No abstract

We solve fundamental problems in the Oka theory by establishing an implicit function theorem for sprays. As the first application of our implicit function theorem, we obtain an elementary proof of the fact that approximation yields interpolation. This proof and Lárusson’s elementary proof of the converse give an elementary proof of the equivalence between approximation and interpolation. The second application concerns the Oka property of a blowup. We prove that the blowup of an algebraically Oka manifold along a smooth algebraic center is Oka. In the appendix, equivariantly Oka manifolds are characterized by the equivariant version of Gromov’s condition [Formula: see text], and the equivariant localization principle is also given.

Aims Increased left atrial pressure leads to pulmonary congestion. Although the B-lines in lung ultrasound (LUS) are useful in detecting pulmonary congestion, data regarding the association between B-lines and invasive hemodynamics are inconsistent. This study aimed to explore the correlation of the B-line count by LUS with pulmonary capillary wedge pressure (PCWP) stratified for preserved and reduced ejection fraction (EF) in acute heart failure patients. Methods and Results We performed a prospective observational study on 116 hospitalized patients with acute heart failure (mean age, 75.2 ± 10.3 years), who underwent right heart catheterization before discharge. LUS was performed in eight zones within 4 h of right heart catheterization and compared with PCWP separately in each EF group. Cardiac events were recorded 1 year after discharge. PCWP revealed a clear pivot point at which the B-lines began to increase in the overall cohort and each EF. Specific thresholds of the increase in B-lines were identified at 19 and 25 mmHg for preserved and reduced EF, respectively. Residual congestion at discharge was defined as the presence of ≥6 B-lines. Patients with residual congestion had a higher risk for cardiac events than those without residual congestion (hazard ratio, 12.6; 95% CI, 4.71–33.7; log-rank, P < 0.0001). Conclusions A clear pivot point was associated with increased B-lines count in PCWP at 19 and 25 mmHg for preserved and reduced EF, respectively. Moreover, the increased B-line count above the defined cutoff used to quantify residual congestion was associated with significantly worse outcomes.

Abstract. We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain Ω ⋐ C n and any connected complex manifold Y , the space O(Ω, Y ) contains a dense holomorphic disc. Our second result states that Y is an Oka manifold if and only if for any Stein space X there exists a dense entire curve in every path component of O(X, Y ).In the second half of this paper, we apply the above results to the theory of universal functions. It is proved that for any bounded convex domain Ω ⋐ C n , any fixed-point-free automorphism of Ω and any connected complex manifold Y , there exists a universal map Ω → Y . We also characterize Oka manifolds by the existence of universal maps.

We study the Oka properties of complements of closed countable sets in C n (n > 1) which are not necessarily discrete. Our main result states that every tame closed countable set in C n (n > 1) with a discrete derived set has an Oka complement. As an application, we obtain non-elliptic Oka manifolds which negatively answer a long-standing question of Gromov. Moreover, we show that these examples are not even weakly subelliptic. It is also proved that every finite set in a Hopf manifold has an Oka complement and an Oka blowup.