QED: Chiral transition and the issue of triviality

I give a review and progress report on studies of lattice QED. I emphasize analytical results and methods that are applied in data analysis. Also, I derive some bounds for the critical exponents and establish their connection with scaling violations. Triviality, as realized in $\phi^4$ theory, is ruled out on theoretical grounds. I show that the present data, if analyzed correctly, all lead to the same conclusions. They are compatible with power law scaling with nongaussian exponents.Comment: 6 pages, 7 figures (not included), ILL-(TH)-93-2

CHILDREN ATTITUDES TOWARD VARIOUS FORMS OF RESISTANCE TRAINING

Despite the belief that resistance training was dangerous or ineffective for children, the safety and effectiveness of such programs are now well documented. The goal of this study was to examine the attitudes of children toward different forms of resistance training in which they were involved. One hundred 3rd and 4th grade children served as participants (age 9.5 years). Before filling out a questionnaire, the students were involved in five different resistance exercises types: exercises with their own body weight, exercises with barbells 1 kg in weight each, exercises with elastic bands, exercises with a partner and exercises with a BOSU ball (under unstable conditions). The questionnaire with a Likert scale of 5 degrees with responses ranging from 1 (strongly agree) to 5 (strongly disagree) consisted of questions exploring attitudes and degree of motivation toward various modalities of resistance training and their use in physical education classes. All of the selected modalities were evaluated positively by the children.  Over 50% of the children stated that they strongly like all of the selected resistance training modalities. Exercises on a BOSU ball were the children’s first choice (51%) followed by rubber bands (15%) while exercise with body weights were their last choice (9%). Within the limitations of the study, the data show that various modalities of resistance training exercises have the potential to increase physical activity and establish healthy physical activity patterns. The desire to experience new and different activities provided a significant role towards choice of modality of resistance training

Compositeness, Triviality and Bounds on Critical Exponents for Fermions and Magnets

We argue that theories with fundamental fermions which undergo chiral symmetry breaking have several universal features which are qualitatively different than those of theories with fundamental scalars. Several bounds on the critical indices $\delta$ and $\eta$ follow. We observe that in four dimensions the logarithmic scaling violations enter into the Equation of State of scalar theories, such as $\lambda\phi^4$, and fermionic models, such as Nambu-Jona-Lasinio, in qualitatively different ways. These observations lead to useful approaches for analyzing lattice simulations of a wide class of model field theories. Our results imply that $\lambda\phi^4$ {\it cannot} be a good guide to understanding the possible triviality of spinor $QED$.Comment: 12 pages, 3 figures (not included), ILL-(TH)-93-2

Universal Properties of Chiral Simmetry Breaking

We discuss chiral symmetry breaking critical points from the perspective of PCAC, correlation length scaling and the chiral equation of state. A scaling theory for the ratio $R_\pi$ of the pion to sigma masses is presented. The Goldstone character of the pion and properties of the longitudinal and transverse chiral susceptibilities determine the ratio $R_\pi$ which can be used to locate critical points and measure critical indices such as $\delta$. We show how PCAC and correlation length scaling determine the pion mass' dependence on the chiral condensate and lead to a practical method to measure the anomalous dimension $\eta$. These tools are proving useful in studies of the chiral transition in lattice QED and the quark-gluon plasma transition in lattice QCD.Comment: 19 pages, 4 figures. CERN-TH.6630/92 ILL-(TH)-92-1

DIFFERENCES IN EXPLOSIVE STRENGTH OF LEGS BETWEEN FOOTBALL AND FUTSAL PLAYERS

Football and futsal belong to the group of polystructural activities of a complex character. From the motor aspect, both games are defined by a complex structure, comprised of various movements of the cyclic and acyclic type. Football and futsal are characterized by specific movements of the lower limbs, which are used to regulate possession of the ball (leading, passing) as well as the movement of the torso and hitting the ball with the head. The movement structure is comprised of various activities: running, jumping, turning, reception and shooting the ball. The aim of this research is to establish whether there are statistically significant differences in the explosive strength of the legs in football and futsal players. The analysis involved a sample of 37 participants, divided into two subsamples, the first being senior football players (first lineup) of FC "Radnički" from Niš – 23, and the second being senior futsal players (first lineup) of Futsal Club "Kopernikus" from Niš – 14 participants. The explosive strength of the lower limbs was estimated through the following tests: Squat Jump (SJ), Counter Movement Jump without arms swing (CMJ) and Counter Movement Jump with arms swing (CMJS). The Multivariate Analysis of Variance method(МАNOVA) was used to determine the differences between the groups, while the Analysis of Variance method (ANOVA) was used for the differences between the groups in terms of separate measuringt instruments. It has been determined that there are differences in the explosive strength of the legs between football players and futsal players

Multistep generalized transformation method applied to solving equations of discrete and continuous time-fractional enzyme kinetics

In this paper, Caputo based Michaelis–Menten kinetic model based on Time Scale Calculus (TSC) is proposed. The main reason for its consideration is a study of tumor cells population growth dynamics. In the particular case discrete-continuous time kinetics, Michaelis–Menten model is numerically treated, using a new algorithm proposed by authors, called multistep generalized difference transformation method (MSGDETM). In addition numerical simulations are performed and is shown that it represents the upgrade of the multi-step variant of generalized differential transformation method (MSGDTM). A possible conditions for its further development are discussed and possible experimental verification is described.This is the peer-reviewed version of the article: Vosika, Z., Mitić, V.V., Vasić, A., Lazović, G., Matija, L., Kocić, L.M., 2017. Multistep generalized transformation method applied to solving equations of discrete and continuous time-fractional enzyme kinetics. Communications in Nonlinear Science and Numerical Simulation 44, 373–389. [https://doi.org/10.1016/j.cnsns.2016.08.024

Looking for the Logarithms in Four-Dimensional Nambu-Jona-Lasinio Models

We study the problem of triviality in the four dimensional Nambu-Jona-Lasinio model with discrete chiral symmetry using both large-N expansions and lattice simulations. We find that logarithmic corrections to scaling appear in the equation of state as predicted by the large-N expansion. The data from $16^4$ lattice simulations is sufficiently accurate to distinguish logarithmically trivial scaling from power law scaling. Simulations on different lattice sizes reveal an interesting interplay of finite size effects and triviality. We argue that such effects are qualitatively different for theories based on fundamental scalar rather than fermion fields. Several lessons learned here can be applied to simulations and analyses of more challenging field theories.Comment: 25 pages, 14 ps figure

Supplementary data for article: Veselinović, J. B.; Kocić, G. M.; Pavic, A.; Nikodinovic-Runic, J.; Senerovic, L.; Nikolić, G. M.; Veselinović, A. M. Selected 4-Phenyl Hydroxycoumarins: In Vitro Cytotoxicity, Teratogenic Effect on Zebrafish (Danio Rerio) Embryos and Molecular Docking Study. Chemico-Biological Interactions 2015, 231, 167–174. https://doi.org/10.1016/j.cbi.2015.02.011

Supplementary material for: [https://doi.org/10.1016/j.cbi.2015.02.011]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/1699

Phenomenological interaction between current quarks

We construct a phenomenological model which describes the dynamical chiral symmetry breaking (DCSB) of QCD vacuum and reproduces meson spectra. Quark condensates, the pion decay constant, and meson spectra are well reproduced by phenomenological interaction which consists of a linear confining potential, a Coulombic potential, and the 't Hooft determinant interaction. In this model, the 't Hooft determinant interaction plays a important role not to only \eta,\eta' mass difference, but other meson masses through DCSB.Comment: 18 pages, LaTe

Phase Transitions at Finite Temperature and Dimensional Reduction for Fermions and Bosons

In a recent Letter we discussed the fact that large-$N$ expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This was seen to be a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. In this article we present more evidence, both theoretical and numerical, that this result is correct. We develop a physical picture for our results and discuss the width of the scaling region (Ginzburg criterion), $1/N$ corrections, and differences between the dynamics of BCS superconductors and Gross-Neveu models. Lattices as large as $12 \times 72^2$ are simulated for both the $N=12$ and $N=4$ cases and the numerical evidence for mean field scaling is quite compelling. We point out that the amplitude ratio for the model's susceptibility is a particulartly good observable for distinguishing between the dimensional reduction and the mean field scenerios, because this universal quantity differs by almost a factor of $20$ in the two cases. The simulations are done close to the critical point in both the symmetric and broken phases, and correlation lengths of order $10$ are measured. The critical indices $\beta_{mag}$ and $\delta$ also pick out mean field behavior. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the composite character of the mesons in the model. We point out that our results should be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics. We also simulated the $O(2)$ model on $8 \times 16^3$ lattices to establish that our methods give the results of dimensional reduction in purely bosonicComment: 47 pages, latex, 23 figures in one uuencoded fil