Precision calculation for e+ e- -> 2f: the KK MC project

We present the current status of the coherent exclusive (CEEX) realization of the YFS theory for the processes in e+ e- -> 2f via the KK MC. We give a brief summary of the CEEX theory in comparison to the older (EEX) exclusive exponentiation theory and illustrate recent theoretical results relevant to the LEP2 and LC physics programs.Comment: 5 pages, 4 figures, 2 diagrams - presented by BFLW at RADCOR0

Coherent Exclusive Exponentiation of 2f Processes in e+e- Annihilation

In the talk we present the Coherent Exclusive Exponentiation (CEEX) which is implemented in the KK MC event generator for the process e+e- to f bar f +n gamma, f=mu,tau,d,u,s,c,b for center of mass energies from tau lepton threshold to 1TeV, that is for LEP1, LEP2, SLC, future Linear Colliders, b,c,tau-factories etc. We will attempt a short discussion of the theoretical concepts necessary in our approach, in particular the relations between the rigorous calculation of spin amplitudes (perturbation expansion), phase space parametrisation and exponentiation. In CEEX effects due to photon emission from the initial beams and outgoing fermions are calculated in QED up to second-order, including all interference effects. Electroweak corrections are included in first-order, at the amplitude level. The beams can be polarised longitudinally and transversely, and all spin correlations are incorporated in an exact manner. Precision predictions, in particular the photon emission at LEP2 energies, are also shown.Comment: latex 9 pages, including 6 eps tables/figure

On inequalities associated with the Jordan-von Neumann functional equation

Summary.: For a group $(G, \cdot)$ and a real or complex inner product space $(E, \langle\cdot, \cdot\rangle)$ with norm $\def\lr{[\!]} \lr.\lr$ we consider the functional inequality $$\def\lr{[\!]} \def\lo{\longrightarrow} f:G\lo E,\;\lr 2f(x) + 2f(y)-f(xy^{-1})\lr\le\lr f(xy)\lr\qquad(\forall x,y\in G)\qquad {\rm (I)}$$ and describe situations in which (I) implies the Jordan-von Neumann parallelogram equation $$ \def\lo{\longrightarrow} f:G\lo E,\; 2f(x)+2f(y)=f(xy)+f(xy^{-1})\qquad(\forall x,y\in G).\qquad {\rm (JvN)} $

Desempenho de crianças do ensino fundamental na solução de problemas aritméticos

Performance of children of the elementary school in arithmetics problems solving This study compared the performance of students of the first year of the elementary school (groups 1F and 1IN) and students of the second year of elementary school (groups 2F and 2IN), tested at the beginning (IN) or at the end of the school year (F), in mathematical problems solving. Thirty eight participants divided into 4 groups were submitted to the same procedure, that consisted in mathematical problems oral presentation. After each answer the participants were asked about form of solution. Data was analysed related to the amount of correct answers and the strategies employed. Correct answers and the use of writing were more frequent in Group 2F and less frequent in Group 1IN. Groups 2F and 1F showed a more frequent use of algorithms. Results also show a better performance of Group 1F related to Group 2IN, suggesting that the history of recent frequency to school favours the performance of the participants.Este estudo buscou comparar o desempenho de alunos da primeira série do ensino fundamental (Grupos 1F e 1IN) e alunos da segunda série do ensino fundamental (Grupos 2F e 2IN), testados no início (IN) ou final do ano letivo (F), na solução de problemas matemáticos. Trinta e oito alunos divididos em 4 grupos foram submetidos ao mesmo procedimento, que consistia da apresentação oral de problemas matemáticos. Após cada resposta, o aluno era questionado sobre a forma de solução. Os dados foram analisados quanto ao índice de acertos e às estratégias empregadas. Os acertos e o uso da escrita foram maiores no Grupo 2F e menores no Grupo 1IN. Os grupos 2F e 1F apresentaram uso mais freqüente de algoritmos. Os resultados também indicam melhor desempenho do Grupo 1F em relação ao Grupo 2IN, sugerindo que a história de freqüência recente à escola favorece o desempenho dos alunos

Hypercontractivity for perturbed diffusion semigroups

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are studied

Coherent Exclusive Exponentiation for Precision Monte Carlo Calculations of Fermion Pair Production / Precision Predictions for (Un)stable W+W- Pairs

We present the new Coherent Exclusive Exponentiation (CEEX), in comparison to the older Exclusive Exponentiation (EEX) and the semi-analytical Inclusive Exponentiation (IEX), for the process e+e- -> f-bar f + n(gamma), f=mu,tau,d,u,s,c,b, with validity for centre of mass energies from tau lepton threshold to 1 TeV. We analyse 2f numerical results at the Z-peak, 189 GeV and 500 GeV. We also present precision calculations of the signal processes e+e- -> 4f in which the double resonant W+W- intermediate state occurs using our YFSWW3-1.14 MC. Sample 4f Monte Carlo data are explicitly illustrated in comparison to the literature at LEP2 energies. These comparisons show that a TU for the signal process cross section of 0.4 percent is valid for the LEP2 200 GeV energy. LC energy results are also shown.Comment: 5 pages, 4 figures, Presented at ICHEP200

On the nonexistence of quasi-Einstein metrics

We study complete Riemannian manifolds satisfying the equation $Ric+\nabla^2 f-\frac{1}{m}df\otimes df=0$ by studying the associated PDE $\Delta_f f + m\mu e^{2f/m}=0$ for $\mu\leq 0$. By developing a gradient estimate for $f$, we show there are no nonconstant solutions. We then apply this to show that there are no nontrivial Ricci flat warped products with fibers which have nonpositive Einstein constant. We also show that for nontrivial steady gradient Ricci solitons, the quantity $R+|\nabla f|^2$ is a positive constant.Comment: Final version: Improved exposition of Section 2, corrected minor typo