Existence of periodic solutions of pendulum-like ordinary and functional differential equations

The equation $$x''(t)=a(t,x(t))+b(t,x)+d(t,x)e(x'(t))$$ is considered, where $a:\mathbb{R}^2\to\mathbb{R}$, $b,d:\mathbb{R}\times C(\mathbb{R},\mathbb{R})\to\mathbb{R}$, $e:\mathbb{R}\to\mathbb{R}$ are continuous, and $a,b,d$ are $T$-periodic with respect to $t$. Using the Leray–Schauder degree theory we prove that a sign condition, in which $a$ dominates $b$, is sufficient for the existence of a $T$-periodic solution. The main theorem is applied to the equation of the forced damped pendulum

Measurement of CP violation parameters in B0 → DK*0 decays

An analysis of B 0 → D K * 0 decays is presented, where D represents an admixture of D 0 and ¯ D 0 mesons reconstructed in four separate final states: K − π + , π − K + , K + K − and π + π − . The data sample corresponds to 3.0     fb − 1 of proton-proton collision, collected by the LHCb experiment. Measurements of several observables are performed, including C P asymmetries. The most precise determination is presented of r B ( D K * 0 ) , the magnitude of the ratio of the amplitudes of the decay B 0 → D K + π − with a b → u or a b → c transition, in a K π mass region of ± 50     MeV / c 2 around the K ∗ ( 892 ) mass and for an absolute value of the cosine of the K * 0 helicity angle larger than 0.4

Measurement of CPCP violation parameters in B0→DK∗0{B}^{0}\rightarrow{}D{K}^{*0} decays

An analysis of ${B}^{0}\rightarrow{}D{K}^{*0}$ decays is presented, where $D$ represents an admixture of ${D}^{0}$ and ${\overline{D}}^{0}$ mesons reconstructed in four separate final states: ${K}^{-{}}{\pi{}}^{+}$, ${\pi{}}^{-{}}{K}^{+}$, ${K}^{+}{K}^{-{}}$ and ${\pi{}}^{+}{\pi{}}^{-{}}$. The data sample corresponds to $3.0\text{ }\text{ }{\mathrm{fb}}^{-{}1}$ of proton-proton collision, collected by the LHCb experiment. Measurements of several observables are performed, including $CP$ asymmetries. The most precise determination is presented of ${r}_{B}(D{K}^{*0})$, the magnitude of the ratio of the amplitudes of the decay ${B}^{0}\rightarrow{}D{K}^{+}{\pi{}}^{-{}}$ with a $b\rightarrow{}u$ or a $b\rightarrow{}c$ transition, in a $K\pi{}$ mass region of $\pm50 \text{ }\mathrm{MeV}/{c}^{2}$ around the ${K}^{*}(892)$ mass and for an absolute value of the cosine of the ${K}^{*0}$ helicity angle larger than 0.4

Faster Algorithms for the Geometric Transportation Problem

Let R, B be a set of n points in R^d, for constant d, where the points of R have integer supplies, points of B have integer demands, and the sum of supply is equal to the sum of demand. Let d(.,.) be a suitable distance function such as the L_p distance. The transportation problem asks to find a map tau : R x B --> N such that sum_{b in B}tau(r,b) = supply(r), sum_{r in R}tau(r,b) = demand(b), and sum_{r in R, b in B} tau(r,b) d(r,b) is minimized. We present three new results for the transportation problem when d(.,.) is any L_p metric: * For any constant epsilon > 0, an O(n^{1+epsilon}) expected time randomized algorithm that returns a transportation map with expected cost O(log^2(1/epsilon)) times the optimal cost. * For any epsilon > 0, a (1+epsilon)-approximation in O(n^{3/2}epsilon^{-d}polylog(U)polylog(n)) time, where U is the maximum supply or demand of any point. * An exact strongly polynomial O(n^2 polylog n) time algorithm, for d = 2

Study of the suppressed decays B-->[K+pi(-)](D)K- and B-->[K+pi(-)](D)pi(-) - art. no. 09160

We report a study of the suppressed decays B- -> [K(+)pi(-)](D)K- and B- -> [K+ pi(-)](D)pi(-), where [K+ pi(-)](D) indicates that the K(+)pi(-) pair originates from a neutral D meson. These decay modes are sensitive to the unitarity triangle angle phi(3). We use a data sample containing 275x10(6) B (B) over bar pairs recorded at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric e(+)e(-) storage ring. The signal for B- -> [K+ pi(-)](D)K- is not statistically significant, and we set a limit r(B) (D) over bar K-0(-))/A(B- -> (DK-)-K-0)vertical bar. We observe a signal with 6.4 sigma statistical significance in the related mode, B- -> [K(+)pi(-)](D)pi(-)