purpose: to report two cases of granulomatosis with polyangiitis (gpa) presented ocular manifestations. cases report: we report two cases of scleritis with red eye, one of them was a 30 years old female patient with saddle nose and positive c-anca and the other one was a 56 year-old female patient with lung cavitation and positive c-anca. both cases undergone corticosteroid and immunosuppressiv...

The string method originally proposed for the computation of minimum energy paths (MEPs) is modified to find saddle points around a given minimum on a potential energy landscape using the location of this minimum as only input. In the modified method the string is evolved by gradient flow in path space, with one of its end points fixed at the minimum and the other end point (the climbing image)...

The reaction path is an important concept of theoretical chemistry. We employ the definitions of the intrinsic reaction coordinate (IRC), the gradient extremal (GE), and the Newton trajectory (NT). The usual imagination in chemistry is that a minimum energy path is in a convex region of the potential energy surface. We describe different schemes of convexity to handle the situation. It comes ou...

We compute, from first principles, the quantum fluctuations about instanton saddle points of the Euclidean path integral for Einstein gravity coupled to a scalar field. The Euclidean two-point correlator is analytically continued into the Lorentzian region where it describes the quantum mechanical vacuum fluctuations in the state described by no boundary proposal initial conditions. We concentr...

We perform a first principles computation of the spectrum of gravity waves produced in open inflationary universes. The background spacetime is taken to be the continuation of an instanton saddle point of the Euclidean no boundary path integral. The two-point tensor correlator is computed directly from the path integral and is shown to be unique and well behaved in the infrared. We discuss the ...

When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom, a saddle point (called the Stark saddle point) appears. For energies slightly above the saddle point energy, one can find classical orbits that are located in the vicinity of this point. We follow those so-called quasi-Penning orbits to high energies and field strengths, observing structural chan...

Abstract The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation the system results in periodic, quasi-periodic, chaotic and unbounded behavior. An explicit Poincaré map constructed an implicit constraint on switching time. stability fixed points corresponding to period-one solutions By varying parameters, we observed saddle-center pitchfork bifu...

The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according to the sign of the cosmological constant. For 3 > 0, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For 3 < 0, on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the cont...

We compute the capacity of entanglement in bipartite random pure state model using replica method. find exact expression which is valid for a finite dimension Hilbert space. argue that gravitational path integral, receives contributions only from sub-leading saddle points corresponding to partially connected geometries.