9 research outputs found
Optimal Graphs for Connectedness under Random Edge Deletion
No full textPerforming percolation on a finite graph G means independently keeping or
discarding each edge according to a probability parameter p. The focus is the
probability Pc(G, p) that a percolation outcome turns out to be a connected
graph. Specifically, if we fix p, the number of vertices n and the number of edges
m, we try to find the graph(s) with the highest such probability. We call such
graphs the most stable or the (n, m, p)-optimal graphs. It is shown that any
(n, m, p)-optimal graph consists of a single so-called block.
For m = n, m = n + 1 and m = n + 2 respectively, we show the existence
of a unique optimal graph, which is actually independent of p. However, in
general, the relative stability of two (n,m)-graphs is p-dependent. We make
some investigations into when this is the case
A new framework for identifying most reliable graphs and a correction to the -theorem
No full textGiven a multigraph , the all-terminal reliability is the probability that remains connected under percolation with parameter . Fixing the number of vertices and edges , we investigate which graphs maximize -- such graphs are called optimal -- paying particular attention to uniqueness and to whether the answer depends upon . We generalize the concept of a distillation and build a framework with which we identify all optimal graphs for which . These graphs are uniformly optimal in . Most have been previously identified, but with serious problems, especially when . We obtain partial results for .
For , the optimal graphs were incorrectly identified by Wang in 1994, in the infinite number of cases where and . This erroneous result concerns subdivisions of and has been cited extensively, without any mistake being detected. While the optimal graphs were correctly described for other , the proof is fundamentally flawed. Our proof of the rectified statement is self-contained.
For , the optimal graphs were recently shown to depend upon for infinitely many . We find a new such set of -values, which gives a different perspective on why this phenomenon occurs and leads us to conjecture that uniformly optimal graphs exist only for finitely many . However, for , we conjecture that there are again infinitely many uniformly optimal graphs.44 pages, 26 figures. Some shortened arguments, clarifications, copyediting, two new figures. Comments welcom
Transport Company Awareness of e-CMR Adoption Opportunities and Benefits
No full textLõputöö eesmärk oli uurida, transpordiettevõtte teadlikkus elektroonilise kaubaveoteabe määrusest (eFTI) ja elektroonilisest veokirjast (e-CMR) ning selle kasutusele võtmise võimalused ja kasutegurid. Lõputöö käigus autor püstitas järgmised küsimused:
• Millisel tasemel transpordiettevõtted valdavad infot elektroonilise kaubaveoteabe määrusest (eFTI) ja elektroonilisest veokirjast (e-CMR)?
• Kas transpordiettevõtted valmis e-CMR-ile üleminekuks?
• Millist kasu saavad transpordiettevõtted e-CMRist ja eFTI määrusest?
Lõputöö eesmärgi saavutamiseks ja uurimisküsimustele vastamiseks, esiteks, autor tegi teoreetiline ülevaade elektroonilise veoselehest ja elektroonilise kaubaveoteabe määrusest. Teises peatükis tutvustab autor valitud uurimismeetodeid. Autor kasutas kvalitatiivne uurimis meetod. Uurimus keskendus ühe objekti süvaanalüüsile, transpordiettevõttele ning nende teadlikkusele elektroonilise kaubaveoteabe määrusest (eFTI) ja elektroonilisest veokirjast (e-CMR). Antud lõputöös andmed oli kogunud intervjuude kaudu. Lõputöö raames oli viinud läbi kokku viis intervjuud erinevate transpordiettevõtete töötajatega. Intervjuu eesmärk oli uurida üldine tehnoloogiline areng transpordiettevõttes ning nende teadlikus e-CMRi kohta. Viimaseks etappiks, autor analüüsib intervjuu tulemused ning selle põhjal teeb järeldused.
Intervjuu käigus selgus, et transpordiettevõtetel teadmised e-CMRi vastuvõtmisest ja eFTI määrusest keskmisel tasemel. See tähendab, et transpordiettevõtte töötajad kursis, et varsti on võimalik kõikidele Euroopa Liidu riikide esitada digitaalseid veodokumente, aga täpsemalt info puudub. Lähtudes sellest, autor teeb järelduse, et transpordiettevõtted ei ole veel valmis elektroonilise veoselehele täielikult üleminekuks. Neil on üldised teadmised, mis ei ole piisavalt, et töötada elektroonilise veoselehega. Nende teadmised põhinevad oletustel. Nagu vastajad ütlesid, neil on raske praegu kujutada ette, kuidas see kõik toimib. Aga kõik transpordiettevõtted väga ootavad seda digilahendust, sest siiamaani küllaltki palju dokumente liigub paberkandjal ning pidurdab tööprotsessid ja langeb efektiivsus. Transpordiettevõtted väga hästi saavad aru elektroonilise veoselehe eelised ning ootavad, millal oleks juba võimalik kasutada neid oma töös.
Selleks, et transpordiettevõtted saaksid lihtsalt ja kiiresti üle minna elektroonilisele veoselehele, on vaja juba praegu uurida informatsiooni selle kohta. Praegu kõik on arendusetapil, sellepärast, avalikus ei ole nii palju infot. See tähendab, et on vaja rohkem infot levitada meedias, et rohkem inimesi sellest teaks. Tulevikus konkurentsieelis on suurem ettevõtetel, kes kasutab erinevaid digilahendused oma töös, sest see on paratamatu tulevik logistikavaldkonnas. Mida varem transpordiettevõtted võtavad kasutusele elektroonilised veoselehed, seda suurem nende konkurents eelis.
Lõputööst saavad kasu kõigepealt ettevõtted, kes tegelevad protsesside digitaliseerimisega logistikasektoris. Nende jaoks, oleks hea teada transpordiettevõtte valmisolek e-CMRi üleminek ning nende teadlikkus sellest. Teiseks, saavad kasu transpordiettevõtted, saavad rohkem teada elektroonilise veoselehest ning elektroonilise kaubaveoteabe määrusest, sest avalikult ei ole mii palju infot selle kohta.
Lõputöö tulemusena selgub, et e-CMR kasutusele võtmine tooks ettevõttele kasu. Peamised eelised e- CMRi kasutamisel on aja ja ressurssi kokkuhoid, andmete kogumine ja sisestamine, dokumentide ettevalmistamine kõik need tegevused võtavad palju aega. Elektroonilise veoselehega on võimaik kõik need toimingud teha paar minuti jooksul. Teiseks on keskkonnasäästlikkus, tänapäeval väga suur probleem terve maailmas on keskkonnareostus, isegi kui logistikasektor keeldub paberdokumentidest, on see juba suur samm keskkonna keskkonnasäästlikkuse suunda. Suureneb läbipaistvus ja efektiivsus, elektrooniline veoseleht võimaldab reaalajas jälgida saadetisi kogu tarneahela ning saada tarne kinnitust, et kaup jõudis kohale. Elektrooniline veoseleht kohe kättesaadav kõigile tarneahelas osalejatele ning võimaldab kiirendada arvete esitamise protsessi. Viimaseks, on avalikule sektorile kasu. On võimalik kontrollida digitaalseid dokumente veokit peatamata, see tähendab, et juhil ei ole vaja raisata oma tööaega andmete kontrollimiseks. Seega suureneb andmete kättesaadavust, kiirendab kontrolliprotsessi ja loob paremat statistikat logistikast.Digitalization of processes is an inevitable future in logistics that awaits all transport companies. Every day in logistics moves a huge amount of information, the processing of which takes a lot of time and resources. Digitalization makes it possible to simplify logistics processes, reducing time and resource consumption and in the same time making them accurate and environmental. By 2025, the European Union has set a goal to adopt e-CMR and start to use them in logistics.
Due to the fact that the author of this thesis, works in logistics company and deals with CMR documents in daily work, the author became interested in CMR digitalization. Explore the possibilities of digitization in logistics in order to reduce time and resource consumption. Since e-CMR will be introduced in the near future, the author set a goal to investigate the transport company's awareness of the Electronic Freight Transport Information Regulation (eFTI) and e-CMR, possibilities and benefits of its implementation.
In order to achieve the goal of the thesis and to answer the research questions, firstly, the author makes a theoretical overview of the e-CMR and of the Electronic Freight Transport Information Regulation (eFTI). In the second part of the thesis, the author introduces the research strategy and methods. The author used a qualitative research method. The research focused on an in-depth analysis of one object, a transport company, and their awareness of eFTI and e-CMR. Data had been collected through interviews with people working in different transport companies. For interviews with companies, the author chose a semi-structured interview. The purpose of the interview was to investigate the general technological development in the transport companies and their awareness of e-CMR. As the last stage, the author analyzes the results of the interview and draws conclusions based on this.
By the results of the interview, found out, that transport companies have knowledge about the adoption of e-CMR and the eFTI at an average level. This means that the employees of the transport companies are aware that it will soon be possible to use electronic CMR to all European Union countries, but there is no more detailed information. Based on this, the author concludes that transport companies are not ready yet for a full transition to an e-CMR. They have general knowledge, which is not enough to work with an e-CMR. Their knowledge is based on assumptions. Transport companies understand very well the advantages of electronic CMR and looking forward to this digital solution, because til now quite a lot of documents are moving on paper, which takes a lot of time and slows down work processes.
In order for transport companies to easily and quickly go over to e-CMR, it is necessary to search information about it. Currently, everything is in the development stage, that's why there is not so much information in the media. This means that more information needs to be disseminated in the media so that more people know about it. Companies that use various digital solutions in their work will have a competitive advantage in the future, because this is the inevitable future in the logistics.
Benefit of this thesis will get first of all, the companies that are involved in the digitalization of processes in the logistics sector. For them, it would be good to know the readiness of the transport company for e- CMR transition and their awareness of it. Secondly, transport companies will benefit, they will learn more about the e-CMR and eFTI, because there is not much information about it publicly.
As a result of the thesis, found out that electronic CMR would bring benefits to companies. The main advantages of using electronic CMR are saving time and resources, because collecting and entering data, preparing documents, all these activities take a lot of time. With the e-CMR, it is possible to perform all these actions within a few minutes. The second is environmental sustainability, nowadays a very big problem in the whole world is environmental pollution, even if the logistics sector refuses paper documents, this is already a big step in the direction of environmental sustainability. Transparency and efficiency increase, the electronic CMR allows real-time tracking of shipments throughout the supply chain and confirmation of delivery. The electronic CMR is immediately available to all participants in the supply chain and allows to speed up the invoicing process. Finally, there are benefits to the public sector. It is possible to check digital documents without stopping the truck, which means that the driver does not need to waste his working time checking the data
Gleasons sats
No full textThis paper aims to present Gleason’s theorem and a full proof, by the most elementary
methods of analysis possible. Gleason’s theorem is an important theorem in the mathematical
foundations of quantum mechanics. It characterizes measures on closed subspaces
of separable Hilbert spaces of dimension at least 3. The theorem can be formulated in
terms of so-called frame functions. It states that all bounded frame functions, on the
specified Hilbert spaces, must have the form hAx, xi, for some self-adjoint operator A.
The theorem is proved by first proving the statement in R3, through mostly geometric
arguments on the unit sphere, and methods relating to convergence of sequences. It is
then shown that this implies the theorem in general Hilbert spaces of higher dimension.
The bulk of our proof follows the ideas of Cooke, Keane and Moran [2] with some own
additions and clarifications in order to make it more accessible and correct. A lemma of
single-variable analysis has been expanded, an oversight in the proof of the geometric
lemma 5 (Piron) has been fixed and an erroneous topological argument has led to the
much rewritten proposition 2 about extremal values of frame functions. The motivation
for the sufficiency of the proof in R3 for higher-dimensional Hilbert spaces follows the
ideas of the original proof by Andrew M. Gleason
Gleasons sats
No full textThis paper aims to present Gleason’s theorem and a full proof, by the most elementary methods of analysis possible. Gleason’s theorem is an important theorem in the mathematical foundations of quantum mechanics. It characterizes measures on closed subspaces of separable Hilbert spaces of dimension at least 3. The theorem can be formulated in terms of so-called frame functions. It states that all bounded frame functions, on the specified Hilbert spaces, must have the form hAx, xi, for some self-adjoint operator A. The theorem is proved by first proving the statement in R3, through mostly geometric arguments on the unit sphere, and methods relating to convergence of sequences. It is then shown that this implies the theorem in general Hilbert spaces of higher dimension. The bulk of our proof follows the ideas of Cooke, Keane and Moran [2] with some own additions and clarifications in order to make it more accessible and correct. A lemma of single-variable analysis has been expanded, an oversight in the proof of the geometric lemma 5 (Piron) has been fixed and an erroneous topological argument has led to the much rewritten proposition 2 about extremal values of frame functions. The motivation for the sufficiency of the proof in R3 for higher-dimensional Hilbert spaces follows the ideas of the original proof by Andrew M. Gleason
Radiofrequency/optical double resonance spactroscopy of .
No full text[1] D. R. Yarkony, J. Chem. Phys. 90, 7164 (1989). [2] D. C. Lorents, S. R. Keiding, and N. Bjerre, J. Chem. Phys. 90, 3096 (1989).Author Institution: Institute of Physics and Astronomy, Aarhus UniversityUsing a Ti-sapphire laser and a radiofrequency wave guide in combination with a fast, mass-selected beam of in the meta-stable a state, we have measured the fine structure splittings in the a and levels to a precision better than 15 kHz. The experimental spin-spin and spin-rotation coupling parameters and (in MHz) are well represented as second order polynomial in the internuclear separation, R (in atomic units): and Using these polynomial and the nuclear wavefunctions calculated from the a-state potential of Yarkony [1], we can reproduce the experimental values of and within 0.01 MHz. The laser excites molecules from the a-state to quasibound levels in the state, which decay by tunneling through the potential barrier of the c-state. The experimental linewidths agree well with those calculated using the empirical c-state potential of Lorents et al. [2
Espaces critiques pour le système des equations de Navier-Stokes incompressibles
No full textNo modification to the text. This work was done when the first author was at Université de Picardie.In this work, we exhibit abstract conditions on a functional space E who insure the existence of a global mild solution for small data in E or the existence of a local mild solution in absence of size constraints for a class of semi-linear parabolic equations, which contains the incompressible Navier-Stokes system as a fundamental example. We also give an abstract criterion toward regularity of the obtained solutions. These conditions, given in terms of Littlewood-Paley estimates for products of spectrally localized elements of , are simple to check in all known cases: Lebesgue, Lorents, Besov, Morrey... spaces. These conditions also apply to non-invariant spaces E and we give full details in the case of some 2-microlocal spaces. The following comments did not show on the first version: This article was written around 1998-99 and never published, because at that time, Koch and Tataru announced their result on well-posedness of Navier-stokes equations with initial data in . We believe though that some results and counterexamples here are of independent interest and we make them available electronically
OBSERVATION OF THE TRANSITION IN XeF
No full textAuthor Institution: Molecular Physics Laboratory, SRI International, produced by KrF Laser hotodissociation of , is excited by a doubled dye-laser to and and the broad-band and fluorescence is detected. The B and C states are distinguished by their differing decay rates at low pressure. Through its fluorescence excitation spectrum the transition is observed for the first time. The vibrational analysis of the C-X bands locates the level at below the level, and yields the first experimental vibrational constants for the C state and . A bandshape analysis of the C-X bands suggests that the equilibrium internuclear separation of the C state lies around 2.45 \AA. Vibrational relaxation and vibrationally resolved collision-induced dissociation of are also observed. Supported by the Defense Advanced Research Projects Agency under contract N0014-80-C-0506,through the office of Naval Research
Teach Yourself? Language Learning through Self-Instruction Manuals in Nineteenth-Century Scandinavia
No full textTo learn a foreign language from a self-instruction manual (teach-yourself book) is not as easy as the publishers will have us believe. Despite this, the genre has endured for many centuries. This thesis argues that the robustness of self-instruction language manuals is due to their ability to adapt to the personal circumstances of their readers. By surveying ordinary nineteenth-century Scandinavians, it is established that they turned to self-directed learning as a consequence of social and economic developments in the region.
At the time, early globalisation was felt in terms of increased travel and trade. As a consequence, people needed to acquire foreign languages for the purpose of everyday communication. Because this area of second language acquisition was practical and took place outside formal education, it has not been accepted as part of the history of applied linguistics. I argue that ‘utilitarian language learning’ deserves to be included as an example of the current theory of autonomous learning. I also draw the conclusion that autonomy is actually one of the reasons why self-instruction manuals are not as effective as traditional language teaching, because the learners take charge of their own learning process and as a result often suffer from lack of motivation and opportunities to practise the language. I do, however, maintain that the works themselves are not inherently inept. The nineteenth-century methods were actually an improvement upon existing methods by focusing on the spoken rather than the written language.
Finally, I investigate why abstract notions of language, culture and identity were not present in works that could essentially disseminate elitist ideas to the general population. I argue that because the genre was highly commercialised, the authors deliberately chose to exclude topics that had political undertones and the potential to alienate parts of the readership
