Fourier transform on finite groupsIn mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform of a function at a representation of is For each representation of , is a matrix, where is the degree of . The inverse Fourier transform at an element of is given by The convolution of two functions is defined as The Fourier transform of a convolution at any representation of is given by For functions , the Plancherel formula states where are the irreducible representations of .
Discrete sine transformIn mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample. A family of transforms composed of sine and sine hyperbolic functions exists.
Fonction point d'interrogationLa fonction point d'interrogation, ou fonction de Minkowski, est, en mathématiques, une fonction, notée ? (ou ). Cette fonction fut définie par Hermann Minkowski en 1904 afin d'obtenir une application continue de l'ensemble des irrationnels quadratiques de l'intervalle ]0, 1[ vers l'ensemble des nombres rationnels du même intervalle. La définition courante actuelle fut posée par Arnaud Denjoy en 1938. Sa restriction aux nombres rationnels est une fonction strictement croissante, dérivable, et de dérivée partout nulle.
Structural proof theoryIn mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof, a kind of proof whose semantic properties are exposed. When all the theorems of a logic formalised in a structural proof theory have analytic proofs, then the proof theory can be used to demonstrate such things as consistency, provide decision procedures, and allow mathematical or computational witnesses to be extracted as counterparts to theorems, the kind of task that is more often given to model theory.
Racine dentairevignette|300px|Détail d'une molaire humaine.1. Dent 2. Émail dentaire 3. Dentine 4. Pulpe dentaire 5. 6. 7. Cément 8. Couronne 9. 10. 11. collet 12. Racine dentaire 13. 14. 15. 16. Sulcus gingivae17. Parodonte 18.Gencive 19. 20. 21. 22. Ligament alvéolo-dentaire 23. Os alvéolaire 24. 25. 26. 27. canal alvéolaire La racine d'une dent est la portion de la dent qui se trouve dans l'os alvéolaire, situé dans l'os basal du maxillaire ou de la mandibule. Surmontée de la couronne dentaire, la racine sert de pilier à la dent.
