LEADER 01088nam2 22002893i 450 001 NAP0161004 005 20231121125559.0 010 $a8820704803 100 $a20141021d1977 ||||0itac50 ba 101 | $aita 102 $ait 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $a˜2: œEdifici in cemento armato$fMichele Pagano 210 $aNapoli$cLiguori$d1977 215 $aVIII, 278 p., \5! c. di tav.$cill.$d24 cm. 461 1$1001NAP0161005$12001 $aTeoria degli edifici$elezioni del corso di complementi di tecnica delle costruzioni$fMichele Pagano$v2 606 $aCemento armato$2FIR$3RMLC173495$9I 676 $a624.18341$9$v21 801 3$aIT$bIT-01$c20141021 850 $aIT-FR0099 899 $aBiblioteca Area Ingegneristica$bFR0099 912 $aNAP0161004 950 2$aBiblioteca Area Ingegneristica$d 54DMS 624.1 PAG II$e 54VM 0000113685 VM barcode:ING436M. - Inventario:436m. - Fondo:CONVM$fA $h20020128$i20121204 977 $a 54 996 $aEdifici in cemento armato$9978503 997 $aUNICAS LEADER 04571nam 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 physics 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$aQuantum physics. 615 14$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