The optimal treatment for profound hyponatraemia remains uncertain. Recent clinical studies have demonstrated that a standardized bolus of hypertonic saline is effective, but relying solely on this approach may not fully address the individual variability of hyponatraemia among patients. We evaluated the effectiveness of rapid bolus (RB) administration of hypertonic saline followed by predictive correction (PC) using an infusate and fluid loss formula identical to the Barsoum-Levine formula based on the Edelman equation (RB-PC) for managing profound hyponatraemia. In this retrospective observational cohort study, we evaluated 276 patients aged >18 years with s[Na] levels ≤120 mEq/L (January 2014-December 2023). Using propensity score matching (PSM), we assessed s[Na] elevations at 6 h post-treatment initiation and the rate of appropriate hyponatraemia correction between the RB-PC and PC groups. We defined the appropriate correction as a change in s[Na] in the range of 4-10 mEq/L within the first 24 h and ≤18 mEq/L within the first 48 h following corrective treatment initiation. Among 276 patients with profound hyponatraemia (s[Na] ≤120 mEq/L), 49 and 108 underwent treatment with RB-PC therapy and with PC therapy without RB, respectively. Post-PSM, 84 patients were selected and allocated to the RB-PC (n = 42) or PC group (n = 42). In PSM analysis, patients with RB-PC experienced a higher elevation in s[Na] at 6 h after treatment initiation than PC (4.0 vs 2.4 mEq/L, P < 0.001). The rate of appropriate correction was similar between the RB-PC and PC groups (90.5% vs 90.5%, P = 1). RB-PC can quickly elevate s[Na] levels and achieve appropriate correction of s[Na] in patients with profound hyponatraemia.
Abstract We consider the Fock–Bargmann–Hartogs domain D n,m which is defined by the inequality where (z, ζ) ∈ ℂ n × ℂ m and μ > 0. We give an explicit formula for the Bergman kernel of the domain in terms of the polylogarithm functions. Moreover, using the interlacing property, we describe how the existence of zeros of the Bergman kernel depends on the integers m and n. Keywords: Bergman kernelweighted Bergman kernelFock–Bargmann spacepolylogarithm functionLu Qi-Keng problemForelli–Rudin constructionAMS Subject classifications: 32A2532A07 Acknowledgements The author would like to express his sincere gratitude to Professors Hideyuki Ishi and Hiroyuki Ochiai and Dr Daisuke Shiomi for their helpful advice and discussions. The author also acknowledges the encouragement and helpful comments by Professor Takeo Ohsawa on this study.
This note gives a concise proof of a classical Poincaré′s theorem which asserts that the unit ball 픹2 and the polydisk 픻 × 픻 are not holomorphically equivalent.
In the study of the holomorphic automorphism groups, many researches have been carried out inside the category of bounded or hyperbolic domains. On the contrary to these cases, for unbounded non-hyperbolic cases, only a few results are known about the structure of the holomorphic automorphism groups. Main result of the present paper gives a class of unbounded non-hyperbolic Reinhardt domains with non-compact automorphism groups, Cartan's linearity theorem and explicit Bergman kernels. Moreover, a reformulation of Cartan's linearity theorem for finite volume Reinhardt domains is also given.
We develop a group-theoretic method of generalizing the Laplace-Beltrami operators on the classical domains. In [18], we defined the generalized Poisson-Cauchy transforms on the classical domains. We show that the generalized Poisson-Cauchy transforms give us eigenfunctions of the generalized Laplacians defined in this paper.
We develop a group-theoretic method to generalize the Laplace-Beltrami operators on the classical domains. In K. Okamoto, "Harmonic analysis on homogeneous vector bundles," Lecture Notes in Mathematics, Springer-Verlag, 266 (1971), 255–271, inspired by Helgason's paper, "A duality for symmetric spaces with applications to group representations," Advan. Math. 5 (1970), 1–154, we defined the "Poisson transforms" for homogeneous vector bundles over symmetric spaces. In K. Okamoto, M. Tsukamoto and K. Yokota, "Generalized Poisson and Cauchy kernel functions on classical domains," Japan. J. Math. 26 No. 1 (2000), 51–103., we defined the generalized Poisson-Cauchy transforms for homogeneous holomorphic line bundles over hermitian symmetric spaces and computed explicitly the kernel functions for each type of the classical domains. In E. Imamura, K. Okamoto, M. Tsukamoto and A. Yamamori, "Generalized Laplacians for Generalized Poisson-Cauchy transforms on classical domains," Proc. Japan Acad., 82, Ser. A (2006), 167–172., making use of the Casimir operator, we defined the "generalized Laplacians" on homogeneous holomorphic line bundles over hermitian symmetric spaces and showed that the generalized Poisson-Cauchy transforms give rise to eigenfunctions of the "generalized Laplacians". In this paper, using the canonical coordinates for each type of the classical domains, we carry out the direct computation to obtain the explicit formulas of (line bundle valued) invariant differential operators which we call the generalized Laplacians and compute their eigenvalues evaluated at the generalized Poisson-Cauchy kernel functions
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