The endomorphism semiring of a semilattice

We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element

Extremális struktúrák = Extremal structures

Kutatásaink témája elsősorban extremális gráfelmélet, Ramsey elmélet gráfokra és hipergráfokra, ezek alkalmazására például számelméletben, illetve az ezekhez kapcsolódó módszerek, elsősorban a regularitási lemmák elmélete és alkalmazása, a pszeudovéletlen gráfok elmélete, és a gráf-limeszek elméletének és alkalmazásainak kiépítésére, illetve vizsgálatára/alkalmazására irányult. Kiemelendő a pontos tételek bizonyítása hipergráfok extremális, illetve Ramsey gráfproblémákra (Füredi-Simonovits-Pikhurko, Haxell at al), A gráf-limeszek elméletének kidolgozása/alkalmazása, (Borgs, Chayes, Lovász, T. Sós, Vesztergombi cikksorozat, Lovász-T. Sós, Lovász-Szegedy cikkek, illetve Elek-Szegedy cikkek, az utóbbiak nem tartoznak pályázatunkhoz.) A számelméleti alkalmazások között említjük Győri extrém gráfelméleti és hipergráfelméleti eredményeit. További eredményeink közül kiemelendő a T. Sós és Saks által indított Bollobás-Balogh-Sós eredmények a gráfok az öröklődő gráf-tulajdonságokkal definiált gráf-izomorfiaoszályok számainak és a tipikus szerkezeteiknek kapcsolatáról, illetve a Balogh-Bollobás-Simonovits eredmények, melyek Erdós-Frankl-Rődl tételt messze megjavítva struktúrális leírást adnak a tipikus gráf-szerkezetről. | Extremal structures OTKA closing report T-032810} Miklós Simonovits Our research was primarily concentrated on extremal graph theory, Ramsey Theory, Extremal hypergraph theory their applications, e.g., in Number Theory, and the methods connected to these areas. Large part of our research is connected to quasirandom structures, Szemeredi Regularity Lemma, their connection. Recently much of the research was extended to a wider area around the Regularity Lemma, and also to the theory of graph homomorphisms, and graph limits, strongly connected to the above areas. See the results of Borgs, Chayes, Lovász, T. Sós, Vesztergombi of Lovász-T. Sós, etc. We have proved several sharp hypergraph extremal and Ramsey theorems. Füredi-Simonovits-Pikhurko, Haxell at al. We also mention our applications to number theory e.g. Győri's C_6 theorem, and related hypergraph results, and some coloring results. Some number theoretical analogies led to some results of T. Sós és Saks, connected also to the results of Bollobás-Balogh-Sós-Saks on hereditary properties of unlabelled graphs. Finally, we mention the improvements of the Erdős-Frankl-Rődl results, given by Balogh-Bollobás-Simonovits, on the typical structure of L-free graphs

Diszkrét matematika = Discrete mathematics

A pályázat résztvevői igen aktívak voltak a 2006-2008 években. Nemcsak sok eredményt értek el, miket több mint 150 cikkben publikáltak, eredményesen népszerűsítették azokat. Több mint 100 konferencián vettek részt és adtak elő, felerészben meghívott, vagy plenáris előadóként. Hagyományos gráfelmélet Több extremális gráfproblémát oldottunk meg. Új eredményeket kaptunk Ramsey számokról, globális és lokális kromatikus számokról, Hamiltonkörök létezéséséről. a crossig numberről, gráf kapacitásokról és kizárt részgráfokról. Véletlen gráfok, nagy gráfok, regularitási lemma Nagy gráfok "hasonlóságait" vizsgáltuk. Különféle metrikák ekvivalensek. Űj eredeményeink: Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit. Hipergráfok, egyéb kombinatorika Új Sperner tipusú tételekte kaptunk, aszimptotikusan meghatározva a halmazok max számát bizonyos kizárt struktőrák esetén. Több esetre megoldottuk a kizárt hipergráf problémát is. Elméleti számítástudomány Új ujjlenyomat kódokat és bioinformatikai eredményeket kaptunk. | The participants of the project were scientifically very active during the years 2006-2008. They did not only obtain many results, which are contained in their more than 150 papers appeared in strong journals, but effectively disseminated them in the scientific community. They participated and gave lectures in more than 100 conferences (with multiplicity), half of them were plenary or invited talks. Traditional graph theory Several extremal problems for graphs were solved. We obtained new results for certain Ramsey numbers, (local and global) chromatic numbers, existence of Hamiltonian cycles crossing numbers, graph capacities, and excluded subgraphs. Random graphs, large graphs, regularity lemma The "similarities" of large graphs were studied. We show that several different definitions of the metrics (and convergence) are equivalent. Several new results like the Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit were proved Hypergraphs, other combinatorics New Sperner type theorems were obtained, asymptotically determining the maximum number of sets in a family of subsets with certain excluded configurations. Several cases of the excluded hypergraph problem were solved. Theoretical computer science New fingerprint codes and results in bioinformatics were found

Spin gap and Luttinger liquid description of the NMR relaxation in carbon nanotubes

Recent NMR experiments by Singer et al. [Singer et al. Phys. Rev. Lett. 95, 236403 (2005).] showed a deviation from Fermi-liquid behavior in carbon nanotubes with an energy gap evident at low temperatures. Here, a comprehensive theory for the magnetic field and temperature dependent NMR 13C spin-lattice relaxation is given in the framework of the Tomonaga-Luttinger liquid. The low temperature properties are governed by a gapped relaxation due to a spin gap (~ 30K), which crosses over smoothly to the Luttinger liquid behaviour with increasing temperature.Comment: 5 pages, 1 figure, 1 tabl

Individual burner air/fuel ratio control optical adaptive feedback control system

On cover : Combustion Research Facility.Conventional combustion control systems for multiburner installations which rely on monitoring the average C02 and/or 02 content of the gases have a number of inherent limitations on their ability to maintain efficient plant operation. Air infiltration'into the flue or sampling lines has the same effect as an instrumental error in causing the control system to adjust the stoichiometry to an incorrect level. Even' when the overall stoichiometry of the furnace is correctly and accurately controlled it is still extremely difficult to ensure that no individual burners are operating inefficiently due to local maldistributions of air or fuel, or to poor nozzle spray characteristics. The potential for fuel savings and for'improved limitation of pollutant emissions has provided strong incentive for the development of individual burner fuel/air ratio control systems which would eliminate the shortcomings associated with the global control method. The present report first reviews past attempts to identify some unique property of an individual flame which can be reliably interpreted as an indicator of the flame behavior over a wide range of operating conditions.. Information potentially usable in this manner could be contained in the acoustic characteristics of the flame, in the local distribution of key chemical species, or in the electromagnetic radiation or absorption behavior of regions of the flame. For many reasons the previous studies have tended to concentrate on the optical portion of the electromagnetic spectrum, with particular emphasis on emission from flames over much of the ultraviolet (u.v.), visible and infrared (i.r.) wavelength regions. A brief review is given of the pioneering work of Penzias and his associates, and of the later work carried out at Sheffield University by Smith which led to the development of the LandTM control system. All of these studies dealt with the infrared emission from flames, wilth particular emphasis on the CO2 barnd at 4.3 pm, and on the H0/CO2 binds near 2.8 m. The report then addresses the experimental work carried out at M.I.T under the sponsorship of five utility companies supporting the M.I.T. Energy Laboratory Electric Power Program. This focused initially on attempts to use a Land control system in the Combustion Research Facility (CRF), with limited success in terms of achieving stability and adequacy of control when operating conditions were varied over a moderate range. The experiments in the CRF also yielded very useful data on the intensities and sources of u.v. emission from No. 6 fuel oil flames over a wide range of fuel equivalence ratio. One other set of experiments carried out in the CRF made use of equipment and personnel supplied by the Foxboro Company, and results of this work are discussed. Also included in the report is a summary of measurements carried out on a small methane-fueled burner which add appreciably to the available information on the dependence of the infrared emission on viewing location relative to the flame front and on fuel equivalence ratio. The overall results obtained under this program do not leave the prospect of individual fuel/air ratio controllers within immediate grasp, but they substantially advance the state of knowledge required for attainment of such control. They give a strong indication that satisfactory control could be obtained over a wide range of furnace operating conditions if both i.r. and u.v. signals were monitored and used in the control system

Congruence modularity implies cyclic terms for finite algebras

An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than vertical bar A vertical bar

Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption

Extremális és véletlen struktúrák = Extremal and random structures

Résztvevők: T. Sós Vera, akadémikus, Szemerédi Endre, akadémikus, Füredi Zoltán akadémikus, Győri Ervin, a tudományok doktora, Elek Gábor a tudományok doktora, és témavezetőként Simonovits Miklós (akadémikus). Menetközben csatlakozott a pályázathoz Patkós Balázs. Itt, a rövid beszámolóban csak a legfontosabb témákat említem, Klasszikus Extremális és Ramsey problémák megoldása, ill. ezekkel rokon problémák. A Szemerédi Regularitási Lemma alkalmazásai, az extremális és Ramsey típusú kérdések kapcsolata, ezek kapcsolata a kvázivéletlenséggel, ""tulajdonság-teszteléssel"". Az extrém gráfelmélettel szoros kapcsolatban álló Erdős-Kleitman-Rothschild típusú tételek. A gráflimesz vizsgálata, alkalmazásai Hasonlóságok és különbségek a sűrű és ritka gráfok limesz-elméletében. ,,Sporadikus kérdések,'' pl. algebrai és geometriai alkalmazások. | Project leader: Miklós Simonovits Participants: Vera T. Sós , Endre Szemerédi, Zoltán Füredi, Ervin Győri, Gábor Elek. Balázs Patkós joined our group later. Here I have space only to mention the topics breafly. We were interested primarily in the connection, similarities and differences between deterministic and randomlike structures. Large part of our research was related to the Szemerédi Regularity Lemma and its various versions, and the applications of it, among others, in classical extremal graph and hypergraph problems. We also investigated the application of this lemma in quasi-randomness, property testing, and other related fields. We investigated the graph-limit theory, both for dense and veryy sparse graph sequences. Beside these, we investigated several ``Sporadic question,'' e.g. applications of our methods in algebra and geometry

Screening of bat faeces for arthropod-borne apicomplexan protozoa: Babesia canis and Besnoitia besnoiti-like sequences from Chiroptera

Background : 45 Microbats (Chiroptera: Microchiropte ra) are among the most eco - epidemiologically important 46 mammals, owing to their presence in human settlements and ani mal keeping facilities . 47 Roosting of bats in buildings may bring pathogens of veterinary - medical importance into the 48 environment of domestic animals and humans. In this context bats have long been studied as 49 carriers of various pathogen groups. However, despite their close association with arthropods 50 (both in their f oo d and as their ectoparasites), only a few molecular surveys have been 51 publish ed on their role as carriers of vector - borne protozoa. The aim of the present study was 52 to compensate for this scarcity of information. 53 Findings : 54 Altogether 221 (mostly individual) bat faecal samples were collected in Hungary and the 55 Netherlands. The DNA w as extracted , and analysed with PCR and sequencing for the 56 presence of arthropod - borne apicomplexan protozoa. Babesia canis canis (with 99 - 100% 57 homology) was identified in five samples, all from Hungary. Because it was excluded with an 58 Ixodidae - specific PC R that the relevant bats consumed ticks, these sequences derive either 59 from insect carriers of Ba. canis , or from the infection of bats. In one bat faecal sample from 60 the Netherlands a sequence having the highest (99%) homology to Besnoitia besnoiti was 61 am plified. 62 Conclusions : 63 The se findings suggest that some aspects of the epidemiology of canine babesiosis are 64 underestimated or unknown, i.e. the potential role of insect - borne mechanical transmission 65 and/or the susceptibility of bats to Ba. canis . In addit ion, b ats need to be added to future 66 studies in the quest for the final host of Be. besnoiti

Steady-State Analysis of Load Balancing with Coxian-22 Distributed Service Times

This paper studies load balancing for many-server ($N$ servers) systems. Each server has a buffer of size $b-1,$ and can have at most one job in service and $b-1$ jobs in the buffer. The service time of a job follows the Coxian-2 distribution. We focus on steady-state performance of load balancing policies in the heavy traffic regime such that the normalized load of system is $\lambda = 1 - N^{-\alpha}$ for $0<\alpha<0.5.$ We identify a set of policies that achieve asymptotic zero waiting. The set of policies include several classical policies such as join-the-shortest-queue (JSQ), join-the-idle-queue (JIQ), idle-one-first (I1F) and power-of-$d$-choices (Po$d$) with $d=O(N^\alpha\log N)$. The proof of the main result is based on Stein's method and state space collapse. A key technical contribution of this paper is the iterative state space collapse approach that leads to a simple generator approximation when applying Stein's method