Suppose that an n-by-n regular matrix pencil A − λB has n distinct eigenvalues. Then determining a defective pencil E−λF which is nearest to A−λB is widely known as Wilkinson’s problem. It is shown that the pencil E − λF can be constructed from eigenvalues and eigenvectors of A − λB when A − λB is unitarily equivalent to a diagonal pencil. Further, in such a case, it is proved that the distance...

We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skewsymmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another ske...

∼= P, where g(x, y, z) = 0 is a homogeneous equation of the curve Z and (λ, μ) ∈ P. Then a general curve in P is birational to an elliptic curve. Remark 1.1. The construction of pencil P can be generalized to the case when C has at most ordinary double points and the points P1, · · · , P9 are not necessarily distinct (see [3]). The pencil P is called a standard Halphen pencil. Definition 1.2. A...

Low-cost electrochemical platform for sensitive Pb(II) and Cd(II) detection in aqueous solution were fabricated using pencil graphite leads. Cyclic voltammetry (CV) impedance spectroscopy (EIS) applied to characterization of the Pencil Graphite Electrode (PGE). Average electroactive surface was determined as 2.58 times its geometrical area. Parameters lead cadmium ions optimized Anodic Strippin...

Given a regular matrix pencil A + μE, we consider the problem of determining the nearest singular matrix pencil with respect to the Frobenius norm. We present new approaches based on the solution of matrix differential equations for determining the nearest singular pencil A+∆A+ μ(E +∆E), one approach for general singular pencils and another one such that A+∆A and E + ∆E have a common left/right...

We have designed a toolbox that provides an environment for testing radiotherapy optimization techniques, objective functions, and constraints. A set of three-dimensional (3D) pencil beam dose distributions have been computed for a cylindrical phantom. The 6 MV pencil beams were computed using a superposition-based dose engine commissioned for an Elekta SL20 linear accelerator. Due to the cylin...

Mirror therapy is one of the promising rehabilitation therapeutic interventions but the neural basis of the therapeutic effect remains unknown. It has been reported that the 20-Hz rhythmic activity is induced in the primary motor cortex after median nerve stimulation and the amount of the induced activity is decreased when the primary motor cortex is activated. In the present study, to elucidat...

Due to their electrochemical and economical characteristics, pencil graphite electrodes (PGEs) gained in recent years a large applicability to the analysis of various types of inorganic and organic compounds from very different matrices. The electrode material of this type of working electrodes is constituted by the well-known and easy commercially available graphite pencil leads. Thus, PGEs ar...