Bulk correlation functions in 2D quantum gravity

We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville gravity with non-rational matter central charge c<1, following and comparing two approaches. The continuous CFT approach exploits the action on the tachyons of the ground ring generators deformed by Liouville and matter ``screening charges''. A by-product general formula for the matter 3-point OPE structure constants is derived. We also consider a ``diagonal'' CFT of 2D quantum gravity, in which the degenerate fields are restricted to the diagonal of the semi-infinite Kac table. The discrete formulation of the theory is a generalization of the ADE string theories, in which the target space is the semi-infinite chain of points.Comment: 14 pages, 2 figure

On the Yang-Lee and Langer singularities in the O(n) loop model

We use the method of `coupling to 2d QG' to study the analytic properties of the universal specific free energy of the O(n) loop model in complex magnetic field. We compute the specific free energy on a dynamical lattice using the correspondence with a matrix model. The free energy has a pair of Yang-Lee edges on the high-temperature sheet and a Langer type branch cut on the low-temperature sheet. Our result confirms a conjecture by A. and Al. Zamolodchikov about the decay rate of the metastable vacuum in presence of Liouville gravity and gives strong evidence about the existence of a weakly metastable state and a Langer branch cut in the O(n) loop model on a flat lattice. Our results are compatible with the Fonseca-Zamolodchikov conjecture that the Yang-Lee edge appears as the nearest singularity under the Langer cut.Comment: 38 pages, 16 figure

Ontogenija usnog aparata salmo faroides and salmo macedonicus gajenih u mrestilištu tokom ranih faza razvitka

Continuing losses of natural production from over harvesting, habitat degradation and disappearance of spawning habitat due to hydroelectric development, irrigation, logging and transportation are increasingly showing the importance of hatchery operations in many countries. Few years ago, the Republic of Macedonia started with captive breeding programs for salmons. This program involves capturing wild fish of species as Salmo faroides and Salmo macedonicus from their native habitats and subsequent culturing the offspring from captive broodstocks which are then stocked into ancestral streams at the juvenile stage. From a practical point of view, the importance of study on how a developing larva copes with the changing functional demands during ontogeny, especially when being reared under artificial conditions, is obvious. Understanding how the locomotor and feeding apparatus is formed during early ontogeny can assist in improving the success of artificial propagation in terms of effective production of high quality juveniles. This would especially be valuable when offspring would be re-introduced into the river ecosystem. On the other hand knowledge on the ontogeny of fishes, especially for the early development of the skeletal system, provides information that can also be useful for solving some taxonomic problems and unravel phylogenetic relationships. For example, it is well known that morphological variation is commonly observed in salmonids. These fishes often form reproductively isolated populations across a diversity of environments and exhibit high levels of phenotypic variation. The final form of a phenotype and its life history are determined during early ontogeny. To better understand the relationship between morphology and ecology studies on the effect on environmentally induced variation in early life stage development within a single species, or study differences in the effect of a single environment in closely related species. Among the Salmo species that are present in the Balkan Peninsula, there is a high level of phenotypic variability, where also phenotypic plasticity is problematic for demarcate species boundaries between previously defined salmon species. Molecular data have confirmed the existence of previously defined species but several nominal species and populations of Balkan trout still remain unresolved. Still, understanding patterns of phenotypic variation that underlies molecular affinities remains essential. Within this context, we analysed the ontogeny of the skeletal system in Salmo faroides and Salmo macedonicus, two species of a still uncertain taxonomic status, reared under controlled condition. We wanted to test to what degree ontogeny of these closely related species is similar. In this study we focus on the early development of the feeding apparatus, from hatching till beginning of the exogenous feedin

Loop models, random matrices and planar algebras

We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar algebra. We apply this construction to compute the generating functions of the Potts model on a random planar map

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Complex Curve of the Two Matrix Model and its Tau-function

We study the hermitean and normal two matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex curve, different from the hyperelliptic curve of the one matrix model. The matrix model quantities are expressed through the periods of meromorphic generating differential on this curve and the partition function of the multiple support solution, as a function of filling numbers and coefficients of the matrix potential, is shown to be the quasiclassical tau-function. The relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multimatrix models with tree-like interactions is considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of J.Phys. A on Random Matrix Theor

Some New/Old Approaches to QCD

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.Comment: 20 page

TG/DTG-DSC and high temperature in-situ XRD analysis of natural thaumasite

This paper investigated thermal properties of natural thaumasite, such as phase composition and reaction mechanism of thermal decomposition using simultaneous TG/DTG-DSC in Ar and Air medium up to 1673 K, coupled with masspectrometer for analysis of evolving gases, and in-situ powder X-ray diffraction measurements. The transitional solid phases, grown with increasing of temperature at thaumasite thermal decomposition, are calcium hydrogen carbonate (Ca(HCO3)2) and hydrogen sulphate (Ca(HSO4)2), calcite, anhydrite, calcium silicates (wolastonite and larnite), calcium silico-carbonate (spurrite), and calcium silico-sulphate (ternesite). The thermal decomposition in both gaseous media includes the stages of dehydration, dehydroxylation, dacarbonation and desulphuration with obtaining a solid residue of varying degrees of crystallinity. The main solid phase, grown at the highest temperatures, is larnite. Based on the obtained results it was proposed the scheme of chemical reactions, which presents the reaction mechanism of thaumasite thermal decomposition. The defined scheme has both fundamental importance by adding new details of reference data, and practical application for thaumasite identification in chemical archaeology, and in the chemistry of cement and cement-based materials