The (h,k)(h,k)-Server Problem on Bounded Depth Trees

We study the $k$-server problem in the resource augmentation setting i.e., when the performance of the online algorithm with $k$ servers is compared to the offline optimal solution with $h \leq k$ servers. The problem is very poorly understood beyond uniform metrics. For this special case, the classic $k$-server algorithms are roughly $(1+1/\epsilon)$-competitive when $k=(1+\epsilon) h$, for any $\epsilon >0$. Surprisingly however, no $o(h)$-competitive algorithm is known even for HSTs of depth 2 and even when $k/h$ is arbitrarily large. We obtain several new results for the problem. First we show that the known $k$-server algorithms do not work even on very simple metrics. In particular, the Double Coverage algorithm has competitive ratio $\Omega(h)$ irrespective of the value of $k$, even for depth-2 HSTs. Similarly the Work Function Algorithm, that is believed to be optimal for all metric spaces when $k=h$, has competitive ratio $\Omega(h)$ on depth-3 HSTs even if $k=2h$. Our main result is a new algorithm that is $O(1)$-competitive for constant depth trees, whenever $k =(1+\epsilon )h$ for any $\epsilon > 0$. Finally, we give a general lower bound that any deterministic online algorithm has competitive ratio at least 2.4 even for depth-2 HSTs and when $k/h$ is arbitrarily large. This gives a surprising qualitative separation between uniform metrics and depth-2 HSTs for the $(h,k)$-server problem, and gives the strongest known lower bound for the problem on general metrics.Comment: Appeared in SODA 201

Lower bounds on geometric Ramsey functions

We continue a sequence of recent works studying Ramsey functions for semialgebraic predicates in $\mathbb{R}^d$. A $k$-ary semialgebraic predicate $\Phi(x_1,\ldots,x_k)$ on $\mathbb{R}^d$ is a Boolean combination of polynomial equations and inequalities in the $kd$ coordinates of $k$ points $x_1,\ldots,x_k\in\mathbb{R}^d$. A sequence $P=(p_1,\ldots,p_n)$ of points in $\mathbb{R}^d$ is called $\Phi$-homogeneous if either $\Phi(p_{i_1}, \ldots,p_{i_k})$ holds for all choices $1\le i_1 < \cdots < i_k\le n$, or it holds for no such choice. The Ramsey function $R_\Phi(n)$ is the smallest $N$ such that every point sequence of length $N$ contains a $\Phi$-homogeneous subsequence of length $n$. Conlon, Fox, Pach, Sudakov, and Suk constructed the first examples of semialgebraic predicates with the Ramsey function bounded from below by a tower function of arbitrary height: for every $k\ge 4$, they exhibit a $k$-ary $\Phi$ in dimension $2^{k-4}$ with $R_\Phi$ bounded below by a tower of height $k-1$. We reduce the dimension in their construction, obtaining a $k$-ary semialgebraic predicate $\Phi$ on $\mathbb{R}^{k-3}$ with $R_\Phi$ bounded below by a tower of height $k-1$. We also provide a natural geometric Ramsey-type theorem with a large Ramsey function. We call a point sequence $P$ in $\mathbb{R}^d$ order-type homogeneous if all $(d+1)$-tuples in $P$ have the same orientation. Every sufficiently long point sequence in general position in $\mathbb{R}^d$ contains an order-type homogeneous subsequence of length $n$, and the corresponding Ramsey function has recently been studied in several papers. Together with a recent work of B\'ar\'any, Matou\v{s}ek, and P\'or, our results imply a tower function of $\Omega(n)$ of height $d$ as a lower bound, matching an upper bound by Suk up to the constant in front of $n$.Comment: 12 page

DC to DC inverter for backup power supplies

Tato diplomová práce se zabývá návrhem DC/DC měniče určeného pro nabíjení superkapacitorů ze zdroje napětí 36 V a následnou zpětnou transformaci napětí ze superkapacitorů na požadovanou výstupní hodnotu. V diplomové práci jsou uvedeny a popsány návrhy snižujícího a zvyšujícího DC/DC měniče včetně schémat zapojení a výpočtů jednotlivých součástek. Dále v textu jsou uvedeny potřebné výpočty superkapacitorů pro splnění podmínky energie 10Wh a balanceru napětí na kondenzátorech. Kompletně navržené zařízení bude sestaveno a odzkoušeno na superkapacitorech s nižší energií.This thesis deals with the design of a DC/DC converter designed for charging supercapacitors from the 36 V voltage source and consequent back transformation of supercapacitors voltage to the required output voltage. In the thesis the designs of decreasing and increasing DC/DC converters including schematics and calculations of individual components are presented and described. The calculations necessary for the supercapacitors to meet the 10Wh energy condition and the voltage balancer on the capacitors are given below. Completely designed equipment will be assembled and tested on supercapacitors with lower energy.

Plasmachemical nitridation of boron precursors

We carried out the plasmachemical nitridation of boron precursor

Competitive algorithms for generalized k-server in uniform metrics

No abstract availabl

SYNTHESIS OF CARBON NANOSTRUCTURES BY PLASMA ENHANCED CHEMICAL VAPOUR DEPOSITION AT ATMOSPHERIC PRESSURE

Carbon nanostructures present the leading field in nanotechnology research. A wide range of chemical and physical methods was used for carbon nanostructures synthesis including arc discharges, laser ablation and chemical vapour deposition. Plasma enhanced chemical vapour deposition (PECVD) with its application in modern microelectronics industry became soon target of research in carbon nanostructures synthesis. Selection of the ideal growth process depends on the application. Most of PECVD techniques work at low pressure requiring vacuum systems. However for industrial applications it would be desirable to work at atmospheric pressure. In this article carbon nanostructures synthesis by plasma discharges working at atmospheric pressure will be reviewed.Uhlíkové nanostruktury patří mezi vedoucí nanotechnologický výzkum. K syntéze uhlíkových nanostruktur lze použít širokou škálu chemických a fyzikálních metod jako například obloukové výboje, laserovou ablaci a CVD. PECVD se svých uplatněním v mikroelektronice se brzy stalo cílem výzkumu i v této oblasti. Výběr metod úzce souvisí s aplikací dané technologie. Ačkoli mnoho metod pracuje při nízkém tlaku, z hlediska aplikací by bylo vhodné použít metodou pracující za atmosférického tlaku. V této publikaci jsou shrnuty metody syntézy uhlíkových nanostruktur za atmosférického tlaku.Carbon nanostructures present the leading field in nanotechnology research. A wide range of chemical and physical methods was used for carbon nanostructures synthesis including arc discharges, laser ablation and chemical vapour deposition. Plasma enhanced chemical vapour deposition (PECVD) with its application in modern microelectronics industry became soon target of research in carbon nanostructures synthesis. Selection of the ideal growth process depends on the application. Most of PECVD techniques work at low pressure requiring vacuum systems. However for industrial applications it would be desirable to work at atmospheric pressure. In this article carbon nanostructures synthesis by plasma discharges working at atmospheric pressure will be reviewed

Hard carbon films: Deposition and diagnostics

We studied the growth of microcrystalline diamond films on pre-treated Si and WC-Co substrates by microwave plasma chemical vapour deposition (MPCVD). The pre-treatment was varied and its effect on diamond film was studied

Atmospheric pressure microwave torch for synthesis of carbon nanotubes

The microwave (mw) plasma torch at atmospheric pressure has been studied for carbon nanotube (CNT) synthesis. The depositions were carried out on silicon substrates with 515 nm thin iron catalytic overlayers from the mixture of argon, hydrogen and methane. The optical emission spectroscopy of the torch showed the presence of C2 and CH radicals as well as carbon and hydrogen excited atoms. The vicinity of the substrate influenced the relative intensities and increased the emission of C2. For fixed mw power, the temperature of the substrate strongly depended on its position with respect to the nozzle electrode and on the gas mixture, particularly the amount of H2. The speed of the substrate heating during an early deposition phase had a significant effect on the CNT synthesis. An abrupt increase of the temperature at the beginning increased the efficiency of theCNTsynthesis. Areas of dense straight standing CNTs, 30 nm in average diameter, with approximately the same sized iron nanoparticles on their tops were found in accordance with the model of growth by plasma enhanced chemical vapour deposition. However, the deposit was not uniform and a place with only several nanometres thick CNTs grown on much larger iron particles was also found. Here, taking into account the gas temperature in the torch, 31003900 K, we can see similarities with the dissolutionprecipitation model of the CNT growth by high temperature methods, arc or laser ablation.Možnosti syntézy uhlíkových nanotrubek(CNTs) byly zkoumány v mikrovlnném výboji buzeném za atmosférického tlaku. Vrstvy byly deponovány na křemíkový substrát s vrstvou železa 5-15 nm sloužící jako katalyzátor ve směsi argonu,vodíku a metanu. Optická emisní spektroskopie výboje prokázala přítomnost radikálů C2 a CH a excitovaných stavů atomů uhlíku a vodíku. Přítomnost substrátu ovlivňovala intenzitu spekter a vedla k vzrůstu intenzity C2 pásu. Při konstantní hodnotě mikrovlnného výkonu byla teplota substrátu silně závislá na vzdálenosti substrátu vůči trysce a průtoku plynů, zejména vodíku. Rychlost zahřívání substrátu v počátení fázi depozice měla významný vliv na depozici CNTs. Prudké zvýšení teploty substrátu na začátku depozice mělo za důsledek zlepšení efektivity depozice CNTs. Na substrátech bylo možno nalézt oblasti hustě uspořádaných CNTs s průměrem okolo 30 nm, které byly na vrcholu ukončeny částicemi katalyzátoru o stejném průměru. Tento výsledek je v souladu s obecně příjmaným růstovým modelem CNTs při použití metody plasma enhanced chemical vapor deposition (PECVD). Deponována vrstva však není uniformní na celé ploše substrátu a byly nalezeny i místa s nanotrubkami, o průměru pouze několika nanometrů, rostoucími na částicích katalyzátoru s mnohem většími rozměry. Vezmeme-li v úvahu teplotu plynu ve výboji, 3100-3900 K, je možno v tomto výsledku spatřovat podobnost s modelem růstu CNTs "dissolution-precipitation" při vysokoteplotních metodách jako jsou obloukový výboj nebo laserová ablace

Tight bounds for Double Coverage against weak adversaries

We study the Double Coverage (DC) algorithm for the k-server problem in tree metrics in the (h,k)-setting, i.e., when DC with k servers is compared against an offline optimum algorithm with h ≤ k servers. It is well-known that in such metric spaces DC is k-competitive (and thus optimal) for h = k. We prove that even if k > h the competitive ratio of DC does not improve; in fact, it increases slightly as k grows, tending to h + 1. Specifically, we give matching upper and lower bounds of (k(h+1)) / (k+1) on the competitive ratio of DC on any tree metric

Synthesis of Carbon Nanotubes in MW Plasma Torch with Different Methods of Catalyst Layer Preparation and their Applications

The microwave plasma torch (2.45 GHz) was used for the synthesis of carbon nanotubes from the mixture of CH4/H2/Ar or C2H2/H2/Ar on different substrates with iron catalyst. Iron catalyst was prepared by vacuum evaporation of iron on Si, Si/SiOx or Si/AlxOy substrates or by deposition of iron oxide nanoparticles on Si/SiOx substrate by decomposion of Fe(CO)5 in gas feed. Such prepared substrates were used for growth of carbon nanotubes. Recostruction of the iron catalyst layer into nanoparticles was also studied in dependence on substrate buffer layer, gas atmosphere and temperature. Samples were studied by scanning and transmission electron microscopy and Raman spectroscopy. Synthesis resulted in rapid growth of MWNTs on all samples but the density, purity and nanotube diameter distribution varied. Such prepared carbon nanotube layers were used for sensing applications.Mikrovlnný plazmový hořák (2,45 GHz) byl použit pro syntézu uhlíkových nanotrubek ze směsi CH4/H2/Ar nebo C2H2/H2/Ar na různých substrátech s železnými katalyzátori. Železný katalyzátor byl připraven vakuovým odpařováním železa na Si, Si/SiOx nebo Si/AlxOy substráty nebo ukládáním nanočástic oxidu železitého Fe (CO) 5 z plynné fáze na Si/SiOx substrát. Takto připravené substráty byly použity pro růst uhlíkových nanotrubek. Vytváření vrstvy katalyzátoru na nanočástice železa byl také studován v závislosti na mezivrstvě , atmosféře a teplotě. Vzorky byly studovány skenovací a transmisní elektronovou mikroskopi a Ramanovskou spektroskopii.The microwave plasma torch (2.45 GHz) was used for the synthesis of carbon nanotubes from the mixture of CH4/H2/Ar or C2H2/H2/Ar on different substrates with iron catalyst. Iron catalyst was prepared by vacuum evaporation of iron on Si, Si/SiOx or Si/AlxOy substrates or by deposition of iron oxide nanoparticles on Si/SiOx substrate by decomposion of Fe(CO)5 in gas feed. Such prepared substrates were used for growth of carbon nanotubes. Recostruction of the iron catalyst layer into nanoparticles was also studied in dependence on substrate buffer layer, gas atmosphere and temperature. Samples were studied by scanning and transmission electron microscopy and Raman spectroscopy. Synthesis resulted in rapid growth of MWNTs on all samples but the density, purity and nanotube diameter distribution varied. Such prepared carbon nanotube layers were used for sensing applications