The Fermion Generations Problem in the Gust in the Free World-Sheet Fermion Formulation

In the framework of the four dimensional heterotic superstring with free fermions we present a revised version of the rank eight Grand Unified String Theories (GUST) which contain the $SU(3)_H$-gauge family symmetry. We also develop some methods for building of corresponding string models. We explicitly construct GUST with gauge symmetry $G = SU(5) \times U(1)\times (SU(3) \times U(1))_H$ and $G = SO(10)\times (SU(3) \times U(1))_H$ or $E(6)\times SU(3)_H$ $\subset E(8)$ and consider the full massless spectrum for our string models. We consider for the observable gauge symmetry the diagonal subgroup $G^{symm}$ of the rank 16 group $G \times G$ $\subset SO(16) \times SO(16)$ or $\subset E(8) \times E(8)$. We discuss the possible fermion matter and Higgs sectors in these theories. We study renormalizable and nonrenormolizable contributions to the superpotential. There has to exist "superweak" light chiral matter ($m_H^f < M_W$) in GUST under consideration. The understanding of quark and lepton mass spectra and family mixing leaves a possibility for the existence of an unusually low mass breaking scale of the $SU(3)_H$ family gauge symmetry (some TeV).Comment: 68 page

The Paths of Unification In The GUST With The G x G Gauge Groups of E(8) x E(8)

In the framework of the four dimensional heterotic superstring with free fermions we discuss the rank eight and/or sixteen Grand Unified String Theories (GUST) which contain the SU(3)_H - gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G x G = [SU(5) x U(1) x (SU(3) x U(1))_H]^2. We show that the GUSTs with the G x G gauge group allow to make the scale of unification to be consistent with the string scale M_SU = g_{string} * 5 * 10^17 GeV.Comment: 18 pages, 2 Postscript figures, uses epsf.st

Математична модель багатоканальної системи масового обслуговування

In the article the mathematical model of the multichannel queuing system with idle on the basis of distributed priorities is proposed.В статье предлагается математическая модель многоканальной системы массового обслуживания с ожиданием на основе распределенных приоритетов.У статті пропонується математична модель багатоканальної системи масового обслуговування з очікуванням на основі розподілених пріоритетів

Asymmetric Orbifolds and Grand Unification

We generalize the rules for the free fermionic string construction to include other asymmetric orbifolds with world-sheet bosons. We use these rules to construct various grand unified string models that involve level-3 current algebras. We present the explicit construction of three classes of 3-chiral-family grand unified models in the heterotic string theory. Each model has 5 left-handed, and two right-handed families, and an adjoint Higgs. Two of them are SO(10) and the third is E_6. With Wilson lines and/or varying moduli, we show how other 3-family grand unified models, such as SO(10) and SU(5), may be constructed from them.Comment: 47 pages, Revtex 3.0, minor misprints corrected (to appear in Phys. Rev. D

A Classification of 3-Family Grand Unification in String Theory I. The SO(10) and E_6 Models

We give a classification of 3-family SO(10) and E_6 grand unification in string theory within the framework of conformal field theory and asymmetric orbifolds. We argue that the construction of such models in the heterotic string theory requires certain Z_6 asymmetric orbifolds that include a Z_3 outer-automorphism, the latter yielding a level-3 current algebra for the grand unification gauge group SO(10) or E_6. We then classify all such Z_6 asymmetric orbifolds that result in models with a non-abelian hidden sector. All models classified in this paper have only one adjoint (but no other higher representation) Higgs field in the grand unified gauge group. In addition, all of them are completely anomaly free. There are two types of such 3-family models. The first type consists of the unique SO(10) model with SU(2) X SU(2) X SU(2) as its hidden sector (which is not asymptotically-free at the string scale). This SO(10) model has 4 left-handed and 1 right-handed 16s. The second type is described by a moduli space containing 17 models (distinguished by their massless spectra). All these models have an SU(2) hidden sector, and 5 left-handed and 2 right-handed families in the grand unified gauge group. One of these models is the unique E_6 model with an asymptotically-free SU(2) hidden sector. The others are SO(10) models, 8 of them with an asymptotically free hidden sector at the string scale.Comment: 35 pages, Revtex 3.0, one eps figure (to appear in Phys. Rev. D

КЛИНИЧЕСКАЯ И УЛЬТРАЗВУКОВАЯ КАРТИНА МНОЖЕСТВЕННОГО ОСТЕОМИЕЛИТА ПРИ СЕПТИКО-ПИЕМИЧЕСКОЙ ФОРМЕ ЗАБОЛЕВАНИЯ У ДЕТЕЙ

Aim of a research diagnostic aspects of acute haematogenic osteomyelitis (AGO) represent a significant problem due more frequent occurrence of multiple osteomyelitis.Objective. Reveal the clinical and ultrasound features of multiple osteomyelitis in purulent-septic form of AGO in children.Material and methods. 59 children aged from birth to 15 years with local (47 peoples) and purulent-septic (12 peoples) form of AGO were studied. Multiple osteomyelitis was diagnosed in four children with purulent-septic form of AGO (11 lesions). Multiple purulent-septic foci were located in the tibia more frequently (4 peoples; 36.4%).Results: Purulent-septic and local forms of AGO were presented qualitatively by intra- and extramedullar inflammatory phase, and extramedullar phase was prevailed (p = 0.181). Purulent-septic form of AGO comparatively local form was observed more frequent in younger children (p = 0.038) and at a later date of disease manifestation (p = 0.009). Multiple osteomyelitis with several septic intra- and intraosseous foci (33.3% and 66.7%, respectively) was observed in children with purulent-septic form of AGO only. The same child could have bone septic foci in one, and in the different phases of the disease.Conclusion. Multiple osteomyelitis occurs in 30–35% of children with purulent-septic form of AGO and it is more frequent in younger children and in later periods from the beginning of the disease clinical man-ifestation. Multiple osteomyelitis is characterized by polymorphism of ultrasound manifestations. Диагностика острого гематогенного остеомиелита (ОГО) представляет существенную проблему ввиду более частого появления множественного остеомиелита. Цель исследования – выявить особенности клинической и ультразвуковой картины множественного остеомиелита при септико-пиемической форме ОГО у детей.Материал и методы. Исследовано 59 детей в возрасте от рождения до 15 лет с местной (47 чело-век) и септико-пиемической (12 человек) формой ОГО. Множественный остеомиелит диагностирован у четырех детей с септико-пиемической формой ОГО (11 локализаций). Множественные септико-пиемические очаги чаще локализовались в большеберцовых костях (4 человека; 36,4%).Результаты. Септико-пиемическая и местная формы ОГО качественно представлены интра- и экстрамедуллярной фазами воспаления с преобладанием последней (p = 0,181). Септико-пиемическая форма ОГО по сравнению с местной чаще наблюдалась у детей в возрасте до 3 лет (p = 0,038) и в более поздние сроки от начала заболевания (p = 0,009). Множественный остеомиелит с наличием нескольких септических очагов внутри- и внекостной локализации (33,3 и 66,7% соответственно) наблюдался только у детей с септико-пиемической формой ОГО. Один и тот же ребенок мог иметь костные септические очаги как в одну, так и в разные фазы заболевания.Заключение. Множественный остеомиелит встречается у 30–35% детей с септико-пиемической формой ОГО, чаще у детей раннего возраста и в поздние сроки от начала манифестации клинических проявлений, характеризуясь полиморфизмом ультразвуковых проявлений

Fermion Mass Hierarchy without Flavour Symmetry

We discuss a supersymmetric grand unified model which has gauge group SU(5) $\times$ SU(5) $\times$ SU(5), with matter fields transforming asymmetrically under different gauge SU(5) groups. We observe that the gauge structure of the model leads to approximate texture zero structures in fermion mass matrices and a natural hierarchy in the Yukawa couplings. The proton lifetime is estimated to be larger than $10^{34}$ years in this model. As in more conventional supersymmetric GUT models with product gauge groups, this model possesses no tensor fields with rank higher than 2, so that it might arise from a level 1 string construction.Comment: 24 pages, REVTex. Eq.(15) Correcte