LEADER 01056nam0-22003011i-450- 001 990002023490403321 005 20021010 035 $a000202349 035 $aFED01000202349 035 $a(Aleph)000202349FED01 035 $a000202349 100 $a20021010d--------km-y0itay50------ba 101 0 $aita 200 1 $aUeber die traubenwickler, (Conchylis ambiguella Hubn. und Polychrosis botrana Schiff) und ihre Bekampfung, mitBerucksichtigung naturlicher Bekampfungsfaktoren.$fSchwangart H. 210 $aJena$cGustav Fischer$d1910 215 $a195 p. 9 tav.$d28 cm 610 0 $aLepidotteri Agraria 610 0 $aLepidotteri 676 $a595.78 700 1$aSchwangart,$bH.$0360238 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990002023490403321 952 $a61 IV G.8/177$b511$fDAGEN 959 $aDAGEN 996 $aUeber die traubenwickler, (Conchylis ambiguella Hubn. und Polychrosis botrana Schiff) und ihre Bekampfung, mitBerucksichtigung naturlicher Bekampfungsfaktoren$9405374 997 $aUNINA DB $aING01 LEADER 04569nam 22006615 450 001 9910686468203321 005 20251113191419.0 010 $a981-19-9527-3 024 7 $a10.1007/978-981-19-9527-9 035 $a(CKB)5840000000241981 035 $a(MiAaPQ)EBC7236610 035 $a(Au-PeEL)EBL7236610 035 $a(DE-He213)978-981-19-9527-9 035 $a(OCoLC)1375994938 035 $a(PPN)269657479 035 $a(MiAaPQ)EBC7235390 035 $a(EXLCZ)995840000000241981 100 $a20230406d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElliptic Extensions in Statistical and Stochastic Systems /$fby Makoto Katori 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023. 215 $a1 online resource (134 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v47 311 08$a981-19-9526-5 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Brownian Motion and Theta Functions -- Biorthogonal Systems of Theta Functions and Macdonald Denominators -- KMLGV Determinants and Noncolliding Brownian Bridges -- Determinantal Point Processes Associated with Biorthogonal Systems -- Doubly Periodic Determinantal Point Processes -- Future Problems. 330 $aHermite's theorem makes it known that there are three levels of mathematical frames in which a simple addition formula is valid. They are rational, q-analogue, and elliptic-analogue. Based on the addition formula and associated mathematical structures, productive studies have been carried out in the process of q-extension of the rational (classical) formulas in enumerative combinatorics, theory of special functions, representation theory, study of integrable systems, and so on. Originating from the paper by Date, Jimbo, Kuniba, Miwa, and Okado on the exactly solvable statistical mechanics models using the theta function identities (1987), the formulas obtained at the q-level are now extended to the elliptic level in many research fields in mathematics and theoretical physics. In the present monograph, the recent progress of the elliptic extensions in the study of statistical and stochastic models in equilibrium and nonequilibrium statistical mechanics and probability theory is shown. At the elliptic level, many special functions are used, including Jacobi's theta functions, Weierstrass elliptic functions, Jacobi's elliptic functions, and others. This monograph is not intended to be a handbook of mathematical formulas of these elliptic functions, however. Thus, use is made only of the theta function of a complex-valued argument and a real-valued nome, which is a simplified version of the four kinds of Jacobi's theta functions. Then, the seven systems of orthogonal theta functions, written using a polynomial of the argument multiplied by a single theta function, or pairs of such functions, can be defined. They were introduced by Rosengren and Schlosser (2006), in association with the seven irreducible reduced affine root systems. Using Rosengren and Schlosser's theta functions, non-colliding Brownian bridges on a one-dimensional torus and an interval are discussed, along with determinantal point processes on a two-dimensional torus. Their scaling limitsare argued, and the infinite particle systems are derived. Such limit transitions will be regarded as the mathematical realizations of the thermodynamic or hydrodynamic limits that are central subjects of statistical mechanics. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v47 606 $aMathematical physics 606 $aStochastic processes 606 $aStatistical physics 606 $aQuantum theory 606 $aMathematical Physics 606 $aStochastic Processes 606 $aStatistical Physics 606 $aQuantum Physics 615 0$aMathematical physics. 615 0$aStochastic processes. 615 0$aStatistical physics. 615 0$aQuantum theory. 615 14$aMathematical Physics. 615 24$aStochastic Processes. 615 24$aStatistical Physics. 615 24$aQuantum Physics. 676 $a515.983 700 $aKatori$b Makoto$f1931-$0755845 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910686468203321 996 $aElliptic Extensions in Statistical and Stochastic Systems$93149417 997 $aUNINA