Root data with group actions

Suppose $k$ is a field, $G$ is a connected reductive algebraic $k$-group, $T$ is a maximal $k$-torus in $G$, and $\Gamma$ is a finite group that acts on $(G,T)$. From the above, one obtains a root datum $\Psi$ on which $\text{Gal}(k)\times\Gamma$ acts. Provided that $\Gamma$ preserves a positive system in $\Psi$, not necessarily invariant under $\text{Gal}(k)$, we construct an inverse to this process. That is, given a root datum on which $\text{Gal}(k)\times\Gamma$ acts appropriately, we show how to construct a pair $(G,T)$, on which $\Gamma$ acts as above. Although the pair $(G,T)$ and the action of $\Gamma$ are canonical only up to an equivalence relation, we construct a particular pair for which $G$ is $k$-quasisplit and $\Gamma$ fixes a $\text{Gal}(k)$-stable pinning of $G$. Using these choices, we can define a notion of taking "$\Gamma$-fixed points" at the level of equivalence classes, and this process is compatible with a general "restriction" process for root data with $\Gamma$-action.Comment: v2: one word inserted, one citation inserted, one reference updated, one misspelling correcte

Large entropy production inside black holes: a simple model

Particles dropped into a rotating black hole can collide near the inner horizon with enormous energies. The entropy produced by these collisions can be several times larger than the increase in the horizon entropy due to the addition of the particles. In this paper entropy is produced by releasing large numbers of neutrons near the outer horizon of a rotating black hole such that they collide near the inner horizon at energies similar to those achieved at the Relativistic Heavy Ion Collider. The increase in horizon entropy is approximately 80 per dropped neutron pair, while the entropy produced in the collisions is 160 per neutron pair. The collision entropy is produced inside the horizon, so this excess entropy production does not violate Bousso's bound limiting the entropy that can go through the black hole's horizon. The generalized laws of black hole thermodynamics are obeyed. No individual observer inside the black hole sees a violation of the second law of thermodynamicsComment: 10 page

A 160-Gb/s OTDM demultiplexer based on parametric wavelength exchange

Parametric wavelength exchange (PWE) has been demonstrated as a versatile device in providing different functionalities. In this paper, we will concentrate, numerically and experimentally, on one of these functionalities, namely, all-optical time demultiplexing of 160-Gb/s return-to-zero (RZ) signals based on a pulsed-pump PWE in a 400 m highly nonlinear dispersion-shifted fiber. Experimental results show power penalties < 2.7 dB at bit-error rate of 10-9 for all demultiplexed 10-Gb/s RZ signals. We also derive theoretical expressions for the conversion/residual efficiencies and investigate the impact of pump pulse width and phase mismatch on these efficiencies. Furthermore, the impacts of pulsed-pump wavelength and power level on the characteristics of the switching window are investigated numerically. As a result, the demultiplexer can be easily upgraded to an add-drop multiplexer because of the complete exchange nature of PWE, which is justified by the surviving channels' waveform performance. © 2009 IEEE.published_or_final_versio

‘Like the stranger at a funeral who cries more than the bereaved’: ethical dilemmas in ethnographic research with children

This article contributes to debates on the practicality and utility of prior ethical review in ethnography and qualitative research using an ethnography of children’s involvement in artisanal gold mining work in Ghana as a case study. Reflecting on dilemmas and obstacles encountered in attempts to employ prescribed institutional ethical guidance modelled for childhood research in the UK during the fieldwork, the discussion brings to attention some of the problems that can arise when ethical guidance is not anchored in the lived realities or value systems of the setting in which fieldwork is conducted. The article seeks to rejuvenate calls for more flexible and socio-culturally responsive ethical review and practice as an alternative to the prescriptive ethical regimes

Improving compliance to colorectal cancer screening using blood and stool based tests in patients refusing screening colonoscopy in Germany

Background Despite strong recommendations for colorectal cancer (CRC) screening, participation rates are low. Understanding factors that affect screening choices is essential to developing future screening strategies. Therefore, this study assessed patient willingness to use non-invasive stool or blood based screening tests after refusing colonoscopy. Methods Participants were recruited during regular consultations. Demographic, health, psychological and socioeconomic factors were recorded. All subjects were advised to undergo screening by colonoscopy. Subjects who refused colonoscopy were offered a choice of non-invasive tests. Subjects who selected stool testing received a collection kit and instructions; subjects who selected plasma testing had a blood draw during the office visit. Stool samples were tested with the Hb/Hp Complex Elisa test, and blood samples were tested with the Epi proColon® 2.0 test. Patients who were positive for either were advised to have a diagnostic colonoscopy. Results 63 of 172 subjects were compliant to screening colonoscopy (37%). 106 of the 109 subjects who refused colonoscopy accepted an alternative non-invasive method (97%). 90 selected the Septin9 blood test (83%), 16 selected a stool test (15%) and 3 refused any test (3%). Reasons for blood test preference included convenience of an office draw, overall convenience and less time consuming procedure. Conclusions 97% of subjects refusing colonoscopy accepted a non-invasive screening test of which 83% chose the Septin9 blood test. The observation that participation can be increased by offering non-invasive tests, and that a blood test is the preferred option should be validated in a prospective trial in the screening setting

True Neutrality as a New Type of Flavour

A classification of leptonic currents with respect to C-operation requires the separation of elementary particles into the two classes of vector C-even and axial-vector C-odd character. Their nature has been created so that to each type of lepton corresponds a kind of neutrino. Such pairs are united in families of a different C-parity. Unlike the neutrino of a vector type, any C-noninvariant Dirac neutrino must have his Majorana neutrino. They constitute the purely neutrino families. We discuss the nature of a corresponding mechanism responsible for the availability in all types of axial-vector particles of a kind of flavour which distinguishes each of them from others by a true charge characterized by a quantum number conserved at the interactions between the C-odd fermion and the field of emission of the corresponding types of gauge bosons. This regularity expresses the unidenticality of truly neutral neutrino and antineutrino, confirming that an internal symmetry of a C-noninvariant particle is described by an axial-vector space. Thereby, a true flavour together with the earlier known lepton flavour predicts the existence of leptonic strings and their birth in single and double beta decays as a unity of flavour and gauge symmetry laws. Such a unified principle explains the availability of a flavour symmetrical mode of neutrino oscillations.Comment: 19 pages, LaTex, Published version in IJT

General Form of the Color Potential Produced by Color Charges of the Quark

Constant electric charge $e$ satisfies the continuity equation $\partial_\mu j^{\mu}(x)= 0$ where $j^\mu(x)$ is the current density of the electron. However, the Yang-Mills color current density $j^{\mu a}(x)$ of the quark satisfies the equation $D_\mu[A] j^{\mu a}(x)= 0$ which is not a continuity equation ($\partial_\mu j^{\mu a}(x)\neq 0$) which implies that a color charge $q^a(t)$ of the quark is not constant but it is time dependent where $a=1,2,...8$ are color indices. In this paper we derive general form of color potential produced by color charges of the quark. We find that the general form of the color potential produced by the color charges of the quark at rest is given by \Phi^a(x) =A_0^a(t,{\bf x}) =\frac{q^b(t-\frac{r}{c})}{r}\[\frac{{\rm exp}[g\int dr \frac{Q(t-\frac{r}{c})}{r}] -1}{g \int dr \frac{Q(t-\frac{r}{c})}{r}}\]_{ab} where $dr$ integration is an indefinite integration, ~~ $Q_{ab}(\tau_0)=f^{abd}q^d(\tau_0)$, ~~$r=|{\vec x}-{\vec X}(\tau_0)|$, ~~$\tau_0=t-\frac{r}{c}$ is the retarded time, ~~$c$ is the speed of light, ~~${\vec X}(\tau_0)$ is the position of the quark at the retarded time and the repeated color indices $b,d$(=1,2,...8) are summed. For constant color charge $q^a$ we reproduce the Coulomb-like potential $\Phi^a(x)=\frac{q^a}{r}$ which is consistent with the Maxwell theory where constant electric charge $e$ produces the Coulomb potential $\Phi(x)=\frac{e}{r}$.Comment: Final version, two more sections added, 45 pages latex, accepted for publication in JHE

Messages from the other side: parasites receive damage cues from their host plants

As sessile organisms, plants rely on their environment for cues indicating imminent herbivory. These cues can originate from tissues on the same plant or from different individuals. Since parasitic plants form vascular connections with their host, parasites have the potential to receive cues from hosts that allow them to adjust defenses against future herbivory. However, the role of plant communication between hosts and parasites for herbivore defense remains poorly investigated. Here we examined the effects of damage to lupine hosts (Lupinus texensis) on responses of the attached hemiparasite (Castilleja indivisa), and indirectly, on a specialist herbivore of the parasite, buckeyes (Junonia coenia). Lupines produce alkaloids as defenses against herbivore that can be taken up by the parasite. We found that damage to lupine host plants by beet armyworm (Spodoptera exigua) significantly increased jasmonic acid (JA) levels in both the lupine host and parasite, suggesting uptake of phytohormones or priming of parasite defenses using host cues. However, lupine host damage did not induce changes in alkaloid levels in the hosts or parasites. Interestingly, the parasite had substantially higher concentrations of JA and alkaloids compared to lupine host plants. Buckeye herbivores consumed more parasite tissue when attached to damaged compared to undamaged hosts. We hypothesize that increased JA due to lupine host damage induced higher iridoid glycosides in the parasite, which are feeding stimulants for this specialist herbivore. Our results demonstrate that damage to hosts may affect both parasites and associated herbivores, indicating cascading effects of host damage on multiple trophic levels

Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe

The effects of generalized uncertainty principle (GUP) on the inflationary dynamics and the thermodynamics of the early universe are studied. Using the GUP approach, the tensorial and scalar density fluctuations in the inflation era are evaluated and compared with the standard case. We find a good agreement with the Wilkinson Microwave Anisotropy Probe data. Assuming that a quantum gas of scalar particles is confined within a thin layer near the apparent horizon of the Friedmann-Lemaitre-Robertson-Walker universe which satisfies the boundary condition, the number and entropy densities and the free energy arising form the quantum states are calculated using the GUP approach. A qualitative estimation for effects of the quantum gravity on all these thermodynamic quantities is introduced.Comment: 15 graghes, 7 figures with 17 eps graph