The Gellerstedt problem is considered for the elliptic-hyperbolic equation with a spectral parameter. There are two inclined-type change lines which form different arbitrary angles
and
with the ...x-axis. The eigenfunctions of this problem are constructed and the corresponding eigenvalues are found. The system of these eigenfunctions is proved to form a Riesz basis in the elliptic domain.
We construct the eigenfunctions of the Tricomi problem for the case in which the type change line of the elliptic-hyperbolic equation is inclined and forms an arbitrary angle
α
with the
x
-axis. ...These eigenfunctions form a basis in the elliptic domain. In addition, we find an integral constraint on the inclined type change line.
Conditions are presented under which two-part trigonometric systems arising in mixed type equations form a Riesz basis in the space of Lebesgue square integrable functions. For such systems, ...biorthogonal systems can be obtained in explicit form. As a result, an integral representation of the solution to the Frankl problem in a special domain can be found. The results are extended to two-part systems of broader functions.
We introduce a new collection of spoken English audio suitable for training speech recognition systems under limited or no supervision. It is derived from open-source audio books from the LibriVox ...project. It contains over 60K hours of audio, which is, to our knowledge, the largest freely-available corpus of speech. The audio has been segmented using voice activity detection and is tagged with SNR, speaker ID and genre descriptions. Additionally, we provide baseline systems and evaluation metrics working under three settings: (1) the zero resource/unsupervised setting (ABX), (2) the semi- supervised setting (PER, CER) and (3) the distant supervision setting (WER). Settings (2) and (3) use limited textual resources (10 minutes to 10 hours) aligned with the speech. Setting (3) uses large amounts of unaligned text. They are evaluated on the standard LibriSpeech dev and test sets for comparison with the supervised state-of-the-art.
The branching fraction ratio R(D^{*})≡B(Bover ¯^{0}→D^{*+}τ^{-}νover ¯_{τ})/B(Bover ¯^{0}→D^{*+}μ^{-}νover ¯_{μ}) is measured using a sample of proton-proton collision data corresponding to 3.0 ...fb^{-1} of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode τ^{-}→μ^{-}νover ¯_{μ}ν_{τ}. The semitauonic decay is sensitive to contributions from non-standard-model particles that preferentially couple to the third generation of fermions, in particular, Higgs-like charged scalars. A multidimensional fit to kinematic distributions of the candidate Bover ¯^{0} decays gives R(D^{*})=0.336±0.027(stat)±0.030(syst). This result, which is the first measurement of this quantity at a hadron collider, is 2.1 standard deviations larger than the value expected from lepton universality in the standard model.
Observations of exotic structures in the J/ψp channel, which we refer to as charmonium-pentaquark states, in Λ_{b}^{0}→J/ψK^{-}p decays are presented. The data sample corresponds to an integrated ...luminosity of 3 fb^{-1} acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude analysis of the three-body final state reproduces the two-body mass and angular distributions. To obtain a satisfactory fit of the structures seen in the J/ψp mass spectrum, it is necessary to include two Breit-Wigner amplitudes that each describe a resonant state. The significance of each of these resonances is more than 9 standard deviations. One has a mass of 4380±8±29 MeV and a width of 205±18±86 MeV, while the second is narrower, with a mass of 4449.8±1.7±2.5 MeV and a width of 39±5±19 MeV. The preferred J^{P} assignments are of opposite parity, with one state having spin 3/2 and the other 5/2.
The first full amplitude analysis of B^{+}→J/ψϕK^{+} with J/ψ→μ^{+}μ^{-}, ϕ→K^{+}K^{-} decays is performed with a data sample of 3 fb^{-1} of pp collision data collected at sqrts=7 and 8 TeV with ...the LHCb detector. The data cannot be described by a model that contains only excited kaon states decaying into ϕK^{+}, and four J/ψϕ structures are observed, each with significance over 5 standard deviations. The quantum numbers of these structures are determined with significance of at least 4 standard deviations. The lightest has mass consistent with, but width much larger than, previous measurements of the claimed X(4140) state.
A measurement of the phase difference between the short- and long-distance contributions to the Formula: see text decay is performed by analysing the dimuon mass distribution. The analysis is based ...on
collision data corresponding to an integrated luminosity of 3Formula: see text collected by the LHCb experiment in 2011 and 2012. The long-distance contribution to the Formula: see text decay is modelled as a sum of relativistic Breit-Wigner amplitudes representing different vector meson resonances decaying to muon pairs, each with their own magnitude and phase. The measured phases of the Formula: see text and Formula: see text resonances are such that the interference with the short-distance component in dimuon mass regions far from their pole masses is small. In addition, constraints are placed on the Wilson coefficients, Formula: see text and Formula: see text, and the branching fraction of the short-distance component is measured.
The data sample of Λ_{b}^{0}→J/ψpK^{-} decays acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3 fb^{-1}, is inspected for the presence of ...J/ψp or J/ψK^{-} contributions with minimal assumptions about K^{-}p contributions. It is demonstrated at more than nine standard deviations that Λ_{b}^{0}→J/ψpK^{-} decays cannot be described with K^{-}p contributions alone, and that J/ψp contributions play a dominant role in this incompatibility. These model-independent results support the previously obtained model-dependent evidence for P_{c}^{+}→J/ψp charmonium-pentaquark states in the same data sample.
A full amplitude analysis of Λ_{b}^{0}→J/ψpπ^{-} decays is performed with a data sample acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3 ...fb^{-1}. A significantly better description of the data is achieved when, in addition to the previously observed nucleon excitations N→pπ^{-}, either the P_{c}(4380)^{+} and P_{c}(4450)^{+}→J/ψp states, previously observed in Λ_{b}^{0}→J/ψpK^{-} decays, or the Z_{c}(4200)^{-}→J/ψπ^{-} state, previously reported in B^{0}→J/ψK^{+}π^{-} decays, or all three, are included in the amplitude models. The data support a model containing all three exotic states, with a significance of more than three standard deviations. Within uncertainties, the data are consistent with the P_{c}(4380)^{+} and P_{c}(4450)^{+} production rates expected from their previous observation taking account of Cabibbo suppression.
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