Gaussian limits for multidimensional random sequential packing at saturation (extended version)

Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is asymptotically normal as $\lambda \to \infty$. We provide a rate of approximation to the normal and show that the finite dimensional distributions of the packing measures converge to those of a mean zero generalized Gaussian field. The method of proof involves showing that the collection of accepted solids satisfies the weak spatial dependence condition known as stabilization.Comment: 31 page

On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

Vicious Walkers and Hook Young Tableaux

We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy--Widom distribution, which is same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.Comment: 23 pages, 5 figure

Search for lepton-flavour-violating decays of Higgs-like bosons.

A search is presented for a Higgs-like boson with mass in the range 45 to 195 GeV/c2 decaying into a muon and a tau lepton. The dataset consists of proton-proton interactions at a centre-of-mass energy of 8 TeV , collected by the LHCb experiment, corresponding to an integrated luminosity of 2 fb-1 . The tau leptons are reconstructed in both leptonic and hadronic decay channels. An upper limit on the production cross-section multiplied by the branching fraction at 95% confidence level is set and ranges from 22 pb for a boson mass of 45 GeV/c2 to 4 pb for a mass of 195 GeV/c2

ЛАПАРОСКОПИЧЕСКАЯ ГАСТРЭКТОМИЯ С ЕЮНОГАСТРОПЛАСТИКОЙ

The arm of the research. To develop a way to perform the laparoscopic total gastrectomy with jejunal interposition (Longmire’s procedure).Material and methods. The study presents the technology of laparoscopic total gastrectomy with a lymph node dissection D1α and jejunal interposition. After removal of the gaster with the tumor through a mini-laparotomy (2 inch), the jejunum was cut approximately45 cm distally to the ligament of Treitz. A circular stapler was used to perform an esophago-jejunostomy with Roux-en-Y reconstruction using a standard technology. The second stage is forming a segment of the small intestine for jejunal interposition. The third stage is entering the head of the circular stapling apparatus into the stump of the duodenum on a probe retrogradely through the afferent loop of the small intestine. The fourth stage is stapled anastomosis between a free segment of the jejunum and the duodenum with the circular stapler. The procedure is finalized with hand-sewn anastomosis between the afferent and efferent loops of the small intestine.Results. The presented technology was used to perform surgery on one patient. The increase in operative time did not lead to increased intraoperative blood loss and longer post-operative bed-days. After 1 year the patient shows no evidence of a tumor progression, manifestations of reflux esophagitis, and dumping syndrome. Conclusion. The proposed technology allows laparoscopic total gastrectomy with jejunal interposition via a mini-invasive technology. Цель исследования – разработать способ выполнения лапароскопической гастрэктомии с сохранением пассажа по ДПК путём пластики сегментом тонкой кишки без формирования резервуара.Материал и методы. Представлена технология лапароскопической гастрэктомии с лимфодиссекцией Д1α и пластикой желудка сегментом тонкой кишки с включением в пассаж двенадцатиперстной кишки без формирования резервуара. Производится лапароскопическая гастрэктомия. После удаления препарата через минидоступ первым этапом накладывается циркулярным аппаратом эзофагоэнтероанастомоз на Ру-петле по стандартной технологии. Вторым этапом формируется интерпонируемый сегмент тонкой кишки из Рупетли. Третьим этапом в культю двенадцатиперстной кишки вводится головка циркулярного сшивающего аппарата ретроградно на зонде через приводящую петлю тонкой кишки. Четвёртым этапом накладывается аппаратный еюнодуоденоанастомоз между сегментом тонкой кишки и двенадцатиперстной кишкой. Операция завершается наложением анастомоза между приводящей и отводящей петлями тонкой кишки.Результаты. По описанной технологии прооперирован один пациент. Увеличение времени операции не привело к увеличению интраоперационной кровопотери и удлинению послеоперационного койко-дня. Через 1 год у больного нет признаков опухолевого прогрессирования, проявлений рефлюкс-эзофагита и демпинг-синдрома.Заключение. Предлагаемая схема лапароскопической гастрэктомии позволяет выполнить операцию с еюногастропластикой по мини-инвазивной технологии.

Observation of an Excited Bc+ State

Using pp collision data corresponding to an integrated luminosity of 8.5 fb-1 recorded by the LHCb experiment at center-of-mass energies of s=7, 8, and 13 TeV, the observation of an excited Bc+ state in the Bc+π+π- invariant-mass spectrum is reported. The observed peak has a mass of 6841.2±0.6(stat)±0.1(syst)±0.8(Bc+) MeV/c2, where the last uncertainty is due to the limited knowledge of the Bc+ mass. It is consistent with expectations of the Bc∗(2S31)+ state reconstructed without the low-energy photon from the Bc∗(1S31)+→Bc+γ decay following Bc∗(2S31)+→Bc∗(1S31)+π+π-. A second state is seen with a global (local) statistical significance of 2.2σ (3.2σ) and a mass of 6872.1±1.3(stat)±0.1(syst)±0.8(Bc+) MeV/c2, and is consistent with the Bc(2S10)+ state. These mass measurements are the most precise to date

Bose-Einstein correlations of same-sign charged pions in the forward region in pp collisions at √s=7 TeV

Bose-Einstein correlations of same-sign charged pions, produced in protonproton collisions at a 7 TeV centre-of-mass energy, are studied using a data sample collected by the LHCb experiment. The signature for Bose-Einstein correlations is observed in the form of an enhancement of pairs of like-sign charged pions with small four-momentum difference squared. The charged-particle multiplicity dependence of the Bose-Einstein correlation parameters describing the correlation strength and the size of the emitting source is investigated, determining both the correlation radius and the chaoticity parameter. The measured correlation radius is found to increase as a function of increasing charged-particle multiplicity, while the chaoticity parameter is seen to decreas

Study of J /ψ production in Jets

The production of J/ψ mesons in jets is studied in the forward region of proton-proton collisions using data collected with the LHCb detector at a center-of-mass energy of 13 TeV. The fraction of the jet transverse momentum carried by the J/ψ meson, z(J/ψ)≡pT(J/ψ)/pT(jet), is measured using jets with pT(jet)>20 GeV in the pseudorapidity range 2.5<η(jet)<4.0. The observed z(J/ψ)distribution for J/ψ mesons produced in b-hadron decays is consistent with expectations. However, the results for prompt J/ψ production do not agree with predictions based on fixed-order nonrelativistic QCD. This is the first measurement of the pT fraction carried by prompt J/ψ mesons in jets at any experiment

Study of charmonium production in b -hadron decays and first evidence for the decay Bs0

Using decays to φ-meson pairs, the inclusive production of charmonium states in b-hadron decays is studied with pp collision data corresponding to an integrated luminosity of 3.0 fb−1, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. Denoting byBC ≡ B(b → C X) × B(C → φφ) the inclusive branching fraction of a b hadron to a charmonium state C that decays into a pair of φ mesons, ratios RC1C2 ≡ BC1 /BC2 are determined as Rχc0ηc(1S) = 0.147 ± 0.023 ± 0.011, Rχc1ηc(1S) =0.073 ± 0.016 ± 0.006, Rχc2ηc(1S) = 0.081 ± 0.013 ± 0.005,Rχc1 χc0 = 0.50 ± 0.11 ± 0.01, Rχc2 χc0 = 0.56 ± 0.10 ± 0.01and Rηc(2S)ηc(1S) = 0.040 ± 0.011 ± 0.004. Here and below the first uncertainties are statistical and the second systematic.Upper limits at 90% confidence level for the inclusive production of X(3872), X(3915) and χc2(2P) states are obtained as RX(3872)χc1 < 0.34, RX(3915)χc0 < 0.12 andRχc2(2P)χc2 < 0.16. Differential cross-sections as a function of transverse momentum are measured for the ηc(1S) andχc states. The branching fraction of the decay B0s → φφφ is measured for the first time, B(B0s → φφφ) = (2.15±0.54±0.28±0.21B)×10−6. Here the third uncertainty is due to the branching fraction of the decay B0s → φφ, which is used for normalization. No evidence for intermediate resonances is seen. A preferentially transverse φ polarization is observed.The measurements allow the determination of the ratio of the branching fractions for the ηc(1S) decays to φφ and p p asB(ηc(1S)→ φφ)/B(ηc(1S)→ p p) = 1.79 ± 0.14 ± 0.32