Particle velocity in noncommutative space-time

We investigate a particle velocity in the $\kappa$-Minkowski space-time, which is one of the realization of a noncommutative space-time. We emphasize that arrival time analyses by high-energy $\gamma$-rays or neutrinos, which have been considered as powerful tools to restrict the violation of Lorentz invariance, are not effective to detect space-time noncommutativity. In contrast with these examples, we point out a possibility that {\it low-energy massive particles} play an important role to detect it.Comment: 16 pages, corrected some mistake

The initial zones of the atrioventricular node: really neglected anatomical features of potential clinical significance?

The constant evolution of medical knowledge and accompanying development of diagnostic and treatment possibilities for arrhythmias and conduction disturbances has reawakened interest in the structure and function of the conduction system of the human heart, especially in the region of the atrioventricular (AV) junction and within the junction itself. Of the large number of studies dealing with the AV junction few focus on the initial zones of the AV node. These were described for the first time by Tawara in 1906. Similarly, Anderson et al. distinguished two origins of the AV node, the left one running towards the basis of the mitral valve and the right one leading towards the tricuspid valve. The differences in length and scale could be the result of the adoption of different reference points. The study was carried out on the material of 50 human hearts, of both sexes and ranging in age from 22 to 93, which were fixed in 10% formalin and 98% ethanol solution. The tissue obtained was fixed in the 10% formalin solution and, after being sunk in the paraffin, was cut into layers of about 10 μm thick. According to the age of the hearts, every 10th or 6th section was stained by the Masson-Goldner method. The preparations were examined under a LEICA 2000 and BIOLAR 2 microscope at magnifications of 2× to 400×. Each of the 50 examined hearts contained the atrioventricular node and its initial parts. We observed that the initial zone of the AV node is created by an assembly of cells typical for a conduction system that can create three groups that are initially independent of each other and are always arranged around the AV nodal artery. In all the hearts examined we found at least two initial parts of the node: the superior and inferior. These two groups were present in 45 hearts (90%). In the last 5 cases (10%) there was also a middle group. No cases were found either with a single initial group or without any initial groups. In the sections examined the superior group appeared to be first in 27 hearts (54%), while in 23 cases (46%) the inferior group was first. The length of each group was measured from its first appearance to its first direct contact with the second part. The length of the superior part varied from 0.15 to 2.91 mm (mean 0.90 ± 0.6 mm), the inferior from 0.11 to 2.41 mm (mean 0.88 ± 0.6 mm) and the middle from 0.67 to 2.21 mm (mean 1.04 ± 0.7 mm). As mentioned above, in all 50 hearts there was a direct connection between the atrial muscle and the upper origin of AV node. Furthermore, in all sections (100%) the same part of the interatrial septal muscle was connected to the compact part of the node. Additionally, in 3 cases (6%) we were able to observe direct connections between the muscle fibres running from the fasciculus limbicus inferior to the initial zone of the AV node: in 2 cases (4%) with the superior group and in 1 case (2%) with the inferior group. In 8% of the material the atrial muscle of the supra-orificial zone made direct contact with the superior initial group and the compact zone of the node and in 10% there was contact between the suborificial muscle and the inferior group and the compact part of the node. This configuration was not observed in relation to the middle and inferior groups

Development of the interatrial wall during the ontogenesis of foetuses and children up to one year of age

Background: The foramen ovale, present in foetal interatrial septum, plays an important role during foetal life. During delivery, foramen ovale closes and becomes fossa ovalis, starting the pulmonary circulation. The aim of our study was to describe the growth of the interatrial wall and changes in location of the foramen ovale, and fossa ovalis during the ontogenesis in the human hearts.Materials and methods: The study was performed on post-mortem material obtained from 92 human hearts from 22nd week of foetal life up to 1 year of age, fixed in a 4% formalin solution.Results: The interatrial wall size in the studied development period was greater in the horizontal than in the vertical dimension. During ontogenesis up to 1 year old, the anterior and inferior parts of the interatrial wall increased their shares considerably by 8% and 6%, respectively. The percentage participation of foramen ovale in the interatrial wall construction in the foetal period formed more than 50% of its size and fairly decreased reaching in infants about 39%.Conclusions: Our study demonstrated that during ontogenesis, from the foetal period to infancy, the parts of the interatrial wall increase their dimensions unevenly. The foramen ovale growth is smaller, compared to the rest of the interatrial wall development. On the basis of our data we can assume that the foramen ovale centre tends to be found in the postero-inferior quadrant of the interatrial wall (foetuses) and in postero-superior quadrant of the interatrial wall — in infants

Prognosis of Hypothermic Patients Undergoing ECLS Rewarming-Do Alterations in Biochemical Parameters Matter?

While ECLS is a highly invasive procedure, the identification of patients with a potentially good prognosis is of high importance. The aim of this study was to analyse changes in the acid-base balance parameters and lactate kinetics during the early stages of ECLS rewarming to determine predictors of clinical outcome. This single-centre retrospective study was conducted at the Severe Hypothermia Treatment Centre at John Paul II Hospital in Krakow, Poland. Patients ≥18 years old who had a core temperature (Tc) < 30 °C and were rewarmed with ECLS between December 2013 and August 2018 were included. Acid-base balance parameters were measured at ECLS implantation, at Tc 30 °C, and at 2 and 4 h after Tc 30 °C. The alteration in blood lactate kinetics was calculated as the percent change in serum lactate concentration relative to the baseline. We included 50 patients, of which 36 (72%) were in cardiac arrest. The mean age was 56 ± 15 years old, and the mean Tc was 24.5 ± 12.6 °C. Twenty-one patients (42%) died. Lactate concentrations in the survivors group were significantly lower than in the non-survivors at all time points. In the survivors group, the mean lactate concentration decreased -2.42 ± 4.49 mmol/L from time of ECLS implantation until 4 h after reaching Tc 30 °C, while in the non-survivors' group (p = 0.024), it increased 1.44 ± 6.41 mmol/L. Our results indicate that high lactate concentration is associated with a poor prognosis for hypothermic patients undergoing ECLS rewarming. A decreased value of lactate kinetics at 4 h after reaching 30 °C is also associated with a poor prognosis

Noncommutative Differential Forms on the kappa-deformed Space

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher-order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded-commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well-defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.Comment: to appear in J. Phys. A: Math. Theo

On the definition of velocity in doubly special relativity theories

We discuss the definition of particle velocity in doubly relativity theories. The general formula relating velocity and four-momentum of particle is given.Comment: 7 page

A Renormalization Group Approach to Relativistic Cosmology

We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a "3+1" formalism and invokes the coarse graining arguments, provided and supported by the real-space Renormalization Group (RG) methods. Block variables are introduced and the recursion relations written down explicitly enabling us to characterize the corresponding RG flow. To leading order, the RG flow is provided by the Ricci-Hamilton equations studied in connection with the geometry of three-manifolds. The properties of the Ricci-Hamilton flow make it possible to study a critical behaviour of cosmological models. This criticality is discussed and it is argued that it may be related to the formation of sheet-like structures in the universe. We provide an explicit expression for the renormalized Hubble constant and for the scale dependence of the matter distribution. It is shown that the Hubble constant is affected by non-trivial scale dependent shear terms, while the spatial anisotropy of the metric influences significantly the scale-dependence of the matter distribution.Comment: 57 pages, LaTeX, 15 pictures available on request from the Author

Exotic smooth structures and symplectic forms on closed manifolds

We give a short proof of the (known) result that there are no Kaehler structures on exotic tori. This yields a negative solution to a problem posed by Benson and Gordon. W discuss the symplectic version of the problem and analyze results which yield an evidence for the conjecture that there are no symplectic structures on exotic tori.Comment: AMSLaTeX, 16 pages, a new version. A survey of the symplectic version of the problem is adde

Covariant realizations of kappa-deformed space

We study a Lie algebra type $\kappa$-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. Space deformation depends on an arbitrary vector. Infinitely many covariant realizations in terms of commuting coordinates of undeformed space and their derivatives are constructed. The corresponding coproducts and star products are found and related in a new way. All covariant realizations are physically equivalent. Specially, a few simple realizations are found and discussed. The scalar fields, invariants and the notion of invariant integration is discussed in the natural realization.Comment: 31 pages, no figures, LaTe

Arterial hypertension and remodeling of the right ventricle

Background: In case of long-term and physiological loads (e.g. during pregnancy or regular athletics training), reversible morphological changes occur in the heart - cardiomyocytes undergo hypertrophy, however, this is not accompanied by impairment of left ventricular function or myocyte metabolism. However, in the course of various pathological processes, as time goes by, gradually permanent morphological changes occur. These changes are referred to as remodeling of the heart muscle, which, regardless of the primary cause, can lead to the development of chronic heart failure. Materials and methods: The study was performed on post-mortem material of 35 human hearts obtained from forensic sections and anatomopathological sections of people who died of non-cardiac causes (mainly traffic accidents, suicide attempts, strokes, acute infections); material was fixed in a 4% formalin solution. The hearts were subjected to macro- and microscopic assessment. During microscopic assessment the features of remodeling were evaluated. Results and conclusions: In vivo and echocardiographic tests, as well as macroscopic evaluation of post-mortem material, suggest the presence of some kind of right ventricular muscle remodeling, however classic microscopic observations, presented in this study do not provide such unambiguous evidence. Thus, the question arises: why and how the right ventricular function is disturbed, sometimes at early stages of arterial hypertension