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

Intelligent machining methods for Ti6Al4V: a review

Digital manufacturing is a necessity to establishing a roadmap for the future manufacturing systems projected for the fourth industrial revolution. Intelligent features such as behavior prediction, decision- making abilities, and failure detection can be integrated into machining systems with computational methods and intelligent algorithms. This review reports on techniques for Ti6Al4V machining process modeling, among them numerical modeling with finite element method (FEM) and artificial intelligence- based models using artificial neural networks (ANN) and fuzzy logic (FL). These methods are intrinsically intelligent due to their ability to predict machining response variables. In the context of this review, digital image processing (DIP) emerges as a technique to analyze and quantify the machining response (digitization) in the real machining process, often used to validate and (or) introduce data in the modeling techniques enumerated above. The widespread use of these techniques in the future will be crucial for the development of the forthcoming machining systems as they provide data about the machining process, allow its interpretation and quantification in terms of useful information for process modelling and optimization, which will create machining systems less dependent on direct human intervention.publishe

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(-)