First we prove a general spectral theorem for the linear NavierStokes (NS) operator in both 2D and 3D. The spectral theorem says that the spectrum consists of only eigenvalues which lie in a parabolic region, and the eigenfunctions (and higher order eigenfunctions) form a complete basis in H (l = 0, 1, 2, · · · ). Then we prove the existence of invariant manifolds. We are also interested in a m...

L, White HD. Troponin concentrations for stratification of patients with acute coronary syndromes in relation to therapeutic efficacy of tirofiban. PRISM Study Investigators. Platelet Receptor Inhibition in Ischemic Syndrome Management. Lancet 1999; 354: 1757–62. [8] The PURSUIT Trial Investigators. Inhibition of platelet glycoprotein IIb/IIIa with eptifibatide in patients with acute coronary s...

Most human cancers contain mutations in the transcription factor p53 and majority of these are missense and located in the DNA binding core domain. In this study, the stabilities of all core domain missense mutations are predicted and are used to infer their likely inactivation mechanisms. Overall, 47.0% non-PRO/GLY mutants are stable (DeltaDeltaG < 1.0 kT) and 36.3% mutants are unstable (Delta...

We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton (localized pulse) through one cell of the link is described by an analytically derived map. Multiple numerical iterations of the map reveal that, at values of the system’s stepsi...

We study the existence of Hopf bifurcations in a model of a regenerative vibrating machine tool, by using the same methods as in the Bifurcation Theorem and in the theory of central varieties. In a paper published in 1984, H. M. Shi and S. A. Tobias [6] have studied the theory of finite amplitude machine tool instability. They considered there some experimental results and have shown that there...

Etomidate is a commonly used anesthetic agent often utilized to induce anesthesia as it has a short half-life and allows for central nervous system depression without causing major cardiovascular disturbances, making it one of the preferred medications for trauma and hemodynamically unstable patients. Thus, etomidate is commonly found during a postmortem drug screen conducted for medicolegal re...

Spherical and axisymmetric accretion onto black holes is discussed. Physical processes in various families of solutions are explained and their characteristics are summarized. Recently discovered solutions of axisymmetric flow provide us with various radiation efficiency and spectrum, which may successfully model diverse accretion systems. Possible role of preheating is also speculated. The var...

We study numerically and theoretically (on a heuristic level) the time evolution of a gas confined to a cube of size L divided into two parts by a piston with mass ML ’ L which can only move in the x-direction. Starting with a uniform ‘‘double-peaked’’ (non Maxwellian) distribution of the gas and a stationary piston, we find that (a) after an initial quiescent period the system becomes unstable...

We study the influence of a wall on the dynamics of a low-Reynolds-number three-sphere swimmer. A far swimmer whose arm makes an angle theta with the horizon experiences the wall presence as an angle-dependent quadrupole force proportional to (a/L)(2)(L/z)(2)cos theta, where a, L, and z are the radius of spheres, the arm length, and the swimmer distance to the wall, respectively. The wall-induc...

Let fa,L : R→ R be such that (1) fa,L : θ 7→ θ + a + L ln |Φ(θ)| where a ∈ [0, 1], L ∈ R are real parameters and Φ(θ) is such that Φ(θ + 1) = Φ(θ). We assume that Φ(θ) is a Morse function and the graph of y = Φ(θ) is transversal to the θ-axis. The functions fa,L induce a two parameter family of 1D maps from S1 to S1 where S1 = R/Z is the unit circle. In this paper we prove that there exists an ...