7 results for “Gibbs Measure”

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Research ArticleOpen accessPhrase in the titleConstructing Gibbs Measure in a Rigorous WayFarida Kachapova, Ilias KachapovEquilibrium statistical mechanics studies mathematical models for physical systems with many particles interacting with an external force and with one another. In this paper we describe an interaction model that generalizes several of these models in one model. An infinite model is constructed as the limiting case of finite interaction models, that is as a thermodynamic limit. The key point … …Journal of Mathematics and Statistics, Vol. 15, Issue 1 · 29 Oct 2019 · 6,591 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsInteraction Model in Statistical MechanicsFarida Kachapova, Ilias KachapovStatistical mechanics considers several models such as Ising model, Potts model, Heisenberg model etc. A rigorous mathematical approach based on the axiomatic foundation of probability would benefit the study and applications of these models. In this paper we use this approach to generalize some of these models into one construction named an interaction model. We introduce a mathematically rigorous definition … …Journal of Mathematics and Statistics, Vol. 13, Issue 4 · 4 Nov 2017 · 7,054 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsConvergence of Renormalization Group Transformations of Gibbs Random FieldFarida Kachapova, Ilias KachapovStatistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group transformation. Here we consider a thermodynamic limit of a lattice model with weak interaction and we use semi-invariants to prove that random fields transformed by renormalization … …Journal of Mathematics and Statistics, Vol. 12, Issue 3 · 27 Jul 2016 · 7,012 accessesView PDF Cite

EditorialOpen accessIn the abstractBig Data and Parkinson’s Disease - from Understanding of Disease to Personalised MedicineYen F. Tai, Nicola PaveseThe advancement of information technology in recent years has generated a huge amount of datasets in all areas of scientific research. This has led to new opportunities to harness the 'Big Data' to improve our understanding of diseases - from investigating disease mechanisms to monitoring treatment responses. The Big Data approach is a data-driven and often hypothesis-free, way of studying … …Neuroscience International, Vol. 7, Issue 1 · 27 Jul 2016 · 7,755 accessesView PDF Cite

Research ArticleOpen accessIn the abstractToward a Hierarchical Bayesian Framework for Modelling the Effect of Regional Diversity on Household ExpenditurePudji Ismartini, Nur Iriawan, Setiawan, Brodjol Sutijo Supri UlamaProblem statement: Household expenditure analysis was highly demanding for government in order to formulate its policy. Since household data was viewed as hierarchical structure with household nested in its regional residence which varies inter region, the contextual welfare analysis was needed. This study proposed to develop a hierarchical model for estimating household expenditure in an attempt to measure the effect … …Journal of Mathematics and Statistics, Vol. 8, Issue 2 · 25 Jun 2012 · 7,304 accessesView PDF Cite

Research ArticleOpen accessIn the abstractMolecular Interaction Studies of H-Bonded Complexes of Benzamide in 1,4-Dioxan with Alcohols From Acoustic and Thermodynamic ParametersAN. Kannappan, R. Kesavasamy, V. PonnuswamyThe ultrasonic velocity, density and viscosity measurements were carried out for the mixtures of benzamide with Propan-2-ol, butan-1-ol, 1-pentanol and n-hexanal in 1,4-dioxan at 303, 308 and 313K. The derived acoustic and thermodynamic parameters namely adiabatic compressibility, free length, free volume, internal pressure, viscous relaxation time and Gibbs free energy were evaluated with a view to investigate the nature of … …American Journal of Engineering and Applied Sciences, Vol. 1, Issue 2 · 30 Jun 2008 · 7,277 accessesView PDF Cite

Research ArticleOpen accessAll words, across the recordA Comparison of Spatio-Temporal Bayesian Models for Reconstruction of Rainfall Fields in a Cloud Seeding ExperimentSujit k. sahu, Giovanna Jona Lasinio, Arianna orasi, Kanti V. MardiaIn response to the drought experienced in Southern Italy a rain seeding project has been setup and developed during the years 1989-1994. The initiative was taken with the purpose of applying existing methods of rain enhancement technology to regions of south Italy including Puglia. The aim of this study is to provide statistical support for the evaluation of the experimental … …Journal of Mathematics and Statistics, Vol. 1, Issue 4 · 31 Dec 2005 · 6,810 accessesView PDF Cite