Linear relations with conjugates of a Salem number

In this paper we consider linear relations with conjugates of a Salem number $\alpha$. We show that every such a relation arises from a linear relation between conjugates of the corresponding totally real algebraic integer $\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem number with a nontrivial relation between its conjugates is $8$, whereas the smallest length of a nontrivial linear relation between the conjugates of a Salem number is $6$.Comment: v1, 12 page

Menonas: dorybė kaip οὐσία ir εἶδος

The article is an interpretation of the first part of the Meno (70a-79e), in which Plato deals with the problem of knowledge of virtue. Parmenides’ being, constituted by Justice, becomes a reference point for reflecting on the ontological and cognitive profile of virtue. The polemic with the sophists forces Plato to reflect on the subject of philosophizing and to realize that it is existentially rooted in the ontologised language. Here Plato finds the concept of οὐσία, which becomes for him the cognitive prototype of virtue. For οὐσία as a possession presupposes the property of a thing whose meaning is determined not by the sensually ascertainable properties of a thing, but by its social significance, which is relatively constant and correlated with justice. The distinction between the meanings of a thing and of its possession in the same object conveys the idea that virtue as a human possession, i.e., οὐσία, cannot be known in everyday thinking that hypertrophies the senses, but should be present in an alternative layer of thinking, and thus imply an alternative mode of knowledge. It can therefore be surmised that Plato’s discovery of the duality of the concept of οὐσία inspired in him both the idea of an autonomous world of ideas and the idea of a specific way of accessing it, i.e. the theory of anamnesis.Straipsnyje interpretuojama Menono pirmoji dalis (70a – 79e), kurioje Platonas gvildena dorybės pažinimo problemą. Teisybės steigiama parmenidiškoji būtis tampa orientyru aptariant dorybės būtiškąjį bei pažintinį profilį. Polemika su sofistais verčia Platoną apmąstyti filosofavimo subjektą bei įsisąmoninti, kad šis yra egzistenciškai įsišaknijęs ontologizuotai traktuojamoje kalboje. Čia Platonas suranda οὐσία sąvoką, kuri jam tampa dorybės pažintiniu provaizdžiu. Mat οὐσία kaip nuo-savybė numano daikto ar dalyko savybę, kurios reikšmę lemia ne jusliškai konstatuojamos daikto savybės, o jos poliškasis reikšmingumas, kuris yra santykiškai pastovus ir pamatuotas teisingumu. Daikto ir nuosavybės reikšmių išsiskyrimas tame pačiame objekte perša mintį, kad dorybė kaip žmogaus nuo-savybė, t. y. οὐσία, negali būti pažinta jusliškumą hipertrofuojančiame kasdieniame mąstyme, bet turėtų būti alternatyviame mąstymo klode, tad ir numanyti alternatyvų pažinimo būdą. Todėl galima spėti, kad Platono aptiktas οὐσία sąvokos dvilypumas inspiravo jam tiek mintį apie autonomišką idėjų pasaulį, tiek mintį apie specifinę prieigą prie jo, t. y. anamnezės teoriją

The Effects of Biogeotextiles on the Stabilization of Roadside Slopes in Lithuania.

Soil erosion, Water erosion, Soil conservation, Geotextiles, Geotextile mats, Roadside slopes, Vegetation cover, Biogeotextiles , Palm mat geotextiles - Borassus aethiopum - Mauritia flexuosa - Buriti mats - BORASSUS Project - LithuaniaBiogeotextiles constructed from the leaves of Borassus aethiopum and Mauritia flexuosa are investigated at the Kaltinėnai Research Station of the Lithuanian Institute of Agriculture, which is participating in the EU-funded BORASSUS Project. Biogeotextiles are potentially excellent biodegradable and environmentally-friendly materials useful for soil conservation. Field studies on a steep (21–25°) roadside slope in Lithuania suggest biogeotextile mats are an effective and sustainable soil conservation technique. Biogeotextiles have a potential as a biotechnical soil conservation method for slope stabilization and protection from water erosion on steep industrial slopes and may be integrated with the use of perennial grasses to optimize protection from water erosion. The investigations demonstrated that a cover of Borassus and Buriti mats improved the germination and growth of sown perennial grasses. The biomass of perennial grasses increased by 52.0–63.4% under cover of Borassus mats and by 18.6–28.2% under cover of Buriti mats. Over 2 years, the biogeotextiles (Borassus and Buruti, respectively) decreased soil losses from bare fallow soil by 90.8% and 81.5% and from plots covered by perennial grasses by 87.9% and 79.0%, respectively

Struvite Precipitation modelling using Extended Quadrature Method of Moments and Drift-Flux Model

The primary fertilisers used in the agricultural industry are phosphorus based. The production of phosphorus is mainly based on the mining operations, however it is a current consensus that in 50 − 100 years time the quality and the availability of phosphorus ores will decrease substantially and the deposits will be either completely depleted or the quality of the obtainable phosphorus will be too toxic to be used in the agriculture. Taking into account the current population growth trends the food production will have to be increased even more and therefore the global food shortage is an event of high potential. To address that alternative sources of phosphorus based fertilisers must be found and numerous technological research have been taking place to limit the impact that phosphorus shortage might cause in the future. The aim of this study is to present a potential technology that could be used for phosphorus recovery. It is known that there is a significant amount of phosphorus in the wastewater therefore most of the technological developments have been focussed towards the recovery of phosphorus from the wastewater streams. The Hydrodynamic Vortex Separator (HDVS) is a product developed by Hydro International® that is primarily used for solid-liquid separation. However this study proposes the potential use of the HDVS as a reaction vessel for phosphorus recovery through magnesium-ammonium-phosphate precipitation. The study presents a development and application of a mathematical model of the two-phase system that is coupled with the formation of a dispersed phase through a precipitation process. Hydrodynamics of the system is modelled using an Eulerian approach, specifically the drift flux mixture model (DFM)[81]. The precipitation process and the change of the dispersed phase properties, namely the mean diameter of the particulates, is modelled using the Population Balance Equation (PBE), which is solved using the Extended Quadrature Method of Moments (EQMOM) method. The affects of the changes observed in the dispersed phase properties were coupled to the hydrodynamics using two new settling models that depend on the size of the particulate phase. The model has been applied to a horizontal settling tank and the HDVS geometries in order to understand the potential of the precipitation process in these type of wastewater treatment tools. In both of the cases the model predicted reasonable values of the dispersed phase mean diameter.Engineering and Physical Sciences Research Council (EPSRC

Multi-objective biopharma capacity planning under uncertainty using a flexible genetic algorithm approach

This paper presents a flexible genetic algorithm optimisation approach for multi-objective biopharmaceutical planning problems under uncertainty. The optimisation approach combines a continuous-time heuristic model of a biopharmaceutical manufacturing process, a variable-length multi-objective genetic algorithm, and Graphics Processing Unit (GPU)-accelerated Monte Carlo simulation. The proposed approach accounts for constraints and features such as rolling product sequence-dependent changeovers, multiple intermediate demand due dates, product QC/QA release times, and pressure to meet uncertain product demand on time. An industrially-relevant case study is used to illustrate the functionality of the approach. The case study focused on optimisation of conflicting objectives, production throughput, and product inventory levels, for a multi-product biopharmaceutical facility over a 3-year period with uncertain product demand. The advantages of the multi-objective GA with the embedded Monte Carlo simulation were demonstrated by comparison with a deterministic GA tested with Monte Carlo simulation post-optimisation