Comparison of the ability of two continuous cardiac output monitors to detect stroke volume index: Estimated continuous cardiac output estimated by modified pulse wave transit time and measured by an arterial pulse contour-based cardiac output device

BACKGROUND: Estimated continuous cardiac output (esCCO), a non-invasive technique for continuously measuring cardiac output (CO), is based on modified pulse wave transit time, which is determined by pulse oximetry and electrocardiography. OBJECTIVE: We examined the ability of esCCO to detect stroke volume index (SVI) and changes in SVI compared with currently available arterial waveform analysis methods. METHODS: We retrospectively reanalysed 15 of the cases from our previous study on esCCO measurement. SVI was calculated using an esCCO system, measured using the arterial pressure-based CO (APCO) method, and compared with a corresponding intermittent bolus thermodilution CO (ICO) method. Percentage error measurement and statistical methods, including concordance analysis and polar plot analysis, were performed. RESULTS: The difference in the SVI values between esCCO and ICO was -3.0 ± 8.8 ml (percentage error, 33.5%). The mean angular bias was 0.8 and the radial limits of agreement were ± 27.3. The difference in the SVI values between APCO and ICO was 0.9 ± 11.2 ml (percentage error, 42.6%). The mean angular bias was -6.8 and the radial limits of agreement were ± 44.1. CONCLUSION: This study demonstrated that the accuracy, precision, and dynamic trend of esCCO are better than those of APCO.

On some Lambert-like series

International audience In this note, we study radial limits of power and Laurent series which are related to the Lerch zeta-function or polylogarithm function. As has been pointed out in [CKK18], there have appeared many instances in which the imaginary part of the Lerch zeta-function was considered by eliminating the real part by considering the odd part only. Mordell studied the properties of the power series resembling Lambert series, and in particular considered whether the limit function is a rational function or not. Our main result is the elucidation of the threshold case of b_n = 1/n studied by Mordell [Mor63], revealing that his result is the odd part of Theorem 1.1 in view of the identities (1.9), (1.5). We also refer to Lambert series considered by Titchmarsh [Tit38] in connection with Estermann's zeta-functions.

Third-order mock theta functions

In [G. E. Andrews and B. C. Berndt, Ramanujan’s Lost Notebook, Part II (Springer, New York, 2009), Entry 3.4.7, p. 67; Y.-S. Choi, The basic bilateral hypergeometric series and the mock theta functions, Ramanujan J. 24(3) (2011) 345–386; B. Chen, Mock theta functions and Appell–Lerch sums, J. Inequal Appl. 2018(1) (2018) 156; E. Mortenson, Ramanujan’s radial limits and mixed mock modular bilateral [Formula: see text]-hypergeometric series, Proc. Edinb. Math. Soc. 59(3) (2016) 1–13; W. Zudilin, On three theorems of Folsom, Ono and Rhoades, Proc. Amer. Math. Soc. 143(4) (2015) 1471–1476], the authors found the bilateral series for the universal mock theta function [Formula: see text]. In [Choi, 2011], the author presented the bilateral series connected with the odd-order mock theta functions in terms of Appell–Lerch sums. However, the author only derived the associated bilateral series for the fifth-order mock theta functions. The purpose of this paper is to further derive different types of bilateral series for the third-order mock theta functions. As applications, the identities between the two-group bilateral series are obtained and the bilateral series associated to the third-order mock theta functions are in fact modular forms. Then, we consider duals of the second type in terms of Appell–Lerch sums and duals in terms of partial theta functions defined by Hickerson and Mortenson of duals of the second type in terms of Appell–Lerch sums of such bilateral series associated to some third-order mock theta functions that Chen did not discuss in [On the dual nature theory of bilateral series associated to mock theta functions, Int. J. Number Theory 14 (2018) 63–94].

Bilateral series and Ramanujan radial limits of mock (false) theta functions

Ramanujan gave a list of seventeen functions which he called mock theta functions. For one of the third-order mock theta functions [Formula: see text], he claimed that as [Formula: see text] approaches an even order [Formula: see text] root of unity [Formula: see text], then [Formula: see text] He also pointed at the existence of similar properties for other mock theta functions. Recently, [J. Bajpai, S. Kimport, J. Liang, D. Ma and J. Ricci, Bilateral series and Ramanujan’s radial limits, Proc. Amer. Math. Soc. 143(2) (2014) 479–492] presented some similar Ramanujan radial limits of the fifth-order mock theta functions and their associated bilateral series are modular forms. In this paper, by using the substitution [Formula: see text] in the Ramanujan’s mock theta functions, some associated false theta functions in the sense of Rogers are obtained. Such functions can be regarded as Eichler integral of the vector-valued modular forms of weight [Formula: see text]. We find two associated bilateral series of the false theta functions with respect to the fifth-order mock theta functions are special modular forms. Furthermore, we explore that the other two associated bilateral series of the false theta functions with respect to the third-order mock theta functions are mock modular forms. As an application, the associated Ramanujan radial limits of the false theta functions are constructed.