Sharp Riesz-Fej\'er inequality for harmonic Hardy spaces

We prove sharp version of Riesz-Fej\'er inequality for functions in harmonic Hardy space $h^p(\mathbb{D})$ on the unit disk $\mathbb{D}$, for $p>1,$ thus extending the result from \cite{KPK} and resolving the posed conjecture.Comment: 5 pages; this version has been accepted for publication in Potential Analysi

Norm inequalities for vector functions

We study vector functions of ${\mathbb R}^n$ into itself, which are of the form $x \mapsto g(|x|)x\,,$ where $g : (0,\infty) \to (0,\infty)$ is a continuous function and call these radial functions. In the case when $g(t) = t^c$ for some $c \in {\mathbb R}\,,$ we find upper bounds for the distance of image points under such a radial function. Some of our results refine recent results of L. Maligranda and S. Dragomir. In particular, we study quasiconformal mappings of this simple type and obtain norm inequalities for such mappings.Comment: 19 page

H-colouring revisited

In this paper we give a new, shortened proof of NP-completeness of CSP problem for undirected, non bipartite graphs, of interest for generalization to QCSP problem. We also give some illustrative examples

Indeks ALBI kao prediktor preživljenja nakon resekcije hepatocelularnog karcinoma u bolesnika s kompenziranom cirozom jetre: usporedba s indeksima PALBI i MELD

The aim of the study was to explore predictive value of the ALBI, PALBI and MELD scores on survival in patients resected for hepatocellular carcinoma with compensated liver cirrhosis and no macrovascular infi ltration. In this retrospective study, longitudinal survival analysis was performed. We analyzed patient/tumor characteristics and MELD, ALBI and PALBI scores as liver function tests for predicting survival outcome. Survival was analyzed from the date of liver resection until death, liver transplantation, or end of follow-up. Patients were stratifi ed for age, cirrhosis etiology, presence of esophageal varices, hepatocellular carcinoma stage, microvascular invasion, histologic diff erentiation, and resection margins. We identifi ed 38 patients (alcoholic cirrhosis in 84.2% of patients) resected over an 8-year period. Median preoperative MELD score was 8, ALBI score -2.63, and PALBI score -2.38. During the follow-up period, 24 patients died. Estimated median survival time was 36 months. Microvascular invasion was observed in 33 patients. Higher ALBI score was associated with 23.1% higher relative risk of death. PALBI score was associated with 12.1% higher relative risk of death, whereas MELD score was not associated with the risk of death. In conclusion, ALBI score demonstrated signifi cant predictive capabilities for survival in patients with compensated cirrhosis resected for hepatocellular carcinoma.Cilj je bio istražiti prediktivnu vrijednost zbira ALBI, PALBI i MELD za preživljenje bolesnika s kompenziranom cirozom reseciranih zbog hepatocelularnog karcinoma bez makrovaskularne invazije. Provedena je retrospektivna longitudinalna analiza preživljenja. Testirane su karakteristike bolesnika/tumora kao i jetreni funkcijski testovi MELD, ALBI i PALBI za predviđanje preživljenja. Bolesnici su praćeni nakon resekcije jetre do smrti, transplantacije jetre odnosno do kraja vremena praćenja. Bolesnici su kategorizirani po dobi, etiologiji ciroze, prisutnosti varikoziteta jednjaka, stadiju karcinoma, mikrovaskularnoj invaziji, histološkom stadiju i resekcijskim rubovima. Identifi cirali smo 38 bolesnika (alkoholna ciroza kod 84,2% bolenika) reseciranih kroz razdoblje od 8 godina. Medijan prijeoperacijskog zbira MELD bio je 8, zbira ALBI -2,63 i zbira PALBI -2,38. Tijekom praćenja 24 bolesnika su umrla. Očekivani medijan preživljenja iznosio je 36 mjeseci. Mikrovaskularna invazija pronađena je u 33 bolesnika. Veći ALBI je bio povezan s 23,1%, a PALBI s 12,1% većim relativnim rizikom od smrtnog ishoda. MELD nije bio povezan sa smrtnim ishodom. Zbir ALBI je pokazao značajnu prediktivnu vrijednost preživljenja u skupini bolesnika s kompenziranom cirozom reseciranih zbog hepatocelularnog karcinoma

Distance between domains in the sense of Letho is not a metric

In this paper we consider the question whether the quotient of the set of domains conformally equivalent to a halfplane by the group of Möbius transformations with distance in the sense of Lehto is a metric space. The answer is shown to be negative in the general case. However, restricted to analytic domains the question has an afirmative answer

ALBI Score as a Predictor of Survival in Patients with Compensated Cirrhosis Resected for Hepatocellular Carcinoma: Exploratory Evaluation in Relationship to PALBI and MELD Liver Function Scores

The aim of the study was to explore predictive value of the ALBI, PALBI and MELD scores on survival in patients resected for hepatocellular carcinoma with compensated liver cirrhosis and no macrovascular infi ltration. In this retrospective study, longitudinal survival analysis was performed. We analyzed patient/tumor characteristics and MELD, ALBI and PALBI scores as liver function tests for predicting survival outcome. Survival was analyzed from the date of liver resection until death, liver transplantation, or end of follow-up. Patients were stratifi ed for age, cirrhosis etiology, presence of esophageal varices, hepatocellular carcinoma stage, microvascular invasion, histologic diff erentiation, and resection margins. We identifi ed 38 patients (alcoholic cirrhosis in 84.2% of patients) resected over an 8-year period. Median preoperative MELD score was 8, ALBI score -2.63, and PALBI score -2.38. During the follow-up period, 24 patients died. Estimated median survival time was 36 months. Microvascular invasion was observed in 33 patients. Higher ALBI score was associated with 23.1% higher relative risk of death. PALBI score was associated with 12.1% higher relative risk of death, whereas MELD score was not associated with the risk of death. In conclusion, ALBI score demonstrated signifi cant predictive capabilities for survival in patients with compensated cirrhosis resected for hepatocellular carcinoma

Infection as a predictor of mortality in decompensated liver cirrhosis: exploring the relationship to severity of liver failure

Background: Infections are common in patients with liver cirrhosis and increase mortality. We explored the relationship between infection and liver dysfunction in their effects on mortality. ----- Methods: Single-center data on decompensated liver cirrhosis patients hospitalized between March 2014 and December 2017 (index period) were reviewed until death, liver transplantation or 31 December 2018. Infections were classified as community-acquired infection (CAi) or hospital/healthcare associated infection (HCAi). Child-Pugh, model for the end-stage liver disease (MELD) and chronic liver failure-organ failure (CLiF-OF) scores indicated liver (dys)function. ----- Results: We enrolled 155 patients (85% alcoholic liver disease), 65 without infection at first hospitalization, 48 with CAi and 42 with HCAi. Multidrug resistant agents were confirmed in 2/48 (4.2%) CAi and 10/42 (23.8%) HCAi patients. At first hospitalization, infection was independently associated with worse liver dysfunction and vice versa, and with higher 30-day mortality [odds ratio (OR) = 2.73, 95% confidence interval (CI) 1.07-6.94]. The association was reduced with adjustment for MELD/CLiF-OF scores, but mediation analysis detected an indirect (via liver dysfunction) association. Twenty-eight patients were repeatedly hospitalized, 11 with new HCAi. HCAi was independently associated with twice higher risk of medium-term mortality and added an additional risk to any level of liver dysfunction, considering all or patients who survived the first 30 days. In those repeatedly hospitalized, HCAi appeared independently associated with a higher probability of infection and higher MELD scores at subsequent hospitalizations. ----- Conclusion: Infection (particularly HCAi) adds mortality risk to any level of liver dysfunction in decompensated liver cirrhosis patients. Mechanisms of long(er)-term effects (in acute episode survivors) seemingly include enhanced deterioration of liver function

Formulation and Evaluation of Helichrysum italicum Essential Oil-Based Topical Formulations for Wound Healing in Diabetic Rats

As proper wound management is crucial to reducing morbidity and improving quality of life, this study evaluated for the first time the wound healing potential of H. italicum essential oil (HIEO) prepared in the form of ointment and gel in streptozotocin-induced diabetic wound models in rats. After creating full-thickness cutaneous wounds, forty-eight diabetic rats were divided into six groups: (1) negative control; (2) positive control; (3) ointment base; (4) gel base; (5) 0.5% HIEO ointment (6) 0.5% HIEO gel. Wound healing potential was determined by the percentage of wound contraction, hydroxyproline content, redox status, and histological observation. A significant decrease in the wound size was observed in animals treated with HIEO formulations compared with other groups. The HIEO groups also showed a higher level of total hydroxyproline content, and more pronounced restitution of adnexal structures with only the underlying muscle defect indicating the incision site. Hence, our results legitimate the traditional data of the pro-healing effect of HIEO because HIEO in both formulations such as gel and ointment exhibited the significant wound repairing effect in the incision wound model