This paper examines the synthesis of the five degree-of-freedom robot formed by links connected by a revolute, prismatic and spherical joint to form an RPS serial chain. The reachable workspace of this robot is a right circular hyperboloid that defines a constraint equation with 10 dimensional parameters. Evaluating this equation on 10 arbitrary spatial positions yields a polynomial system of t...

In the two-dimensional isotropic parabolic potential barrier V (x, y) = V0 − mγ2(x2 + y2)/2, though it is a model of an unstable system in quantum mechanics, we can obtain the stationary states corresponding to the real energy eigenvalue V0. Further, they are infinitely degenerate. For the first few eigenstates, we will find the stationary flows round a right angle that are expressed by the com...

This paper gives an analytical proof of the conjecture [1]: when the dimension M of the auto-covariance matrix is large, the eigenvalue spectrum from Principal Component Analysis (PCA) of a fractal Brownian motion (fBm) process with Hurst parameter H decays as a power-law: λm ∼ m −(2H+1), m = 1,..., M . This resolves the interesting puzzle why PCA based H estimator can yield right results for f...

We review the major progress in the rigorous analysis of the classical quasispecies model that usually comes in two related but different forms: the Eigen model and the Crow–Kimura model. The model itself was formulated almost 50 years ago, and in its stationary form represents an easy to formulate eigenvalue problem. Notwithstanding the simplicity of the problem statement, we still lack full u...

We propose globally convergent iteration schemes for updating the eigenvalues of a symmetric matrix after a rank-1 modiication. Such calculations are the core of the divide-and-conquer technique for the symmetric tridiagonal eigenvalue problem. We prove the superlinear convergence right from the start of our schemes which allows us to improve the complexity bounds of 3]. The eeec-tiveness of ou...

For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to...

We present a deflated version of the conjugate gradient algorithm for solving linear systems. The new algorithm can be useful in cases when a small number of eigenvalues of the iteration matrix are very close to the origin. It can also be useful when solving linear systems with multiple right-hand sides, since the eigenvalue information gathered from solving one linear system can be recycled fo...

We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our results are compared with known exact results for β=1 finding good agreement. We also consider the case of almost square matrices finding new universal rate functions descri...

We study an eigenvalue problem involving variable exponent growth conditions and a non-local term, on a bounded domain Ω ⊂ RN . Using adequate variational techniques, mainly based on the mountain-pass theorem of A. Ambrosetti and P. H. Rabinowitz, we prove the existence of a continuous family of eigenvalues lying in a neighborhood at the right of the origin. Mathematics subject classification (...

The equation ∆u + λu + g(λ, u)u = 0 is considered in a bounded domain in R2 with a Signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary. It is assumed that g(λ, 0) = 0 for λ ∈ R, λ is a bifurcation parameter. A given eigenvalue of the linearized equation with the same boundary conditions is considered. A smooth local bifurcation b...