An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations

We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic, including applications to coincidence points. An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given

A study of CP violation in B-+/- -> DK +/- and B-+/- -> D pi(+/-) decays with D -> (KSK +/-)-K-0 pi(-/+) final states

A first study of CP violation in the decay modes $B^\pm\to [K^0_{\rm S} K^\pm \pi^\mp]_D h^\pm$ and $B^\pm\to [K^0_{\rm S} K^\mp \pi^\pm]_D h^\pm$, where $h$ labels a $K$ or $\pi$ meson and $D$ labels a $D^0$ or $\overline{D}^0$ meson, is performed. The analysis uses the LHCb data set collected in $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{-1}$. The analysis is sensitive to the CP-violating CKM phase $\gamma$ through seven observables: one charge asymmetry in each of the four modes and three ratios of the charge-integrated yields. The results are consistent with measurements of $\gamma$ using other decay modes

Measurement of the (eta c)(1S) production cross-section in proton-proton collisions via the decay (eta c)(1S) -> p(p)over-bar

The production of the $\eta_c (1S)$ state in proton-proton collisions is probed via its decay to the $p \bar{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5$ GeV/c. The cross-section for prompt production of $\eta_c (1S)$ mesons relative to the prompt $J/\psi$ cross-section is measured, for the first time, to be $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.74 \pm 0.29 \pm 0.28 \pm 0.18 _{B}$ at a centre-of-mass energy $\sqrt{s} = 7$ TeV using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$, and $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{B}$ at $\sqrt{s} = 8$ TeV using 2.0 fb$^{-1}$. The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta_c (1S)$ and $J/\psi$ decays to the $p \bar{p}$ final state. In addition, the inclusive branching fraction of $b$-hadron decays into $\eta_c (1S)$ mesons is measured, for the first time, to be $B ( b \rightarrow \eta_c X ) = (4.88 \pm 0.64 \pm 0.25 \pm 0.67 _{B}) \times 10^{-3}$, where the third uncertainty includes also the uncertainty on the $J/\psi$ inclusive branching fraction from $b$-hadron decays. The difference between the $J/\psi$ and $\eta_c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1$ MeV/c$^2$.The production of the $\eta _c (1S)$ state in proton-proton collisions is probed via its decay to the $p\overline{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5 \mathrm{{\,GeV/}{ c}}$ . The cross-section for prompt production of $\eta _c (1S)$ mesons relative to the prompt ${{ J}}/{\psi }$ cross-section is measured, for the first time, to be $\sigma _{\eta _c (1S)}/\sigma _{{{{ J}}/{\psi }}} = 1.74\, \pm \,0.29\, \pm \, 0.28\, \pm \,0.18 _{{\mathcal{B}}}$ at a centre-of-mass energy ${\sqrt{s}} = 7 {~\mathrm{TeV}}$ using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$ , and $\sigma _{\eta _c (1S)}/\sigma _{{{{ J}}/{\psi }}} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{{\mathcal{B}}}$ at ${\sqrt{s}} = 8 {~\mathrm{TeV}}$ using 2.0 fb$^{-1}$ . The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta _c (1S)$ and ${{ J}}/{\psi }$ decays to the $p\overline{p}$ final state. In addition, the inclusive branching fraction of ${b}$ -hadron decays into $\eta _c (1S)$ mesons is measured, for the first time, to be ${\mathcal{B}}( b {\rightarrow } \eta _c X ) = (4.88\, \pm \,0.64\, \pm \,0.29\, \pm \, 0.67 _{{\mathcal{B}}}) \times 10^{-3}$ , where the third uncertainty includes also the uncertainty on the ${{ J}}/{\psi }$ inclusive branching fraction from ${b}$ -hadron decays. The difference between the ${{ J}}/{\psi }$ and $\eta _c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1 {\mathrm {\,MeV\!/}c^2}$ .The production of the $\eta_c (1S)$ state in proton-proton collisions is probed via its decay to the $p \bar{p}$ final state with the LHCb detector, in the rapidity range $2.0 6.5$ GeV/c. The cross-section for prompt production of $\eta_c (1S)$ mesons relative to the prompt $J/\psi$ cross-section is measured, for the first time, to be $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.74 \pm 0.29 \pm 0.28 \pm 0.18 _{B}$ at a centre-of-mass energy $\sqrt{s} = 7$ TeV using data corresponding to an integrated luminosity of 0.7 fb$^{-1}$, and $\sigma_{\eta_c (1S)}/\sigma_{J/\psi} = 1.60 \pm 0.29 \pm 0.25 \pm 0.17 _{B}$ at $\sqrt{s} = 8$ TeV using 2.0 fb$^{-1}$. The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the $\eta_c (1S)$ and $J/\psi$ decays to the $p \bar{p}$ final state. In addition, the inclusive branching fraction of $b$-hadron decays into $\eta_c (1S)$ mesons is measured, for the first time, to be $B ( b \rightarrow \eta_c X ) = (4.88 \pm 0.64 \pm 0.29 \pm 0.67 _{B}) \times 10^{-3}$, where the third uncertainty includes also the uncertainty on the $J/\psi$ inclusive branching fraction from $b$-hadron decays. The difference between the $J/\psi$ and $\eta_c (1S)$ meson masses is determined to be $114.7 \pm 1.5 \pm 0.1$ MeV/c$^2$

Search for CP violation using T-odd correlations in D-0 -> K+K-pi(+)pi(-) decays

A search for $CP$ violation using $T$-odd correlations is performed using the four-body $D^0 \to K^+K^-\pi^+\pi^-$ decay, selected from semileptonic $B$ decays. The data sample corresponds to integrated luminosities of $1.0\,\text{fb}^{-1}$ and $2.0\,\text{fb}^{-1}$ recorded at the centre-of-mass energies of 7 TeV and 8 TeV, respectively. The $CP$-violating asymmetry $a_{CP}^{T\text{-odd}}$ is measured to be $(0.18\pm 0.29\text{(stat)}\pm 0.04\text{(syst)})\%$. Searches for $CP$ violation in different regions of phase space of the four-body decay, and as a function of the $D^0$ decay time, are also presented. No significant deviation from the $CP$ conservation hypothesis is found

Measurement of CP asymmetry in B-s(0) -> D-s(-/+) K--/+ decays

We report on measurements of the time-dependent CP violating observables in $B^0_s\rightarrow D^{\mp}_s K^{\pm}$ decays using a dataset corresponding to 1.0 fb$^{-1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables $C_f=0.53\pm0.25\pm0.04$, $A^{\Delta\Gamma}_f=0.37\pm0.42\pm0.20$, $A^{\Delta\Gamma}_{\bar{f}}=0.20\pm0.41\pm0.20$, $S_f=-1.09\pm0.33\pm0.08$, $S_{\bar{f}}=-0.36\pm0.34\pm0.08$, where the uncertainties are statistical and systematic, respectively. We use these observables to make the first measurement of the CKM angle $\gamma$ in $B^0_s\rightarrow D^{\mp}_s K^{\pm}$ decays, finding $\gamma$ = (115$_{-43}^{+28}$)$^\circ$ modulo 180$^\circ$ at 68% CL, where the error contains both statistical and systematic uncertainties.We report on measurements of the time-dependent CP violating observables in B$_{s}^{0}$  → D$_{s}^{∓}$ K$^{±}$ decays using a dataset corresponding to 1.0 fb$^{−1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables C$_{f}$ = 0.53±0.25±0.04, A$_{f}^{ΔΓ}$  = 0.37 ± 0.42 ± 0.20, ${A}_{\overline{f}}^{\varDelta \varGamma }=0.20\pm 0.41\pm 0.20$ , S$_{f}$ = −1.09±0.33±0.08, ${S}_{\overline{f}}=-0.36\pm 0.34\pm 0.08$ , where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the B$_{s}^{0}$ mixing phase −2β$_{s}$ leads to the first extraction of the CKM angle γ from B$_{s}^{0}$  → D$_{s}^{∓}$ K$^{±}$ decays, finding γ = (115$_{− 43}^{+ 28}$ )° modulo 180° at 68% CL, where the error contains both statistical and systematic uncertainties.We report on measurements of the time-dependent CP violating observables in $B^0_s\rightarrow D^{\mp}_s K^{\pm}$ decays using a dataset corresponding to 1.0 fb$^{-1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables $C_f=0.53\pm0.25\pm0.04$, $A^{\Delta\Gamma}_f=0.37\pm0.42\pm0.20$, $A^{\Delta\Gamma}_{\bar{f}}=0.20\pm0.41\pm0.20$, $S_f=-1.09\pm0.33\pm0.08$, $S_{\bar{f}}=-0.36\pm0.34\pm0.08$, where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the $B^0_s$ mixing phase $-2\beta_s$ leads to the first extraction of the CKM angle $\gamma$ from $B^0_s \rightarrow D^{\mp}_s K^{\pm}$ decays, finding $\gamma$ = (115$_{-43}^{+28}$)$^\circ$ modulo 180$^\circ$ at 68% CL, where the error contains both statistical and systematic uncertainties

Measurement of Upsilon production in collisions at root s=2.76 TeV

The production of $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ mesons decaying into the dimuon final state is studied with the LHCb detector using a data sample corresponding to an integrated luminosity of 3.3 $pb^{-1}$ collected in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=2.76$ TeV. The differential production cross-sections times dimuon branching fractions are measured as functions of the $\Upsilon$ transverse momentum and rapidity, over the ranges $p_{\rm T} Upsilon(1S) X) x B(Upsilon(1S) -> mu+mu-) = 1.111 +/- 0.043 +/- 0.044 nb, sigma(pp -> Upsilon(2S) X) x B(Upsilon(2S) -> mu+mu-) = 0.264 +/- 0.023 +/- 0.011 nb, sigma(pp -> Upsilon(3S) X) x B(Upsilon(3S) -> mu+mu-) = 0.159 +/- 0.020 +/- 0.007 nb, where the first uncertainty is statistical and the second systematic

Study of forward Z + jet production in pp collisions at √s=7 TeV

A measurement of the $Z(\rightarrow\mu^+\mu^-)$+jet production cross-section in $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 7$ TeV is presented. The analysis is based on an integrated luminosity of $1.0\,\text{fb}^{-1}$ recorded by the LHCb experiment. Results are shown with two jet transverse momentum thresholds, 10 and 20 GeV, for both the overall cross-section within the fiducial volume, and for six differential cross-section measurements. The fiducial volume requires that both the jet and the muons from the Z boson decay are produced in the forward direction ($2.0<\eta<4.5$). The results show good agreement with theoretical predictions at the second-order expansion in the coupling of the strong interaction.A measurement of the $Z(\rightarrow\mu^+\mu^-)$+jet production cross-section in $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 7$ TeV is presented. The analysis is based on an integrated luminosity of $1.0\,\text{fb}^{-1}$ recorded by the LHCb experiment. Results are shown with two jet transverse momentum thresholds, 10 and 20 GeV, for both the overall cross-section within the fiducial volume, and for six differential cross-section measurements. The fiducial volume requires that both the jet and the muons from the Z boson decay are produced in the forward direction ($2.0<\eta<4.5$). The results show good agreement with theoretical predictions at the second-order expansion in the coupling of the strong interaction

ATTRACTORS THEORY FOR AUTONOMOUS SYSTEMS OF HYDRODYNAMICS AND ITS APPLICATION TO BINGHAM MODEL OF FLUID MOTION

In the study of solutions behavior of various mathematical physics equations their limit state when time tends to infinity (so-called attractors) is of particular interest. At the works of russian mathematicians M.I. Vishik and V.V. Chepyzhov and american mathematician G. Sell a new approach for the attractors study based on the consideration of trajectory spaces and trajectory attractors of the corresponding equations was proposed. However, for a large number of hydrodynamics equations this theory could not be applied because of the conditions of the translational invariance and of the closure of a trajectory space. In the introduction of this article a brief summary of the attractors theory for autonomous systems based on the concept of the trajectory space without the assumption of its translational invariance is presented. As an application of this theory, the existence of the global attractor for autonomous model of the Bingham medium motion in the case of periodic spatial variables in proved