Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

Experimental and numerical study of the effect of conjugate heat transfer on film cooling

Combined convection heat transfer and thermal conduction for film cooling of a flat plate with 45° ribs on one wall was investigated experimentally and numerically. The flat plate surface temperature was measured using thermochromic liquid crystals. The results show that the film cooling is the main mechanism for the local cooling with a very low thermal conductivity while the convection heat transfer of the coolant in the coolant channel is the dominant heat transfer mechanism for the high thermal conductivity plate, with both film cooling and convection heat transfer by the coolant being important with medium thermal conductivity walls.     

The effect of increasing the excitation level of the sodium atom on the structure of the NaArn polyatomic exciplexes

In this work, the geometrical structures, the formation energies, and electronic states of the Na(ms)Ar_n polyatomic exciplexes with m = 3-6 and n = 2-5 are studied by using a quantum-classical method. The interaction potential between an electronically excited sodium atom and argon atoms are calculated by using a one-electron model involving electron-Ar and electron-Na⁺ pseudopotentials, in which the Hamiltonian is diagonalized at every optimization step in the Basin Hopping algorithm. The relationship between the position of the electronically excited levels and the cluster geometry is investigated as a function of the excitation level and of the spatial extension of the excited electron orbital. We show that the equilibrium structures of the ground state Na(3s)Ar_n and those of the electronically excited states Na(4s)Ar_n, Na(5s)Ar_n, and Na(6s)Ar_n are significantly different. As a result of the detailed examination of the relationships between the geometrical structure and density distribution of the Na valence electron of the Na^∗Ar_n with n = 2-5 polyatomic exciplexes, we can see that for the Na(4s)Ar_n polyatomic exciplexes, the two extreme geometries, neutral Na(3s)Ar_n and ionic Na⁺Ar_n compete. It appears that none of them is the actual one. For Na(5s)Ar_n and Na(6s)Ar_n the valence electron is very weakly bound to the ionic core and described by a more diffused orbital so that the geometry and the formation energies of this excited state called Rydberg states converge towards those of the ionic cores.     

Observation of B(s)0-->K+ K- and measurements of branching fractions of charmless two-body decays of B0 and B(s)0 mesons in pp collisions at square root of s = 1.96 TeV

We search for decays of the type B(s)0-->h+ h'- (where h,h' = K or pi) in 180 pb(-1) of pp collisions collected at the Tevatron by the upgraded Collider Detector at Fermilab. We report the first observation of the new mode B(s)0-->K+ K- with a yield of 236+/-32 events, corresponding to (fs/fd) x B(B(s)0-->K+ K-)/B(B0-->K+ pi-) = 0.46+/-0.08stat+/-0.07syst, where fs/fd is the ratio of production fractions of B(s)0 and B0. We find results in agreement with world averages for the B0 modes, and set the following new limits at 90% C.L.: B(B(s)0-->K- pi+) < 5.6 x 10(-6) and B(B(s)0-->pi+ pi-) < 1.7 x 10(-6).     

Measurement of the Bs0-Bs0 oscillation frequency

We present the first precise measurement of the Bs0-Bs0 oscillation frequency Deltams. We use 1 fb-1 of data from pp collisions at sqrts=1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. The sample contains signals of 3600 fully reconstructed hadronic Bs decays and 37,000 partially reconstructed semileptonic Bs decays. We measure the probability as a function of proper decay time that the Bs decays with the same, or opposite, flavor as the flavor at production, and we find a signal consistent with Bs0-Bs0 oscillations. The probability that random fluctuations could produce a comparable signal is 0.2%. Under the hypothesis that the signal is due to Bs0-Bs0 oscillations, we measure Deltams=17.31(-0.18)+0.33(stat)+/-0.07(syst) ps-1 and determine |Vtd/Vts|=0.208(-0.002)+0.001(expt)-0.006(+0.008)(theor).     

Observation of B(0)(s)-->Psi(2S)Phi and measurement of the ratio of branching fractions Beta(B(0)(s)-->Psi(2S)Phi)/Beta(B(0)(s)-->J/PsiPhi)

We report the first observation of B(0)(s)-->Psi(2S)Phi decay in p(p_) collisions at square root of 8=1.96 TeV using 360 pb(-1) of data collected by the CDF II detector at the Fermilab Tevatron. We observe 20.2 +/- 5.0 and 12.3 +/- 4.1 B(0)(s)-->Psi(2S)Phi candidates, in Psi(2S)-->mu(+)mu(-) and Phi(2S)-->J/Phipi(+)pi(-) decay modes, respectively. We present a measurement of the relative branching fraction Beta(B(0)(s)-->Psi(2S)Phi)/Beta(B(0)(s)-->J/PsiPhi)=0.52 +/- 0.13(stat) +/- 0.04(syst) +/- 0.06(BR) using the Psi(2S)-->mu(+)mu(-) decay mode.     

Search for high-mass resonances decaying to emu in pp collisions at square root = 1.69 TeV

We describe a general search for resonances decaying to a neutral emu final state in pp collisions at a center-of-mass energy of 1.96 TeV. Using a data sample representing 344 pb(-1) of integrated luminosity recorded by the Collider Detector at Fermilab II experiment, we compare standard model predictions with the number of observed events for invariant masses between 50 and 800 GeV/c2. Finding no significant excess (5 events observed vs 7.7 +/- 0.8 expected for M(emu) > 100 GeV/c2 ), we set limits on sneutrino and Z' masses as functions of lepton family number violating couplings.     

Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.