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American Institute of Mathematical Sciences

November  2010, 14(4): 1337-1359. doi: 10.3934/dcdsb.2010.14.1337

Analysis of a conservation law modeling a highly re-entrant manufacturing system

 1 Institut universitaire de France and Université Pierre et Marie Curie-Paris VI, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu, Paris, F-75005, France 2 Arizona State University, Tempe, Arizona 85287-1804, United States 3 Fudan University and Université Pierre et Marie Curie-Paris VI, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu, Paris, F-75005, France

Received  July 2009 Revised  March 2010 Published  August 2010

This article studies a hyperbolic conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. Characteristic features are the nonlocal character of the velocity and that the influx and outflux constitute the control and output signal, respectively. We prove the existence and uniqueness of solutions for $L^1$-data, and study their regularity properties. We also prove the existence of optimal controls that minimizes in the $L^2$-sense the mismatch between the actual and a desired output signal. Finally, the time-optimal control for a step between equilibrium states is identified and proven to be optimal.
Citation: Jean-Michel Coron, Matthias Kawski, Zhiqiang Wang. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1337-1359. doi: 10.3934/dcdsb.2010.14.1337
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2018 Impact Factor: 1.008


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# 13.6: Shopping for Homeowners Insurance

• Anonymous
• LibreTexts

Learning Objectives

In this section we elaborate on strategies for acquiring the most suitable insurance at the lowest relative cost

You can buy insurance for your home from many different sources, and premiums can vary greatly. As with any kind of purchase, price is not the sole consideration, but the possibility of saving 40 or 50 percent a year on your home insurance is worth some effort. The range of prices may not be as great where you live, but there is likely enough variation to justify shopping around. The startling difference between high and low prices clearly demonstrates that it pays to shop for home insurance.

There are three steps to shopping for homeowners coverage:

• Figure out what you have
• Figure out what you want

These steps are illustrated in the case of the Smith family mentioned earlier in the chapter. You will need to inventory your possessions and organize all the information the insurer will need. Taking photos of your property and keeping the photos in a safe place away from your home is a good method of maintaining an inventory list. Figure $$\PageIndex{1}$$ shows the information about your property that you will need to provide to your insurer, including details such as construction (brick, frame), access to fire hydrants, location, age, and security. The location of the property is important and may cause you to have to pay higher premiums. The issue of redlining—higher premiums for homes in inner cities—is discussed in the box “Redlining: Urban Discrimination Myth or Reality?”

Next, you need to decide what insurance you want and the amounts of coverage, for example:

• Coverage A (dwelling) $100,000 • Coverage E (liability)$25,000
• Coverage F (medical payments) $500 per person You will also need to choose your deductibles, such as$100, $250, and$500, and limits on coverages E and F, such as $100,000 or$300,000 on coverage E.

Finally, collect quotes from potential insurers. You might choose a couple of online or direct-mail insurers, some independent agents, and some exclusive-agency companies. Taking into account any differences in coverage, compare annual premiums and decide which company will provide what you want at the best price, as is demonstrated in Case 1 of "23: Cases in Holistic Risk Management".

## Key Takeaways

In this section you studied the general notion of liability and the related legal aspects thereof:

• It is worth shopping around for home insurance because savings can amount to 40 to 50 percent per year.
• The first step in seeking coverage is to perform a thorough inventory of possessions and gather information pertinent to an insurer.
• The second step is deciding on the insurance, the amounts of coverage desired, and the deductibles.
• The final step is to collect quotes from potential insurers.

## Discussion Questions

1. What might account for cost differentials between policies that offer the same limits of coverage?
2. In your experience, is cost the bottom line when it comes to the purchase of insurance? Does service factor into the decision?

This page titled 13.6: Shopping for Homeowners Insurance is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Anonymous.

format: plain


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0

# How to make a round script?

I was wondering how to make a round script that NEVER Ends, so The game can continue.

3

There are a few ways to do this. The first method is using a while loop.

while true do
PlayRound()
end

This will constantly execute any code in the PlayRound function (which will need to be defined above the while loop), and for your case, the code to play your game in rounds will go inside. Another method is an infinite for loop:

for i = 1, math.huge do
PlayRound()
end

Another would be the repeat-until loop:

repeat
PlayRound()
until false

One other option you have is a recursive call to your round function.

function PlayRound()
-- code in here to play the round

PlayRound() -- start the next round
end

PlayRound() -- start the first round

You'll notice above that the PlayRound function actually calls itself. This will happen infinitely unless (like all other methods) there is an error in your script.

Which method you pick is up to you. The while loop is the easiest to understand, while the recursive function (the last example) would be highly beneficial to learn. It's your call, though.

0
Thanks! stanford7787 0 — 7y
while true do


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# Homology with local coefficients and flat bundles

I have a problem in understanding Prop.1.10 in https://pages.uoregon.edu/sadofsky/691/sseq-local-coefficients.pdf My interpretation is as follows:

Let $$X$$ be a smooth n-manifold and $$U\to X$$ be its universal cover. Notice that $$U$$ is a $$\pi_1 X$$ principal bundle. Let $$\rho: \pi_1 X\to Aut(S)$$ be a an action of $$\pi_1 X$$ on the group $$S$$. Then we can form the associated bundle $$\tilde{X}=U\times_\rho S$$. The proposition 1.10 says that $$H_*(X,S) \simeq H_*(\tilde{X},\mathbb{Z})$$ where the LHS is the homology with twisted coefficients in $$S$$.

Problem: If $$S=V$$ is a vector space then $$\tilde{X}=U\times_{\rho} V$$ is the flat bundle associated to the flat connection induced by $$\rho.$$ This is a vector bundle over $$X$$ hence it retract over $$X$$ therefore $$H_*(X,V) \simeq H_*(\tilde{X},\mathbb{Z})\simeq H_*(X, \mathbb{Z}).$$ Which is not true for any flat connection.

• The highlighted proposition 1.10 is false as stated. – Moishe Kohan Jan 9 '20 at 18:16
• @MoisheKohan, am I interpreting it wrongly? Or is the proposition in the document false as well? – Warlock of Firetop Mountain Jan 10 '20 at 9:27

What is true is that if $$A = \Bbb Z[\pi_1(X)/H]$$ as a $$\pi_1(X)$$-module, and $$p: X' \to X$$ is the covering space associated to the subgroup $$H \subset \pi_1(X)$$, then $$\mathcal A = \tilde X \times_{\pi_1 X} A$$ gives a local coefficient system over $$X$$ (if you like to think of a local coefficient system as being a bundle of abelian groups over $$X$$). Then we have $$H_*(X;\mathcal A) \cong H_*(X'; \Bbb Z).$$
• @WarlockofFiretopMountain Sorry, I don't, I picked up most of this by brute-force computation. It might be a nice exercise for you to compute the homology of the circle equipped with a local coefficient system with fiber $\Bbb C^n$, and $1 \in \pi_1 S^1$ acting by $A \in GL_n(\Bbb C)$. Also, if you use the definition of the local-coefficient chain complex from bundle of groups, I suggest you show explicitly that we have an isomorphism of chain complexes $C_*(X;\mathcal A) \cong C_*(X';\Bbb Z)$, it's not too hard and is revealing. – Jacque Lemure Jan 11 '20 at 18:22


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## Saturday, June 29, 2019

### Question from Material Science (Summer 2019) AMIE Exam

At room temperature, the electrical conductivity of PbS is 25 (Ω.m)-1, whereas the electron and hole mobilities are 0.06 and 0.02 m2/V.s, respectively. Calculate the intrinsic carrier concentration for PbS at room temperature. (AMIE, Material Science, Summer 2019)

Solution
$\begin{array}{l}\sigma = 25{(\Omega m)^{ - 1}}\\{\mu _e} = 0.06{m^2}/Vs\\{\mu _h} = 0.02{m^2}/Vs\end{array}$
In the intrinsic region
$n = p = {n_i}$
So, $\sigma = {n_i}\left| e \right|({\mu _e} + {\mu _h})$
$\therefore {n_i} = \frac{\sigma }{{\left| e \right|({\mu _e} + {\mu _h})}} = \frac{{25}}{{1.6x{{10}^{ - 19}}(0.06 + 0.02)}} = 1.95x{10^{21}}{m^{ - 3}}$

Study material for AMIE Exams


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# [OS X TeX] How to mark = as just a symbol

Herbert Schulz herbs at wideopenwest.com
Sun Jan 17 10:35:21 EST 2016

> On Jan 17, 2016, at 9:25 AM, Alain Schremmer <schremmer.alain at gmail.com> wrote:
>
> I am running into an error with tcolorbox--a fantastic package--but,  in fact, I suspect that this has nothing to do with the package and just with my general ignorance:
>
> \begin{tcolorbox}[title=$5$]
> Text
> \end{tcolorbox}
>
> works but
>
> \begin{tcolorbox}[title=$=5$]
> Text
> \end{tcolorbox}
>
>
> does not.
>
> I suspect that the second = should somehow be marked as being a mere symbol. Which I don't know how to do.
>
> Embarrassed regards
> --schremmer

Howdy,

Don't know exactly why but it probably has to do with the way the arguments are processed but

title={$=5$}

works fine. When in doubt, isolate! :-)

Good Luck,

Herb Schulz
(herbs at wideopenwest dot com)


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Posts Tagged presence

Recent Postings from presence

The Effects of Lyman-Limit Systems on the Evolution and Observability of the Epoch of Reionization

We present the first large-scale, full radiative transfer simulations of the reionization of the intergalactic medium in the presence of Lyman-limit systems (LLSs). To illustrate the impact of LLS opacity, possibly missed by previous simulations, we add either a uniform or spatially-varying hydrogen bound-free opacity. This opacity, implemented as the mean free path (mfp) of the ionizing photons, extrapolates the observed, post-reionization redshift dependence into the epoch of reionization. In qualitative agreement with previous studies, we find that at late times the presence of LLSs slows down the ionization fronts, and alters the size distribution of H II regions. We quantitatively characterize the size distribution and morphological evolution of H II regions and examine the effects of the LLSs on the redshifted 21-cm signal from the patchy reionization. The presence of LLSs extends the ionization history by $\Delta z \sim 0.8$. The LLS absorbers significantly impede the late-time growth of the H II regions. The position dependent LLS distribution slows reionization further and additionally limits the late growth of the ionized regions. However, there is no "freeze out" of the H II regions and the largest regions grow to the size of the simulation volume. The 21-cm power spectra show that at large scales the power drops by a factor of 2 for 50% and 75% ionization stages (at $k = 0.1$ $\text{h} \, \text{Mpc}^{-1}$) reflecting the limiting effect of the LLSs on the growth of ionized patches. The statistical observables such as the RMS of the brightness temperature fluctuations and the peak amplitudes of the 21-cm power spectra at large-scales ($k = 0.05 - 0.1$ $\text{h} \, \text{Mpc}^{-1}$) are diminished by the presence of LLS.

A pragmatic Bayesian perspective on correlation analysis: The exoplanetary gravity - stellar activity case

We apply the Bayesian framework to assess the presence of a correlation between two quantities. To do so, we estimate the probability distribution of the parameter of interest, $\rho$, characterizing the strength of the correlation. We provide an implementation of these ideas and concepts using python programming language and the pyMC module in a very short ($\sim$130 lines of code, heavily commented) and user-friendly program. We used this tool to assess the presence and properties of the correlation between planetary surface gravity and stellar activity level as measured by the log($R'_{\mathrm{HK}}$) indicator. The results of the Bayesian analysis are qualitatively similar to those obtained via p-value analysis, and support the presence of a correlation in the data. The results are more robust in their derivation and more informative, revealing interesting features such as asymmetric posterior distributions or markedly different credible intervals, and allowing for a deeper exploration. We encourage the reader interested in this kind of problem to apply our code to his/her own scientific problems. The full understanding of what the Bayesian framework is can only be gained through the insight that comes by handling priors, assessing the convergence of Monte Carlo runs, and a multitude of other practical problems. We hope to contribute so that Bayesian analysis becomes a tool in the toolkit of researchers, and they understand by experience its advantages and limitations.

Luminous blue variables: An imaging perspective on their binarity and near environment

Context. Luminous blue variables (LBVs) are rare massive stars with very high luminosity. They are characterized by strong photo-metric and spectroscopic variability related to transient eruptions. The mechanisms at the origin of these eruptions is not well known. In addition, their formation is still problematic and the presence of a companion could help to explain how they form. Aims. This article presents a study of seven LBVs (about 20% of the known Galactic population), some Wolf-Rayet stars, and massive binaries. We probe the environments that surround these massive stars with near-, mid-, and far-infrared images, investigating potential nebula/shells and the companion stars. Methods. To investigate large spatial scales, we used seeing-limited and near diffraction-limited adaptive optics images to obtain a differential diagnostic on the presence of circumstellar matter and to determine their extent. From those images, we also looked for the presence of binary companions on a wide orbit. Once a companion was detected, its gravitational binding to the central star was tested. Tests include the chance projection probability, the proper motion estimates with multi-epoch observations, flux ratio, and star separations. Results. We find that two out of seven of LBVs may have a wide orbit companion. Most of the LBVs display a large circumstellar envelope or several shells. In particular, HD168625, known for its rings, possesses several shells with possibly a large cold shell at the edge of which the rings are formed. For the first time, we have directly imaged the companion of LBV stars.

Landau Levels in graphene in the presence of emergent gravity [Replacement]

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.

Molecular jet emission and a spectroscopic survey of S235AB

Context. The S235AB star forming region houses a massive young stellar object which has recently been reported to exhibit possible evidence of jet rotation - an illusive yet crucial component of disk aided star formation theories. Aims. To confirm the presence of a molecular counterpart to the jet and to further study the molecular environment in in S235AB. Methods. We search for velocity wings in the line emission of thermal SiO (J=2-1, v=0), a tracer of shocked gas, which would indicate the presence of jet activity. Utilising other lines detected in our survey we use the relative intensities of intra species transitions, isotopes and hyperfine transitions to derive opacities, temperatures, column densities and abundances of various molecular species in S235AB. Results. The SiO (J=2-1, v=0) emission exhibits velocity wing of up to 75 km/s above and below the velocity of the star, indicating the presence of a jet. The molecular environment describes an evolutionary stage resemblant of a hot molecular core.

Investigating Particle Acceleration in Protostellar Jets: The Triple Radio Continuum Source in Serpens

While most protostellar jets present free-free emission at radio wavelengths, synchrotron emission has been also proposed to be present in a handful of these objects. The presence of non-thermal emission has been inferred by negative spectral indices at centimeter wavelengths. In one case (the HH 80-81 jet arising from a massive protostar), its synchrotron nature was confirmed by the detection of linearly polarized radio emission. One of the main consequences of these results is that synchrotron emission implies the presence of relativistic particles among the non-relativistic material of these jets. Therefore, an acceleration mechanism should be taking place. The most probable scenario is that particles are accelerated when the jets strongly impact against the dense envelope surrounding the protostar. Here, we present an analysis of radio observations obtained with the Very Large Array of the Triple Radio Source in the Serpens star-forming region. This object is known to be a radio jet arising from an intermediate-mass protostar. It is also one of the first protostellar jets where the presence of non-thermal emission was proposed. We analysed the dynamics of the jet as well as the nature of the emission and discuss these issues in the context of the physical parameters of the jet and the particle acceleration phenomenon.

Spectra of accelerated particles at supernova shocks in the presence of neutral hydrogen: the case of Tycho

The presence of neutral hydrogen in the shock proximity changes the structure of the shock and affects the spectra of particles accelerated through the first order Fermi mechanism. This phenomenon has profound implications for the interpretation of the multifrequency spectra of radiation from supernova remnants. Neutrals that undergo charge exchange with hot ions downstream of the shock may result in fast neutrals moving towards the upstream gas, where they can suffer additional charge exchange or ionisation reactions, thereby depositing energy and momentum upstream. Here we discuss the implications of this neutral return flux, already predicted in our previous work on neutral mediated supernova shocks and show how the spectra of accelerated particles turn out to be appreciably steeper than $p^{-4}$, thereby affecting the gamma ray spectra from supernova remnants in general and from Tycho specifically. The theory that describes non-linear diffusive shock acceleration in the presence of neutral hydrogen has been developed in the last few years. Here we use this semi-analytical theory and specialise our predictions to the case of the Tycho supernova shock, where there is evidence from gamma ray observations that the spectrum of the parent cosmic rays is steeper than expected from the traditional theory of diffusive shock acceleration. We show that, if the fraction of neutral hydrogen in the vicinity of the Tycho supernova shock is, as suggested by observations, $\sim 70-90\%$, then spectra of accelerated protons steeper than $p^{-4}$ may be a natural consequence of charge exchange reactions and the associated neutral return flux. The spectral shape is affected by this phenomenon for particles with energies below $\sim 100-1000$ GeV, for which the diffusion length is smaller than or at most comparable with the pathlength of charge exchange and ionisation upstream of the shock.

The HARPS search for southern extra-solar planets. XXXIX. HD175607 b, the most metal-poor G dwarf with an orbiting sub-Neptune

Context. The presence of a small-mass planet (M$_p<$0.1\,M$_{Jup}$) seems, to date, not to depend on metallicity, however, theoretical simulations have shown that stars with subsolar metallicities may be favoured for harbouring smaller planets. A large, dedicated survey of metal-poor stars with the HARPS spectrograph has thus been carried out to search for Neptunes and super-Earths. Aims. In this paper, we present the analysis of \object{HD175607}, an old G6 star with metallicity [Fe/H] = -0.62. We gathered 119 radial velocity measurements in 110 nights over a time span of more than nine years. Methods. The radial velocities were analysed using Lomb-Scargle periodograms, a genetic algorithm, a Markov chain Monte Carlo analysis, and a Gaussian processes analysis. The spectra were also used to derive stellar properties. Several activity indicators were analysed to study the effect of stellar activity on the radial velocities. Results. We find evidence for the presence of a small Neptune-mass planet (M$_{p}\sin i = 8.98\pm1.10$\,M$_{\oplus}$) orbiting this star with an orbital period $P = 29.01\pm0.02$\, days in a slightly eccentric orbit ($e=0.11\pm0.08$). The period of this Neptune is close to the estimated rotational period of the star. However, from a detailed analysis of the radial velocities together with the stellar activity, we conclude that the best explanation of the signal is indeed the presence of a planetary companion rather than stellar related. An additional longer period signal ($P\sim 1400$\,d) is present in the data, for which more measurements are needed to constrain its nature and its properties. Conclusions. HD\,175607 is the most metal-poor FGK dwarf with a detected low-mass planet amongst the currently known planet hosts. This discovery may thus have important consequences for planet formation and evolution theories.

The Ch-class asteroids: Connecting a visible taxonomic class to a 3-{\mu}m band shape

Asteroids belonging to the Ch spectral taxonomic class are defined by the presence of an absorption near 0.7 {\mu}m, which is interpreted as due to Fe-bearing phyllosilicates. Phyllosilicates also cause strong absorptions in the 3-{\mu}m region, as do other hydrated and hydroxylated minerals and H2O ice. Over the past decade, spectral observations have revealed different 3-{\mu}m band shapes the asteroid population. Although a formal taxonomy is yet to be fully established, the "Pallas-type" spectral group is most consistent with the presence of phyllosilicates. If Ch class and Pallas type are both indicative of phyllosilicates, then all Ch-class asteroids should also be Pallas-type. In order to test this hypothesis, we obtained 42 observations of 36 Ch-class asteroids in the 2- to 4-{\mu}m spectral region. We found that 88% of the spectra have 3-{\mu}m band shapes most consistent with the Pallas-type group. This is the first asteroid class for which such a strong correlation has been found. Because the Ch class is defined by the presence of an absorption near 0.7 {\mu}m, this demonstrates that the 0.7-{\mu}m band serves not only as a proxy for the presence of a band in the 3-{\mu}m region, but specifically for the presence of Pallas-type bands. There is some evidence for a correlation between band depth at 2.95 {\mu}m and absolute magnitude and/or albedo. However, we find only weak correlations between 2.95-{\mu}m band depth and semi-major axis. The connection between band depths in the 0.7- and 3-{\mu}m regions is complex and in need of further investigation.

The Ch-class asteroids: Connecting a visible taxonomic class to a 3-{\mu}m band shape [Replacement]

Asteroids belonging to the Ch spectral taxonomic class are defined by the presence of an absorption near 0.7 {\mu}m, which is interpreted as due to Fe-bearing phyllosilicates. Phyllosilicates also cause strong absorptions in the 3-{\mu}m region, as do other hydrated and hydroxylated minerals and H2O ice. Over the past decade, spectral observations have revealed different 3-{\mu}m band shapes the asteroid population. Although a formal taxonomy is yet to be fully established, the "Pallas-type" spectral group is most consistent with the presence of phyllosilicates. If Ch class and Pallas type are both indicative of phyllosilicates, then all Ch-class asteroids should also be Pallas-type. In order to test this hypothesis, we obtained 42 observations of 36 Ch-class asteroids in the 2- to 4-{\mu}m spectral region. We found that 88% of the spectra have 3-{\mu}m band shapes most consistent with the Pallas-type group. This is the first asteroid class for which such a strong correlation has been found. Because the Ch class is defined by the presence of an absorption near 0.7 {\mu}m, this demonstrates that the 0.7-{\mu}m band serves not only as a proxy for the presence of a band in the 3-{\mu}m region, but specifically for the presence of Pallas-type bands. There is some evidence for a correlation between band depth at 2.95 {\mu}m and absolute magnitude and/or albedo. However, we find only weak correlations between 2.95-{\mu}m band depth and semi-major axis. The connection between band depths in the 0.7- and 3-{\mu}m regions is complex and in need of further investigation.

Mono-jet, -photon and -Z Signals of a Supersymmetric (B-L) model at the Large Hadron Collider

Search for invisible final states produced at the Large Hadron Collider (LHC) by new physics scenarios are normally carried out resorting to a variety of probes emerging from the initial state, in the form of single-jet, -photon and -$Z$ boson signatures. These are particularly effective for models of Supersymmetry (SUSY) in presence of $R$-parity conservation, owing to the presence in their spectra of a stable neutralino as dark matter candidate. We assume here as theoretical framework Supersymmetric ($B-L$) extension of the Standard Model (BLSSM), wherein a mediator for invisible decays can be $Z'$ boson. The peculiarity of the signal is thus that the final state objects carry a very large (transverse) missing energy, since the $Z'$ is naturally massive and constrained by direct searches and electro-weak precision tests to be at least in TeV scale region. Under these circumstances the efficiency in accessing the invisible final state and rejecting the standard model background is very high. This somehow compensates the rather meagre production rates. Another special feature of this invisible BLSSM signal is its composition, which is often dominated by sneutrino decays (alongside the more traditional neutrino and neutralino modes). Sensitivity of the CERN machine to these two features can therefore help disentangling the BLSSM from more popular SUSY models. We assess in this analysis the scope of the LHC in establishing the aforementioned invisible signals through a sophisticated signal-to-background simulation carried out in presence of parton shower, hadronisation and detector effects. We find that significant sensitivity exists already after 300 fb$^{-1}$ during Run 2. We find that mono-jet events can be readily accessible at the LHC, so as to enable one to claim a prompt discovery, while mono-photon and -$Z$ signals can be used as diagnostic tools of the underlying scenario.

Boundary effects on radiative processes of two entangled atoms [Cross-Listing]

We analyze radiative processes of a quantum system composed by two identical two-level atoms interacting with a massless scalar field prepared in the vacuum state in the presence of perfect reflecting flat boundaries. We consider that the atoms are prepared in a stationary maximally entangled state. We investigate the spontaneous transition rates from the entangled states to its collective ground state induced by vacuum fluctuations. In the empty-space case, the spontaneous decay rates can be enhanced or inhibited depending on the specific entangled state and changes with the distance between the atoms. Next, we consider the presence of perfect mirrors and impose Dirichlet boundary conditions on such surfaces. In the presence of a single boundary the transition rate for the symmetric state undergoes a strong reduction, whereas for the antisymmetric state our results indicate a slightly enhancement. For completeness we also investigate the case of two perfect mirrors.

Boundary effects on radiative processes of two entangled atoms [Replacement]

We analyze radiative processes of a quantum system composed by two identical two-level atoms interacting with a massless scalar field prepared in the vacuum state in the presence of perfect reflecting flat boundaries. We consider that the atoms are prepared in a stationary maximally entangled state. We investigate the spontaneous transition rates from the entangled states to its collective ground state induced by vacuum fluctuations. In the empty-space case, the spontaneous decay rates can be enhanced or inhibited depending on the specific entangled state and changes with the distance between the atoms. Next, we consider the presence of perfect mirrors and impose Dirichlet boundary conditions on such surfaces. In the presence of a single boundary the transition rate for the symmetric state undergoes a strong reduction, whereas for the antisymmetric state our results indicate a slightly enhancement. For completeness we also investigate the case of two perfect mirrors.

Chern--Simons--Yang--Mills system in presence of Gribov horizon with fundamental Higgs matter

In this work we study the behaviour of Yang--Mills--Chern--Simons theory coupled to a Higgs field in the fundamental representation by taking into account the effects of the presence of the Gribov horizon. By analyzing the infrared structure of the gauge field propagator, both confined and de-confined regions can be detected. The confined region corresponds to the appearance of complex poles in the propagators, while the de-confined one to the presence of real poles. One can move from one region to another by changing the parameters of the theory.

Hydrogen recombination in the early Universe in the presence of a magnetic field

Hydrogen recombination in the early Universe in the presence of a magnetic field is studied. An equation for the temperature of recombination in the presence of a magnetic field is derived. Limiting cases of weak and strong fields are considered. It is demonstrated that there exists a critical magnetic field, above which the system stays in the phase of atomic hydrogen for all temperatures. The relative shift of the temperature of recombination in the presence of a magnetic field is estimated and it is demonstrated that this shift is small.

Hydrogen recombination in the early Universe in the presence of a magnetic field [Cross-Listing]

Hydrogen recombination in the early Universe in the presence of a magnetic field is studied. An equation for the temperature of recombination in the presence of a magnetic field is derived. Limiting cases of weak and strong fields are considered. It is demonstrated that there exists a critical magnetic field, above which the system stays in the phase of atomic hydrogen for all temperatures. The relative shift of the temperature of recombination in the presence of a magnetic field is estimated and it is demonstrated that this shift is small.

First discovery of a magnetic field in a main sequence delta Scuti star: the Kepler star HD188774

The Kepler space mission provided a wealth of {\delta} Sct-{\gamma} Dor hybrid candidates. While some may be genuine hybrids, others might be misclassified due to the presence of a binary companion or to rotational modulation caused by magnetism and related surface inhomogeneities. In particular, the Kepler {\delta} Sct-{\gamma} Dor hybrid candidate HD 188774 shows a few low frequencies in its light and radial velocity curves, whose origin is unclear. In this work, we check for the presence of a magnetic field in HD 188774. We obtained two spectropolarimetric measurements with ESPaDOnS at CFHT. The data were analysed with the least squares deconvolution method. We detected a clear magnetic signature in the Stokes V LSD profiles. The origin of the low frequencies detected in HD 188774 is therefore most probably the rotational modulation of surface spots possibly related to the presence of a magnetic field. Consequently, HD 188774 is not a genuine hybrid {\delta} Sct-{\gamma} Dor star, but the first known magnetic main sequence {\delta} Sct star. This makes it a prime target for future asteroseismic and spot modelling. This result casts new light on the interpretation of the Kepler results for other {\delta} Sct-{\gamma} Dor hybrid candidates.

Dynamical Heating Induced by Dwarf Planets on Cold Kuiper Belt-like Debris Disks

With the use of long-term numerical simulations, we study the evolution and orbital behavior of cometary nuclei in cold Kuiper belt-like debris disks under the gravitational influence of dwarf planets (DPs); we carry out these simulations with and without the presence of a Neptune-like giant planet. This exploratory study shows that in the absence of a giant planet, 10 DPs are enough to induce strong radial and vertical heating on the orbits of belt particles. On the other hand, the presence of a giant planet close to the debris disk, acts as a stability agent reducing the radial and vertical heating. With enough DPs, even in the presence of a Neptune-like giant planet some radial heating remains; this heating grows steadily, re-filling resonances otherwise empty of cometary nuclei. Specifically for the solar system, this secular process seems to be able to provide material that, through resonant chaotic diffusion, increase the rate of new comets spiraling into the inner planetary system, but only if more than the $\sim10$ known DP sized objects exist in the trans-Neptunian region.

Timelike geodesics of a modified gravity black hole immersed in an axially symmetric magnetic field

We investigate the dynamics of a neutral and a charged particle around a black hole in modified gravity immersed in magnetic field. Our focus is on the scalar-tensor-vector theory as modified gravity. We are interested to explore the conditions on the energy of the particle under which it can escape to infinity after collision with another neutral particle in the vicinity of the black hole. We calculate escape velocity of particle orbiting in the innermost stable circular orbit (ISCO) after the collision. We study the effects of modified gravity on the dynamics of particles. Further we discuss how the presence of magnetic field in the vicinity of black hole, effects the motion of the orbiting particle. We show that the stability of ISCO increases due to presence of magnetic field. It is observed that a particle can go arbitrary close to the black hole due to presence of magnetic field. Furthermore ISCO for black hole is more stable as compared with Schwarzschild black hole. We also discuss the Lyapunov exponent and the effective force acting on the particle in the presence of magnetic field.

IKT 16: the first X-ray confirmed composite SNR in the SMC

Aims: IKT 16 is an X-ray and radio-faint supernova remnant (SNR) in the Small Magellanic Cloud (SMC). A detailed X-ray study of this SNR with XMM-Newton confirmed the presence of a hard X-ray source near its centre, indicating the detection of the first composite SNR in the SMC. With a dedicated Chandra observation we aim to resolve the point source and confirm its nature. We also acquire new ATCA observations of the source at 2.1 GHz with improved flux density estimates and resolution. Methods: We perform detailed spatial and spectral analysis of the source. With the highest resolution X-ray and radio image of the centre of the SNR available today, we resolve the source and confirm its pulsar wind nebula (PWN) nature. Further, we constrain the geometrical parameters of the PWN and perform spectral analysis for the point source and the PWN separately. We also test for the radial variations of the PWN spectrum and its possible east west asymmetry. Results: The X-ray source at the centre of IKT 16 can be resolved into a symmetrical elongated feature centering a point source, the putative pulsar. Spatial modeling indicates an extent of 5.2 arcsec of the feature with its axis inclined at 82 degree east from north, aligned with a larger radio feature consisting of two lobes almost symmetrical about the X-ray source. The picture is consistent with a PWN which has not yet collided with the reverse shock. The point source is about three times brighter than the PWN and has a hard spectrum of spectral index 1.1 compared to a value 2.2 for the PWN. This points to the presence of a pulsar dominated by non-thermal emission. The expected E_{dot} is ~ 10^37 erg s^-1 and spin period < 100 ms. However, the presence of a compact nebula unresolved by Chandra at the distance of the SMC cannot completely be ruled out.

Gravitational Lensing in Plasmic Medium [Cross-Listing]

The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.

Gravitational Lensing in Plasmic Medium

The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.

Optical properties of black hole in the presence of plasma: shadow [Replacement]

We have studied photon motion around axially symmetric rotating Kerr black hole in the presence of plasma with radial power-law density. It is shown that in the presence of plasma the observed shape and size of shadow changes depending on i) plasma parameters, ii) black hole spin and iii) inclination angle between observer plane and axis of rotation of black hole. In order to extract pure effect of plasma influence on black hole image the particular case of the Schwarzschild black hole has also been investigated and it has been shown that i) the photon sphere around the spherical symmetric black hole is left unchanged under the plasma influence, ii) however the Schwarzschild black hole shadow size in plasma is reduced due to the refraction of the electromagnetic radiation in plasma environment of black hole. The study of the energy emission from the black hole in plasma shows that in the presence of plasma the maximal energy emission rate from the black hole decreases.

Optical properties of black hole in the presence of plasma: shadow [Replacement]

We have studied photon motion around axially symmetric rotating Kerr black hole in the presence of plasma with radial power-law density. It is shown that in the presence of plasma the observed shape and size of shadow changes depending on i) plasma parameters, ii) black hole spin and iii) inclination angle between observer plane and axis of rotation of black hole. In order to extract pure effect of plasma influence on black hole image the particular case of the Schwarzschild black hole has also been investigated and it has been shown that i) the photon sphere around the spherical symmetric black hole is left unchanged under the plasma influence, ii) however the Schwarzschild black hole shadow size in plasma is reduced due to the refraction of the electromagnetic radiation in plasma environment of black hole. The study of the energy emission from the black hole in plasma shows that in the presence of plasma the maximal energy emission rate from the black hole decreases.

Signature of the presence of a third body orbiting around XB 1916-053

The ultra-compact dipping source \object{XB 1916-053} has an orbital period of close to 50 min and a companion star with a very low mass (less than 0.1 M$_{\odot}$). The orbital period derivative of the source was estimated to be $1.5(3) \times 10^{-11}$ s/s through analysing the delays associated with the dip arrival times obtained from observations spanning 25 years, from 1978 to 2002. The known orbital period derivative is extremely large and can be explained by invoking an extreme, non-conservative mass transfer rate that is not easily justifiable. We extended the analysed data from 1978 to 2014, by spanning 37 years, to verify whether a larger sample of data can be fitted with a quadratic term or a different scenario has to be considered. We obtained 27 delays associated with the dip arrival times from data covering 37 years and used different models to fit the time delays with respect to a constant period model.We find that the quadratic form alone does not fit the data. The data are well fitted using a sinusoidal term plus a quadratic function or, alternatively, with a series of sinusoidal terms that can be associated with a modulation of the dip arrival times due to the presence of a third body that has an elliptical orbit. We infer that for a conservative mass transfer scenario the modulation of the delays can be explained by invoking the presence of a third body with mass between 0.10-0.14 M$_{\odot}$, orbital period around the X-ray binary system of close to 51 yr and an eccentricity of $0.28 \pm 0.15$. In a non-conservative mass transfer scenario we estimate that the fraction of matter yielded by the degenerate companion star and accreted onto the neutron star is $\beta = 0.08$, the neutron star mass is $\ge 2.2$ M$_{\odot}$, and the companion star mass is 0.028 M$_{\odot}$. (Abridged)

Enhancing the Cosmic Shear Power Spectrum

Applying a transformation to a non-Gaussian field can enhance the information content of the resulting power spectrum, by reducing the correlations between Fourier modes. In the context of weak gravitational lensing, it has been shown that this gain in information content is significantly compromised by the presence of shape noise. We apply clipping to mock convergence fields, a technique which is known to be robust in the presence of noise and has been successfully applied to galaxy number density fields. When analysed in isolation the resulting convergence power spectrum returns degraded constraints on cosmological parameters. However substantial gains can be achieved by performing a combined analysis of the power spectra derived from both the original and transformed fields. Even in the presence of realistic levels of shape noise, we demonstrate that this approach is capable of reducing the area of likelihood contours within the $\Omega_m - \sigma_8$ plane by more than a factor of three.

Enhancing the Cosmic Shear Power Spectrum [Replacement]

Applying a transformation to a non-Gaussian field can enhance the information content of the resulting power spectrum, by reducing the correlations between Fourier modes. In the context of weak gravitational lensing, it has been shown that this gain in information content is significantly compromised by the presence of shape noise. We apply clipping to mock convergence fields, a technique which is known to be robust in the presence of noise and has been successfully applied to galaxy number density fields. When analysed in isolation the resulting convergence power spectrum returns degraded constraints on cosmological parameters. However substantial gains can be achieved by performing a combined analysis of the power spectra derived from both the original and transformed fields. Even in the presence of realistic levels of shape noise, we demonstrate that this approach is capable of reducing the area of likelihood contours within the $\Omega_m - \sigma_8$ plane by more than a factor of three.

No evidence for activity correlations in the radial velocities of Kapteyn's star

Stellar activity may induce Doppler variability at the level of a few m/s which can then be confused by the Doppler signal of an exoplanet orbiting the star. To first order, linear correlations between radial velocity measurements and activity indices have been proposed to account for any such correlation. The likely presence of two super-Earths orbiting Kapteyn's star was reported in Anglada et al. (2014, MNRAS 443L, 89A), but this claim was recently challenged by Robertson et al. (2015, ApJ 805L, 22R) arguing evidence of a rotation period (143 days) at three times the orbital period of one of the proposed planets (Kapteyn's b, P=48.6 days), and the existence of strong linear correlations between its Doppler signal and activity data. By re-analyzing the data using global optimization methods and model comparison, we show that such claim is incorrect given that; 1) the choice of a rotation period at 143 days is unjustified, and 2) the presence of linear correlations is not supported by the data. We conclude that the radial velocity signals of Kapteyn's star remain more simply explained by the presence of two super-Earth candidates orbiting it. We also advocate for the use of global optimization procedures and objective arguments, instead of claims lacking of a minimal statistical support.

Imprint of inflation on galaxy shape correlations [Replacement]

We show that intrinsic (not lensing-induced) correlations between galaxy shapes offer a new probe of primordial non-Gaussianity and inflationary physics which is complementary to galaxy number counts. Specifically, intrinsic alignment correlations are sensitive to an anisotropic squeezed limit bispectrum of the primordial perturbations. Such a feature arises in solid inflation, as well as more broadly in the presence of light higher spin fields during inflation (as pointed out recently by Arkani-Hamed and Maldacena). We present a derivation of the all-sky two-point correlations of intrinsic shapes and number counts in the presence of non-Gaussianity with general angular dependence, and show that a quadrupolar (spin-2) anisotropy leads to the analog in galaxy shapes of the well-known scale-dependent bias induced in number counts by isotropic (spin-0) non-Gaussianity. Moreover, in presence of non-zero anisotropic non-Gaussianity, the quadrupole of galaxy shapes becomes sensitive to far superhorizon modes. These effects come about because long-wavelength modes induce a local anisotropy in the initial power spectrum, with which galaxies will correlate. We forecast that future imaging surveys could provide constraints on the amplitude of anisotropic non-Gaussianity that are comparable to those from the Cosmic Microwave Background (CMB). These are complementary as they probe different physical scales. The constraints, however, depend on the sensitivity of galaxy shapes to the initial conditions which we only roughly estimate from observed tidal alignments.

Imprint of inflation on galaxy shape correlations

We show that intrinsic (not lensing-induced) correlations between galaxy shapes offer a new probe of primordial non-Gaussianity and inflationary physics which is complementary to galaxy number counts. Specifically, intrinsic alignment correlations are sensitive to an anisotropic squeezed limit bispectrum of the primordial perturbations. Such a feature arises in solid inflation, as well as more broadly in the presence of light higher spin fields during inflation (as pointed out recently by Arkani-Hamed and Maldacena). We present a derivation of the all-sky two-point correlations of intrinsic shapes and number counts in the presence of non-Gaussianity with general angular dependence, and show that a quadrupolar (spin-2) anisotropy leads to the analog in galaxy shapes of the well-known scale-dependent bias induced in number counts by isotropic (spin-0) non-Gaussianity. Moreover, in presence of non-zero anisotropic non-Gaussianity, the quadrupole of galaxy shapes becomes sensitive to far superhorizon modes. These effects come about because long-wavelength modes induce a local anisotropy in the initial power spectrum, with which galaxies will correlate. We forecast that future imaging surveys could provide constraints on the amplitude of anisotropic non-Gaussianity that are comparable to those from the Cosmic Microwave Background (CMB). These are complementary as they probe different physical scales. The constraints, however, depend on the sensitivity of galaxy shapes to the initial conditions which we only roughly estimate from observed tidal alignments.

Higher dimensional dilaton black holes in the presence of exponential nonlinear electrodynamics

We examine the higher dimensional action in which gravity is coupled to the exponential nonlinear electrodynamic and a scalar dilaton field. We construct a new class of $n$-dimensional static and spherically symmetric black hole solutions of this theory in the presence of the dilaton potential with two Liouville-type terms. In the presence of two Liouville-type dilaton potential, the asymptotic behavior of the obtained black holes are neither flat nor (A)dS. Due to the nonlinear nature of electrodynamic field, the electric field has finite value near the origin where $r\rightarrow0$ and goes to zero as $r\rightarrow\infty$. Interestingly enough, we find that in the absence of the dilaton field, the electric field has a finite value at $r=0$, while as soon as the dilaton field is taken into account, the electric field diverges as $r\rightarrow 0$. This implies that the presence of the dilaton field changes the behaviour of the electric field near the origin. In the limiting case where the nonlinear parameter $\beta$ goes to infinity, our solutions reduce to dilaton black holes of Einstein-Maxwell-dilaton gravity in higher dimensions. We compute the conserved and thermodynamic quantities of the solutions and show that these quantities satisfy the first law of black holes thermodynamics on the horizon.

Possible scenarios that the New Horizons spacecraft may find in its close encounter with Pluto

Next year, 2015, the New Horizons spacecraft will have a close encounter with Pluto. In the present study we discuss some possibilities regarding what the spacecraft may encounter during its approach to Pluto. Among them we should include: the presence of geological activity due to heat generated by tides; the unlikely presence of an intrinsic magnetic field; the possibility of a plasmasphere and a plasmapause; the position of an ionopause; the existence of an ionospheric trans-terminator flow similar to that at Venus and Mars; and the presence of a Magnus force that produces a deflection of Pluto plasma wake. This deflection oscillates up and down in its orbit around the sun.

The telegraph approximation for focused cosmic-ray transport in the presence of boundaries [Cross-Listing]

Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term. Analytical and numerical solutions of illustrative boundary problems are presented. The applicability and accuracy of the telegraph approximation for focused cosmic-ray transport in the presence of boundaries are discussed, and potential applications to modeling cosmic-ray transport are noted.

Peculiarities of massive vectormesons and their zero mass limits [Replacement]

Massive QED, in contrast with its massless counterpart, possesses two conserved charges; one is a screened (vanishing) Maxwell charge which is directly associated with the massive vector mesons through the identically conserved Maxwell current, while the presence of a particle-antiparticle counting charge depends on the matter . A somewhat peculiar situation arises for couplings of Hermitian matter fields to massive vector potentials; in that case the only current is the screened Maxwell current and the coupling disappears in the massless limit. In case of selfinteracting massive vector mesons the situation becomes even more peculiar in that the usually renormalizability guaranteeing validity of the first order power-counting criterion breaks down in second order and requires the compensatory presence of additional Hermitian H-fields. Some aspect of these observation have already been noticed in the BRST gauge theoretic formulation, but here we use a new setting based on string-local vector mesons which is required by Hilbert space positivity ("off-shell unitarity"). This new formulation explains why spontaneous symmetry breaking cannot occur in the presence of higher spin fields. The coupling to H-fields induces Mexican hat like selfinteractions; they are not imposed but rather consequences of the foundational causal localization properties realized in a Hilbert space setting. In case of selfinteracting massive vectormesons their presence is required in order to maintain the first order power-counting restriction of renormalizability also in second order. The presentation of the new Hilbert space setting for vector mesons which replaces gauge theory is the main motivation for this work.

Peculiarities of massive vectormesons and their zero mass limits [Replacement]

Massive QED, in contrast with its massless counterpart, possesses two conserved charges; one is a screened (vanishing) Maxwell charge which is directly associated with the massive vector mesons through the identically conserved Maxwell current, while the presence of a particle-antiparticle counting charge depends on the matter . A somewhat peculiar situation arises for couplings of Hermitian matter fields to massive vector potentials; in that case the only current is the screened Maxwell current and the coupling disappears in the massless limit. In case of selfinteracting massive vector mesons the situation becomes even more peculiar in that the usually renormalizability guaranteeing validity of the first order power-counting criterion breaks down in second order and requires the compensatory presence of additional Hermitian H-fields. Some aspect of these observation have already been noticed in the BRST gauge theoretic formulation, but here we use a new setting based on string-local vector mesons which is required by Hilbert space positivity ("off-shell unitarity"). This new formulation explains why spontaneous symmetry breaking cannot occur in the presence of higher spin fields. The coupling to H-fields induces Mexican hat like selfinteractions; they are not imposed but rather consequences of the foundational causal localization properties realized in a Hilbert space setting. In case of selfinteracting massive vectormesons their presence is required in order to maintain the first order power-counting restriction of renormalizability also in second order. The presentation of the new Hilbert space setting for vector mesons which replaces gauge theory is the main motivation for this work.

On the stability of gravity with Dirichlet walls

Dirichlet walls -- timelike boundaries at finite distance from the bulk on which the induced metric is held fixed -- have been used to model AdS spacetimes with a finite cutoff. In the context of gauge/gravity duality, such models are often described as dual to some novel UV-cufoff version of a corresponding CFT that maintains local Lorentz invariance. We study linearized gravity in the presence of such a wall and find it to differ significantly from the seemingly-analogous case of Dirichlet boundary conditions for fields of spins zero and one. In particular, using the Kodama-Ishibashi formalism, the boundary condition that must be imposed on scalar-sector master field with harmonic time dependence depends explicitly on their frequency. That this feature first arises for spin-2 appears to be related to the second-order nature of the equations of motion. It gives rise to a number of novel instabilities, though both global and planar Anti-de Sitter remain (linearly) stable in the presence of large-radius Dirichlet cutoffs. The instabilities arise on the outside of spherical Dirichlet walls, and also inside sufficiently large such spherical walls in de Sitter space. We analyze both inside and outside of flat and spherical walls in Minkowski, de Sitter, and anti-de Sitter space, as well as in certain black hole spacetimes and find stability for cases not mentioned above. In particular, we find no linear instabilities in the presence of flat walls. We also find evidence supporting the conjecture that neutral black holes are repelled by Dirichlet walls.

Evidence for Early Filamentary Accretion from the Andromeda Galaxy's Thin Plane of Satellites

Recently it has been shown that a large fraction of the dwarf satellite galaxies orbiting the Andromeda galaxy are surprisingly aligned in a thin, extended and kinematically coherent planar structure. The presence of such a structure seems to challenge the current Cold Dark Matter paradigm of structure formation, which predicts a more uniform distribution of satellites around central objects. We show that it is possible to obtain a thin, extended, rotating plane of satellites resembling the one in Andromeda in cosmological collisionless simulations based on the Cold Dark Matter model. Our new high resolution simulations show a correlation between the formation time of the dark matter halo and the thickness of the plane of satellites. Our simulations have a high incidence of satellite planes as thin, extended, and as rich as the one in Andromeda and with a very coherent kinematic structure when we select high concentration/early forming halos. By tracking the formation of the satellites in the plane we show that they have been mainly accreted onto the main object along thin dark matter filaments at high redshift. Our results show that the presence of a thin, extended, rotating plane of satellites is not a challenge for the Cold Dark Matter paradigm, but actually supports one of the predictions of this paradigm related to the presence of filaments of dark matter around galaxies at high redshift.

Evidence for Early Filamentary Accretion from the Andromeda Galaxy's Thin Plane of Satellites [Replacement]

Recently it has been shown that a large fraction of the dwarf satellite galaxies orbiting the Andromeda galaxy are surprisingly aligned in a thin, extended and kinematically coherent planar structure. The presence of such a structure seems to challenge the current Cold Dark Matter paradigm of structure formation, which predicts a more uniform distribution of satellites around central objects. We show that it is possible to obtain a thin, extended, rotating plane of satellites resembling the one in Andromeda in cosmological collisionless simulations based on the Cold Dark Matter model. Our new high resolution simulations show a correlation between the formation time of the dark matter halo and the thickness of the plane of satellites. Our simulations have a high incidence of satellite planes as thin, extended, and as rich as the one in Andromeda and with a very coherent kinematic structure when we select high concentration/early forming halos. By tracking the formation of the satellites in the plane we show that they have been mainly accreted onto the main object along thin dark matter filaments at high redshift. Our results show that the presence of a thin, extended, rotating plane of satellites is not a challenge for the Cold Dark Matter paradigm, but actually supports one of the predictions of this paradigm related to the presence of filaments of dark matter around galaxies at high redshift.

Discovery of blue companions to two southern Cepheids: WW Car and FN Vel

A large number of high-dispersion spectra of classical Cepheids were obtained in the region of the CaII H+K spectral lines. The analysis of these spectra allowed us to detect the presence of a strong Balmer line, H$\epsilon$, for several Cepheids, interpreted as the signature of a blue companion: the presence of a sufficiently bright blue companion to the Cepheid results in a discernible strengthening of the CaII H + Hepsilon line relative to the CaII K line. We investigated 103 Cepheids, including those with known hot companions (B5-B6 main-sequence stars) in order to test the method. We could confirm the presence of a companion to WW Car and FN Vel (the existence of the former was only suspected before) and we found that these companions are blue hot stars. The method remains efficient when the orbital velocity changes in a binary system cannot be revealed and other methods of binarity detection are not efficient.

Anisotropic Propagator for the Goldstone Modes in Color-flavor Locked Phase in the Presence of a Magnetic Field

We consider the phase diagram of QCD at very high baryon density and at zero temperature in the presence of a strong magnetic field. The state of matter at such high densities and low temperatures is believed to be a phase known as the color-flavor locked phase which breaks color and electromagnetic gauge invariance leaving a linear combination of them unbroken. Of the 9 quarks (three flavors and three colors), five are neutral under this unbroken generator and four are oppositely charged. In the presence of a magnetic field corresponding to the unbroken generator however, the properties of the condensate changes and a new phase known as the magnetic color flavor locked (MCFL)phase is realized. This phase breaks some of the color-flavor symmetry of the Lagrangian spontaneously, giving rise to 6 Goldstone modes, 5 of which are pseudo Goldstone modes. These Goldstone modes are composed of excitations that correspond to both neutral quarks and charged quarks. Hence it is natural to expect that the propagators of these Goldstone modes get affected in the presence of a magnetic field and their speed becomes considerably anisotropic. Although this anisotropy is self-evident from symmetry arguments, it has not been quantified yet. We calculate this anisotropy in the speed of the Goldstone modes using an NJL model type of interaction between the quarks and comment on the impact of such anisotropic modes on the transport properties of the MCFL phase.

Anisotropic Propagator for the Goldstone Modes in Color-flavor Locked Phase in the Presence of a Magnetic Field [Cross-Listing]

We consider the phase diagram of QCD at very high baryon density and at zero temperature in the presence of a strong magnetic field. The state of matter at such high densities and low temperatures is believed to be a phase known as the color-flavor locked phase which breaks color and electromagnetic gauge invariance leaving a linear combination of them unbroken. Of the 9 quarks (three flavors and three colors), five are neutral under this unbroken generator and four are oppositely charged. In the presence of a magnetic field corresponding to the unbroken generator however, the properties of the condensate changes and a new phase known as the magnetic color flavor locked (MCFL)phase is realized. This phase breaks some of the color-flavor symmetry of the Lagrangian spontaneously, giving rise to 6 Goldstone modes, 5 of which are pseudo Goldstone modes. These Goldstone modes are composed of excitations that correspond to both neutral quarks and charged quarks. Hence it is natural to expect that the propagators of these Goldstone modes get affected in the presence of a magnetic field and their speed becomes considerably anisotropic. Although this anisotropy is self-evident from symmetry arguments, it has not been quantified yet. We calculate this anisotropy in the speed of the Goldstone modes using an NJL model type of interaction between the quarks and comment on the impact of such anisotropic modes on the transport properties of the MCFL phase.

Four Dimensional Supersymmetric Theories in Presence of a Boundary

In this paper, we study $\mathcal{N} =1$ supersymmetric theories in four dimensions in presence of a boundary. We demonstrate that it is possible to preserve half the supersymmetry of the original theory by suitably modifying it in presence of a boundary. This is done by adding new boundary terms to the original action, such that the supersymmetric variation of the new terms exactly cancels the boundary terms generated by the supersymmetric transformation of the original bulk action. We also analyze the boundary projections of such supercharges used in such a theory. Finally, we study super-Yang-Mills theories in presence of a boundary using these results. We explicitly construct the action for the modified super-Yang-Mills theory, which preserves half the supersymmetry of the original theory, in presence of a boundary.

Four Dimensional Supersymmetric Theories in Presence of a Boundary [Replacement]

In this paper, we study $\mathcal{N} =1$ supersymmetric theories in four dimensions in presence of a boundary. We demonstrate that it is possible to preserve half the supersymmetry of the original theory by suitably modifying it in presence of a boundary. This is done by adding new boundary terms to the original action, such that the supersymmetric variation of the new terms exactly cancels the boundary terms generated by the supersymmetric transformation of the original bulk action. We also analyze the boundary projections of such supercharges used in such a theory. We study super-Yang-Mills theories in presence of a boundary using these results. Finally, we study the Born-Infeld action in presence of a boundary. We analyse the boundary effects for the Born-Infeld action coupled to a background dilaton and an axion field. We also analyse the boundary effects for an non-abelian Born-Infeld action. We explicitly construct the actions for these systems in presence of a boundary. This action preserves half of the original supersymmetry.

Non pertubative effects of local structure on the Hubble parameter in presence of a cosmological constant [Replacement]

In order to estimate the effects of local structure on the Hubble parameter we calculate the low-redshift expansion for $H(z)$ and $\frac{\delta H}{H}$ for an observer at the center of a spherically symmetric matter distribution in presence of a cosmological constant. We then test the accuracy of the formulae comparing them with fully relativistic non pertubative numerical calculations for different cases for the density profile. Our analytical approach does not involve perturbation theory, and is based on the use of exact solutions of Einstein's field equations. The formulae can be used to take into account the non linear effects on the Hubble expansion parameter due to the monopole component of the local structure. The physical implications and the relation with cosmic acceleration are discussed, both in presence and absence of the cosmological constant, respectively as non pertubative effects within the standard cosmological model or as constraints on inhomogeneous models as alternative to dark energy.

Non pertubative effects of local structure on the Hubble parameter in presence of a cosmological constant [Replacement]

In order to estimate the effects of local structure on the Hubble parameter we calculate the low-redshift expansion for $H(z)$ and $\frac{\delta H}{H}$ for an observer at the center of a spherically symmetric matter distribution in presence of a cosmological constant. We then test the accuracy of the formulae comparing them with fully relativistic non pertubative numerical calculations for different cases for the density profile. Our analytical approach does not involve perturbation theory, and is based on the use of exact solutions of Einstein's field equations. The formulae can be used to take into account the non linear effects on the Hubble expansion parameter due to the monopole component of the local structure. The physical implications and the relation with cosmic acceleration are discussed, both in presence and absence of the cosmological constant, respectively as non pertubative effects within the standard cosmological model or as constraints on inhomogeneous models as alternative to dark energy.

Searching for signatures of planet formation in stars with circumstellar debris discs

(Abridged) Tentative correlations between the presence of dusty debris discs and low-mass planets have been presented. In parallel, detailed chemical abundance studies have reported different trends between samples of planet and non-planet hosts. We determine in a homogeneous way the metallicity, and abundances of a sample of 251 stars including stars with known debris discs, with debris discs and planets, and only with planets. Stars with debris discs and planets have the same [Fe/H] behaviour as stars hosting planets, and they also show a similar <[X/Fe]>-Tc trend. Different behaviour in the <[X/Fe]>-Tc trend is found between the samples of stars without planets and the samples of planet hosts. In particular, when considering only refractory elements, negative slopes are shown in cool giant planet hosts, whilst positive ones are shown in stars hosting low-mass planets. Stars hosting exclusively close-in giant planets show higher metallicities and positive <[X/Fe]>-Tc slope. A search for correlations between the <[X/Fe]>-Tc slopes and the stellar properties reveals a moderate but significant correlation with the stellar radius and as well as a weak correlation with the stellar age. The fact that stars with debris discs and stars with low-mass planets do not show neither metal enhancement nor a different <[X/Fe]>-Tc trend might indicate a correlation between the presence of debris discs and the presence of low-mass planets. We extend results from previous works which reported differences in the <[X/Fe]>-Tc trends between planet hosts and non hosts. However, these differences tend to be present only when the star hosts a cool distant planet and not in stars hosting exclusively low-mass planets.

Cosmology in presence of dark energy in an emergent gravity scenario

We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence of dark energy. The background metric is taken to be Friedman-Lemaitre-Robertson-Walker (FLRW). We show that if $\dot\phi ^{2}$ is the dark energy density (in units of the critical density) then (a) for total energy density greater than the pressure (non-relativistic scenario, matter domination) the deceleration parameter $q(t)\approx\frac {1}{2} [1 + 27 \dot\phi ^{2}+...] > \frac{1}{2}$ (b) for total energy density equal to 3 times the pressure (relativistic case, radiation domination), the deceleration parameter $q(t)\approx 1 + 18\dot\phi ^{2} +... > 1$ and (c) for total energy density equal to the negative of the pressure (dark energy scenario), the deceleration parameter $q(t)< -1$. Our results indicate that many aspects of standard cosmology can be accommodated with the presence of dark energy right from the beginning of the universe where the time parameter $t\equiv \frac{t}{t_{0}}$, $t_{0}$ being the present epoch.


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# Magnetosome

Magnetite magnetosomes in Gammaproteobacteria strain SS-5. (A) Chain of highly elongated magnetosomes. (B) Part of a magnetosome chain. (C) The magnetosome in the lower right in (B), viewed along the ${\displaystyle \scriptstyle [1{\overline {1}}0]}$ direction, with its Fourier transform in the lower right.[1]

Magnetosome chains are membranous prokaryotic structures present in magnetotactic bacteria. They contain 15 to 20 magnetite crystals that together act like a compass needle to orient magnetotactic bacteria in geomagnetic fields, thereby simplifying their search for their preferred microaerophilic environments. Each magnetite crystal within a magnetosome is surrounded by a lipid bilayer, and specific soluble and transmembrane proteins are sorted to the membrane. Recent research has shown that magnetosomes are invaginations of the inner membrane and not freestanding vesicles.[2] Magnetite-bearing magnetosomes have also been found in eukaryotic magnetotactic algae, with each cell containing several thousand crystals.

Overall, magnetosome crystals have high chemical purity, narrow size ranges, species-specific crystal morphologies and exhibit specific arrangements within the cell. These features indicate that the formation of magnetosomes is under precise biological control and is mediated biomineralization.

Magnetotactic bacteria usually mineralize either iron oxide magnetosomes, which contain crystals of magnetite (Fe3O4), or iron sulfide magnetosomes, which contain crystals of greigite (Fe3S4). Several other iron sulfide minerals have also been identified in iron sulfide magnetosomes—including mackinawite (tetragonal FeS) and a cubic FeS—which are thought to be precursors of Fe3S4. One type of magnetotactic bacterium present at the oxic-anoxic transition zone (OATZ) of the southern basin of the Pettaquamscutt River Estuary, Narragansett, Rhode Island, United States is known to produce both iron oxide and iron sulfide magnetosomes.[3][4]

The particle morphology of magnetosome crystals varies, but is consistent within cells of a single magnetotactic bacterial species or strain. Three general crystal morphologies have been reported in magnetotactic bacteria on the basis: roughly cuboidal, elongated prismatic (roughly rectangular), and tooth-, bullet- or arrowhead-shaped.

Magnetosome crystals are typically 35–120 nm long, which makes them single-domain. Single-domain crystals have the maximum possible magnetic moment per unit volume for a given composition. Smaller crystals are superparamagnetic—that is, not permanently magnetic at ambient temperature, and domain walls would form in larger crystals. In most magnetotactic bacteria, the magnetosomes are arranged in one or more chains. Magnetic interactions between the magnetosome crystals in a chain cause their magnetic dipole moments to orient parallel to each other along the length of the chain. The magnetic dipole moment of the cell is usually large enough such that its interaction with Earth's magnetic field overcomes thermal forces that tend to randomize the orientation of the cell in its aqueous surroundings. Magnetotactic bacteria also use aerotaxis, a response to changes in oxygen concentration that favors swimming toward a zone of optimal oxygen concentration. In lakes or oceans the oxygen concentration is commonly dependent on depth. As long as the Earth's magnetic field has a significant downward slant, the orientation along field lines aids the search for the optimal concentration. This process is called magneto-aerotaxis.

While a single magnetosome chain would appear to be ideal for magneto-aerotaxis, a number of magnetotactic bacteria have magnetosomes or magnetosome arrangements that depart from the ideal.[5] One reported example includes large (up to 200 nm) magnetosomes found in coccoid cells in Brazil. These cells have enough magnetosomes so that the calculated magnetic dipole moment of the cell is about 250 times larger than that of a typical cell of Magnetospirillum magnetotacticum. There are also examples of magnetotactic bacteria that contain hundreds of magnetosomes, many more than required for orientation. One large, rod-shaped organism, Magnetobacterium bavaricum, contains up to 1000 bulletshaped magnetosomes arranged in several chains traversing the cell. Some bacteria have magnetosomes that are not arranged in chains, but are clustered on one side of the cell. In such an arrangement, the shape anisotropy of each crystal provides the stability against remagnetization, rather than the overall shape anisotropy in the magnetosome chain arrangement. These non-ideal arrangements may be pointing to additional, currently unknown functions of magnetosomes, possibly related to metabolism.

## References

1. ^ Pósfai, Mihály; Lefèvre, Christopher T.; Trubitsyn, Denis; Bazylinski, Dennis A.; Frankel, Richard B. (2013). "Phylogenetic significance of composition and crystal morphology of magnetosome minerals". Frontiers in Microbiology. 4. doi:10.3389/fmicb.2013.00344.
2. ^ Komeili, A., Zhuo Li and D. K. Newman "Magnetosomes Are Cell Membrane Invaginations Organized by the Actin-Like Protein MamK" Science, 311, Jan. 2006, p. 242-245
3. ^ Bazylizinki, D. A.; Heywood, B. R.; Mann, S.; Frankel, R. B. (1993). "Fe304 and Fe3S4 in a bacterium". Nature. 366 (6452): 218. Bibcode:1993Natur.366..218B. doi:10.1038/366218a0.
4. ^ Bazylinski, D. A.; Frankel, R. B.; Heywood, B. R.; Mann, S.; King, J. W.; Donaghay, P. L.; Hanson, A. K. (1995). "Controlled Biomineralization of Magnetite (Fe(inf3)O(inf4)) and Greigite (Fe(inf3)S(inf4)) in a Magnetotactic Bacterium". Applied and Environmental Microbiology. 61 (9): 3232–3239. PMC . PMID 16535116.
5. ^ R. Frankel "Biological Permanent Magnets" Hyperfine Interactions 151/152: 145–153, 2003


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# Fundamental thinking is required

Number Theory Level 2

Find the sum of all integers greater than 1 such that $$\frac{2^{n} + 1}{n^{2}}$$ is an integer

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GATE CSE 1998 Which of the following is an example of spooled device? GATE CSE 1996 The process state transition diagram in Figure is representative of ... GATE CSE 1996 Which scheduling policy is most suitable for a time-shared operating systems? GATE CSE 1995 ## Marks 2 More Which of the following standard C library functions will always invoke a system call when executed from a single-threade... GATE CSE 2021 Set 1 Consider the following set of processes, assumed to have arrived at time 0. Consider the CPU scheduling algorithms Short... GATE CSE 2020 Consider the following four processes with arrival times (in milliseconds) and their length of CPU bursts (in millisecon... GATE CSE 2019 Consider the following processes, with the arrival time and the length of the CPU burst given in milliseconds. The sched... GATE CSE 2016 Set 2 For the processes listed in the following table, which of the following scheduling schemes will give the lowest average ... 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# Peano on Wronskians: A Translation - On the Wronskians

Author(s):
Susannah M. Engdahl (Wittenberg University) and Adam E. Parker (Wittenberg University)

The addition of such a confusing footnote (Passage 4) certainly obscured the main point of Peano’s first article. He responded with a letter, part of which was published under the name Sur les Wronskiens in the same issue of Mathesis as the original note. The letter consists of three sections: in the first part, Peano argued that Mansion’s suggested language does not lead to a true statement; next, he presented another counterexample to the contested proposition which avoids the issue that at every point of the domain, at least one of the functions will evaluate to zero; finally, he referred to the above “proof” of Mansion’s proposition, and stated the most general theorem that can actually be proved using Mansion’s reasoning.

6. On the Wronskians (Excerpt from a letter by M.G. Peano). The note added to the end of my brief article on the Wronskians (Mathesis, p. 75-76), if it contributes to the clarity, it adds nothing to the rigor of the contested proposition; and I must return to the subject. I. The proposition I contest is the following: If the determinant formed with $$n$$ functions $$x_1,\dots, x_n$$ of the same variable $$t,$$ and their derivatives of orders $$1,\dots, (n-1)$$ is zero for all values of $$t,$$ there is between these functions a homogeneous linear relationship with constant coefficients; in other words, one can determine $$n$$ constants, $$C_1,\dots, C_n ,$$ all of which cannot equal zero at the same time, such that $$C_1 x_1+\cdots + C_n x_n =0$$ for all values of $$t.$$

He then particularly attacked the footnote (Passage 4) appended by Mansion to his previous article. He showed that adding the words “one of the functions is identically zero” (he quoted Mansion’s footnote) does not change the validity of the proposition at all. Lest readers would be confused by the way he phrased the proposition, Peano restated the (false) theorem in multiple ways, including a geometric argument similar to what he used to show that two functions were linearly independent.

If one of the functions, for example $$x_1,$$ is identically zero, these functions are connected by the linear relation $$x_1+0x_2 +\cdots +0x_n =0.$$ Thus the conclusion of the proposition in question is not at all modified if one adds the words: or one of the functions is identically zero. This proposition may again be expressed in this way: If the Wronskian of the functions $$x_1,\dots, x_n$$ is identically zero, the determinant formed with the values of the functions, when one gives the variable $$n$$ ordinary values, is also zero. A particular case of the general theorem is as follows: If the determinant formed with the derivatives of orders $$1, 2, 3$$ of the functions $$x, y, z$$ of the same variable $$t$$ is identically zero, the curve described by the coordinate point $$x, y, z$$ is planar.

Peano then reiterated his previous example (Passage 1), and explained that since neither of the two functions is identically zero, Mansion’s addition does not apply to his two functions, and hence his example still shows that the proposition in question is not true.

However, Peano did note that while neither of his functions is “identically zero,” for every value of $$t,$$ at least one of them is.  Realizing that this might be confusing to the reader, he gave a second example, which is merely half the sum and difference of his original.  These no longer have the odd property that one of them is zero at any $$t$$ value, yet they still satisfy that the Wronskian is always zero. Recall that $$\, {\rm mod}\, t$$ denotes the absolute value of $$t.$$

II. To demonstrate that these propositions are not always true, I have indicated in my previous note, an example in which I consider only two functions $$x$$ and $$y$$ of the variable $$t;$$ the determinant $$x{y^\prime} – {x^\prime} y$$ is identically zero; but between them there exists no linear relation. Neither one nor the other of the two functions is identically zero, because $$x>0$$ if $$t>0,$$ and $$y>0$$ if $$t<0.$$ But these two functions present this unusual characteristic that, for all values of $$t,$$ one or the other is zero. To make this anomaly disappear, we propose $X={t^2},\quad Y=t{\, {\rm mod}\, t}.$ These two functions of $$t$$ satisfy the condition $$X{Y^\prime}-{X^\prime}Y=0 ;$$ they only cancel for $$t=0,$$ and between them there is no homogeneous linear relation. The sum and the difference of these functions are the functions of my first example; the coordinate point $$(X,Y)$$ now describes the two half-bisectors of the axes.

Passage 5

In the third part of this note, Peano explained that the “proofs” of all the false propositions make the assumption that the Wronskians of the functions taken $$n-1$$ at a time are either all zero or never zero, referring explicitly to Mansion’s work as an example of one of these incorrect proofs.  He again suggests that readers start looking for additional hypotheses that make the proposition true.

III. The given demonstrations of the proposition, including yours, only allow us to prove that it is true if one of the minor determinants of the last line is always equal to zero, or if it is never equal to zero. For determinants of the second order, one can demonstrate the proposition, except where, for any value of the independent variable, the two given functions and their derivatives each cancel at the same time. It would be interesting to identify all the cases in which the proposition holds true.

Peano finally noted that he had never seen this fact accurately conveyed, and gave several additional citations. We think he was being very generous, because when one reads these three passages, one sees that the issue is not whether the proposition is “clearly expressed,” but rather that it is clearly incorrect!

I believed it necessary to publish this brief note on the Wronskians, because I have never seen the proposition clearly expressed. (See Hermite, Cours d’Analyse, p. 133; Jordan, Cours d’Analyse, III, p. 150; Laurent, Traité d’Analyse, I, p. 183.)

We turn our attention to these three textbooks now.

Susannah M. Engdahl (Wittenberg University) and Adam E. Parker (Wittenberg University), "Peano on Wronskians: A Translation - On the Wronskians," Loci (April 2011), DOI:10.4169/loci003642