BackgroundSeveral inflammatory biomarkers, especially a high preoperative neutrophil-to-lymphocyte count ratio (NLR) and platelet-to-lymphocyte count ratio (PLR), are known to be indicator of poor prognosis in several cancers. However, very few studies have evaluated the significance of the NLR and PLR in papillary thyroid cancer (PTC). We evaluated the association of the preoperative NLR and PLR with clinicopathological characteristics in patients with PTC.MethodsThis study included 1,066 female patients who underwent total thyroidectomy for PTC. Patients were stratified into 4 quartiles by preoperative NLR and PLR. And the combination of preoperative NLR and PLR was calculated on the basis of data obtained value of tertile as follows: patients with both an elevated PLR and an elevated NLR were allocated a score of 2, and patients showing one or neither were allocated a score of 1 or 0, respectively.ResultsThe preoperative NLR and PLR were significantly lower in patients aged ≥45 years and in patients with Hashimoto's thyroiditis. The PLR was significantly higher in patients with tumor size >1 cm (P=0.021).When the patients were categorized into the aforementioned four groups, the group with the higher preoperative PLR was found to have a significantly increased incidence of lateral lymph node metastasis (LNM) (P=0.018). However, there are no significant association between the combination of preoperative NLR and PLR and prognostic factors in PTC patients.ConclusionThese results suggest that a preoperative high PLR were significant associated with lateral LNM in female patients with PTC.

Abstract. We formulate and solve a transonic regular reflection problem for the unsteadytransonic small disturbance equation, using a free boundary problem approach. Our method applies to self-similar shock reflection when the incident shock angle is large enough to permit a regular reflection configuration with a subsonic state behind the reflected shock. For the small-disturbance approximation in weak shock reflection, this corresponds to relatively large wedge angles. One contribution of this paper is the development of an asymptotic formula for the reflected shock, far from the reflection point, and for the subsonic state far downstream. These asymptotic series are valid for the small-disturbance approximation, for any incident shock angles.The main result in the paper is an existence theorem for the nonuniform subsonic flow behind the reflected shock. The flow velocity satisfies a quasilinear elliptic equation which is coupled to the Rankine-Hugoniot equations for the reflected shock, forming a free boundary problem on part of the boundary. Because the equation is not uniformly elliptic in the entire domain, we introduce a cut off to give a bounded domain, and also cut offs to the coefficients.Our result is incomplete in the following sense: we have been unable to remove the cut offs entirely. However, we prove that the flow we have constructed solves the original problem in a domain of finite size around the reflection point.1. Introduction. This paper is inspired by work of Cathleen Morawetz, [17], which analyses the bifurcation patterns in shock reflection by a wedge. Morawetz considers weak shocks and small wedge angles, for which the transonic full potential equation provides a good model, as entropy and vorticity vanish to third order in the shock strength. In the shock interaction region, the equation reduces further to the unsteady transonic small disturbance (UTSD) equation, the model we consider here. Our results are complementary to those in [17]: While that paper establishes values of the wedge angle parameter at which regular or Mach reflection occurs, we consider only the range in which regular reflection is expected to occur. While Morawetz identifies two types of regular reflection, weak and strong, and shows that entropy considerations favor the occurrence of weak reflection, we focus on transonic reflection, which is the strong case except for a narrow range of wedge angles near the transition, where both the weak and the strong reflection are transonic. Finally, while Morawetz assumes the existence of nonconstant subsonic flows, we verify this assumption in the particular case we study.For technical reasons involving the theory of oblique derivative boundary value problems in elliptic equations, we are restricted to using the UTSD equation, although there is no reason to suppose these results could not be extended to other elliptic problems such as the subsonic full potential equation. However, to our knowledge the machinery is not yet in place for this.Analysis near* the shock interactio...

SUMMARYIn this paper, we present a mathematical analysis of the quasilinear e ects arising in a hyperbolic system of partial di erential equations modelling blood ow through large compliant vessels. The equations are derived using asymptotic reduction of the incompressible Navier-Stokes equations in narrow, long channels.To guarantee strict hyperbolicity we ÿrst derive the estimates on the initial and boundary data which imply strict hyperbolicity in the region of smooth ow. We then prove a general theorem which provides conditions under which an initial-boundary value problem for a quasilinear hyperbolic system admits a smooth solution. Using this result we show that pulsatile ow boundary data always give rise to shock formation (high gradients in the velocity and inner vessel radius). We estimate the time and the location of the ÿrst shock formation and show that in a healthy individual, shocks form well outside the physiologically interesting region (2:8 m downstream from the inlet boundary). In the end we present a study of the in uence of vessel tapering on shock formation. We obtain a surprising result: vessel tapering postpones shock formation. We provide an explanation for why this is the case.

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We study a family of two-dimensional Riemann problems for compressible flow modeled by the nonlinear wave system. The initial constant states are separated by two jump discontinuities, x = ±κay, which develop into two interacting shock waves. We consider shock angles in a range where regular reflection is not possible. The solution is symmetric about the y-axis and on each side of the y-axis consists of an incident shock, a reflected compression wave, and a Mach stem. This has a clear analogy with the problem of shock reflection by a ramp. It is well known that no triple point structure exists in which incident, reflected, and Mach stem shocks meet at a point. In this paper, we model the reflected wave by a continuous function with a singularity in the derivative. This fails to be a weak solution across the sonic line. We show that a solution to the free boundary problem for the Mach stem exists, and we conjecture that the global solution can be completed by the construction of a reflected shock, by a similar free boundary technique.The point of our paper is the capability to deal analytically with a Mach stem by solving a free boundary problem. The difficulties associated with the analysis of solutions containing Mach stems include (1) loss of obliqueness in the derivative boundary condition corresponding to the jump conditions across the Mach stem, and (2) loss of ellipticity at the formation point of the Mach stem.We use barrier functions to show that for sufficiently large values of κa the subsonic solution is continuous up to the sonic line at the Mach stem.