LEADER 03640nam 2200529 450 001 9910793296603321 005 20220525075748.0 010 $a1-4704-4815-7 035 $a(CKB)4100000007133848 035 $a(MiAaPQ)EBC5571101 035 $a(Au-PeEL)EBL5571101 035 $a(OCoLC)1065073359 035 $a(RPAM)20662073 035 $a(PPN)231946023 035 $a(EXLCZ)994100000007133848 100 $a20220525d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic Q-groups as abstract groups /$fOlivier Fre?con 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2018] 210 4$dİ2018 215 $a1 online resource (v, 99 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vNumber 1219 300 $a"September 2018 . Volume 255 . Number 1219 (second of 7 numbers)." 311 $a1-4704-2923-3 320 $aIncludes bibliographical references and index. 327 $aCover -- Title page -- Chapter 1. Introduction -- 1.1. Related work -- 1.2. The field of definition -- 1.3. Overview of the paper -- Chapter 2. Background material -- 2.1. Groups of finite Morley rank -- 2.2. Fundamental theorems -- 2.3. Decent tori and pseudo-tori -- 2.4. Unipotence -- Chapter 3. Expanded pure groups -- Chapter 4. Unipotent groups over \ov{\Q} and definable linearity -- Chapter 5. Definably affine groups -- 5.1. Definition and generalities -- 5.2. The subgroup ( ) -- 5.3. The subgroup ( ) -- Chapter 6. Tori in expanded pure groups -- Chapter 7. The definably linear quotients of an -group -- 7.1. The subgroups ( ) and ( ) -- 7.2. The nilpotence of ( ) -- 7.3. The subgroup ( ) when the ground field is \ov{\Q} -- 7.4. The subgroups ( ) and ( ) in positive characteristic -- Chapter 8. The group _{ } and the Main Theorem for =\ov{\Q} -- Chapter 9. The Main Theorem for =?\ov{\Q} -- Chapter 10. Bi-interpretability and standard isomorphisms -- 10.1. Positive characteristic and bi-interpretability -- 10.2. Characteristic zero -- Acknowledgements -- Bibliography -- Index of notations -- Index -- Back Cover. 330 $aThe author analyzes the abstract structure of algebraic groups over an algebraically closed field K. For K of characteristic zero and G a given connected affine algebraic \overline{\mathbb Q}-group, the main theorem describes all the affine algebraic \overline{\mathbb Q} -groups H such that the groups H(K) and G(K) are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic \overline{\mathbb Q} -groups G and H, the elementary equivalence of the pure groups G(K) and H(K) implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when K is either \overline {\mathbb Q} or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited. 410 0$aMemoirs of the American Mathematical Society ;$vNumber 1219. 606 $aAlgebra 606 $aFinite groups 606 $aIsomorphisms (Mathematics) 615 0$aAlgebra. 615 0$aFinite groups. 615 0$aIsomorphisms (Mathematics) 676 $a512.9 700 $aFre?con$b Olivier$f1974-$01544050 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793296603321 996 $aAlgebraic Q-groups as abstract groups$93797936 997 $aUNINA LEADER 02075oam 2200421zu 450 001 9910146791603321 005 20241212215307.0 010 $a9781509098682 010 $a1509098682 035 $a(CKB)1000000000022769 035 $a(SSID)ssj0000454430 035 $a(PQKBManifestationID)12192111 035 $a(PQKBTitleCode)TC0000454430 035 $a(PQKBWorkID)10397899 035 $a(PQKB)10260246 035 $a(NjHacI)991000000000022769 035 $a(EXLCZ)991000000000022769 100 $a20160829d2005 uy 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 00$a2005 IEEE Ultrasonics Symposium 210 31$a[Place of publication not identified]$cI E E E$d2005 215 $a1 online resource $cillustrations 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9780780393820 311 08$a0780393821 330 $aApplication of piezoelectric flexural mechanical resonators such as tuning forks to accurate measurements of liquid physical properties is discussed. It was shown earlier that liquid properties such as viscosity, density and dielectric constant can be obtained by measuring the resonator AC impedance within certain frequency range and fitting it to the resonator equivalent circuit model [1]. Error sources for the liquid property measurements and their influence on the measured value are investigated. It is shown experimentally that the reproducibility of the viscosity and density measurements using this technique can meet and often exceed the one delivered by the well established analytical instrumentation. It is also demonstrated here that better performance is resulting from the use of the whole impedance curve over a frequency range, which produces better statistics and natural averaging of the noise. 606 $aUltrasonics$vCongresses 615 0$aUltrasonics 676 $a534 801 0$bPQKB 906 $aPROCEEDING 912 $a9910146791603321 996 $a2005 IEEE Ultrasonics Symposium$92541612 997 $aUNINA