-GTP with the RhoGAP domain, reduces the hydrolysis of RhoA-GTP, the binding of other DLC1 ligands, and the colocalization of DLC1 with focal adhesions and attenuates tumor suppressor activity. DLC1 is a critical AKT target in DLC1-positive cancer because AKT inhibition has potent antitumor activity in the DLC1-positive transgenic cancer model and in a DLC1-positive cancer cell line but not in an isogenic DLC1-negative cell line

Relation of alleles of the collagen type Ialpha1 gene to bone density and the risk of osteoporotic fractures in postmenopausal women

BACKGROUND: Osteoporosis is a common disorder with a strong genetic component. One way in which the genetic component could be expressed is through polymorphism of COLIA1, the gene for collagen type Ialpha1, a bone-matrix protein. METHODS: We determined the COLIA1 genotypes SS, Ss, and ss in a population-based sample of 177

Tomography of pairing symmetry from magnetotunneling spectroscopy -- a case study for quasi-1D organic superconductors

We propose that anisotropic $p$-, $d$-, or $f$-wave pairing symmetries can be distinguished from a tunneling spectroscopy in the presence of magnetic fields, which is exemplified here for a model organic superconductor ${(TMTSF)}_{2}X$. The shape of the Fermi surface (quasi-one-dimensional in this example) affects sensitively the pairing symmetry, which in turn affects the shape (U or V) of the gap along with the presence/absence of the zero-bias peak in the tunneling in a subtle manner. Yet, an application of a magnetic field enables us to identify the symmetry, which is interpreted as an effect of the Doppler shift in Andreev bound states.Comment: 4 papegs, 4 figure

Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

In this paper we obtain topological static solutions of some kind of pure $F(R)$ gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-$\Lambda$-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-$\Lambda$ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure $F(R)$ gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at $r=0$. We should note that the Kreschmann scalar of charged solutions goes to infinity as $r \rightarrow 0$, but with a rate slower than that of uncharged solutions.Comment: 21 pages, 4 figures, generalization to higher dimensions, references adde

Gluino Contribution to Radiative B Decays: Organization of QCD Corrections and Leading Order Results

The gluino-induced contributions to the decay b-> s gamma are investigated in supersymmetric frameworks with generic sources of flavour violation. It is shown that, when QCD corrections are taken into account, the relevant operator basis of the Standard Model effective Hamiltonian gets enlarged to contain: i) magnetic and chromomagnetic operators with a factor of alpha_s and weighted by a quark mass m_b or m_c; ii) magnetic and chromomagnetic operators of lower dimensionality, also containing alpha_s; iii) four-quark operators weighted by a factor alpha_s^2. Numerical results are given, showing the effects of the leading order QCD corrections on the inclusive branching ratio for b-> s gamma. Constraints on supersymmetric sources of flavour violation are derived.Comment: 36 pages including 16 postscript figures; uses epsf; journal version: one ref. added; rephrasing of a couple of paragraph

'To live and die [for] Dixie': Irish civilians and the Confederate States of America

Around 20,000 Irishmen served in the Confederate army in the Civil War. As a result, they left behind, in various Southern towns and cities, large numbers of friends, family, and community leaders. As with native-born Confederates, Irish civilian support was crucial to Irish participation in the Confederate military effort. Also, Irish civilians served in various supporting roles: in factories and hospitals, on railroads and diplomatic missions, and as boosters for the cause. They also, however, suffered in bombardments, sieges, and the blockade. Usually poorer than their native neighbours, they could not afford to become 'refugees' and move away from the centres of conflict. This essay, based on research from manuscript collections, contemporary newspapers, British Consular records, and Federal military records, will examine the role of Irish civilians in the Confederacy, and assess the role this activity had on their integration into Southern communities. It will also look at Irish civilians in the defeat of the Confederacy, particularly when they came under Union occupation. Initial research shows that Irish civilians were not as upset as other whites in the South about Union victory. They welcomed a return to normalcy, and often 'collaborated' with Union authorities. Also, Irish desertion rates in the Confederate army were particularly high, and I will attempt to gauge whether Irish civilians played a role in this. All of the research in this paper will thus be put in the context of the Drew Gilpin Faust/Gary Gallagher debate on the influence of the Confederate homefront on military performance. By studying the Irish civilian experience one can assess how strong the Confederate national experiment was. Was it a nation without a nationalism

BMD loci contribute to ethnic and developmental differences in skeletal fragility across populations: Assessment of evolutionary selection pressures

Bone mineral density (BMD) is a highly heritable trait used both for the diagnosis of osteoporosis in adults and to assess bone health in children. Ethnic differences in BMD have been documented, with markedly higher levels in individuals of African descent, which partially explain disparity in osteoporosis risk across populations. To date, 63 independent genetic variants have been associated with BMD in adults of Northern-European ancestry. Here, we demonstrate that at least 61 of these variants are predictive of BMD early in life by studying their compound effect within two multiethnic pediatric cohorts. Furthermore, we show that within these cohorts and across populations worldwide the frequency of those alleles associated with increased BMD is systematically elevated in individuals of Sub-Saharan African ancestry. The amount of differentiation in the BMD genetic scores among Sub-Saharan and non-Sub-Saharan populations together with neutrality tests, suggest that these allelic differences are compatible with the hypothesis of selective pressures acting on the genetic determinants of BMD. These findings constitute an explorative contribution to the role of selection on ethnic BMD differences and likely a new example of polygenic adaptation acting on a human trait

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Detector Description and Performance for the First Coincidence Observations between LIGO and GEO

For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave detectors were operated in coincidence to produce their first data for scientific analysis. Although the detectors were still far from their design sensitivity levels, the data can be used to place better upper limits on the flux of gravitational waves incident on the earth than previous direct measurements. This paper describes the instruments and the data in some detail, as a companion to analysis papers based on the first data.Comment: 41 pages, 9 figures 17 Sept 03: author list amended, minor editorial change