In this paper, tuning of power system stabilizer (PSS) and thyristor controlled series capacitor (TCSC) is studied. The analysis of mode controllability is used to select the effective location for TCSC. The performances of TCSC equipped with a proportional-integral-derivative controller (P-I-D controller) and proportional-integral-derivative power system stabilizer (P-I-D PSS) are investigated...

‎in this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in lorentzian plane $mathbb{l}^{2}.$ then the‎ ‎special curves mentioned above are studied in lorentzian plane $mathbb{l}%‎‎^{2}.$ finally some characterizations of these special curves are given in‎ ‎$mathbb{l}^{2}.$‎

Let M be a C∞ manifold (without corners) and let E ⊆ TM be a subbundle of the tangent bundle. In class we discussed the notion of integral manifolds for E in M (as well as maximal ones), essentially as a generalization of the theory of integral curves for vector fields. Roughly speaking, in the special case that E is a trivial line bundle we are in the setup of integral curves for (non-vanishin...

The arithmetic of quaternions is recalled from a constructive point of view. A Hecke module is introduced, defined as a free abelian group on right ideal classes of a quaternion order, together with a natural action of Hecke operators. An equivalent construction in terms of Shimura curves is then introduced, and the quaternion construction is applied to the analysis of specific modular and Shim...

We describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential operators have an S-integral solution. These differential operators are naturally associated with Teichmüller curves in genus 2. They are counterexamples to conjectures by Chudnovsky–Chudnovsky and Dwork. We also det...

This paper studies the discontinuity in the behavior of neighboring integral curves. Discontinuity is measured by a number of selected attributes of the integral curves. A variety of attribute fields are defined. The attribute value at any given spatio-temporal point in these fields is assigned the attribute of the integral curve that passes through this point. This encodes the global behavior ...

Sarabia et al. (1999) present a basic model to create ordered families of Lorenz curves, along with basic theorems that describe the conditions for the models to satisfy the definition of the Lorenz curve. Using these basic models, they suggest a family which includes several well-known Lorenz models as special cases. This paper first shows that their basic theorems can be generalized. The pape...

In this work we prove the existence of an autonomous Hamiltonian vector field in $W^{1,r}(\mathbb T^d; \mathbb R^d)$ with $r < d-1$ and $d \geq 4$ for which associated transport equation has non-unique positive solutions. As a consequence Ambrosio's superposition principle [2], show that integral curves Lebesgue measure set initial data moreover, is not constant along these curves.