41 research outputs found
Dilogarithm Identities in Conformal Field Theory
Dilogarithm identities for the central charges and conformal dimensions exist
for at least large classes of rational conformally invariant quantum field
theories in two dimensions. In many cases, proofs are not yet known but the
numerical and structural evidence is convincing. In particular, close relations
exist to fusion rules and partition identities. We describe some examples and
ideas, and present some conjectures useful for the classification of conformal
theories. The mathematical structures seem to be dual to Thurston's program for
the classification of 3-manifolds.Comment: 14 pages, BONN-preprint. (a few minor changes, two major corrections
in chapter 3, namely: (3.10) only holds in the case of the A series,
Goncharovs conjecture is not an equivalence but rather an implication and a
theorem
Towards more sustainable small holder farmer livelihoods by using infrared spectroscopy for soil analytical advisory services
Steps towards Lattice Virasoro Algebras: su(1,1)
An explicit construction is presented for the action of the su(1,1)
subalgebra of the Virasoro algebra on path spaces for the c(2,q) minimal
models. In the case of the Lee-Yang edge singularity, we show how this action
already fixes the central charge of the full Virasoro algebra. For this case,
we additionally construct a representation in terms of generators of the
corresponding Temperley-Lieb algebra.Comment: 15 pages, plain TeX, 4 typos correcte
Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
We present fermionic sum representations of the characters
of the minimal models for all relatively prime
integers for some allowed values of and . Our starting point is
binomial (q-binomial) identities derived from a truncation of the state
counting equations of the XXZ spin chain of anisotropy
. We use the Takahashi-Suzuki method to express
the allowed values of (and ) in terms of the continued fraction
decomposition of (and ) where stands for
the fractional part of These values are, in fact, the dimensions of the
hermitian irreducible representations of (and )
with (and We also establish the duality relation and discuss the action of the Andrews-Bailey transformation in the
space of minimal models. Many new identities of the Rogers-Ramanujan type are
presented.Comment: Several references, one further explicit result and several
discussion remarks adde
Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)
We prove polynomial identities for the N=1 superconformal model SM(2,4\nu)
which generalize and extend the known Fermi/Bose character identities. Our
proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic
side and a recently introduced very general method of producing recursion
relations for q-series on the fermionic side. We use these polynomials to
demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and
M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is
expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments
added; misprints eliminate
T-systems and Y-systems in integrable systems
The T and Y-systems are ubiquitous structures in classical and quantum
integrable systems. They are difference equations having a variety of aspects
related to commuting transfer matrices in solvable lattice models, q-characters
of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras
with coefficients, periodicity conjectures of Zamolodchikov and others,
dilogarithm identities in conformal field theory, difference analogue of
L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem,
AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace
sequence in discrete geometry, Fermionic character formulas and combinatorial
completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics,
analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and
so forth. This review article is a collection of short reviews on these topics
which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5,
eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical
review) also needs these correction
A global spectral library to characterize the world's soil
Soil provides ecosystem services, supports human health and habitation, stores carbon and regulates emissions of greenhouse gases. Unprecedented pressures on soil from degradation and urbanization are threatening agro-ecological balances and food security. It is important that we learn more about soil to sustainably manage and preserve it for future generations. To this end, we developed and analyzed a global soil visible-near infrared (vis-NIR) spectral library. It is currently the largest and most diverse database of its kind. We show that the information encoded in the spectra can describe soil composition and be associated to land cover and its global geographic distribution, which acts as a surrogate for global climate variability. We also show the usefulness of the global spectra for predicting soil attributes such as soil organic and inorganic carbon, clay, silt, sand and iron contents, cation exchange capacity, and pH. Using wavelets to treat the spectra, which were recorded in different laboratories using different spectrometers and methods, helped to improve the spectroscopic modelling. We found that modelling a diverse set of spectra with a machine learning algorithm can find the local relationships in the data to produce accurate predictions of soil properties. The spectroscopic models that we derived are parsimonious and robust, and using them we derived a harmonized global soil attribute dataset, which might serve to facilitate research on soil at the global scale. This spectroscopic approach should help to deal with the shortage of data on soil to better understand it and to meet the growing demand for information to assess and monitor soil at scales ranging from regional to global. New contributions to the library are encouraged so that this work and our collaboration might progress to develop a dynamic and easily updatable database with better global coverage. We hope that this work will reinvigorate our community's discussion towards larger, more coordinated collaborations. We also hope that use of the database will deepen our understanding of soil so that we might sustainably manage it and extend the research outcomes of the soil, earth and environmental sciences towards applications that we have not yet dreamed of
Fertilidade química de um substrato tratado com lodo de esgoto e composto de resíduos domésticos
Improving the design of long-term monitoring experiments in forests: a new method for the assessment of local soil variability by combining infrared spectroscopy and dendrometric data
Gepner Modelle und W-Algebren
SIGLEAvailable from TIB Hannover: RN 4852(92-20) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman