Funkcje prawie ortogonalnie addytywne

W czterech pracach stanowiących rozprawę, dwóch napisanych tylko przeze mnie oraz dwóch napisanych wspólnie z Tomaszem Kochankiem, zajmuję się funkcjami prawie ortogonalnie addytywnymi z rozumieniem słowa prawie na dwa różne sposoby

Orthogonally Pexider functions modulo a discrete subgroup

A result from [J. Brzdęk, Pacific J. Math. 181 (1997), no. 2, 247–267; MR1486531] provides, under some assumptions, a description of functions f:G→H such that f(x+y)−f(x)−f(y)∈K for x,y∈G with x⊥y. In the present paper, the author considers the Pexider difference f(x+y)−g(x)−h(y) instead of the Cauchy one

Decoupling Hypothesis and the Financial Crisis

The purpose of this paper was to present the decoupling hypothesis which says that the performance of emerging economies becomes relatively independent of the changes in advanced economies, and to empirically verify this hypothesis. The Christiano-Fitzgerald band-pass filter and spectral analyses have been applied to examine the hypothesis. On the basis of obtained results, comparing the deviations of GDPs from their long-term trend, it seems that the synchronization of cycles between emerging and advanced economies was already high before the crisis. The last global crisis, especially if time shifts between the countries are taken into account, even increased the synchronization of the economies. Therefore, this paper presents evidence against the decoupling hypothesis, and at the same time it raises doubts whether the high GDP growth rates in emerging economies can be sustainable in the presence of the slow-down in the advanced economies. The paper analyzes the situation from the Poland’s point of view as the country which is on the verge of joining the ERM2 system and adopting the euro (synchronization divagations are important for this decision) and because Poland is a good example of an emerging economy

Chapter 6 Challenges for the education system in the era of the Fourth Industrial Revolution

The fourth industrial revolution, characterized by digitization, artificial intelligence and augmented reality, and megatrends such as globalization, urbanization, demographic changes and the knowledge-based economy, will trigger a series of profound technological, economic, social and environmental changes that will permanently and irreversibly change the role of the state in meeting social needs. Industry 4.0 will also change the type, nature, and scope of public goods and how they are produced, financed, delivered, and consumed. This book redefines the current paradigm of public goods. It proposes a model of production and distribution of public goods that acknowledges the participation of entities from the public, private, and nonprofit sectors. The authors argue that these entities would participate in the production, financing, distribution, and consumption of such goods. From a theoretical point of view, such an inclusive approach involving the expansion of the classical state - market dichotomy with new entities, including citizens themselves, leads to a new conceptualization and approach towards public goods. The model assumes shared responsibility, subsidiarity, and paternalistic libertarianism, and it allows the state to create new entities of an educational or fiscal nature, while remaining the regulator of public services and distribution. Additionally, the book analyzes changes regarding the perception of public goods, in the era of the fourth industrial revolution, across selected sectors such as healthcare and pension systems, education, local public goods, and public utility services. The book is primarily addressed to researchers, scholars and students across social and technical sciences, and it will also be a useful guide for central and local administration bodies responsible for public policy

Zespół samotnego wrzodu odbytnicy i enterocele u 13-letniego chłopca

Zespół samotnego wrzodu odbytnicy (solitary rectal ulcer syndrome - SURS) jest rzadkim schorzeniem u dzieci i młodzieży. Zwykle objawia się zaburzeniami oddawania stolca i bólami brzucha. Powszechnie uważa się, że w patogenezie tego schorzenia odgrywają rolę zaburzenia defekacji. W niniejszej pracy przedstawiono opis przypadku 13-letniego chłopca z zespołem nadpobudliwości psychoruchowej i SURS. Głównymi objawami, które zgłaszał pacjent, były: zwiększona częstość oddawania stolca z obecnością śluzu, okresowe krwawienia z odbytnicy, uczucie parcia na stolec i niepełnego wypróżnienia oraz bóle brzucha. W badaniu kolonoskopowym stwierdzono okrężne owrzodzenie i uniesioną, nieregularną zmianę sięgającą esicy z typowym dla SURS obrazem mikroskopowym. Defekografia uwidoczniła typowy dla enterocele obraz wpuklenia się pętli jelita cienkiego w ścianę prostnicy. Chłopcu i jego matce wyjaśniono łagodny, chociaż przewlekły, charakter schorzenia. Leczenie zachowawcze obejmowało zalecenie unikania wysiłkowego oddawania stolca oraz stosowanie diety bogatobłonnikowej, aby zapobiegać zaparciom. W SURS obraz zmian makroskopowych jest bardziej różnorodny, niż powszechnie się uważa. Ustalenie właściwego rozpoznania zależy w dużej mierze od wnikliwości zarówno klinicysty, jak i patologa.Solitary rectal ulcer syndrome (SRUS) is a rare disorder of childhood, which usually presents with any of the manifestations of anorectal disease, bowel habit alteration and abdominal pain. It is commonly accepted that pathogenesis is associated with disturbances of defecation. We describe a 13-year-old boy with attention deficit hyperactivity disorder (ADHD) and SRUS. He complained of increased stool frequency associated with the passage of blood and mucus, tenesmus, sensation of incomplete defecation and abdominal pain. Circumferential ulcer and flat lesion extending up to the sigmoid colon with typical microscopic findings were revealed upon colonoscopy. Defecography showed an opacified small bowel invaginating into the rectal wall, the pictures consistent with enterocele. Conservative treatment, including reassuring the patient and his mother of the benign nature of the disease, recommendation to avoid straining defecation and use of a high-fiber diet to prevent constipation, was applied. The macroscopic appearance of rectal lesions in SRUS are much more variable than is usually realized. An early diagnosis requires a high index of suspicion both for clinicians and the pathologist

Ultrasound variants of autoimmune thyroiditis in children and adolescents and their clinical implication in relation to papillary thyroid carcinoma development

Background The prevalence of autoimmune thyroiditis (AIT) and papillary thyroid carcinoma (PTC) is rising in children and adolescents, and the coincidence of AIT and PTC is as high as 6.3-43%. Objective To investigate the ultrasound manifestation of AIT in relation to PTC development in paediatric patients. Patients 179 paediatric patients (133 females), mean (SD) age: 13.9 (3.03) years diagnosed with AIT and referred for ultrasound evaluation. Eight patients were diagnosed with PTC (6 females). Methods Retrospective analysis of thyroid ultrasound scans of patients diagnosed with AIT. Thyroid and autoimmune status was assessed based on TSH, fT4, fT3 and increased aTPO and/or aTG and/or TRAB levels. In patients with PTC, total thyroidectomy was performed. Results Analysis of thyroid US scans revealed that the following five ultrasound variants of AIT were observed in 179 patients: the most common in 35.2%-diffuse thyroiditis with hypoechogenic background and normoechogenic parenchyma, in 30.2%-diffuse thyroiditis with irregular background, in 18.9% nodular variant with normoechogenic background, in 11.7%-micronodulations and in 3.9%-diffuse hypoechogenic background. Eight cases of PTC were diagnosed in nodular variant of AIT with normoechogenic irregular background. Conclusion Patients with AIT and nodular variant with normoechogenic irregular background of the thyroid gland on US scans are in the risk group of developing PTC and should be followed up with regular neck US assessment

Schizencephaly—diagnostics and clinical dilemmas

Background Schizencephaly is an uncommon congenital disorder of cerebral cortical development. The defect is characterized by the presence of a cleft in the brain extending from the surface of the pia mater to the cerebral ventricles. The margins of the cleft are lined with heterotropic, dysplastic gray matter. The causes of schizencephaly are heterogeneous and can include teratogens, prenatal infection, maternal trauma, or EMX2 mutations. Method In the present paper, the authors described difficulties in employing diagnostic imaging in differentiating between type II (open-lip) schizencephaly and much more common intracranial fluid spaces of a different origin (arachnoid cysts and hydrocephalus). Result In all the three cases, the treatment consisted in implantation of a shunt system; nevertheless, it should be emphasized that a surgical intervention in the third presented case (type II schizencephaly) aimed at relieving the symptoms of intracranial hypertension—a directly life-threatening condition—since shunting is not a method of treating schizencephaly itself. Conclusions Although proper interpretation of the character of intracranial fluid spaces is of significance for further therapeutic management, yet, the key decision as to the surgical intervention is made based on clinical presentation, predominantly on symptoms of intracranial hypertension