Let $(Omega, mu)$ be a measure space and $\{\tau_\alpha\}_{\alpha\in \Omega}$ be a normalized continuous Bessel family for a real Hilbert space $\mathcal{H}$. If the diagonal $\Delta \{(\alpha, \alpha):\alpha \in \Omega\}$ is measurable in the measure space $\Omega\times \Omega$, then we show that \begin{align}\label{CRBA} \sup _{\alpha, \beta \in \Omega, \alpha\neq \beta}\langle \tau_\alpha, \tau_\beta\rangle \geq \frac{-(\mu\times\mu)(\Delta)}{(\mu\times\mu)((\Omega\times\Omega)\setminus\Delta)}. \end{align} We call Inequality (1) as continuous Rankin bound. It improves 76 years old result of Rankin [Ann. of Math., 1947]. It also answers one of the questions asked by K. M. Krishna in the paper [Continuous Welch bounds with applications, Commun. Korean Math. Soc., 2023]. We also derive Banach space version of Inequality (1).

Controlling Nutritional Status (CONUT) Score is useful for the nutritional screening. We aimed to explore whether the CONUT score may predict a 3-month functional outcome in hemorrhagic stroke (AHS). Totally, 349 patients with incident AHS were consecutively recruited, and their malnutrition risks were determined using a high CONUT score of ≥ 2. Poor functional outcomes were defined as the modified Rankin Scale (mRS) score of ≥ 3 at 3 months. A total of 328 patients (mean age, 60.4 ± 12.83 years; 66.8% male) were included, 172 (52.40%) patients at malnutrition risk and 104 (31.7%) patients with a poor prognosis. High-CONUT patients had lower total lymphocyte counts and total cholesterol levels than low-CONUT patients (p < 0.001 and p = 0.012). At 3-month post discharge, patients with malnutrition risk had higher hospitalization costs (p = 0.021), lower Barthel Index (p = 0.001), and more infectious complications (p = 0.002) than those without, and there was a greater risk for poor functional outcomes in the high-CONUT compared with the low-CONUT patients at admission (adjusted odds ratio: 2.32, 95% confidence interval: 1.28-4.17). High-CONUT scores predict a 3-month poor prognosis in AHS, which may help identify the AHS patients who need additional nutritional managements.

The paper presents the results of energy and environmental analysis of geothermal CHP plant operation in Polish conditions. As the most favorable, for the geothermal conditions prevailing in Poland, the variant of CHP plant based on Organic Rankine Cycle (ORC) has been taken into consideration. As the case study the existing geothermal well located in the town of Konin in the Wielkopolska voivodship has been chosen. The conceptual design of CHP plant has been proposed and evaluated from energy and environmental point of view. As energy performance criteria the non-renewable primary energy consumption has been chosen. In case of environmental performance carbon dioxide emission has been taken as evaluation criteria. The analysis has been performed for different operating conditions and three working fluids.

In advanced world stroke is one of the disabling cause of death that can be managed with thrombolysis if presents early despite further risk of intracerebral haemorrhage. Secondary prevention is an important objective in ischaemic stroke where recurrence is very high with subsequent stroke. Carotid End Arterectomy impact a definitive and effective role for both symptomatic and asymptomatic carotid stenosis for secondary stroke prevention in selective cases. Thrombolysis is a potential primary management for certain group whereas carotid surgery employs secondary preventative measure in a specified ischaemic stroke group.