Geometric Properties of Cesro Function and Sequence Spaces

Theory of Banach spaces as a branch of Functional Analysis was founded at the beginning of the 20th century and since then it has been extensively developed and applied. Banach lattices, in particular Banach function and sequence spaces, like classical Lebesgue spaces or Orlicz, Lorentz, Musielak-Orlicz spaces, are of special interest and importance for applications. In this dissertation we study Cesàro function and sequence spaces which, unlike many other classical spaces, are not rearrangement invariant. This makes them a very interesting object to explore with possible applications to some functional analysis problems. Cesàro function and sequence spaces appeared for the first time in 1968 in the Dutch Mathematical Society Journal as a problem to find a representation of their dual space. This problem, in case of sequences, was solved in 1974 by Jagers. Since then, Cesàro sequence spaces have gain an attention among Banach space theory specialists. For example, in the nineties several geometric properties of them were studied. During the last decade, more general spaces, Cesàro-Orlicz sequence spaces, have been explored as well. Cesàro function spaces attracted a wider attention only since 2008 when Astashkin and Maligranda published series of interesting papers on their geometrical and topological properties. In this dissertation we study geometric properties of Cesàro function spaces with general weight. We find an isometric description of the dual of Cesàro function space. This description involves a new concept of essential Psi-concave majorant of a measurable function which we define and study. We show, among others, that every non empty relatively open subset (and hence every slice) of the unit ball of Cesàro function space has diameter 2. In particular these spaces do not have the Radon-Nikodym property. Also, they are strictly convex Banach spaces while the unit sphere does not have strongly extreme points. This shows rather unexpected differences between Cesàro function and sequence spaces since the latter are known to have the Radon-Nikodym property and to be locally uniformly rotund.We also explore Cesàro-Orlicz sequence spaces. We show that they are not B-convex and investigate under what conditions there is an isometric or isomorphic copy of ∞ in these spaces

Stężenie parathormonu w surowicy krwi u środkowoeuropejskich pacjentów z nie-niedokrwienną niewydolnością serca jako potencjalny czynnik ciężkości choroby i złego rokowania

Introduction: Parathyroid hormone (PTH) might be considered as a potential marker of disease severity and worse prognosis in heart failure (HF) patients. The aim of the study was to assess PTH, vitamin D, phosphorus (P), and total calcium (Ca2+) serum concentrations in Central European patients suffering from HF of non-ischaemic origin compared to non-HF volunteers.To evaluate potential correlations among the enumerated parameters, established markers of worse prognosis and declared sun exposure. Material and methods: Serum intact-PTH, 25-OH vitamin D, P, and total Ca2+ concentrations were assessed in a group of HF patients and non-HF volunteers. Patients described their daily profile of sun exposure during the previous eight weeks as “above” or “below” seven hours a week. Results: The mean PTH concentrations in the non-ischaemic HF group and control group were 79.5 pg/mL and 59.6 pg/mL, respectively (P = 0.009). Non-HF volunteers declaring higher sun exposure time had higher serum concentrations of vitamin D compared to those with lower sun exposure time (30.3 vs. 23.8 ng/mL, P < 0.05), unlike the HF patients (24.1 ng/mL vs. 23.2 ng/mL, P = ns). Multiple regression analysis revealed the relationship between age, NT-proBNP (N-terminal pro-brain natriuretic peptide), P, and PTH as a dependent variable. Conclusions: PTH is significantly elevated in non-ischaemic HF patients compared to non-HF volunteers and correlates with established factors of worse prognosis, including age, estimated glomerular filtration rate (eGFR), aspartate aminotransferase (AST), serum concentrations of creatinine, and NT-proBNP. Declared sun exposure did not affect the serum concentration of vitamin D in the HF group, in contrast to the control group.Wstęp: Podwyższone stężenie parathormonu (PTH) jest uważane za potencjalny marker ciężkości choroby i złego rokowania u chorych z niewydolnością serca (NS). Celem pracy była ocena stężenia PTH, witaminy D, całkowitego wapnia (Ca2+) i fosforu (P) w surowicy krwi środkowoeuropejskich chorych z nie-niedokrwienną NS w porównaniu z grupą bez NS. Określenie potencjalnych zależności wymienionych parametrów z ustalonymi markerami złego rokowania oraz deklarowanym czasem ekspozycji na słońce. Materiał i metody: W obu grupach oznaczono stężenie aktywnego biologicznie PTH, 25-OH witaminy D, Ca2+ i P. Pacjenci deklarowali czas ekspozycji na słońce w ciągu ostatnich ośmiu tygodni jako „powyżej” lub „poniżej” siedmiu godzin w tygodniu. Wyniki: Średnie stężenie PTH było wyższe w grupie badanej (79,5 vs. 59,6 pg/ml, p = 0,009). W grupie bez niewydolności serca u osób deklarujących czas ekspozycji na słońce > 7h/tygodniu obserwowano wyższe stężenie witaminy D (30,3 vs. 23,8 ng/ml, p < 0,05), zależność ta nie zachodziła u pacjentów z NS (24,1 ng/ml vs. 23,2 ng/ml, p = ns). Analiza regresji wieloczynnikowej wykazała zależność między wiekiem, stężeniem N-końcowego fragmentu prohormonu peptydu natriuretycznego (NT-proBNP), P oraz PTH jako zmienną zależną. Wnioski: Stężenie PTH jest wyższe w grupie pacjentów z nie-niedokrwienną NS w porównaniu z ochotnikami bez NS. Stężenie PTH koreluje z ustalonymi czynnikami złego rokowania jak wiek, estymowany wskaźnik filtracji kłębkowej (eGFR), stężenie kreatyniny, aminotransferazy asparaginianowej oraz NT-proBNP. W przeciwieństwie do grupy kontrolnej, deklarowana ekspozycja na słońce nie wpływa na stężenie witaminy D u pacjentów z NS

Percutaneous direct thrombin injection with hydrodissection to manage type II endoleak after endovascular abdominal aortic aneurysm repair

Type II endoleak is the most common complication after endovascular abdominal aortic aneurysm repair (EVAR). The management remains controversial. We present a case in which endoleak was successfully treated by direct percutaneous thrombin injection with hydrodissection. This method seems to be a safe and feasible alternative method for treatment of type II endoleak

Electroretinographic findings in day-blind dogs

Cone degeneration (cd; day blindness) is one of the inherited retinal diseases of dogs. Its diagnosis is based on vision testing, fundoscopy, electroretinography (ERG) and, for some breeds, on genetic tests. Typical signs of the disease are day blindness and cone dysfunction during ERG while fundoscopy does not show any abnormalities. The aim of this study was to compare behavioural findings, fundoscopic lesions and electroretinographic alterations in 12 cd-affected dogs (Alaskan Malamute, Labrador Retriever, German Shepherd, Dachshund, Yorkshire Terrier, Shih Tzu, Siberian Husky and crossbreeds) examined at our clinic. None of the examined dogs had any fundoscopic lesions, and all of them had normal scotopic vision with strongly impaired or absent photopic vision. Light-adapted transient, cone-mediated and steady-state, 31-Hz cone flicker ERGs were much below the 5th percentile limits of normality or even unrecordable, while the rod-driven ERGs were within normal values. Vision test and ERG results corresponded to each other and, combined with the results of fundoscopy, were typical of cd. To date, our research is one of the few studies in the world presenting ERG alterations compared with vision test findings and fundoscopic results in the course of cd

Is rosuvastatin better than atorvastatin and simvastatin in the prevention of in-stent restenosis and atherosclerosis progression in patients after superficial femoral artery stenting due to chronic lower limb ischaemia? The preliminary case-control study

Introduction. Statins effect on the outcome of endovascular intervention due to chronic lower limb ischaemia (CLLI) is still uncertain. The aim of this study was to determine the effect of statin type on the late outcome of superficial femoral artery (SFA) stenting in patients with CLLI. Material and methods. Retrospective analysis of the medical documentation of 275 consecutive patients treated with SFA stenting due to CLLI, including 125 (45%) patients with critical limb ischaemia (CLI). Measured outcomes were: target lesion revascularization (TLR), target extremity revascularization (TER), and target limb amputation (TLA). Results. Statins were used by 267 (97%) of the patients, respectively: atorvastatin (n = 191, 70%), simvastatin (n = 31, 11%) and rosuvastatin (n = 45, 16%). During the 675.0 ± 569.7 days of follow-up, TLR was required by 79 (29%) patients, TER by 109 (39%), and TLA by 27 (10%). Patients treated with rosuvastatin in comparison with those treated with atorvastatin, in spite of greater initial LDL and triglyceride levels, required TER (p = 0.01) and TLR (p = 0.03) less frequently. The risk of TER in patients treated with rosuvastatin was significantly (p = 0.016) lower than in individuals treated with atorvastatin and simvastatin, as shown in the Kaplan-Meier analysis. Cox’s proportional hazards regression showed that therapy with rosuvastatin was the strongest factor (HR 0.40 ± 95% CI; 0.2-0.81) decreasing the likelihood of TER. Conclusions. Rosuvastatin after SFA stenting seems to have the strongest effect on reduction in reintervention risk but without influence on limb salvage.

Participation of fire protection units in Poland in ensuring the continuous operation of ventilators for home use — a 7-year observation

Introduction: After each weather front with gales all over Poland, firemen have to perform a few hundred or so interventions. The life of persons covered by a specialistic treatment — home mechanical ventilation HMV — depends upon stable supplies of electricity. In case of breakdowns, indispensable aid is given by firemen who deliver generating sets available in Rescue and Firefighting Units (RFU). Aim of the study: Analysis and a statistical presentation of interventions of fire protection units to support the correct operation of home medical machines in case of temporary power failure. Material and methods: Data obtained from the Decision Support System of the State Fire Service (SFS DSS), made available to the authors by the Operational Planning Bureau at the Headquarters of the State Fire Service. In graphical presentations utilized were materials from the Head Office of Geodesy and Cartography, Law on Geodesy and Cartography, viz. Database for Topographic Objects, National Register of Borders. Medical data consistent with the purpose of the study were collected from the analysis of reports compiled by the person in charge of a rescue action of the State Fire Service, which is not the leading service in medical interventions. Results: In 2015–2021 were 1490 local hazards in which case it was necessary to support the operation — in most cases of ventilators for home use among people requiring ventilator-based therapy. The data show a constantly rising trend, the number of such actions increased by 64.29% — from 163 to 276 [mean (M) = 215.86, standard deviation (SD) = 66.35]. The average waiting time for undertaking intervention in these types of events was 910.68 seconds (15 min, 10 s). Conclusions: A significant element of rescue actions are volunteer fire brigade squads for being better deployed in rural areas, provided with generating sets; they can ensure faster an emergency electricity source. Persons in charge of a rescue action should draw up the medical part of a report more accurately (concerning the victim and the disease entity) while performing qualified first aid procedures