Classification of algebraic solutions of irregular Garnier systems

We prove that algebraic solutions of Garnier systems in the irregular case are of two types. The classical ones come from isomonodromic deformations of linear equations with diagonal or dihedral differential Galois group; we give a complete list in the rank-2 case (two indeterminates). The pull-back ones come from deformations of coverings over a fixed degenerate hypergeometric equation; we provide a complete list when the differential Galois group is $\text{SL}_{2}(\mathbb{C})$. As a byproduct, we obtain a complete list of algebraic solutions for the rank-2 irregular Garnier systems.

Impact of radiological morphology of clinical T1 renal cell carcinoma on the prediction of upstaging to pathological T3

Objectives Previous studies have reported that cases with clinical T1 renal cell cancer upstaging to pathological T3 are a risk factor to predicting postoperative recurrence after partial nephrectomy. The aim of our study was to investigate the impact of the radiological morphology of the enhanced CT scan of clinical T1 renal cell cancer on predicting upstaging to pathological T3. Methods Three hundred sixty-seven cases with clinical T1 renal cell cancer diagnosed from enhanced CT scans were enrolled in this study. Based on the findings from the enhanced CT scan, the cases were classified into ‘round’, the margins of which were smooth and round; ‘lobular’, one or more findings of smooth dent and no spiky dent were identified on the margin of the tumor; and ‘irregular’, one or more spiky dent were identified on the margin of the tumor. The association of postoperative upstaging with these radiological morphology and other clinical characteristics of each case was analyzed. Results Eighteen cases (4.9%) pathologically upstaged to T3a. Two round case (0.7%), 3 lobular cases (10.0%) and 13 irregular cases (22.0%) pathologically upstaged (P < 0.001, round + lobular versus irregular). Four of 17 cases (23.5%) with hilar tumors pathologically upstaged, while 14 of 350 cases (4%) with tumors pathologically upstaged in other sites (P < 0.001). Multivariate analysis revealed that irregular case was an independent factor in predicting upstaging to pathological T3a (P < 0.001). Conclusions Evaluation of the radiological morphology of clinical T1 renal cell cancer based on enhanced CT scans is useful for predicting pathological upstaging.

Pustules on the back possibly triggering toxic-shock syndrome

We herein describe an irregular case of toxic-shock syndrome (TSS). A previously healthy 28-year-old Japanese man developed a sudden-onset high fever. The patient was suffering from conjunctival hyperaemia, gastrointestinal symptoms such as vomiting and diarrhoea, and systemically diffused macular erythroderma. Further physical examination detected pustules on his back, which self-destructed over time. Laboratory revealed multiple organ failures. Subsequently, scalded skin on the face and desquamation in the limb extremities emerged by day 10, leading to the diagnosis of TSS, despite his stable circulatory dynamics through the course. Learning points for clinicians include that they should recall TSS as a possible disease concurrently causing high fever, systemic rash and multiple organ dysfunctions, even without being in a state of shock. The characteristic desquamations emerged in the limb extremities after hospitalisation were of help in diagnosing TSS.

An Operator Based Approach to Irregular Frames of Translates

We consider translates of functions in L 2 ( R d ) along an irregular set of points, that is, { ϕ ( · − λ k ) } k ∈ Z —where ϕ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.

NUMERICAL MODELING OF NON-COHESIVE CONTACT IN MULTI-BODY HYDRODYNAMIC SYSTEMS WITH SPH

Enforcing solid boundary conditions is one of the most challenging parts of the Smoothed Particle Hydrodynamics (SPH) method and many different approaches have been recently developed. Better understanding of interaction forces between solid bodies is of great importance in the investigation of structural stability and armor layer displacement in breakwaters. In this study, performance of repulsive force and dynamic boundary conditions have been investigated and showed that non-physical results are presented in non-cohesive contact. In this paper, a non-cohesive contact model in multi-body hydrodynamic systems has been developed and validated against other common boundary conditions. Using the developed contact model, the effect of regular and irregular placement of cubic concrete armors has been investigated. Also, comparison has been made with Van Buchem (2009) experimental results and concluded that in the irregular case it is more possible that a unit moves toward instability.

Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.