Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

Nestemäisten jätteiden vastaanotto ja käsittely Tarastenjärven jätekeskuksessa : Selvitys vaihtoehtoisista menetelmistä

Nestemäiset jätteet ovat erilaisia loka-autoilla kuljetettavia jätteitä, jotka koostuvat nesteestä ja kiintoaineksesta. Tällaisia jätteitä ovat esimerkiksi hiekan- ja rasvanerotuskaivoista imetyt nesteet sekä teollisuudessa syntyvät jätevesilietteet. Nestemäisiä jätteitä ei ole Valtioneuvoston päätöksestä enää vuoden 2002 jälkeen saanut sijoittaa sellaisenaan kaatopaikkapenkkaan, vaan ne on tullut esikäsitellä nesteen poistamiseksi. Tähän asti nestemäiset jätteet on käsitelty Tarastenjärven jätekeskuksessa painovoimaisesti erottelemalla. Menetelmä on ollut toimiva, mutta on päivityksen tarpeessa. Tämän opinnäytetyön tarkoituksena olikin tutkia erilaisia vaihtoehtoja nestemäisten jätteiden vastaanotolle sekä käsittelylle Tarastenjärven jätekeskuksessa, sekä arvioida eri vaihtoehtojen kustannuksia mikäli mahdollista. Myös tarvetta haitta-aineiden, kuten metallien ja öljyjen poistamiselle tutkittiin. Työn laatimisessa hyödynnettiin olemassa olevaa tieteellistä kirjallisuutta sekä asiantuntijahaastatteluja. Työn tilaajana toimi Pirkanmaan Jätehuolto Oy. Selvitystyön tuloksena kävi ilmi, että yleisimmät menetelmät nesteiden ja kiinteiden ainesten erottamiseen ovat painovoimainen erottelu ja suodatus. Painovoimaiset erottelijat ovat useimmiten kiinteäseinäisiä altaita, joissa kiintoaines laskeutuu painovoimaisesti altaan pohjalle ja pinnalle jäänyt kirkastunut neste ohjataan ylivuotona jatkokäsittelyyn. Kiintoaineksen ollessa kevyempää kuin vesi, se erottuu nesteen pinnalle. Suodattimien toiminta taas perustuu puoliläpäisevään suodatusmediaan, joka päästää nesteen läpi, mutta jättää kiintoaineksen suodattimeen. Suodattimet voivat olla esimerkiksi paineistettuja tai painovoimalla toimivia. Geotuubit ovat eräänlaisia paineistettuja säkkisuodattimia, joita on käytössä myös jätekeskuksissa. Useissa käsittelymenetelmissä käytetään apuna myös saostuskemikaaleja, jotka edistävät kiintoaineksen erottumista nesteestä. Haitta-aineiden osalta helpoin ratkaisu on poistaa ne kiintoaineksen mukana ja käsitellä ne pilaantuneiden maiden kanssa jätekeskuksessa. Mikäli haitta-aineet ovat nesteessä liukoisessa muodossa, voidaan apuna käyttää saostuskemikaaleja, kuten alumiini- tai rautasuoloja. Öljyjen erottamisessa olisi mahdollista hyödyntää öljynerotuskaivoa. Kirjallisuuden sekä haastattelujen perusteella päivitetty versio painovoimaisesta erottelujärjestelmästä sekä geotuubimenetelmä vaikuttavat parhailta käytettävissä olevilta ratkaisuilta. Suurin haaste jätekeskuksen nestemäisten jätteiden käsittelyssä on kuitenkin se, että nesteiden ominaisuudet eroavat kuormittain hyvin paljon toisistaan. Tähän voitaisiin vaikuttaa jätteiden tarkemmalla lajittelulla vastaanottovaiheessa. Käsittelymenetelmää valittaessa tulee kuitenkin pohtia järjestelmän kuluja sekä hyötyjä pitkällä aikavälillä niin, että päästään parhaaseen mahdolliseen puhdistuslopputulokseen.Liquid wastes are solid-liquid mixtures such as wastes from sand and grease separation wells and industrial wastewaters. Since 2002 liquid wastes have no longer been allowed to be placed at a waste disposal site according to the decree 1049/1999 of the Finnish Council of State. Therefore liquid wastes have to be dewatered before final disposal. At the moment liquid wastes are treated at the Tarastenjärvi waste management centre with gravitational separation but the system needs updating. The aim of this study was to provide Pirkanmaan Jätehuolto Oy with different methods of liquid waste handling as well as evaluate the costs of a new system if possible. Also the need for contaminant removal was taken into consideration. The study was carried out by literature reviews and interviewing professionals of the industry. The results showed that the most common methods of solid-liquid separation are gravitational separation and filtration. Gravitational separators are usually containers in which the solid matter is allowed to separate either by sedimentation or flotation. Filters have a semi-permeable filter media which traps the solid matter but allows the liquid to flow through. Geotubes are an example of filters that are currently being used in several waste management centres. Many separation methods also require the use of polymers or flocculants to operate effectively. When contaminants are in a settleable form they are rather easy to be removed and treated with the solid matter. If the contaminants are dissolved in the liquid it might be possible to make them settle by adding aluminium or iron sulphate. Also an oil separation well could be used to separate oils from the liquid phase. Based on the literature reviews and interviews an upgraded gravitational system or the geotube method seem to be the best options. However, more tests should be conducted to see if these methods would work in practice. The biggest challenge is that the incoming liquid waste loads at Tarastenjärvi are not homogenous which makes it difficult to choose a solution that works well for all of them. The situation could be improved with more precise classification of the waste loads and handling them separately according to their characteristics. The most important aspect is to find a long-term cost-effective solution that can provide sufficient handling of the liquid wastes

The effect of ISM turbulence on the gravitational instability of galactic discs

We investigate the gravitational instability of galactic discs, treating stars and cold interstellar gas as two distinct components, and taking into account the phenomenology of turbulence in the interstellar medium (ISM), i.e. the Larson-type scaling relations observed in the molecular and atomic gas. Besides deriving general properties of such systems, we analyse a large sample of galaxies from The HI Nearby Galaxy Survey (THINGS), and show in detail how interstellar turbulence affects disc instability in star-forming spirals. We find that turbulence has a significant effect on both the inner and the outer regions of the disc. In particular, it drives the inner gas disc to a regime of transition between two instability phases and makes the outer disc more prone to star-dominated instabilities.Comment: MNRAS, in press. Moderate revision to match the accepted versio

In-medium relativistic kinetic theory and nucleon-meson systems

Within the $\sigma-\omega$ model of coupled nucleon-meson systems, a generalized relativistic Lenard--Balescu--equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium effects as well as flucuation effects. It contains all possible processes due to one meson exchange and special attention is kept to the off--shell character of the particles. As a new feature of many particle effects, processes are possible which can be interpreted as particle creation and annihilation due to in-medium one meson exchange. In-medium cross sections are obtained from the generalized derivation of collision integrals, which possess complete crossing symmetries.Comment: See nucl-th/9310032 for revised version which the authors incompetently resubmitted rather than correctly replacing thi

A spectroscopic and proper motion search of Sloan Digital Sky Survey : red subdwarfs in binary systems

Red subdwarfs in binary systems are crucial for both model calibration and spectral classification. We search for red subdwarfs in binary systems from a sample of high proper motion objects with Sloan Digital Sky Survey spectroscopy. We present here discoveries from this search, as well as highlight several additional objects of interest. We find 30 red subdwarfs in wide binary systems including: two with spectral type of esdM5.5, 6 companions to white dwarfs and 3 carbon-enhanced red subdwarfs with normal red subdwarf companions. 15 red subdwarfs in our sample are partially resolved close binary systems. With this binary sample, we estimate the low limit of the red subdwarf binary fraction of similar to 10 per cent. We find that the binary fraction goes down with decreasing masses and metallicities of red subdwarfs. A spectroscopic esdK7 subdwarf + white dwarf binary candidate is also reported. 30 new M subdwarfs have spectral type of >= M6 in our sample. We also derive relationships between spectral types and absolute magnitudes in the optical and near-infrared for M and L subdwarfs, and we present an M subdwarf sample with measured U, V, W space velocities.Peer reviewe

Global impacts of tropospheric halogens (Cl, Br, I) on oxidants and composition in GEOS-Chem [Discussion paper]

We present a simulation of the global present-day composition of the troposphere which includes the chemistry of halogens (Cl, Br, I). Building on previous work within the GEOS-Chem model we include emissions of inorganic iodine from the oceans, anthropogenic and biogenic sources of halogenated gases, gas phase chemistry, and a parameterised approach to heterogeneous halogen chemistry. Consistent with Schmidt et al. (2016) we do not include sea-salt debromination. Observations of halogen radicals (BrO, IO) are sparse but the model has some skill in reproducing these. Modelled IO shows both high and low biases when compared to different datasets, but BrO concentrations appear to be modelled low. Comparisons to the very sparse observations dataset of reactive Cl species suggest the model represents a lower limit of the impacts of these species, likely due to underestimates in emissions and therefore burdens. Inclusion of Cl, Br, and I results in a general improvement in simulation of ozone (O3) concentrations, except in polar regions where the model now underestimates O3 concentrations. Halogen chemistry reduces the global tropospheric O3 burden by 18.6 %, with the O3 lifetime reducing from 26 to 22 days. Global mean OH concentrations of 1.28  ×  106 molecules cm−3 are 8.2 % lower than in a simulation without halogens, leading to an increase in the CH4 lifetime (10.8 %) due to OH oxidation from 7.47 to 8.28 years. Oxidation of CH4 by Cl is small (∼  2 %) but Cl oxidation of other VOCs (ethane, acetone, and propane) can be significant (∼  15–27 %). Oxidation of VOCs by Br is smaller, representing 3.9 % of the loss of acetaldehyde and 0.9 % of the loss of formaldehyde

Wormholes and Ringholes in a Dark-Energy Universe

The effects that the present accelerating expansion of the universe has on the size and shape of Lorentzian wormholes and ringholes are considered. It is shown that, quite similarly to how it occurs for inflating wormholes, relative to the initial embedding-space coordinate system, whereas the shape of the considered holes is always preserved with time, their size is driven by the expansion to increase by a factor which is proportional to the scale factor of the universe. In the case that dark energy is phantom energy, which is not excluded by present constraints on the dark-energy equation of state, that size increase with time becomes quite more remarkable, and a rather speculative scenario is here presented where the big rip can be circumvented by future advanced civilizations by utilizing sufficiently grown up wormholes and ringholes as time machines that shortcut the big-rip singularity.Comment: 11 pages, RevTex, to appear in Phys. Rev.