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The $\mathrm{^2H}(d,p)\mathrm{^3H}$ bare nucleus astrophysical S(E) factor has been measured indirectly at energies from about 500 keV down to several keV by means of the Trojan-horse method applied to the quasi-free process $\mathrm{^2H({}^6Li},pt)\mathrm{^4He}$ induced at the lithium beam energy of 11 and 9.5 MeV, which makes the virtual binary process incident energy $\mathrm {E}_{dd}^{qf}$ go much closer to the zero-quasi-free-energy point than that in the previous similar experiment. The obtained results are compared with direct data as well as with previous indirect investigation of the same binary reactions. It shows that the precision of S(E) data in low energy range extracted via the same Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$ ) becomes better when the incident energy decreases from high value down to the zero-quasi-free-energy point. The very good agreement between data extracted from different Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$ vs. $\mathrm{^3He}=(d \oplus p)$) gives a strong updated test for the independence of the binary indirect cross section on the chosen Trojan horse nucleus at low energies., Comment: 6 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1503.08672

The study of d(d,p)t reaction is very important for the nucleosynthesis in both standard Big Bang and stellar evolution, as well as for the future fusion reactors planning of energy production. The d(d,p)t bare nucleus astrophysical S(E) factor has been measured indirectly at energies from about 400 keV down to several keV by means of the Trojan horse method applied to the quasi-free process $\rm {}^2H({}^6Li,pt){}^4He$ induced at a lithium beam energy of 9.5 MeV, which is closer to the zero quasi-free energy point. An accurate analysis leads to the determination of the $\rm S_{bare}(0)=56.7 \pm 2.0 keV \cdot b$ and of the corresponding electron screening potential $\rm U_e = 13.2 \pm 4.3 eV$. In addition, this work gives an updated test for the Trojan horse nucleus invariance comparing with previous indirect investigations using $\rm {}^3He=(d+p)$ breakup., Comment: 6 pages, 7 figures

The Coulomb barrier and electron screening cause difficulties in directly measuring nuclear reaction cross sections of charged particles in astrophysical energies. The Trojan-horse method has been introduced to solve the difficulties as a powerful indirect tool. In order to understand experimental spectra better, Geant4 is employed to simulate the method for the first time. Validity and reliability of the simulation are examined by comparing the experimental data with simulated results. The Geant4 simulation can give useful information to understand the experimental spectra better in data analysis and is beneficial to the design for future related experiments., Comment: 4 pages, 5 figures

The $^{10}$B(p,$\alpha_0$)$^7$Be bare nucleus astrophysical S(E)-factor has been measured for the first time at energies from about 100 keV down to about 5 keV by means of the Trojan Horse Method (THM). In this energy region, the S(E)-factor is strongly dominated by the 8.699 MeV $^{11}$C level (J$^{\pi}$=$\frac{5}{2}$$^+$), producing an s-wave resonance centered at about 10 keV in the entrance channel. Up to now, only the high energy tail of this resonant has been measured, while the low-energy trend is extrapolated from the available direct data. The THM has been applied to the quasi-free $^2$H($^{10}$B,$\alpha_0$$^7$Be)n reaction induced at a boron-beam energy of 24.5 MeV. An accurate analysis brings to the determination of the $^{10}$B(p,$\alpha_0$)$^7$Be S(E)-factor and of the corresponding electron screening potential $U_e$, thus giving for the first time an independent evaluation of it., Comment: Authors thank the (anonymous) referee for detailed comments and suggestions. The paper is already submitted to Physical Review C

We consider a natural mechanical system on a Finsler manifold and study its \emph{curvature} using the intrinsic Jacobi equations (called \emph{Jacobi curves}) along the extremals of the least action of the system. The curvature for such a system is expressed in terms of the Riemann curvature and the Chern curvature (involving the gradient of the potential) of the Finsler manifold and the Hessian of the potential w.r.t. a Riemannian metric induced from the Finslerian metric. As an application, we give sufficient conditions for the Hamiltonian flows of the least action to be hyperbolic and show new examples of Anosov flows., Comment: We used (3.4.4) in Bao&Chern&Chen GTM 200 to clarify some formulae

We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for a natural sub-Riemannian structure defined on Sasakian manifolds. This generalizes the earlier work for the three dimensional case., Comment: 38 pages

Measure contraction properties are generalizations of the notion of Ricci curvature lower bounds in Riemannian geometry to more general metric measure spaces. In this paper, we give sufficient conditions for a Sasakian manifold equipped with a natural sub-Riemannian distance to satisfy these properties. Moreover, the sufficient conditions are defined by the Tanaka-Webster curvature. This generalizes the earlier work in \cite{AgLe1} for the three dimensional case and in \cite{Ju} for the Heisenberg group. To obtain our results we use the intrinsic Jacobi equations along sub-Riemannian extremals, coming from the theory of canonical moving frames for curves in Lagrangian Grassmannians \cite{LiZe1, LiZe2}. The crucial new tool here is a certain decoupling of the corresponding matrix Riccati equation. It is also worth pointing out that our method leads to exact formulas for the measure contraction in the case of the corresponding homogeneous models in the considered class of sub-Riemannian structures., Comment: 25 pages

A new video coding method based on compressive sampling is proposed. In this method, a video is coded using compressive measurements on video cubes. Video reconstruction is performed by minimization of total variation (TV) of the pixelwise DCT coefficients along the temporal direction. A new reconstruction algorithm is developed from TVAL3, an efficient TV minimization algorithm based on the alternating minimization and augmented Lagrangian methods. Video coding with this method is inherently scalable, and has applications in mobile broadcast., Comment: 9 pages, 12 figures

Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf fibration naturally appear in quantum mechanics. We study the curvature maps for such a sub-Riemannian structure and express them using the Riemannian curvature tensor of the Fubini-Study metric of the complex projective space and the curvature form of the Hopf fibration. We also estimate the number of conjugate points of a sub-Riemannian extremal in terms of the bounds of the sectional curvature and the curvature form. It presents a typical example for the study of curvature maps and comparison theorms for a general corank 1 sub-Riemannian structure with symmetries done by C.Li and I.Zelenko., Comment: 6 pages. arXiv admin note: substantial text overlap with arXiv:0908.4397

The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrange distribution) on the symplectic manifold. It is shown that the negativity of the reduced curvature implies the hyperbolicity of any compact invariant set of the Hamiltonian flow restricted to a prescribed energy level. We consider the Hamiltonian flows of the curve of least action of natural mechanical systems in sub-Riemannian structures with symmetries. We give sufficient conditions for the reduced flows (after reduction of the first integrals induced from the symmetries) to be hyperbolic and show new examples of Anosov flows.

The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical bundle of moving frames and the complete system of symplectic invariants, called curvature maps, for parametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural equation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the normal form for the Jacobi equation along this extremal and the curvature maps can be seen as the "coefficients" of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form (a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields., Comment: 27 pages

Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions., Comment: 26 pages