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991.
992.
If f∈Lp[0, 1], let fp be its best Lp-approximant by convex functions. It is shown that if
exists uniformly on closed subintervals of (0,1).
This research was partially supported by Grant No. 020-033-58 from the Faculty Research Committee, Idaho State University. 相似文献
993.
We prove that the Mellin transform of a function log-concave (convex) is, after division by (+1), where is the argument of the transform, itself log-concave (convex) in . This theorem is first applied to the moments of the ground state wave function of the Schrödinger equation where the Laplacian of the central potential has a given sign, and generalized to other situations. This is used to derive inequalities linking thel
th derivative of the ground state wave function at the origin for angular momentuml and the expectation value of the kinetic energy, and applied to quarkonium physics. A generalization to higher radial excitations is shown to be plausible by using the WKB approximation. Finally, new bounds on ground-state energies in power potentials are obtained. 相似文献
994.
Martin Bordemann 《Communications in Mathematical Physics》1990,135(1):201-216
We generalize the usual Lax equationd/dt L=[M, L] byd/dt L=–(M)L, where is an arbitrary representation of a Lie algebra g (the values ofM) in a representation spaceV (the values ofL). The usual classicalr-matrix programme for Hamiltonian integrable systems is generalized tor-matrices taking values in gV. Ther-matrices are then considered as left invariant torsion-free covariant derivatives on a Lie groupK (with Lie algebraV
*). The Classical Yang-Baxter Equation (CYBE) is equivalent to the flatness ofK whereas the Modified CYBE implies thatK is an affine locally symmetric space. An example is discussed. 相似文献
995.
996.
997.
998.
Anjos JC Appel JA Bean A Bracker SB Browder TE Cremaldi LM Duboscq JE Elliott JR Escobar CO Gibney MC Hartner GF Karchin PE Kumar BR Losty MJ Luste GJ Mantsch PM Martin JF McHugh S Menary SR Morrison RJ Nash T Ong P Pinfold J Punkar G Purohit MV Santoro AF Sidhu JS Sliwa K Sokoloff MD Souza MH Spalding WJ Streetman ME Stundia AB Witherell MS 《Physical review letters》1990,64(24):2885-2888
999.
1000.
N. Gray D. J. Broadhurst W. Grafe K. Schilcher 《Zeitschrift fur Physik C Particles and Fields》1990,48(4):673-679
We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN F?1 light quarks of massesM i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections. 相似文献