Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory

System of classical nonlinear oscillators as a coarse-grained quantum system

Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of the corresponding classical system on a sufficiently large scale

A constructive geometry in teaching of mathematics

Konstruktivna geometrija ima svoju nezamjenjivu ulogu u nastavi matematike. U ovomu radu uvodimo aksiome konstruktivne geometrije tj. usustavljujemo pravila kojima se u nastavi geometrije služimo kao nepisanim pravilima. Time konstruktivna geometrija postaje disciplina koja se bavi realizacijom klasičnog modela Euklidske geometrije. Ona nam pomaže pri naslučivanju i dokazivanju istina koje vrijede u tom, a onda i u bilo kojem drugom, modelu Euklidske geometrije. Napose, algebarskim jezikom možemo opisati rješivost geometrijskih problema konstruktivnim metodama.Constructive geometry plays an important role in teaching mathematics. In this paper we give axioms of constructive geometry, i.e. we incorporate all unwritten rules into a deductive system. In such manner constructive geometry becomes a mathematical discipline dealing with one particular realization of the classical model of Euclidian geometry. Its methods provide research into this model of geometry. Solvability of constructive geometry problems is characterized in a rather algebraic way

Assessment of the effectiveness of low level laser in the treatment of alveolar osteitis

Background/Aim. Alveolar osteitis (AO) is the extraction wound healing disorder with a presence of severe pain. Low level laser therapy stimulates cell metabolism and microcirculation, have has pronounced analgesic, antiedematous and anti-inflammatory effect and speeds up wound healing process. The aim of this study was to present results of clinical research that examined the effectiveness of low level laser in pain relief and healing of extraction wounds with alveolar osteitis in the lower jaw which was formed on the second day after tooth extraction. Methods. The study was conducted on 60 subjects divided into the study and the control group. In both groups extraction wounds were processed in similar way, except that in the study group was applied daily treatment of low level laser with a total of eight sessions of radiation, while in the control group extraction wounds were dressed with zinc oxide eugenol paste, which was changed every 48 hours up to the pain cessation. Measurement of pain intensity was done with a visual analogue scale (VAS) 10 min prior to processing of extraction wounds and daily for the next eight days. Assessment of the effectiveness of low level laser on healing of extraction wounds was performed on the day eight of the treatment. Results. On the day five after beginning of the treatment of extraction wounds with alveolar osteitis in the patients of the study group a lower average value of pain as compared to the control group was registered. This difference was increased within the following days. Extraction wounds healing in the study group was more successful and faster than in the control group. Conclusion. This study suggested that the reduction of pain was more pronounced in the patients with alveolar osteitis whose extraction wounds were subjected to low level laser radiation in comparison to those in which extraction wounds were treated with zinc oxide eugenol paste

A constructive geometry in teaching of mathematics

Konstruktivna geometrija ima svoju nezamjenjivu ulogu u nastavi matematike. U ovomu radu uvodimo aksiome konstruktivne geometrije tj. usustavljujemo pravila kojima se u nastavi geometrije služimo kao nepisanim pravilima. Time konstruktivna geometrija postaje disciplina koja se bavi realizacijom klasičnog modela Euklidske geometrije. Ona nam pomaže pri naslučivanju i dokazivanju istina koje vrijede u tom, a onda i u bilo kojem drugom, modelu Euklidske geometrije. Napose, algebarskim jezikom možemo opisati rješivost geometrijskih problema konstruktivnim metodama.Constructive geometry plays an important role in teaching mathematics. In this paper we give axioms of constructive geometry, i.e. we incorporate all unwritten rules into a deductive system. In such manner constructive geometry becomes a mathematical discipline dealing with one particular realization of the classical model of Euclidian geometry. Its methods provide research into this model of geometry. Solvability of constructive geometry problems is characterized in a rather algebraic way

Mean field approximation for noisy delay coupled excitable neurons

Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by $N\gg 1$ stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.Comment: 15 pages, 3 figure

Hamiltonian Quantum Dynamics With Separability Constraints

Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a special submanifold of $P {\cal H}$. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton's operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed

Okularni pseudoeksfolijativni sindrom i unutarnje sistemske bolesti

The aim of the study was to assess the association between the presence of ocular pseudoexfoliation syndrome and internal systemic diseases, i.e. arterial hypertension, angina pectoris, myocardial infarction, heart arrhythmias, diabetes mellitus, stroke and transient ischemic attacks. This prospective study included 646 patients aged =50 examined at a general ophthalmology clinic in Knin. Ophthalmologic examination included visual acuity testing and refraction, slit lamp examination, fundus examination and applanation tonometry. The diagnosis of pseudoexfoliation syndrome was based on the presence of characteristic whitish, granular deposits on the anterior segment structures of the eye. Data on the presence of internal systemic disease were collected by interview with patients and from internist and neurological medical records. All data collected were statistically analyzed by use of c2-test and ANOVA. In patients with pseudoexfoliation syndrome, the prevalence of arterial hypertension (p=0.468), ischemic heart disease (p=0.372), cerebrovascular disease (p=0.485), diabetes mellitus (p=0.492) was not statistically significantly higher in comparison with patients without pseudoexfoliation syndrome. However, the prevalence of heart arrhythmia was statistically significantly higher in patients with than in those without pseudoexfoliation syndrome (p=0.001). Based on the results of this and other studies, the question of whether the presence of ocular pseudoexfoliation syndrome could be used as a marker in detecting individuals with heart arrhythmias or internal disease remains open.Cilj studije bio je ispitati povezanost između okularnog pseudoeksfolijativnog sindroma i unutarnjih sistemskih bolesti arterijske hipertenzije, ishemične bolesti srca (angina pektoris i infarkt miokarda), srčanih aritmija, šećerne bolesti i cerebrovaskularnih bolesti (moždani udar i tranzitorne ishemične atake). Ova prospektivna studija uključila je 646 bolesnika u dobi od 50 ili više godina pregledanih u općoj oftalmološkoj ambulanti u Kninu. Oftalmološki pregled bolesnika uključio je ispitivanje vidne oštrine i refrakcije, pregled na biomikroskopu, pregled očne pozadine i aplanacijsku tonometriju. Dijagnoza okularnog pseudoeksfolijativnog sindroma postavljena je na temelju prisutnosti znakovitih bjelkastih granularnih nakupina na strukturama prednjeg segmenta oka. Podaci o postojanju unutarnjih sistemskih bolesti prikupljeni su anamnestički i uvidom u internističku i neurološku medicinsku dokumentaciju. Svi prikupljeni podaci obrađeni su statistički pomoću ÷2-testa i ANOVA. Nismo utvrdili statistički značajnu razliku u učestalosti arterijske hipertenzije (p=0,468), ishemične bolesti srca (p=0,372), cerebrovaskularnih bolesti (p=0,485) i šećerne bolesti (p=0,492) u bolesnika s pseudoeksfolijativnim sindromom u odnosu na učestalost tih bolesti u bolesnika bez pseudoeksfolijativnog sindroma. Učestalost srčanih aritmija bila je statistički značajno viša u pacijenata s pseudoeksfolijativnim sindromom u odnosu na učestalost srčanih aritmija u bolesnika bez pseudoeksfolijativnog sindroma (p=0,001). S obzirom na rezultate ove i drugih studija ostaje otvoreno pitanje bi li okularni pseudoeksfolijativni sindrom mogao poslužiti kao biljeg u otkrivanju osoba s poremećajem srčanog ritma odnosno osoba s unutarnjim bolestima

Okularni pseudoeksfolijativni sindrom i unutarnje sistemske bolesti

The aim of the study was to assess the association between the presence of ocular pseudoexfoliation syndrome and internal systemic diseases, i.e. arterial hypertension, angina pectoris, myocardial infarction, heart arrhythmias, diabetes mellitus, stroke and transient ischemic attacks. This prospective study included 646 patients aged =50 examined at a general ophthalmology clinic in Knin. Ophthalmologic examination included visual acuity testing and refraction, slit lamp examination, fundus examination and applanation tonometry. The diagnosis of pseudoexfoliation syndrome was based on the presence of characteristic whitish, granular deposits on the anterior segment structures of the eye. Data on the presence of internal systemic disease were collected by interview with patients and from internist and neurological medical records. All data collected were statistically analyzed by use of c2-test and ANOVA. In patients with pseudoexfoliation syndrome, the prevalence of arterial hypertension (p=0.468), ischemic heart disease (p=0.372), cerebrovascular disease (p=0.485), diabetes mellitus (p=0.492) was not statistically significantly higher in comparison with patients without pseudoexfoliation syndrome. However, the prevalence of heart arrhythmia was statistically significantly higher in patients with than in those without pseudoexfoliation syndrome (p=0.001). Based on the results of this and other studies, the question of whether the presence of ocular pseudoexfoliation syndrome could be used as a marker in detecting individuals with heart arrhythmias or internal disease remains open.Cilj studije bio je ispitati povezanost između okularnog pseudoeksfolijativnog sindroma i unutarnjih sistemskih bolesti arterijske hipertenzije, ishemične bolesti srca (angina pektoris i infarkt miokarda), srčanih aritmija, šećerne bolesti i cerebrovaskularnih bolesti (moždani udar i tranzitorne ishemične atake). Ova prospektivna studija uključila je 646 bolesnika u dobi od 50 ili više godina pregledanih u općoj oftalmološkoj ambulanti u Kninu. Oftalmološki pregled bolesnika uključio je ispitivanje vidne oštrine i refrakcije, pregled na biomikroskopu, pregled očne pozadine i aplanacijsku tonometriju. Dijagnoza okularnog pseudoeksfolijativnog sindroma postavljena je na temelju prisutnosti znakovitih bjelkastih granularnih nakupina na strukturama prednjeg segmenta oka. Podaci o postojanju unutarnjih sistemskih bolesti prikupljeni su anamnestički i uvidom u internističku i neurološku medicinsku dokumentaciju. Svi prikupljeni podaci obrađeni su statistički pomoću ÷2-testa i ANOVA. Nismo utvrdili statistički značajnu razliku u učestalosti arterijske hipertenzije (p=0,468), ishemične bolesti srca (p=0,372), cerebrovaskularnih bolesti (p=0,485) i šećerne bolesti (p=0,492) u bolesnika s pseudoeksfolijativnim sindromom u odnosu na učestalost tih bolesti u bolesnika bez pseudoeksfolijativnog sindroma. Učestalost srčanih aritmija bila je statistički značajno viša u pacijenata s pseudoeksfolijativnim sindromom u odnosu na učestalost srčanih aritmija u bolesnika bez pseudoeksfolijativnog sindroma (p=0,001). S obzirom na rezultate ove i drugih studija ostaje otvoreno pitanje bi li okularni pseudoeksfolijativni sindrom mogao poslužiti kao biljeg u otkrivanju osoba s poremećajem srčanog ritma odnosno osoba s unutarnjim bolestima

Mean field approximation of two coupled populations of excitable units

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the inter-ensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical inter-population couplings.Comment: 5 figure