Mathematik und Statistikhttp://kops.uni-konstanz.de:80/handle/123456789/392023-02-08T23:47:34Z2023-02-08T23:47:34ZExamination of the Connection Between the Horn Problem and the Lax ConjectureHess, Sarahpop257145123456789/600212023-02-02T04:00:14Z2020Examination of the Connection Between the Horn Problem and the Lax Conjecture
Hess, Sarah
In this Master's thesis, we introduce the additive and multiplicative Horn's Problem and verify the equivalence of both formulations as given by Klyachko. Furthermore, we present a solution to the Horn's Problem following Knutson and Tao and establish the famous Lax conjecture. We provide a solution to the latter as it is given by Grinshpan et al. in the Helton-Vinnikov Theorem. Lastly, we elaborate on the connection between the multiplicative Horn's Problem and Vinnikov curves following Speyer and draw our own conclusions about the connection between the Horn's problem and the Lax conjecture.
2020Hess, Sarah510In this Master's thesis, we introduce the additive and multiplicative Horn's Problem and verify the equivalence of both formulations as given by Klyachko. Furthermore, we present a solution to the Horn's Problem following Knutson and Tao and establish the famous Lax conjecture. We provide a solution to the latter as it is given by Grinshpan et al. in the Helton-Vinnikov Theorem. Lastly, we elaborate on the connection between the multiplicative Horn's Problem and Vinnikov curves following Speyer and draw our own conclusions about the connection between the Horn's problem and the Lax conjecture.MSC_THESISurn:nbn:de:bsz:352-2-160cfrqubrq6n2eng2023-02-01T07:47:17+01:00123456789/392023-02-01T06:47:17ZElliptic Curves and Their Application in Key-Exchange CryptographyHess, Sarahpop257145123456789/600202023-02-02T04:00:12Z2018Elliptic Curves and Their Application in Key-Exchange Cryptography
Hess, Sarah
In this Bachelor's thesis, we introduce elliptic curves over the field of real numbers and finite fields and present numerical methods for mathematical calculations over these. Furthermore, we establish the discrete logarithm problem and analyze various key-exchange crypto-systems in terms of their security. In particular, the Diffie-Hellman key-exchange, the Massey-Omura key-exchange and the ElGamal key-exchange are considered.
2018Hess, Sarah510In this Bachelor's thesis, we introduce elliptic curves over the field of real numbers and finite fields and present numerical methods for mathematical calculations over these. Furthermore, we establish the discrete logarithm problem and analyze various key-exchange crypto-systems in terms of their security. In particular, the Diffie-Hellman key-exchange, the Massey-Omura key-exchange and the ElGamal key-exchange are considered.BSC_THESISurn:nbn:de:bsz:352-2-gulfjde9kdan6eng2023-02-01T07:44:04+01:00123456789/392023-02-01T06:44:04ZA note on stability in three-phase-lag heat conductionQuintanilla, RamonRacke, Reinhardpop03677123456789/714.22023-01-31T13:51:02Z2008A note on stability in three-phase-lag heat conduction
Quintanilla, Ramon; Racke, Reinhard
In this note we consider two cases in the theory of the heat conduction models with three-phase-lag. For each one we propose a suitable Lyapunov function. These functions are relevant tools which allow to study several qualitative properties. We obtain conditions on the material parameters to guarantee the exponential stability of solutions. The spectral analysis complements the results and we show that if the conditions obtained to prove the exponential stability are not satisfied, then we can obtain the instability of solutions for suitable domains. We believe that this kind of results is fundamental to clarify the applicability of the models.
2008Quintanilla, RamonRacke, Reinhard510In this note we consider two cases in the theory of the heat conduction models with three-phase-lag. For each one we propose a suitable Lyapunov function. These functions are relevant tools which allow to study several qualitative properties. We obtain conditions on the material parameters to guarantee the exponential stability of solutions. The spectral analysis complements the results and we show that if the conditions obtained to prove the exponential stability are not satisfied, then we can obtain the instability of solutions for suitable domains. We believe that this kind of results is fundamental to clarify the applicability of the models.ElsevierJOURNAL_ARTICLEeng10.1016/j.ijheatmasstransfer.2007.04.0450017-93101879-21892429511-2International Journal of Heat and Mass Transfer2023-01-31T14:51:02+01:00123456789/39International Journal of Heat and Mass Transfer ; 51 (2008), 1-2. - S. 24-29. - Elsevier. - ISSN 0017-9310. - eISSN 1879-2189true2023-01-31T13:51:02ZtrueA monotone convergence theorem for strong Feller semigroupsBudde, ChristianDobrick, AlexanderGlück, JochenKunze, Markuspop258479123456789/599522023-01-27T04:00:22Z2022A monotone convergence theorem for strong Feller semigroups
Budde, Christian; Dobrick, Alexander; Glück, Jochen; Kunze, Markus
For an increasing sequence (Tn) of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the strong Feller property carries over from the approximating semigroups to the limit semigroup if the resolvent of the latter maps 1 to a continuous function. This is instrumental in the study of elliptic operators on Rd with unbounded coefficients: our abstract result enables us to assign a semigroup to such an operator and to show that the semigroup is strongly Feller under very mild regularity assumptions on the coefficients. We also provide counterexamples to demonstrate that the assumptions in our main result are close to optimal.
2022Budde, ChristianDobrick, AlexanderGlück, JochenKunze, Markus510For an increasing sequence (Tn) of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the strong Feller property carries over from the approximating semigroups to the limit semigroup if the resolvent of the latter maps 1 to a continuous function. This is instrumental in the study of elliptic operators on Rd with unbounded coefficients: our abstract result enables us to assign a semigroup to such an operator and to show that the semigroup is strongly Feller under very mild regularity assumptions on the coefficients. We also provide counterexamples to demonstrate that the assumptions in our main result are close to optimal.SpringerJOURNAL_ARTICLEeng10.1007/s10231-022-01293-90373-31141618-1891Annali di Matematica Pura ed Applicata2023-01-26T15:18:56+01:00123456789/39Annali di Matematica Pura ed Applicata ; 2022. - Springer. - ISSN 0373-3114. - eISSN 1618-1891true2023-01-26T14:18:56Ztrue