Convergence of eigenfunction expansions corresponding to nonlinear Sturm-Liouville operators

It is well known that the classical linear Sturm-Liouville eigenvalue problem is self-adjoint and possesses a family of eigenfunctions which form an orthonormal basis for the space L. A natural question is to ask if a similar result holds for nonlinear problems. In the present paper, we examine the basis property for eigenfunctions of nonlinear Sturm-Liouville equations subject to general linear, separated boundary conditions

Transverse Electronic Transport through DNA Nucleotides with Functionalized Graphene Electrodes

Graphene nanogaps and nanopores show potential for the purpose of electrical DNA sequencing, in particular because single-base resolution appears to be readily achievable. Here, we evaluated from first principles the advantages of a nanogap setup with functionalized graphene edges. To this end, we employed density functional theory and the non-equilibrium Green's function method to investigate the transverse conductance properties of the four nucleotides occurring in DNA when located between the opposing functionalized graphene electrodes. In particular, we determined the electrical tunneling current variation as a function of the applied bias and the associated differential conductance at a voltage which appears suitable to distinguish between the four nucleotides. Intriguingly, we observe for one of the nucleotides a negative differential resistance effect.Comment: 19 pages, 7 figure

Early protein intake predicts functional connectivity and neurocognition in preterm born children

© 2021, The Author(s). Nutritional intake can promote early neonatal brain development in very preterm born neonates (\u3c 32 weeks’ gestation). In a group of 7-year-old very preterm born children followed since birth, we examined whether early nutrient intake in the first weeks of life would be associated with long-term brain function and neurocognitive skills at school age. Children underwent resting-state functional MRI (fMRI), intelligence testing (Wechsler Intelligence Scale for Children, 5th Ed) and visual-motor processing (Beery-Buktenica, 5th Ed) at 7 years. Relationships were assessed between neonatal macronutrient intakes, functional connectivity strength between thalamic and default mode networks (DMN), and neuro-cognitive function using multivariable regression. Greater functional connectivity strength between thalamic networks and DMN was associated with greater intake of protein in the first week (β = 0.17; 95% CI 0.11, 0.23, p \u3c 0.001) but lower intakes of fat (β = − 0.06; 95% CI − 0.09, − 0.02, p = 0.001) and carbohydrates (β = − 0.03; 95% CI − 0.04, − 0.01, p = 0.003). Connectivity strength was also associated with protein intake during the first month (β = 0.22; 95% CI 0.06, 0.37, p = 0.006). Importantly, greater thalamic-DMN connectivity strength was associated with higher processing speed indices (β = 26.9; 95% CI 4.21, 49.49, p = 0.02) and visual processing scores (β = 9.03; 95% CI 2.27, 15.79, p = 0.009). Optimizing early protein intake may contribute to promoting long-term brain health in preterm-born children

Evidence for the h_b(1P) meson in the decay Upsilon(3S) --> pi0 h_b(1P)

Using a sample of 122 million Upsilon(3S) events recorded with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at SLAC, we search for the $h_b(1P)$ spin-singlet partner of the P-wave chi_{bJ}(1P) states in the sequential decay Upsilon(3S) --> pi0 h_b(1P), h_b(1P) --> gamma eta_b(1S). We observe an excess of events above background in the distribution of the recoil mass against the pi0 at mass 9902 +/- 4(stat.) +/- 2(syst.) MeV/c^2. The width of the observed signal is consistent with experimental resolution, and its significance is 3.1sigma, including systematic uncertainties. We obtain the value (4.3 +/- 1.1(stat.) +/- 0.9(syst.)) x 10^{-4} for the product branching fraction BF(Upsilon(3S)-->pi0 h_b) x BF(h_b-->gamma eta_b).Comment: 8 pages, 4 postscript figures, submitted to Phys. Rev. D (Rapid Communications

Study of Upsilon(3S,2S) -> eta Upsilon(1S) and Upsilon(3S,2S) -> pi+pi- Upsilon(1S) hadronic trasitions

We study the Upsilon(3S,2S)->eta Upsilon(1S) and Upsilon(3S,2S)->pi+pi- Upsilon(1S) transitions with 122 million Upsilon(3S) and 100 million Upsilon(2S) mesons collected by the BaBar detector at the PEP-II asymmetric energy e+e- collider. We measure B[Upsilon(2S)->eta Upsilon(1S)]=(2.39+/-0.31(stat.)+/-0.14(syst.))10^-4 and Gamma[Upsilon(2S)->eta Upsilon(1S)]/Gamma[Upsilon(2S)-> pi+pi- Upsilon(1S)]=(1.35+/-0.17(stat.)+/-0.08(syst.))10^-3. We find no evidence for Upsilon(3S)->eta Upsilon(1S) and obtain B[Upsilon(3S)->eta Upsilon(1S)]<1.0 10^-4 and Gamma[Upsilon(3S)->eta Upsilon(1S)]/Gamma[Upsilon(3S)->pi+pi- Upsilon(1S)]<2.3 10^-3 as upper limits at the 90% confidence level. We also provide improved measurements of the Upsilon(2S) - Upsilon(1S) and Upsilon(3S) - Upsilon(1S) mass differences, 562.170+/-0.007(stat.)+/-0.088(syst.) MeV/c^2 and 893.813+/-0.015(stat.)+/-0.107(syst.) MeV/c^2 respectively.Comment: 8 pages, 16 encapsulated postscript figures, submitted to Phys.Rev.

Evidence for the η_b(1S) Meson in Radiative Υ(2S) Decay

We have performed a search for the η_b(1S) meson in the radiative decay of the Υ(2S) resonance using a sample of 91.6 × 10^6 Υ(2S) events recorded with the BABAR detector at the PEP-II B factory at the SLAC National Accelerator Laboratory. We observe a peak in the photon energy spectrum at E_γ = 609.3^(+4.6)_(-4.5)(stat)±1.9(syst) MeV, corresponding to an η_b(1S) mass of 9394.2^(+4.8)_(-4.9)(stat) ± 2.0(syst) MeV/c^2. The branching fraction for the decay Υ(2S) → γη_b(1S) is determined to be [3.9 ± 1.1(stat)^(+1.1)_(-0.9)(syst)] × 10^(-4). We find the ratio of branching fractions B[Υ(2S) → γη_b(1S)]/B[Υ(3S) → γη_b(1S)]= 0.82 ± 0.24(stat)^(+0.20)_(-0.19)(syst)

Measurement of the quasi-elastic axial vector mass in neutrino-oxygen interactions

The weak nucleon axial-vector form factor for quasi-elastic interactions is determined using neutrino interaction data from the K2K Scintillating Fiber detector in the neutrino beam at KEK. More than 12,000 events are analyzed, of which half are charged-current quasi-elastic interactions nu-mu n to mu- p occurring primarily in oxygen nuclei. We use a relativistic Fermi gas model for oxygen and assume the form factor is approximately a dipole with one parameter, the axial vector mass M_A, and fit to the shape of the distribution of the square of the momentum transfer from the nucleon to the nucleus. Our best fit result for M_A = 1.20 \pm 0.12 GeV. Furthermore, this analysis includes updated vector form factors from recent electron scattering experiments and a discussion of the effects of the nucleon momentum on the shape of the fitted distributions.Comment: 14 pages, 10 figures, 6 table

Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+

We perform amplitude analyses of the decays $B^0 \to K^+K^-K^0_S$, $B^+ \rightarrow K^+K^-K^+$, and $B^+ \to K^0_S K^0_S K^+$, and measure CP-violating parameters and partial branching fractions. The results are based on a data sample of approximately $470\times 10^6$ $B\bar{B}$ decays, collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory. For $B^+ \to K^+K^-K^+$, we find a direct CP asymmetry in $B^+ \to \phi(1020)K^+$ of $A_{CP}= (12.8\pm 4.4 \pm 1.3)$, which differs from zero by $2.8 \sigma$. For $B^0 \to K^+K^-K^0_S$, we measure the CP-violating phase $\beta_{\rm eff} (\phi(1020)K^0_S) = (21\pm 6 \pm 2)^\circ$. For $B^+ \to K^0_S K^0_S K^+$, we measure an overall direct CP asymmetry of $A_{CP} = (4 ^{+4}_{-5} \pm 2)$. We also perform an angular-moment analysis of the three channels, and determine that the $f_X(1500)$ state can be described well by the sum of the resonances $f_0(1500)$, $f_2^{\prime}(1525)$, and $f_0(1710)$.Comment: 35 pages, 68 postscript figures. v3 - minor modifications to agree with published versio

Measurement of the B+ --> p pbar K+ Branching Fraction and Study of the Decay Dynamics

With a sample of 232x10^6 Upsilon(4S) --> BBbar events collected with the BaBar detector, we study the decay B+ --> p pbar K+ excluding charmonium decays to ppbar. We measure a branching fraction Br(B+ --> p pbar K+)=(6.7+/-0.5+/-0.4)x10^{-6}. An enhancement at low ppbar mass is observed and the Dalitz plot asymmetry suggests dominance of the penguin amplitude in this B decay. We search for a pentaquark candidate Theta*++ decaying into pK+ in the mass range 1.43 to 2.00 GeV/c2 and set limits on Br(B+ --> Theta*++pbar)xBr(Theta*++ --> pK+) at the 10^{-7} level.Comment: 8 pages, 7 postscript figures, submitted to Phys. Rev. D (Rapid Communications

Search for the W-exchange decays B0 --> Ds(*)- Ds(*)+

We report a search for the decays $B^{0} \to D_{s}^{-} D_{s}^{+}$, $B^{0} \to D_{s}^{*-} D_{s}^{+}$, $B^{0} \to D_{s}^{*-} D_{s}^{*+}$ in a sample of 232 million $\Upsilon(4S)$ decays to \BBb ~pairs collected with the \babar detector at the PEP-II asymmetric-energy $e^+ e^-$ storage ring. We find no significant signal and set upper bounds for the branching fractions: ${\cal B}(B^{0} \to D_{s}^{-} D_{s}^{+}) < 1.0 \times 10^{-4}, {\cal B}(B^{0} \to D_{s}^{*-} D_{s}^{+}) < 1.3 \times 10^{-4}$ and ${\cal B}(B^{0} \to D_{s}^{*-} D_{s}^{*+}) < 2.4 \times 10^{-4}$ at 90% confidence level.Comment: 8 pages, 2 figures, submitted to PRD-R