Minimal Subspaces with Maximal Dimensioanal Diameters

Владимир Тодоров - Нека X е компактно метрично пространство с dim X = n. Тогава за n − 1 - мерния диаметър dn−1(X) на X е изпълнено неравенството dn−1(X) > 0, докато dn(X) = 0 (да отбележим, че това е една от характеристиките на размерността на Лебег). От тук се получава, че X съдържа минимално по включване затворено подмножество Y , за което dn−1(Y ) = dn−1(X). Известен резултат е, че от това следва, че Y е Канторово Многообразие. В тази бележка доказваме, че всяко такова (минимално) подпространство Y е даже континуум V^n. Получени са също така някои следствия.

Extended Maximum Principles

2000 Mathematics Subject Classification: 35B50, 35L15.

Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures

2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds

2000 Mathematics Subject Classification: 53C42, 53C55.

Warped Product CR-Submanifolds in Lorentzian para Sasakian Manifolds

2000 Mathematics Subject Classification: 53C15, 53C40, 53C42.

Contact CR-Submanifolds of Kenmotsu Manifolds

2000 Mathematics Subject Classification: 53C15, 53C42.

Formes de contact ayant le même champ de Reeb

2000 Mathematics Subject Classification: 37J55, 53D10, 53D17, 53D35.

Methyl chloride purification for the silicone industry

This study experimentally investigated methyl chloride (MeCl) purification method using an inhouse designed and built volumetric adsorption/desorption rig. MeCl is an essential raw material in the manufacture of silicone however all technical grades of MeCl contain concentrations (0.2 - 1.0 % wt) of dimethyl ether (DME) which poison the process. The project industrial partner had previously exhausted numerous separation methods, which all have been deemed not suitable for various reasons. Therefore, adsorption/desorption separation was proposed in this study as a potential solution with less economic and environmental impact. Pure component adsorption/desorption was carried out for DME and MeCl on six different adsorbents namely: zeolite molecular sieves (types 4 Å and 5 Å); silica gels (35-70 mesh, amorphous precipitated, and 35-60 mesh) and granular activated carbon (type 8-12 mesh). Subsequent binary gas mixture adsorption in batch and continuous mode was carried out on both zeolites and all three silica gels following thermal pre-treatment in vacuum. The adsorbents were tested as received and after being subjected to different thermal and vacuum pre-treatment conditions. The various adsorption studies were carried out at low pressure and temperature ranges of 0.5 - 3.5 atm and 20 - 100 °C. All adsorbents were characterised using Brunauer Emmett Teller (BET), thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and energy dispersive x-ray analysis (EDXA) to investigate their physical and chemical properties. The well-known helium (He) expansion method was used to determine the empty manifold and adsorption cell (AC) regions and respective void volumes for the different adsorbents. The amounts adsorbed were determined using Ideal gas laws via the differential pressure method. The heat of adsorption for the various adsorbate-adsorbent (A-S) interactions was calculated using a new calorimetric method based on direct temperature measurements inside the AC. Further adsorption analysis included use of various empirical and kinetic models to determine and understand the behaviour of the respective interactions. The gas purification behaviour was investigated using gas chromatography and mass spectroscopy (GC-MC) analysis. Binary gas mixture samples were syringed from the manifold iii and AC outlet before and after adsorption/desorption analysis through manual sample injections into the GC-MS to detect and quantify the presence of DME and ultimately observe for methyl chloride purification. Convincing gas purification behaviour was confirmed using two different GC columns, thus giving more confidence on the measurement reliability. From the single pure component adsorption of DME and MeCl on the as received zeolite 4A subjected to 1 h vacuum pre-treatment, both gases exhibited pseudo second order adsorption kinetics with DME exhibiting a rate constant nearly double that of MeCl thus suggesting a faster rate of adsorption. From the adsorption isotherm classification both DME and MeCl exhibited Type II and I adsorption isotherm classifications, respectively. The strength of bonding was confirmed by the differential heat of adsorption measurement, which was found to be 23.30 and 10.21 kJ mol-1 for DME and MeCl, respectively. The former is believed to adsorb heterogeneously through hydrogen bonding whilst MeCl adsorbs homogenously via van der Waal’s (VDW) forces. Single pure component adsorption on as received zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) resulted in similar adsorption/desorption behaviour in similar quantities (mol kg-1). The adsorption isotherms for DME and MeCl on zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) and activated carbon 8-12 exhibited Type I classifications, respectively. Experiments on zeolite 5A indicated that DME adsorbed stronger, faster and with a slightly stronger strength of interaction than MeCl but in lesser quantities. On the silica gels adsorbents, DME exhibited a slightly greater adsorption capacity whilst adsorbing at a similar rate and strength of interaction compared to MeCl. On the activated carbon adsorbent, MeCl exhibited the greater adsorption capacity at a faster rate but with similar heats of adsorption. The effect of prolonged vacuum (15 h), thermal pre-treatment (150 °C) and extended equilibrium time (15 min) were investigated for the adsorption behaviour of DME and MeCl on both zeolites 4A and 5A, respectively. Compared to adsorption on as received adsorbents subjected to 1 h vacuum the adsorption capacities for DME and MeCl were found to increase by 1.95 % and 20.37 % on zeolite 4A and by 4.52 % and 6.69 % on zeolite 5A, respectively. In addition the empirical and kinetic models and differential heats of adsorption resulted in more definitive fitting curves and trends due to the true equilibrium position of the adsorbate with the adsorbent. Batch binary mixture adsorption on thermally and vacuum pre-treated zeolite 4A demonstrated purification behaviour of all adsorbents used for MeCl streams containing DME impurities, with a concentration as low as 0.66 vol. %. The GC-MS analysis showed no DME detection for the tested concentration mixtures at the AC outlet after 15 or 30 min, whereas MeCl was detectable in measurable amounts. Similar behaviour was also observed when carrying out adsorption in continuous mode. On the other hand, similar studies on the other adsorbents did not show such favourable MeCl purification behaviour. Overall this study investigated a wide range of adsorbents (zeolites, silica gels and activated carbon) and demonstrated for the first time potential to purify MeCl streams containing DME impurities using adsorption/desorption separation under different adsorbent pre-treatment and adsorption operating conditions. The study also revealed for the first time the adsorption isotherms, empirical and kinetic models and heats of adsorption for the respective adsorbentsurface (A-S) interactions. In conclusion, this study has shown strong evidence to propose zeolite 4A for adsorptive purification of MeCl. It is believed that with a technical grade MeCl stream competitive yet simultaneous co-adsorption of DME and MeCl occurs with evidence of molecular sieiving effects whereby the larger DME molecules are unable to penetrate through the adsorbent bed whereas the smaller MeCl molecules diffuse through resulting in a purified MeCl stream at the AC outlet. Ultimately, further studies are recommended for increased adsorption capacities by considering wider operating conditions, e.g. different adsorbent thermal and vacuum pre-treatment and adsorbing at temperatures closer to the boiling point of the gases and different conditions of pressure and temperature.

Catalytic applications of waste derived materials

Sustainability has become a watchword and guiding principle for modern society, and with it a growing appreciation that anthropogenic 'waste', in all its manifold forms, can offer a valuable source of energy, construction materials, chemicals and high value functional products. In the context of chemical transformations, waste materials not only provide alternative renewable feedstocks, but also a resource from which to create catalysts. Such waste-derived heterogeneous catalysts serve to improve the overall energy and atom-efficiency of existing and novel chemical processes. This review outlines key chemical transformations for which waste-derived heterogeneous catalysts have been developed, spanning biomass conversion to environmental remediation, and their benefits and disadvantages relative to conventional catalytic technologies.

Improved data visualisation through multiple dissimilarity modelling

Popular dimension reduction and visualisation algorithms rely on the assumption that input dissimilarities are typically Euclidean, for instance Metric Multidimensional Scaling, t-distributed Stochastic Neighbour Embedding and the Gaussian Process Latent Variable Model. It is well known that this assumption does not hold for most datasets and often high-dimensional data sits upon a manifold of unknown global geometry. We present a method for improving the manifold charting process, coupled with Elastic MDS, such that we no longer assume that the manifold is Euclidean, or of any particular structure. We draw on the benefits of different dissimilarity measures allowing for the relative responsibilities, under a linear combination, to drive the visualisation process.

Megmenthető-e az euróövezet? (Can the eurozone be saved?)

Az euró válságának szélesebb globális összefüggései vannak, mind a kiváltó okait, mind a nemzetközi pénzügyi rendszer működésének hiányosságait illetően. Az európai monetáris integráció szilárd reálgazdasági alapokon nyugszik. Az euró teljesítménye mind az árstabilitás, mind az árfolyamok ingadozása tekintetében megfelelőnek tekinthető. Az euróválság szuverénadósság-válság, és leginkább a zóna egyes (déli) országait érinti. Az euróválság okai többrétűek: ezek között az eurózóna hibás konstrukcióját, téves koncepcionális feltételezéseit, a politikai kompromisszumokkal folyamatosan megnyomorított működését említhetjük leginkább. A közös pénz önmagában nem oka a válságnak és nem is bűvös ellenszer. A hibás gazdaságpolitikáért belül ugyanúgy bűnhődni kell, mint kívül. Görögország, vagy Írország elsősorban nem azért került válságba, mert tagjai az eurózónának, hanem mert hibás gazdaságpolitikát folytattak. Nem zárható ki az eurózóna szétesése, de kicsi az esélye. / === / The euro crisis has broad global connections, both in terms of deficiencies of the international monetary system, and of the crisis of the global financial markets. The European monetary integration is based on strong real-economic foundations. The performance of the euro has been satisfactory both in terms of price and exchange rate stability. The present crisis is a sovereign debt crisis, and it is concentrated mainly on some Southern members. The causes of the crisis are manifold: wrong institutional and policy structures, mistaken conceptual assumptions, and the distortion of its operation by continuous political compromises. The contradictions between common monetary policy and the national fiscal policies, the failure of disciplining role of the markets, the weakness of control of national fiscal policies, the dangers of "one size fits all" monetary policy, the failure of finding the proper national policy mixes, particularly in terms of income and structural policies, and the underestimation of social and cultural differences, can be particularly stressed. The common monetary policy failed to secure the necessary equilibrium among liquidity, stability and growth. Greece and Ireland got in crisis not because they are members of the euro zone, but because of their mistaken economic policies. The collapse of the euro zone cannot be excluded, but the chances of it are limited.

Átmenet vagy spontán rend(etlenség)? = Transition or spontaneous order/disorder?

Az írás arra a kérdésre keresi a választ, hogy a két évtized után tartóssá, vagyis trenddé váló gazdasági és társadalmi eltérések a "posztkommunista" országok között milyen okokra vezethetők vissza. Másodsorban azt elemzi, mi a jelentősége e sokrétű különbségek modellszerű kategorizálásának. Ennek alapja az állami szerepvállalás mértéke és minősége. Végül harmadikként azt a kérdéskört vizsgálja, hogy az eltérések milyen következményekkel járnak. A fő következtetés az, hogy a közösségi választások ugyan jelentősek, ezek szerepe azonban a pályafüggőséghez képest sokkal kisebb, mint azt a legtöbb elmélet föltételezi. Az eredmény - Hayekkel szólva (Hayek [1995]) - emberi cselekvés, ámde nem emberi tervezet szülötte. _____ The article seeks to discover what causes can be traced for the economic and social differences that have become permanent or a trend after two decades. Secondly, it analy-ses what importance this model-like categorization of manifold differences bears. Thirdly and lastly, it examines the sphere of questions to do with the consequences of these differences. The main conclusion is that the community choices are significant, but their role is much less, by comparison with career dependence, than most theories assume. Achievement, to quote Hayek (1995) is borne of human endeavour, not human planning.

Munkahelyi motivációk Magyarországon 2013-ban (Workplace motivations in Hungary in 2013)

A motiváció szerepe a szervezetek életében alapvető fontossággal bír. A tanulmány egy friss reprezentatív kutatás eredményeit mutatja be, amelyet a szerzők a magyar munkavállalók körében végeztek annak érdekében, hogy feltárják a hazai motivációs viszonyokat és a munkavállalók számára legfontosabb tényezőket. A korábbi évek felmérései szerint a legfontosabb hazai motivációs tényezők a versenyképes fizetés, a cafeteria, a karrierlehetőség és az előrelépési lehetőségek voltak. A kutatás bizonyította, hogy az elmúlt időszakban átrendeződés figyelhető meg, egyre inkább előtérbe kerülnek olyan tényezők, amelyek a biztonsággal, a stabilitással, a jó munkahelyi légkörrel és a megfelelő kapcsolatokkal függnek össze. A szerzők megvizsgálták egy francia motivációs modell lehetséges magyarországi alkalmazását is, amelynek során szintén megmutatkoztak a magyar sajátosságok. A modell elemei közül bizonyos területek fontosabbak a hazai munkavállalók számára. A modell hazai adaptációja színesítheti a hazai motivációs megoldások kínálatát. ______ Motivation has an essential role in the operation of the organisations. The study represents the results of a recent representative research which was conducted by the authors among Hungarian workers. The aim was to explore the domestic motivational relations and the key motivational factors of employees. According to the surveys of previous years the main Hungarian motivating factors were competitive salary, cafeteria, career opportunities and advancement opportunities. The research has proved that rearrangement could be observed in the last period. Those factors have increasingly come to the forefronts which are related to safety, stability, appropriate work environment and appropriate employee relations. The authors have examined the possible domestic application of a French motivational model, besides the Hungarian specialties were also reflected. Some elements of the model are more important than the others for domestic workers. The adaptation of the model could make the domestic motivational solution offerings more relevant and manifold.

On arterial contractility, energetic requirements of the cardiovascular system, and the formation of arterial sclerosis

The aorta has been viewed as a passive distribution manifold for blood whose elasticity allows it to store blood during cardiac ejection (systole), and release it during relaxation (diastole). This capacitance, or compliance, lowers peak cardiac work input and maintains peripheral sanguine irrigation throughout the cardiac cycle. The compliance of the human and canine circulatory systems have been described either as constant throughout the cycle (Toy et al. 1985) or as some inverse function of pressure (Li et al. 1990, Cappelo et al. 1995). This work shows that a compliance value that is higher during systole than diastole (equivalent to a direct function of pressure) leads to a reduction in the energetic input to the cardiovascular system (CV), even when accounting for the energy required to change compliance. This conclusion is obtained numerically, based on a 3-element lumped-parameter model of the CV, then demonstrated in a physical model built for the purpose. It is then shown, based on the numerical and physical models, on analytical considerations of elastic tubes, and on the analysis of arterial volume as a function of pressure measured in vivo (Armentano et al. 1995), that the mechanical effects of a presupposed arterial contraction are consistent with those of energetically beneficial changes in compliance during the cardiac cycle. Although the amount of energy potentially saved with rhythmically contracting arteries is small (mean 0.55% for the cases studied) the importance of the phenomenon lies in its possible relation to another function of the arterial smooth muscle (ASM): synthesis of wall matrix macromolecules. It is speculated that a reduction in the rate of collagen synthesis by the ASM is implicated in the formation of arteriosclerosis. ^