[a,b]-factorization of a graph

Let a and b be integers such that 0 ? a ? b. Then a graph G is called an [a, b]-graph if a ? d_G(x) ? b for every x ? V(G), and an [a, b]-factor of a graph is defined to be its spanning subgraph F such that a ? d_F(x) ? b for every vertex x, where d_G(x) and d_F(x) denote the degrees of x in G and F, respectively. If the edges of a graph can be decomposed into [a.b]-factors then we say that the graph is [2a, 2a]-factorable. We prove the following two theorems: (i) a graph G is [2a, 2b)-factorable if and only if G is a [2am,2bm]-graph for some integer m, and (ii) every [8m + 2k, 10m + 2k]-graph is [1,2]-factorable.     

Measurement of time-dependent CP-violating asymmetries in B0 --> K(s)0K(s)0K(s)0 decay

We present a measurement of CP-violation parameters in the B0 --> K(s)0K(s)0K(s)0 decay based on a sample of 275 x 10(6) BB pairs collected at the upsilon(4S) resonance with the Belle detector at the KEKB energy-asymmetric e+e- collider. One neutral B meson is fully reconstructed in the decay B0 --> K(s)0K(s)0K(s)0, and the flavor of the accompanying B meson is identified from its decay products. CP-violation parameters are obtained from the asymmetry in the distributions of the proper-time interval between the two B decays: S = +1.26 +/- 0.68(stat) +/- 0.20(syst) and [symbol: see text] = +0.54 +/- 0.34(stat) +/- 0.09(syst).     

Observation of the D1(2420)-->Dpi + pi- decays

We report on the first observation of D0/1(2420)-->D0pi- pi+ and D+/1(2420-->D+ pi- pi+ decays (where the contribution from the dominant known D1-->D*pi decay mode is excluded) in the B- -->D0/1pi-) and (-)B0-->D+/1pi- decays, respectively. The observation is based on 15.2 x 10(7) B(-)B events collected with the Belle detector at the KEKB collider. We also set 90% confidence level upper limits for the branching fractions of the four following decays: B- -->D0/1pi-, D01-->D(*0)pi- pi+, (-)B0-->D+/1pi-, D+/1-->D(*+) pi- pi+, B- -->D(*0)2(2460)pi-, D(*0)2 -->D(*0) pi- pi+, (-)B0-->D(*+)2(2460)pi-, D(*+)2-->D(*+)pi- pi+.     

Observation of a near-threshold omegaJ/psi mass enhancement in exclusive B-->KomegaJ/psi decays

We report the observation of a near-threshold enhancement in the omegaJ/psi invariant mass distribution for exclusive B-->KomegaJ/psi decays. The results are obtained from a 253 fb(-1) data sample that contains 275 x 10(6) BB pairs that were collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e(+)e(-) collider. The statistical significance of the omegaJ/psi mass enhancement is estimated to be greater than 8sigma.     

Search for D0-D0 mixing in D0 --> K+ pi(-) decays and measurement of the doubly-Cabibbo-suppressed decay rate

We have searched for mixing in the D(0)-D (0) system by measuring the decay-time distribution of D(0) --> K(+) pi(-) decays. The analysis uses 90 fb(-1) of data collected by the Belle detector at the KEKB e(+) e(-) collider. We fit the decay-time distribution for the mixing parameters x' and y' and also for the parameter R(D), which is the ratio of the rate for the doubly-Cabibbo-suppressed decay D(0)--> K+ pi(-) to that for the Cabibbo-favored decay D(0)--> K-pi(+). We do these fits both assuming CP conservation and allowing for CP violation. We use a frequentist method to obtain a 95% C.L. region in the x'(2) - y' plane. Assuming no mixing, we measure R(D) = (0.381 +/- 0.017(+0.008)(-0.016))%.     

Singular Fano compactifications of (I)

In this paper we study the singular Fano compactifications of with small Gorenstein singularities and determine the structure of such a compactification in the case of the Fano index r 2.Mathematics Subject Classification (2000): 14J45 , 32J05     

Search for CP violation in the decay B0-->D*+/-D-/+

We report a search for CP-violating asymmetry in B0-->D(*+/-)D-/+ decays. The analysis employs two methods of B0 reconstruction: full and partial. In the full reconstruction method all daughter particles of the B0 are required to be detected; the partial reconstruction technique requires a fully reconstructed D- and only a slow pion from the D(*+)-->D0pi(+)(slow) decay. From a fit to the distribution of the time interval corresponding to the distance between two B meson decay points we calculate the CP-violating parameters and find the significance of nonzero CP asymmetry to be 2.7 standard deviations.     

Uniform convexity of ψ-direct sums of Banach spaces

Let X and Y be Banach spaces and ψ a continuous convex function on the unit interval [0,1] satisfying certain conditions. Let X⊕_ψY be the direct sum of X and Y equipped with the associated norm with ψ. We show that X⊕_ψY is uniformly convex if and only if X,Y are uniformly convex and ψ is strictly convex. As a corollary we obtain that the ?_p,q-direct sum (not p=q=1 nor ∞), is uniformly convex if and only if X,Y are, where ?_p,q is the Lorentz sequence space. These results extend the well-known fact for the ?_p-sum . Some other examples are also presented.     

Transverse instability of solitary waves in the generalized kadomtsev-petviashvili equation

The linear stability of planar solitary waves with respect to long-wavelength transverse perturbations is studied in the framework of the generalized Kadomtsev-Petviashvili equation. It is newly discovered that for some nonlinearities in this family, the solitary waves could be transversely unstable even in a medium with negative dispersion. In the case of positive dispersion, they are found to be always unstable.     

Low temperature dependence of elastic moduli and internal friction for the glassy alloy Zr55Cu30Al10Ni5

Longitudinal and transverse wave velocities, eight kinds of elastic parameters, and dilational and shear internal frictions of Zr₅₅Cu₃₀Al₁₀Ni₅ glassy alloy were simultaneously measured as a function of temperature in the range from 77 to 373 K, using an ultrasonic pulse method. The inflections at around 150 K for wave velocities, anisotropy factor and Poisson's ratio, and the 150 K peak of shear friction seem to correspond to one topological change (pseudo‐transition) associated with an interatomic readjustment or vacancy rearrangements. The behaviors from 77 to 125 K and 125 to 373 K are due to thermal relaxation of squeezed free volumes and entropy elasticity associated with vibrational motions of clusters, respectively, accompanied by an increase in atomic distance. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)