The thermodynamics for a hadronic gas of fireballs with internal color structures and chiral fields

The thermodynamical partition function for a gas of color-singlet bags consisting of fundamental and adjoint particles in both $U(N_c)$ and $SU(N_c)$ group representations is reviewed in detail. The constituent particle species are assumed to satisfy various thermodynamical statistics. The gas of bags is probed to study the phase transition for a nuclear matter in the extreme conditions. These bags are interpreted as the Hagedorn states and they are the highly excited hadronic states which are produced below the phase transition point to the quark-gluon plasma. The hadronic density of states has the Gross-Witten critical point and exhibits a third order phase transition from a hadronic phase dominated by the discrete low-lying hadronic mass spectrum particles to another hadronic phase dominated by the continuous Hagedorn states. The Hagedorn threshold production is found just above the highest known experimental discrete low-lying hadronic mass spectrum. The subsequent Hagedorn phase undergoes a first order deconfinement phase transition to an explosive quark-gluon plasma. The role of the chiral phase transition in the phases of the discrete low-lying mass spectrum and the continuous Hagedorn mass spectrum is also considered. It is found crucial in the phase transition diagram. Alternate scenarios are briefly discussed for the Hagedorn gas undergoes a higher order phase transition through multi-processes of internal color-flavor structure modification.Comment: 110 pages and 13 figures. Added references to the introductio

A predictive formulation of the Nambu--Jona-Lasinio model

A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu--Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated of the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects which are independent of the (arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few ones. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model become predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigma-quark coupling constants.Comment: 38 pages, 1 figure, To appear in Phy.Rev.

Extension of the Nambu--Jona-Lasinio model at high densities and temperatures by using an implicit regularization scheme

Traditional cutoff regularization schemes of the Nambu--Jona-Lasinio model limit the applicability of the model to energy-momentum scales much below the value of the regularizing cutoff. In particular, the model cannot be used to study quark matter with Fermi momenta larger than the cutoff. In the present work an extension of the model to high temperatures and densities recently proposed by Casalbuoni, Gatto, Nardulli, and Ruggieri is used in connection with an implicit regularization scheme. This is done by making use of scaling relations of the divergent one-loop integrals that relate these integrals at different energy-momentum scales. Fixing the pion decay constant at the chiral symmetry breaking scale in the vacuum, the scaling relations predict a running coupling constant that decreases as the regularization scale increases, implementing in a schematic way the property of asymptotic freedom of quantum chromodynamics. If the regularization scale is allowed to increase with density and temperature, the coupling will decrease with density and temperature, extending in this way the applicability of the model to high densities and temperatures. These results are obtained without specifying an explicit regularization. As an illustration of the formalism, numerical results are obtained for the finite density and finite temperature quark condensate, and to the problem of color superconductivity at high quark densities and finite temperature.Comment: 7 pages, 5 eps figures - in version 3, substantial changes in text, results and conclusions unchanged. To be published in Phys. Rev.

Static QˉQ\bar Q Q Potentials and the Magnetic Component of QCD Plasma near TcT_c

Static quark-anti-quark potential encodes important information on the chromodynamical interaction between color charges, and recent lattice results show its very nontrivial behavior near the deconfinement temperature $T_c$. In this paper we study such potential in the framework of the ``magnetic scenario'' for the near Tc QCD plasma, and particularly focus on the linear part (as quantified by its slope, the tension) in the potential as well as the strong splitting between the free energy and internal energy. By using an analytic ``ellipsoidal bag'' model, we will quantitatively relate the free energy tension to the magnetic condensate density and relate the internal energy tension to the thermal monopole density. By converting the lattice results for static potential into density for thermal monopoles we find the density to be very large around Tc and indicate at quantum coherence, in good agreement with direct lattice calculation of such density. A few important consequences for heavy ion collisions phenomenology will also be discussed.Comment: 10 pages, 6 figure

БУХГАЛТЕРСЬКИЙ ОБЛІК ФІНАНСОВИХ РЕЗУЛЬТАТІВ ЯК ПЕРЕДУМОВА ПОПЕРЕДЖЕННЯ БАНКРУТСТВА ПІДПРИЄМСТВА

This paper analyzes the analyzes of the dynamics of the financial results of enterprises, the influence of the factors leading to reduced solvency of domestic enterprises, the necessity of timeliness of financial information as a prerequisite to avoid bankruptcy.Amidst uncertain economic environment one gives much attentionto the bankruptcy issue because many domestic businesses are in crisis or bankruptcy. This is due to the financial failure of the company to overcome the economic crisis. The increasing number of bankrupt enterprises is influenced by most companies, which work with borrowed funds being insolvent and unable to fulfill their obligations not only to suppliers, but also to major creditors.В статье проанализированы аналитическую информацию о динамике финансового результата предприятий, определено влияние факторов, приводящих к снижению платежеспособности отечественных предприятий, обоснована необходимость своевременности предоставления бухгалтерской информации как предпосылки избежания банкротства предприятия.В статті проаналізовано аналітичну інформацію щодо динаміки фінансового результату підприємств, визначено вплив факторів, що призводять до зниження платоспроможності вітчизняних підприємств, обґрунтовано необхідність своєчасності надання бухгалтерської інформації як передумови уникнення банкрутства підприємства

Photon distribution amplitudes and light-cone wave functions in chiral quark models

The leading- and higher-twist distribution amplitudes and light-cone wave functions of real and virtual photons are analyzed in chiral quark models. The calculations are performed in the nonlocal quark model based on the instanton picture of QCD vacuum, as well as in the spectral quark model and the Nambu--Jona-Lasinio model with the Pauli-Villars regulator, which both treat interaction of quarks with external fields locally. We find that in all considered models the leading-twist distribution amplitudes of the real photon defined at the quark-model momentum scale are constant or remarkably close to the constant in the $x$ variable, thus are far from the asymptotic limit form. The QCD evolution to higher momentum scales is necessary and we carry it out at the leading order of the perturbative theory for the leading-twist amplitudes. We provide estimates for the magnetic susceptibility of the quark condensate $\chi_m$ and the coupling $f_{3\gamma}$, which in the nonlocal model turn out to be close to the estimates from QCD sum rules. We find the higher-twist distribution amplitudes at the quark model scale and compare them to the Wandzura-Wilczek estimates. In addition, in the spectral model we evaluate the distribution amplitudes and light-cone wave functions of the $\rho$-meson.Comment: 24 pages, 15 figure

Effects of mesonic correlations in the QCD phase transition

The finite temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T_c the pressure is well described by the mean-field approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed.Comment: 11 pages, 4 figures; version accepted for publication in Yad. Fiz., text extended, 1 figure adde

Глобалізація як фактор розвитку сучасної освіти в Європейському Союзі та Україні

The article examines the impact of globalisation on the development of education in the countries of the European Union and Ukraine. It was determined that globalisation causes a transformation in higher education, forcing higher education institutions to adapt to new requirements and standards imposed by international organisations and market conditions. It has been proven that in the EU, globalisation contributed to the harmonisation of higher education by implementing the Bologna process, which contributed to the growth of mobility of students and teachers and the formation of joint educational programs and research initiatives. It has been studied that Ukraine, trying to integrate into the European educational space, is also implementing reforms aimed at compliance with European standards and improving the quality of education. However, challenges are associated with adapting to international standards, ensuring the quality of education and developing international competitiveness. It has been proven that globalisation contributes to the convergence of educational systems and opens up opportunities for enriching cultural experiences and innovative development.У статті досліджено вплив глобалізації на розвиток освіти в країнах Європейського Союзу та Україні. Визначено, що глобалізація викликає трансформацію у вищій освіті, змушуючи вищі навчальні заклади адаптуватися до нових вимог і стандартів, що висуваються міжнародними організаціями та ринковими умовами. Доведено, що в ЄС глобалізація сприяла гармонізації вищої освіти шляхом впровадження Болонського процесу, що сприяло зростанню мобільності студентів і викладачів та формуванню спільних освітніх програм і дослідницьких ініціатив. Досліджено, що Україна, намагаючись інтегруватися в європейський освітній простір, також проводить реформи, спрямовані на відповідність європейським стандартам та підвищення якості освіти. Проте має виклики, пов’язані з адаптацією до міжнародних стандартів, забезпеченням якості освіти та розвитком міжнародної конкурентоспроможності. Доведено, що глобалізація сприяє конвергенції освітніх систем і відкриває можливості для збагачення культурного досвіду та інноваційного розвитку

Hypernetted-chain study of broken rotational symmetry states for the ν\bm{\nu} = 1/3 fractional quantum Hall effect and other fractionally filled Landau levels

We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at 1/3-filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens.\ Matter {\bf 8}, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LLs a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LLs. Possible connections to the newly discovered liquid crystalline phases in higher LLs are also discussed.Comment: 7 pages including 3 eps figure