Effective bounds for very ample line bundles

Let be an ample line bundle on a non singular projective -fold . It is first shown that is very ample for . The proof develops an original idea of Y.T. Siu and is based on a combination of the Riemann-Roch theorem together with an improved Noetherian induction technique for the Nadel multiplier ideal sheaves. In the second part, an effective version of the big Matsusaka theorem is obtained, refining an earlier version of Y.T. Siu: there is an explicit polynomial bound of degree in the arguments, such that is very ample for . The refinement is obtained through a new sharp upper bound for the dualizing sheaves of algebraic varieties embedded in projective space. Oblatum 30-I-1995 & 18-V-1995     

On the boundary-value problem for a mixed-type equation: Asymptotic analysis and an effective numerical algorithm

A singularly perturbed boundary-value problem for an equation of mixed ellipticparabolic type is considered. The first part of this work is devoted to an asymptotic study of the solution to the problem. Modification of the boundary function method for mixed-type equations with small parameters at the highest derivatives is used. The second part is devoted to creating a numerical method that considers the structure of the solution for small parameter values. The idea of an approximate factorization of an elliptic operator into the product of two parabolic operators is employed. An effective numerical algorithm based on an asymptotic representation of the solution is developed.     

Approximate analytic solutions to Radulet equations for the analysis of electromagnetic transients in single-phase power transmission lines

In this work, an analytic development for a transmission line with a corona effect for simulating an electromagnetic transient is presented. The asymptotic solution for the Radulet equations in which a nonlinear term is presented is obtained. The study is carried out for a single-phase transmission line. The electrical parameters for an overhead line are defined and several formulations for their calculation are presented. The frequency dependence of the electrical parameters is considered. In the first part, the linear problem solution is found; the Fourier and Laplace transforms are applied with respect to distance and time respectively. After finding the solution in the Fourier–Laplace domain, which is expressed in terms of a Green’s function integral, an approximate analytical solution is obtained in the distance–time domain by means of asymptotic methods. Finally, the nonlinear solution is found using as a first approach the linear solution. The results obtained show an attenuation in the voltage wave due to the corona effect.     

Auto-balancing of a rotor with an orthotropic elastic shaft

The self-balancing of a statically unbalanced orthotropic elastic rotor equipped with a ball auto-balancing device is investigated. Equations of motion in fixed and rotating systems of coordinates, as well as equations describing steady motions of the regular precession type, are derived using a simple model of a Jeffcott rotor. Formulae for calculating the amplitude-frequency and phase-frequency characteristics of the precessional motion of the rotor are obtained. It is established that the conditions for a steady balanced mode of motion for an orthotropic rotor to exist have the same form as for an isotropic rotor, but the stability region of such a mode for an orthotropic rotor is narrower than the stability region for an isotropic rotor. The unsteady modes of motion of the rotor in the case of rotation with constant angular velocity and in the case of passage through critical velocities with constant angular acceleration is investigated numerically. It is established that the mode of slow passage through the critical region for an orthotropic rotor is far more dangerous than the similar mode for an isotropic rotor.     

Sensitivity in data envelopment analysis using an approximate inverse matrix

In this paper, sensitivity analysis of the Charnes–Cooper–Rhodes model in data envelopment analysis (DEA) is studied for the case of perturbation of all outputs and of all inputs of an efficient decision-making unit (DMU). Using an approximate inverse of the perturbed optimal basis matrix, an approximate preservation of efficiency for an efficient DMU under these perturbations is considered. Sufficient conditions for an efficient DMU to preserve its efficiency are obtained in that case. An illustrative example is provided.     

Algorithm of Barrier Objective Penalty Function

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm.     

Partial order generalized Marcum Q-function contour integral representation

A new contour integral representation of generalized Marcum Q-function is presented. The obtained expression is valid for an arbitrary positive order of the function and for a specific case of integer order yields a well known result. As an example of practical application the problem of energy base signal detection in presence of fading is considered. A novel closed form analytic expression for an average probability of detection for various channel models is obtained.     

Quasi-concave minimization subject to linear constraints

A finite algorithm is presented for solving the quasi-concave minimization problem subject to linear constraints. The concept of an extreme point is generalized to that of an extreme facet of a polyhedron. Then a search routine is developed for the detection of an extreme facet of the feasible region relative to the polyhedron defined by the current set of cuts. After identifying an extreme facet we cut it off by a cut developed for this purpose. We call this cut the facet cut. The method is both compatible with other cutting procedures and is finite..     

On certain cases of determination of trajectories of plane conservative motion of a particle : PMM vol. 43, no. 6, 1979 pp. 1111–1113

A method is developed for obtaining an incomplete integral of the two-dimensional Hamilton— Jacobi equation for a particle when a particular solution that satisfies a special equation in partial derivatives is known. The equation for the trajectory of dipole particles moving with zero total energy in an arbitrary two-dimensional electrostatic field is obtain, as an example.     

POLES OF ZETA FUNCTIONS OF COMPLETE INTERSECTIONS

51.IntroductionLetF.beafinitefieldofqele~swithcharederisticp.LetXbeanThdilnensionalalgebraicsetdeadedoverF..ThezetafunctionofX/F.isdennedbywhereXOdenotesthesetofclosedpointsOfX/F.and#X(F.d)denotesthenUInberof.F.d-rationalpointsonX.ItiseasytoseethatZ(X,T)isapowerserieswithintegercoefficients.Dwork'srationalltytheoremIg]showsthatthezetafunctionZ(X,T)isrationalinT.ThuS,therearealgebraicintegerspll'.3Pr,pl,'3basuchthatThereisagoodreasonthatwemoantheabovezetafunctionbythepower(--1)"-…