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    Wyświetlanie 1-6 z 6
    Tytuł:
    Embedding Cohen algebras using pcf theory
    Autorzy:
    Shelah, Saharon
    Powiązania:
    https://bibliotekanauki.pl/articles/1204996.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    set theory
    pcf
    forcing
    Opis:
    Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν, adds a generic for the Cohen forcing notion on $ν^+$.
    Źródło:
    Fundamenta Mathematicae; 2000, 166, 1-2; 83-86
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cellularity of free products of Boolean algebras (or topologies)
    Autorzy:
    Shelah, Saharon
    Powiązania:
    https://bibliotekanauki.pl/articles/1205001.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    set theory
    pcf
    Boolean algebras
    cellularity
    product
    colourings
    Opis:
    The aim this paper is to present an answer to Problem 1 of Monk [10], [11]. We do this by proving in particular that if μ is a strong limit singular cardinal, $θ = (2^{cf(μ)})^+$ and $2^μ = μ^+$ then there are Boolean algebras $\mathbb{B}_1,\mathbb{B}_2$ such that
    $c(\mathbb{B}_1) = μ, c(\mathbb{B}_2) < θ but c(\mathbb{B}_1*\mathbb{B}_2)=μ^+$.
    Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if $\mathbb{B}$ is a ccc Boolean algebra and $μ^{ℶ_ω} ≤ λ = cf(λ) ≤ 2^μ$ then $\mathbb{B}$ satisfies the λ-Knaster condition (using the "revised GCH theorem").
    Źródło:
    Fundamenta Mathematicae; 2000, 166, 1-2; 153-208
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong covering without squares
    Autorzy:
    Shelah, Saharon
    Powiązania:
    https://bibliotekanauki.pl/articles/1204997.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    set theory
    covering
    strong covering lemma
    pcf theory
    Opis:
    Let W be an inner model of ZFC. Let κ be a cardinal in V. We say that κ-covering holds between V and W iff for all X ∈ V with X ⊆ ON and V ⊨ |X| < κ, there exists Y ∈ W such that X ⊆ Y ⊆ ON and V ⊨ |Y| < κ. Strong κ-covering holds between V and W iff for every structure M ∈ V for some countable first-order language whose underlying set is some ordinal λ, and every X ∈ V with X ⊆ λ and V ⊨ |X| < κ, there is Y ∈ W such that X ⊆ Y ≺ M and V ⊨ |Y| < κ.
      We prove that if κ is V-regular, $κ^+_V = κ^+_W$, and we have both κ-covering and $κ^+$-covering between W and V, then strong κ-covering holds. Next we show that we can drop the assumption of $κ^+$-covering at the expense of assuming some more absoluteness of cardinals and cofinalities between W and V, and that we can drop the assumption that $κ^+_W = κ^+_V$ and weaken the $κ^+$-covering assumption at the expense of assuming some structural facts about W (the existence of certain square sequences).
    Źródło:
    Fundamenta Mathematicae; 2000, 166, 1-2; 87-107
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fusion splicing: the penalty of increasing the collapse length of the air holes in ESM-12B photonic crystal fibers
    Autorzy:
    Adnan, S. A.
    Abdulwahhab, A. W.
    Ismail, S.N.
    Powiązania:
    https://bibliotekanauki.pl/articles/174083.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    photonic crystal fiber
    PCF
    collapse length
    mode field diameter
    MFD
    fusion splicing
    guiding mechanisms
    Opis:
    For optimum fusion splicing process of a photonic crystal fiber, the collapsing of the air holes at any photonic crystal fiber is the key point of either increasing or decreasing the total splice loss. In this paper, an experimental study has been carried out to investigate the relation between total splice loss or total fiber attenuation due to splice loss and the length of the collapsed region of the air holes. This is done by splicing ESM-12B photonic crystal fiber between two equal lengths of single mode fibers and measuring the attenuation at different arc times and arc powers. The results showed that the increase in the length of the collapsed air holes region results in higher loss, therefore, higher fiber attenuation.
    Źródło:
    Optica Applicata; 2016, 46, 2; 265-275
    0078-5466
    1899-7015
    Pojawia się w:
    Optica Applicata
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Polarity-reversed ultra-wideband monocycle pulse generation with dual-channel multicasting in a photonic crystal fiber
    Autorzy:
    Gong, J
    Hui, Z
    Powiązania:
    https://bibliotekanauki.pl/articles/173791.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    nonlinear optics
    cross-phase modulation (XPM)
    radio frequency photonics
    ultra-wideband (UWB)
    photonic crystal fiber (PCF)
    Opis:
    This paper proposes and demonstrates a novel scheme of a two-channel-output ultra-wideband monocycle pulse generator consisting of a 100 m dispersion-flattened highly nonlinear photonic crystal fiber and two optical bandpass filters. Based on the cross-phase modulation effect in a dispersion-flattened highly nonlinear photonic crystal fiber, two polarity-reversed ultra-wideband monocycle pulses simultaneously output from two different channels are successfully achieved by appropriately locating the probe wavelength at the left linear slope and the right linear slope of the two optical bandpass filters transmission spectra, respectively. The full width at half-maximum and a fractional bandwidth of 24 ps and 260% for a positive pulse, 24 ps and 251% for a negative pulse are obtained. Moreover, the influences of input signal powers, the polarization misalignment between the data light and the continuous wave probe light, and probe wavelength variation on the double output ultra-wideband signals quality are also investigated. The results show that the system has some tolerance to both the input signal power fluctuation and the slight polarization mismatch and even can efficiently operate with a widely tunable wavelength range. This makes it very attractive for engineering applications in future multiuser ultra-wideband-over-fiber communication systems.
    Źródło:
    Optica Applicata; 2015, 45, 1; 25-39
    0078-5466
    1899-7015
    Pojawia się w:
    Optica Applicata
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On what I do not understand (and have something to say): Part I
    Autorzy:
    Shelah, Saharon
    Powiązania:
    https://bibliotekanauki.pl/articles/1204995.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    set theory
    cardinal arithmetic
    pcf theory
    forcing
    iterated forcing
    large continuum
    nep
    nicely definable forcing
    combinatorial set theory
    Boolean algebras
    set-theoretic algebra
    partition calculus
    Ramsey theory
    Opis:
    This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdotes and opinions. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history and side references are erratic, usually kept to a minimum ("see ..." means: see the references there and possibly the paper itself). The base were lectures in Rutgers, Fall '97, and reflect my knowledge then. The other half, [122], concentrating on model theory, will subsequently appear. I thank Andreas Blass and Andrzej Rosłanowski for many helpful comments.
    Źródło:
    Fundamenta Mathematicae; 2000, 166, 1-2; 1-82
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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