Characterizations of second-order differential operators

If $k\geq 2$ is a positive integer, $\Omega \subset \mathbb{R}^{N}$ is a domain then by the well-known properties of the Laplacian and the gradient, we have $$\Delta(f\cdot g)=g \Delta f+f \Delta g+2\langle \nabla f, \nabla g\rangle$$ for all $f, g\in \mathscr{C}^{k}(\Omega, \mathbb{R})$. Due to the results of K\"onig--Milman \cite{KonMil18}, the converse is also true under some assumptions. Thus the main aim is this paper is to provide an extension of this result and to study the corresponding equation $$T(f\cdot g)= fT(g)+T(f)g+2B(A(f), A(g)) \qquad \left(f, g\in P\right),$$ where $Q$ and $R$ are commutative rings and $P$ is a subring of $Q$, further $T\colon P\to Q$ and $A\colon P\to R$ are additive mappings, while $B\colon R\times R\to Q$ is a symmetric and bi-additive mapping. Related identities with one function will also be considered which turn also suitable for characterizing second-order differential operators

Glosa aprobująca do wyroku Sądu Najwyższego z dnia 16 listopada 2017 r., V CSK 81/17

In the judgment of November 16, 2017, Ref. V. CSK 81/17, the Supreme Court ruled that starting a business in the form of running a go-go club in the commune does not violate its good name, even if some activities in its activity are contrary to the law. In addition, there are no grounds to distinguish the personal interest of a legal person in the form of a credible image. The purpose of this opinion is to evaluate the above resolution of the Supreme Court. The author intends to compare the judgment of the Supreme Court with the views of representatives of the doctrine of Polish judicial law and previous case-law

Immune system, immune self. Introduction

The idea that the immune system distinguishes between self and non-self was one of the central assumptions of immunology in the second half of 20 th century. This idea influenced experimental design and data interpretation. However, in the face of new evidence there is a need for a new conceptual framework in immunology

Glosa częściowo krytyczna do uchwały Sądu Najwyższego z dnia 17 marca 2017 r. (III CZP 110/16)

The Supreme Court in the judgment of 17 March 2017, Ref. No. III CZP 110/16, ruled that it is permissible to enter into an agreement to renounce a legal portion in Polish civil law. Until now, it was unacceptable. The Supreme Court ruled that since the inheritance can be renounced, all the more so a legal portion can be renounced. The purpose of this article is to evaluate the above resolution of the Supreme Court. The author intends to compare the judgment of the Supreme Court with the views of the representatives of the doctrine of Polish judicial law and the previous case-law

Glosa krytyczna do wyroku Sądu Najwyższego z dnia 24 maja 2019 r., I CSK 218/18

The Supreme Court in its judgment of 24 May 2019, I CSK 218/18, ruled that the purpose of increase in a lump sum remuneration under Article 632 § 2 of the Polish Civil Code is only to reduce the loss. The purpose of increasing the lump sum remuneration is not to compensate for the entire imminent loss. Such increase should cover that part of the loss which exceeds the normal contractual risk. The aim of this paper is to comment on the above judgment of the Supreme Court. The author compares the Supreme Court judgment with the views of legal scholars and commentators on the Polish judicial law, and with the previous case law

Dobra osobiste osób prawnych w polskim prawie cywilnym

Monografia pt. ,,Dobra osobiste osób prawnych w polskim prawie cywilnym” porusza niezwykle doniosłą i nadal niedostatecznie zbadaną przez polską doktrynę prawa cywilnego problematykę. Zarówno na etapie wykładni jak i stosowania prawa powstaje wiele pytań i dylematów związanych z art. 43 w zw. z art. 23 i 24 Kodeksu cywilnego. Liczne trudności dotyczącą między innymi: określenia dokładnego katalogu dóbr osobistych osób prawnych, wskazania środków ochrony przysługujących osobom prawnym w przypadku naruszenia ich dóbr osobistych, definiowania pojęcia dóbr osobistych osób prawnych czy wyszczególnienia zakresu jaki obejmuje poszczególne dobro osobiste osoby prawnej. Niniejsza publikacja ma na celu udzielenie chociażby częściowej odpowiedzi na powyższe pytania. Wnikliwej analizie poddany został dorobek naukowy polskiej doktryny prawa cywilnego począwszy od okresu dwudziestolecia międzywojennego, a skończywszy na początku lat 20 XXI wieku, a także dorobek orzeczniczy Sądu Najwyższego i sądów powszechnych głównie z okresu ostatnich kilkunastu lat. Mam nadzieję, iż monografia pt. ,,Dobra osobiste osób prawnych w polskim prawie cywilnym” stanowić będzie dla wielu naukowców dobry wstęp do prowadzenia dalszych badań, a praktykom ułatwi prowadzenie spraw sądowych związanych z ochroną dóbr osobistych osób prawnych. Zapraszam do lektury

The potential impact of hereditary hemochromatosis on the heart considering the disease stage and patient age—the role of echocardiography

BackgroundHereditary hemochromatosis (HH) is a genetic disease that leads to increased iron accumulation in several organs. Cardiomyocytes are highly susceptible to this damage owing to their high iron uptake, and cardiovascular complications account for 1/3 of the deaths in the natural course of HH. Additionally, excess iron intake and associated oxidative stress may accelerate the aging of the cardiovascular system, regardless of the age of patients with HH. We aimed to investigate the role of standard and speckle-tracking echocardiography (STE) in revealing heart differences in patients with HH considering the disease stage and the patient age.MethodologyConsecutive patients with HH (n = 58) without heart pathologies (except hypertension) and 29 age- and sex-matched healthy individuals underwent echocardiography. Patients were compared according to the time since HH diagnosis (the recently diagnosed HH group [31 patients] with diagnosed HH for less than 6 months and had no more than one venesection; the medium group [11 patients] with diagnosed HH between 6 and 24 months; and the long-lasting group [16 patients] with diagnosed HH for more than 2 years) and the quartile contribution of their age.ResultsStandard echocardiography revealed differences in diastolic parameters between patients with HH and controls, which were the most prominent between healthy and long-lasting HH patients. Regarding systolic function, left ventricular ejection fraction was lower in HH patients, with the most evident differences between the healthy and recently diagnosed HH patients. STE revealed additional differences in systolic parameters, with LV rotation the worst in recently diagnosed patients and its increase in patients with medium and long-lasting HH. Significantly worse peak systolic longitudinal strain values were observed in all patients with HH. Analyses of the results according to the age quartiles of patients with HH revealed that some changes ocurred earlier than expected according to age.ConclusionsEchocardiography can reveal possible heart damage in HH patients at different stages of the disease and highlight potential features of accelerated myocardial aging in these patients

Baroreflex sensitivity but not microvolt T-wave alternans can predict major adverse cardiac events in ischemic heart failure

Background: Major adverse cardiovascular events (MACE) constitutes the main cause of morbidity and mortality in ischemic heart failure (HF) patients. The prognostic value of the autonomic nervous system (ANS) parameters and microvolt T-wave alternans (MTWA) in this issue has not been identified to date. The aim herein, was to assess the usefulness of the abovementioned parameters in the prediction of MACE in HF patients with left ventricular systolic dysfunction of ischemic origin. Methods: Baroreflex sensitivity (BRS), heart rate variability (HRV), MTWA and other well-known clinical parameters were analyzed in 188 ischemic HF outpatients with left ventricular ejection fraction (LVEF) ≤ 50%. During 34 (14–71) months of follow-up, 56 (30%) endpoints were noted. Results: Univariate Cox analyses revealed BRS (but not HRV), MTWA, age, New York Heart Association III, LVEF, implantable cardioverter-defibrillator presence, use of diuretics and antiarrhythmic drugs, diabetes, and kidney insufficiency were defined as significant predictors of MACE. Pre-specified cut-off values for MACE occurrence for the aforementioned continuous parameters (age, LVEF, and BRS) were: ≥ 72 years, ≤ 33%, and ≤ 3 ms/mmHg, respectively. In a multivariate Cox analysis only BRS (HR 2.97, 95% CI 1.35–6.36, p < 0.006), and LVEF (HR 1.98, 95% CI 0.61–4.52, p < 0.038) maintained statistical significance in the prediction of MACE. Conclusions: BRS and LVEF are independent of other well-known clinical parameters in the prediction of MACE in patients with HF of ischemic origin and LVEF up to 50%. BRS ≤ 3 ms/mmHg and LVEF ≤ 33% identified individuals with the highest probability of MACE during the follow-up period