Algebraic arctic curves in the domain-wall six-vertex model

The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve. Some interesting examples are discussed in detail. The upper bound on the maximal degree of the equation in a generic root-of-unity case is obtained.Comment: 15 pages, no figures; v2: metadata correcte

Functional relations for the six vertex model with domain wall boundary conditions

In this work we demonstrate that the Yang-Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six vertex model with domain wall boundary conditions. The homogeneous limit is studied for small lattices and the properties determining the partition function are also discussed.Comment: 19 pages, v2: typos corrected, new section and appendix added. v3: minor corrections, to appear in J. Stat. Mech

Refined Razumov-Stroganov conjectures for open boundaries

Recently it has been conjectured that the ground-state of a Markovian Hamiltonian, with one boundary operator, acting in a link pattern space is related to vertically and horizontally symmetric alternating-sign matrices (equivalently fully-packed loop configurations (FPL) on a grid with special boundaries).We extend this conjecture by introducing an arbitrary boundary parameter. We show that the parameter dependent ground state is related to refined vertically symmetric alternating-sign matrices i.e. with prescribed configurations (respectively, prescribed FPL configurations) in the next to central row. We also conjecture a relation between the ground-state of a Markovian Hamiltonian with two boundary operators and arbitrary coefficients and some doubly refined (dependence on two parameters) FPL configurations. Our conjectures might be useful in the study of ground-states of the O(1) and XXZ models, as well as the stationary states of Raise and Peel models.Comment: 11 pages LaTeX, 8 postscript figure

On the partition function of the six-vertex model with domain wall boundary conditions

The six-vertex model on an $N\times N$ square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ``reconstruction'' formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.Comment: typos correcte

The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime

An explicit expression for the spatial curve separating the region of ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone) in the six-vertex model with domain wall boundary conditions in its anti-ferroelectric regime is obtained.Comment: 12 pages, 1 figur

ISSUES OF SOCIAL AND ECONOMIC DEVELOPMENT OF OMSK REGION

Issues of the regional economic development are considered in the paper through human resources management as the principal source of competitiveness. A constituent of the Russian Federation – Omsk oblast, an actively developing region with diversified economy in terms of both economic activity and spatial location was selected as a target of research. In the course of research there were revealed some problems existing on the regional labour market, such as intensification of skilled labour force outflows, and worsening of demographic and environmental situation in the region. Discrepancy of the occupational training structure of the educational system with the structure of the regional economy results in deficiency of labour resources of required qualification. It is proposed to resolve the issues revealed on the regional labour market using a series of actions, the primary of which are as follows: proper management of migration flows, engagement of the labour force from other regions and countries, further development of the programme for resettlement of compatriots, strengthening cooperation between regional employers and educational institutions of the city, raising investment attractiveness, development of industrial production and of new types of activity on the territory of the region. Industrial enterprises make the basis for social and economic development of the Omsk region. Statistical data characterizing the situation at industrial enterprises of Omsk oblast are provided in the research (wages, labour conditions, staff turnover, material and technical base etc.). Key problems typical of many industrial enterprises of the city of Omsk were revealed. Recommendations are given in terms of the principal directions for the social and economic development of the region

Criminal narrative experience: relating emotions to offence narrative roles during crime commission

A neglected area of research within criminality has been that of the experience of the offence for the offender. The present study investigates the emotions and narrative roles that are experienced by an offender while committing a broad range of crimes and proposes a model of Criminal Narrative Experience (CNE). Hypotheses were derived from the Circumplex of Emotions (Russell, 1997), Frye (1957), Narrative Theory (McAdams, 1988) and its link with Investigative Psychology (Canter, 1994). The analysis was based on 120 cases. Convicted for a variety of crimes, incarcerated criminals were interviewed and the data were subjected to Smallest Space Analysis (SSA). Four themes of Criminal Narrative Experience (CNE) were identified: Elated Hero, Calm Professional, Distressed Revenger and Depressed Victim in line with the recent theoretical framework posited for Narrative Offence Roles (Youngs & Canter, 2012). The theoretical implications for understanding crime on the basis of the Criminal Narrative Experience (CNE) as well as practical implications are discussed

On FPL configurations with four sets of nested arches

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde

Performance/mathematics: a dramatisation of mathematical methods

This essay conceptualises the notion of performance mathematics in terms of a paradoxical relationship with the constructed notion of truth, which is shared by theatrical and mathematical performance. Specifically, I argue that these two disciplines can and cannot be reconciled with truthfulness. Grounding my comparison on the notion of an axiomatic method common to both disciplines, I argue that theatrical and mathematical performance can speak of truths only when these truths are properly staged or methodologically grounded according to the internal rules and conditions laid out by each discipline. But in the same way that these truths can be constructed, or they can be done, so they can be undone. Arguing that mathematics can be described as a performance of specific outcomes involving abstract objects and functions, I trace a cross-disciplinary comparative analysis of performance elements (especially axioms and functions), drawing on a number of theatre and mathematical theories. Some suggestions are also put forward in terms of the connection between the performance of mathematised texts and computational mathematics, particularly in terms of an inherent poetics and theatricality inside the performance-oriented, mathematised languages of digital computing