Speed measurements in the developing region of an electrohydrodynamic spray using laser diagnostics

Experiments were conducted to assess the ability of a particle-counter-sizer velocimeter (PCSV) to measure droplet speeds in the developing region of an electrohydrodynamic spray. The working fluid, ethanol, was pumped through a stainless steel capillary tube at a constant mass flow rate. The capillary tube was held at various positive potential voltages with respect to an externally grounded funnel located below the tube. Data were acquired at two axial stations, directly under the capillary tip, in the developing region of the subject spray. The results indicated that the PCSV, with an experimental modification to the speed reduction process, performed well in this region. Speeds were measured at the near station within an average uncertainty of 2.2% and a corresponding maximum uncertainty of 3.0%; speeds at the far station were measured within an average uncertainty of 4.6% and a corresponding maximum uncertainty of 6.0%.     

Oscillatory and asymptotic behavior of solutions of differential equations with deviating arguments

The oscillatory and asymptotic behavior of solutions of a class of nth order nonlinear differential equations, with deviating arguments, of the form (E, δ) L_nx(t) + δq(t) f(x[g₁(t)],…, x[g_m(t)]) = 0, where δ = ± 1 and L₀x(t) = x(t), L_kx(t) = a_k(t)(L_{k ? 1}x(t))^., $\text{k = 1, 2,…, n (}{}^{\mathrm{.}}\text{=}\text{d}\text{dt}\text{)}$, is examined. A classification of solutions of (E, δ) with respect to their behavior as t → ∞ and their oscillatory character is obtained. The comparisons of (E, 1) and (E, ?1) with first and second order equations of the form y^.(t) + c₁(t) f(y[g₁(t)],…, y[g_m(t)]) = 0 and (a_{n ? 1}(t)z^.(t))^. ? c₂(t) f(z[g₁(t)],…, z[g_m(t)]) = 0, respectively, are presented. The obtained results unify, extend and improve some of the results by Graef, Grammatikopoulos and Spikes, Philos and Staikos.     

Some exponentially decreasing error bounds for a numerical inversion of the Laplace transform

Convergence properties of a class of least-squares methods for finding approximate inverses of the Laplace transform are obtained by using reproducing kernel Hilbert space techniques (or, alternatively, related minimization techniques) and some classical interpolation results.     

On oscillation of solutions of higher order forced functional differential inequalities

Oscillation criteria for the class of forced functional differential inequalities x(t){L_nx(t) + f(t, x(t), x[g₁(t)],…, x[g_m(t)]) ? h(t)} ? 0, for n even, and x(t){L_nx(t) ? f(t, x(t), x[g₁(t)],…, x[g_m(t)]) ? h(t)} ? 0, for n odd, are established.     

On sequential labelings of graphs

A valuation on a simple graph G is an assignment of labels to the vertices of G which induces an assignment of labels to the edges of G. β-valuations, also called graceful labelings, and α-valuations, a subclass of graceful labelings, have an extensive literature; harmonious labelings have been introduced recently by Graham and Sloane. This paper introduces sequential labelings, a subclass of harmonious labelings, and shows that any tree admitting an α-valuation also admits a sequential labeling and hence is harmonious. Constructions are given for new families of graceful and sequential graphs, generalizing some earlier results. Finally, a conjecture of Frucht is shown to be wrong by exhibiting several graceful labelings of wheels in which the center label is larger than previously thought possible.     

On nonoscillatory solutions of differential inclusions

This paper introduces a nonoscillatory theory for differential inclusions based on fixed point theory for multivalued maps.

     

Simple ABCD matrix treatment for transversely varying saturable gain

We have developed an ABCD matrix that, for the first time to our knowledge, accurately describes the transformation of a Gaussian beam by a medium with transversely varying saturable gain. In contrast with the conventional ABCD matrix, the newly developed matrix is shown to be in excellent agreement with a full beam propagation code over a wide parameter range. Accurate treatment of transversely varying saturable gain in laser resonators is important for the optimization of end-pumped lasers, particularly for efficient diode-pumped solid-state and Kerr-lens mode-locked systems.