Polynomials of Least Deviation from Zero in Sobolev p-Norm

The first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev p-norm ($$1<p<\infty $$ 1 < p < ∞ ) for the case $$p=1$$ p = 1 . Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev p-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that the n-th polynomial of least deviation has at least $$n-\mathbf {d}^*$$ n - d ∗ zeros on the convex hull of the support of the measure, where $$\mathbf {d}^*$$ d ∗ denotes the number of terms in the discrete part.

Acute and sub-chronic oral toxicities of DA.AMLODEPON HVD hard capsule in experimental animals

Assessment of toxicities of DA.AMLODEPON HVD hard capsule on experimental animals. The acute toxicity of DA.AMLODEPON HVD was assessed on Swiss mice according to World Health Organization Guidance, and LD50 determination according to the method of Litchfield – Wilcoxon. The sub-chronic toxicity study of DA.AMLODEPON HVD at two doses (0.42 g/kg/day and 1.26g/kg/day) was conducted in rats for four consecutive weeks. After administration, general conditions and the body weight of rats were evaluated. Blood samples were collected for analyzing serum parameters before treatment (T0), second week (T1), and fourth week (T2). Histopathological analysis of livers and kidneys was observed at the end of the experiment. The results revealed that mice were taken up to a maximum dose of 39.15 g/kg with no symptoms of acute toxicity, LD50 of DA.AMLODEPON HVD has not been determined. The sub-chronic toxicity study at two doses did not change the body weight of rats, general conditions. The parameters for structures and functions of livers and kidneys and microscopic of the livers and kidneys are in a normal range during the study period.

A class of Newton maps with Julia sets of Lebesgue measure zero

Let $$g(z)=\int _0^zp(t)\exp (q(t))\,dt+c$$ g ( z ) = ∫ 0 z p ( t ) exp ( q ( t ) ) d t + c where p, q are polynomials and $$c\in {\mathbb {C}}$$ c ∈ C , and let f be the function from Newton’s method for g. We show that under suitable assumptions on the zeros of $$g''$$ g ′ ′ the Julia set of f has Lebesgue measure zero. Together with a theorem by Bergweiler, our result implies that $$f^n(z)$$ f n ( z ) converges to zeros of g almost everywhere in $${\mathbb {C}}$$ C if this is the case for each zero of $$g''$$ g ′ ′ that is not a zero of g or $$g'$$ g ′ . In order to prove our result, we establish general conditions ensuring that Julia sets have Lebesgue measure zero.

Czas na podjęcie przez sąd decyzji w przedmiocie wniosku o zastosowanie tymczasowego aresztowania

This paper canvasses the problem of adequacy of time limit of 24 hours (as defined in art. 248 § 2 of the Code of Criminal Procedure and Art. 41 sec. 3 of the Constitution) for the court to assess the prosecutor’s request for pre-trial detention. Starting from the historical analysis of such a solution and then going through the characteristics of the scope of activities necessary to be taken by the court in such a short time and recalling selected procedural problems, visible mainly in the extensive penal economic cases, it was indicated that such a short deadline does not create general conditions for a reliable assessment of the legitimacy of the conclusion drawn. At the same time, the risk of transferring the effects of such inability to the suspect was indicated. Against this background, two main directions of possible normative changes are presented, including both the time limit itself and the accompanying solutions, allowing to create conditions for a more effective use of this inherently short period.

RESOURCES-BASED STRATEGIES FOR HEALTH PROMOTION OF STUDENTS WITH DIFFERENT GENERAL CONDITIONS AND DIFFERENT ORIGINS

Background: The aim of this study is to investigate the study-/work-related behavior and experience patterns of students, taking into account their origins as well as the stressful general conditions. Methods: A total of 194 students (41.8% women, 58.2% men, 58.7% German and 41.3% international students) were evaluated to their strains during the study and study-/work-related Behavior and Experience Patterns (AVEM). Four potentially stressful conditions were taken into account. Results: For only 14% of international students, but 45% of German students risk patterns for work-related behavior and experience were found. Study-/work-related behaviour and expe-rience patterns depend on the origin of the students. Resources during study were significantly higher among students of German origin. Conclusions: A study-related strengthening of resources is necessary, which can be viewed as a competitive advantage when choosing a study location.

Convergence in distribution for randomly stopped random fields

Let X \mathbb {X} and Y \mathbb {Y} be two complete, separable, metric spaces, ξ ε ( x ) , x ∈ X \xi _\varepsilon (x), x \in \mathbb {X} and ν ε \nu _\varepsilon be, for every ε ∈ [ 0 , 1 ] \varepsilon \in [0, 1] , respectively, a random field taking values in space Y \mathbb {Y} and a random variable taking values in space X \mathbb {X} . We present general conditions for convergence in distribution for random variables ξ ε ( ν ε ) \xi _\varepsilon (\nu _\varepsilon ) that is the conditions insuring holding of relation, ξ ε ( ν ε ) ⟶ d ξ 0 ( ν 0 ) \xi _\varepsilon (\nu _\varepsilon ) \stackrel {\mathsf {d}}{\longrightarrow } \xi _0(\nu _0) as ε → 0 \varepsilon \to 0 .

Quantum Black Holes and (Re)Solution of the Singularity

Classical general relativity predicts the occurrence of spacetime singularities under very general conditions. Starting from the idea that the spacetime geometry must be described by suitable states in the complete quantum theory of matter and gravity, we shall argue that this scenario cannot be realised physically since no proper quantum state may contain the infinite momentum modes required to resolve the singularity.

Saccharomyces boulardii improves the behaviour and emotions of spastic cerebral palsy rats through the gut-brain axis pathway

Background Cerebral palsy (CP) is a kind of disability that influences motion, and children with CP also exhibit depression-like behaviour. Inflammation has been recognized as a contributor to CP and depression, and some studies suggest that the gut-brain axis may be a contributing factor. Our team observed that Saccharomyces boulardii (S. boulardii) could reduce the inflammatory level of rats with hyperbilirubinemia and improve abnormal behaviour. Both CP and depression are related to inflammation, and probiotics can improve depression by reducing inflammation. Therefore, we hypothesize that S. boulardii may improve the behaviour and emotions of spastic CP rats through the gut-brain axis pathway. Methods Our new rat model was produced by resecting the cortex and subcortical white matter. Seventeen-day-old CP rats were exposed to S. boulardii or vehicle control by gastric gavage for 9 days, and different behavioural domains and general conditions were tested. Inflammation was assessed by measuring the inflammatory markers IL-6 and TNF-α. Hypothalamic–pituitary–adrenal (HPA) axis activity was assessed by measuring adrenocorticotropic hormone and corticosterone in the serum. Changes in the gut microbiome were detected by 16S rRNA. Results The hemiplegic spastic CP rats we made with typical spastic paralysis exhibited depression-like behaviour. S. boulardii treatment of hemiplegic spastic CP rats improves behaviour and general conditions and significantly reduces the level of inflammation, decreases HPA axis activity, and increases gut microbiota diversity. Conclusions The model developed in this study mimics a hemiplegic spastic cerebral palsy. Damage to the cortex and subcortical white matter of 17-day-old Sprague–Dawley (SD) rats led to spastic CP-like behaviour, and the rats exhibited symptoms of depression-like behaviour. Our results indicate that S. boulardii might have potential in treating hemiplegic spastic CP rat models or as an add-on therapy via the gut-brain axis pathway.

The basic liberties: An essay on analytical specification

We characterize, more precisely than before, what Rawls calls the ‘analytical’ method of drawing up a list of basic liberties. This method employs one or more general conditions that, under any just social order whatever, putative entitlements must meet for them to be among the basic liberties encompassed, within some just social order, by Rawls’s first principle of justice (i.e. the liberty principle). We argue that the general conditions that feature in Rawls’s own account of the analytical method, which employ the notion of necessity, are too stringent. They ultimately fail to deliver as basic certain particular liberties that should be encompassed within any fully adequate scheme of liberties. To address this under-generation problem, we provide an amended general condition. This replaces Rawls’s necessity condition with a probabilistic condition and it appeals to the standard liberal prohibition on arbitrary coercion by the state. We defend our new approach both as apt to feature in applications of the analytical method and as adequately grounded in justice as fairness as Rawls articulates the theory’s fundamental ideas.

The influence of liquid rubber on selected properties of rubber compound and its vulcanizates

The aim of the work was to determine the influence of liquid rubber on selected properties of rubber compound and its vulcanizates. Due to the liquid form of this rubber, it is not possible to completely replace the conventional solid rubber used in the mixture because of problems in further processing. In four experimental tests, we used different amounts of liquid rubber in the recipe together with butadiene-styrene rubber and the compounds we mixed according to the general conditions. We studied the curing characteristics of prepared mixture and we measuremend physical and mechanical properties of study vulcanizates and summarized the individual measured values for each parameter and suggested the greatest importance of the recipe for rubber practice.