Elliptic problems with lack of compactness via a new fixed point theorem

AbstractThis paper provides a new fixed point theorem for increasing self-mappings G:B→B of a closed ball B⊂X, where X is a Banach semilattice which is reflexive or has a weakly fully regular order cone X+. By means of this fixed point theorem, we are able to establish existence results of elliptic problems with lack of compactness

Huge thermoelectric effects in ferromagnet-superconductor junctions in the presence of a spin-splitting field

We show that a huge thermoelectric effect can be observed by contacting a superconductor whose density of states is spin-split by a Zeeman field with a ferromagnet with a non-zero polarization. The resulting thermopower exceeds $k_B/e$ by a large factor, and the thermoelectric figure of merit $ZT$ can far exceed unity, leading to heat engine efficiencies close to the Carnot limit. We also show that spin-polarized currents can be generated in the superconductor by applying a temperature bias.Comment: 5 pages, 4 figure

Simple vs complex models in housing market forecasting:empirical evidence from Helsinki metropolitan area

Abstract. This study seeks to examine whether it is possible to gain similar forecasting performance from simple forecasting models compared to more complex specifications in housing market context. Evaluation is conducted by comparing the predictive power of five common modelling techniques out-of-sample: Autoregressive Integrated Moving Average (ARIMA), Simple Regression (SR), Multiple Regression (MR), Vector Autoregression (VAR) and Autoregressive Integrated Moving Average with a vector of explanatory variables (ARIMAX). A set of macroeconomic variables is used with these different modelling techniques to generate ex-post (out-of-sample) forecasts for the housing market of Helsinki Metropolitan Area. The dataset employed in this study is gathered from public sources and covers a period from 1999 to 2018. The ex-post forecasts are generated one, two, three, four and five steps ahead, i.e. from 2016 H2 to 2018 H2, and the forecasting accuracy is assessed by calculating Theil’s U and root-mean-square error (RMSE) values for each of the forecasts. The obtained results imply that added model complexity does not necessarily yield better results, as the more complex run the risk of overfitting small data samples. What is more, the results indicate that while the complex models tend to fit historic data with greater accuracy, the higher historical fit does not always translate into superior forecasting results. However, it seems probable that the shortcomings of the more complex models in this study are aggravated by the very specific features of the utilized dataset. Hence, market participants should acknowledge that the obtained forecasting results are always not only largely dependent on the chosen methodology, but also on the utilized dataset

On a Theory of Truth and on the Regress Problem

A theory of truth is introduced for a first--order language L of set theory. Fully interpreted metalanguages which contain their truth predicates are constructed for L. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. Only ZF set theory, concepts definable in L and classical two-valued logic are used

A theory of truth for a class of mathematical languages and an application

In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT is shown to conform well with the eight norms presented for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)' by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem

A mathematical theory of truth and an application to the regress problem

In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)', by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. Main tools used in proofs are Zermelo-Fraenkel (ZF) set theory and classical logic

Effects of sodium sulphate and potassium chloride fertilizers on the nutritive value of timothy grown on different soils

Third harvest samples from a pot experiment were analysed to study the effects of sodium (Na) (0, 200 and 400 mg dm-3 of soil in a single application as Na2SO4 . 10H2O) and potassium (K) application (0, 100 and 200 mg dm-3 applied at each harvest as KCl) on the nutritive value of timothy grown on three different soil types (clay, loam and organogenic soil). The effects of fertilization on concentrations of crude protein, neutral detergent fibre (NDF) and non-structural carbohydrates, although statistically significant, were relatively minor in absolute terms. Na applications increased and K applications decreased sulphur and phosphorus concentrations, the magnitude of which was dependent on soil type. The increase in sulphur concentration can be attributed to sulphate in Na-fertilizer. The effects of fertilizers on in vitro organic matter digestibility and the potential extent of dry matter (DM) and NDF digestibility were small. Digestion kinetic parameters estimated from fermentative gas production measured using a fully automated system were used in a rumen simulation model to estimate digestibility. Total gas volume and the rate of gas production from the rapidly digestible fraction were negatively correlated with timothy S and N concentrations. Na application had no effect, but K application increased true rumen DM digestibility, the effect being most profound on organogenic soil. The results suggest that Na application does not elicit substantial positive effects on the nutritive value of timothy which has often been reported for perennial ryegrass, but K application can improve the nutritive value of timothy grown on K deficient soil.;Tutkimuksen tavoitteena oli selvitettää natrium- ja kaliumlannoituksen vaikutusta timotein ravintoarvoon. Näytteet olivat Peltovuoren ja Yli-Hallan (1997) astiakokeesta, jossa selvitettiin Na- ja K-lannoituksen vaikutusta timotein Na, K,Ca ja Mg-pitoisuuteen ja satoon savi-, hieta- ja turvemaalla. Käytetyt ravinnemäärät olivat 0, 200 tai 400 mg Na l-1 kokeen alussa natriumsulfaattina ja 0, 100 tai 200 mg K 1-1 joka sadolle kaliumkloridina. Tähän tutkimukseen valittiin kolmannen sadon näytteet, koska niissä Na-pitoisuuden vaihtelu oli suurin (0,16-7,13 g kg-1). Vaikka timotei luetaan ns. natrofobisiin kasveihin, jotka ottavat huonosti natriumia versoihin, nousi timotein natriumpitoisuus huomattavasti. Na- ja K-lannoituksen vaikutusta timotein ravintoarvoon tutkittiin in vitro -kokein ja lisäksi määritettiin typpi, neutraalideterkenttikuitu (NDF), sokeri, rikki ja fosfori. Orgaanisen aineen in vitro -sulavuus määritettiin sellulaasimenetelmällä ja potentiaalinen kuiva-aineen ja NDF:n pötsisulavuus inkuboimalla näytettä 12 vrk nailonpussissa kahden lehmän pötsissä (in situ). Sulatuskinetiikan parametrit määritettiin mikrobikäymisen tuottaman kaasuntuotannon mittauksella ajan funktiona automaattisella mittauslaitteella, ja dynaamisen ja pötsimallin perusteella laskettiin potentiaalisesti sulavan kuiva-aineen pötsisulavuus ja kuiva-aineen todellinen pötsisulavuus. Lannoituksen vaikutus raakavalkuais-, NDF- ja sokeripitoisuuteen oli pieni. Na-lannoitus lisäsi hieman ja K-lannoitus vähensi typpipitoisuutta ja molemmat vähensivät laskennallista sokeripitoisuutta. NDF-pitoisuus nousi hieman Na-lannoituksella. Na-lannoitus lisäsi ja K-lannoitus vähensi rikki- ja fosforipitoisuutta vaikutuksen riippuessa maalajista. Na-lannoituksen vaikutukset orgaanisen aineen in vitro sulavuuteen sekä potentiaaliseen kuiva-aineen ja NDF:n pötsisulavuuteen olivat pieniä, vaikkakin tilastollisesti merkitseviä. Kokonaiskaasutuotanto ja nopeasti sulavan fraktion kaasutuotannon nopeus vähenivät, kun timotein typpi-, rikki-, kalsium-, magnesium-, fosfori- ja natriumpitoisuudet nousivat. Na-lannoituksella ei ollut vaikutusta sulatuskinetiikan parametreihin ja estimoituun potentiaalisesti sulavan kuiva-aineen pötsisulavuuteen tai kuiva-aineen todelliseen pötsisulavuuteen, kun taas K-lannoitus lisäsi hieman nopeasti sulavan fraktion kaasutuotannon nopeutta ja todellista kuiva-aineen pötsisulavuutta. Kaliumin vaikutus oli selvin turvemaalla. Maalajien välillä oli eroja kaasuntuotannon määrässä ja potentiaalisesti sulavan kuiva-aineen ja todellisessa kuiva-aineen pötsisulavuudessa, savimaa ruoho oli huonoiten ja turvemaan ruoho parhaiten sulavaa. Näiden tulosten mukaan Na-lannoituksella ei näytä olevan samanlaisia myönteistä vaikutusta timotein ravintoarvoon kuin brittiläistutkimuksissa on usein esitetty englannin raiheinällä, mutta K-lannoitus voi parantaa timotein ravintoarvoa K-puutteesta kärsivillä mailla