LEADER 03369nam 22004335a 450 001 9910151935103321 005 20091109150325.0 010 $a3-03719-545-2 024 70$a10.4171/045 035 $a(CKB)3710000000953824 035 $a(CH-001817-3)77-091109 035 $a(PPN)17815539X 035 $a(EXLCZ)993710000000953824 100 $a20091109j20080429 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFunctional Equations and Characterization Problems on Locally Compact Abelian Groups$b[electronic resource] /$fGennadiy Feldman 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008 215 $a1 online resource (268 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v5 330 $aThis book deals with the characterization of probability distributions. It is well known that both the sum and the difference of two Gaussian independent random variables with equal variance are independent as well. The converse statement was proved independently by M. Kac and S. N. Bernstein. This result is a famous example of a characterization theorem. In general, characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables. In recent years, a great deal of attention has been focused upon generalizing the classical characterization theorems to random variables with values in various algebraic structures such as locally compact Abelian groups, Lie groups, quantum groups, or symmetric spaces. The present book is aimed at the generalization of some well-known characterization theorems to the case of independent random variables taking values in a locally compact Abelian group X. The main attention is paid to the characterization of the Gaussian and the idempotent distribution (group analogs of the Kac-Bernstein, Skitovich-Darmois, and Heyde theorems). The solution of the corresponding problems is reduced to the solution of some functional equations in the class of continuous positive definite functions defined on the character group of X. Group analogs of the Crame?r and Marcinkiewicz theorems are also studied. The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analysis, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory. 606 $aProbability & statistics$2bicssc 606 $aProbability theory and stochastic processes$2msc 606 $aAbstract harmonic analysis$2msc 606 $aStatistics$2msc 615 07$aProbability & statistics 615 07$aProbability theory and stochastic processes 615 07$aAbstract harmonic analysis 615 07$aStatistics 686 $a60-xx$a43-xx$a62-xx$2msc 700 $aFeldman$b Gennadiy$01071623 801 0$bch0018173 906 $aBOOK 912 $a9910151935103321 996 $aFunctional Equations and Characterization Problems on Locally Compact Abelian Groups$92567867 997 $aUNINA LEADER 04148nam 2200865z- 450 001 9910639989103321 005 20231220164723.0 010 $a3-0365-5870-5 035 $a(CKB)5470000001633463 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/95835 035 $a(EXLCZ)995470000001633463 100 $a20202301d2022 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aShedding Light to the Dark Sides of the Universe: Cosmology from Strong Interactions 210 $aBasel$cMDPI - Multidisciplinary Digital Publishing Institute$d2022 215 $a1 electronic resource (234 pages) 311 $a3-0365-5869-1 330 $aThe theory of quantum chromo dynamics (QCD), an organic part of the standard model (SM) of particle physics, has been validated by many theoretical and experimental studies. The strongly coupled QCD dynamics controls colored particles? (quarks and gluons) collective motion at large spacetime separations and the formation of colorless composite states (hadrons). While QCD theory and the related phenomenology aspects are being intensively studied in laboratory measurements, the possible connections of this important layer of knowledge to cosmology remain rather vague and largely unexplored. No doubt, the physical vacuum has been transformed many times throughout the lifetime of the universe and has affected its history through a sequence of events, such as the cosmic inflation, phase transitions, and the dark-energy-dominated expansion. Strong interactions could play an important role in some of these cosmological events. In particular, the emergence of a new state of matter called the quark-gluon plasma at the LHC is often suggested to provide an important source of empirical knowledge to what the universe looked like in the first few moments after the Big Bang. This Special Issue aims at creating an overview of the recent progress in these directions by focusing on the novel implications of quantum chromo, or more generally, Yang?Mills (YM) dynamics, to the physics of the early universe and critical phenomena in cosmology. 517 $aShedding Light to the Dark Sides of the Universe 606 $aResearch 606 $aPhysics 610 $adynamics of phase transitions 610 $aspinodal instability 610 $aheavy-ion collisions 610 $aneutron stars 610 $adark energy 610 $anon-Abelian gauge theory 610 $acondensate 610 $aQCD 610 $aDGLAP equations 610 $aphysics beyond the standard model 610 $atensorgluons 610 $aextended DGLAP equations 610 $atensorgluon splitting functions 610 $aneutron star 610 $aequation of state 610 $amany-body methods of nuclear matter 610 $aneutron-skin thickness 610 $aGW170817 610 $aWeyl gravity 610 $arenormalization group 610 $ainflation 610 $alight scalar fields 610 $aaxial anomaly 610 $aSU(2) Yang-Mills thermodynamics 610 $ade-percolation of axionic lumps 610 $acosmological and galactic dark-matter densities 610 $acosmology 610 $aparticle physics 610 $aparticle symmetry 610 $astable particles 610 $adark matter 610 $acosmic rays 610 $aQCD in the early universe 610 $aphase transitions 610 $ahydrodynamical evolution 610 $aequation of state of super-dense matter 610 $aclassical Yang-Mills fields 610 $aDark Energy 610 $aDark Matter 610 $agluon condensate 610 $aeffective Yang-Mills action 610 $acosmic inflation 615 0$aResearch. 615 0$aPhysics. 702 $aS?umbera$b Michal 702 $aPasechnik$b Roman 906 $aBOOK 912 $a9910639989103321 996 $aShedding Light to the Dark Sides of the Universe: Cosmology from Strong Interactions$93655968 997 $aUNINA