Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over compact semi-algebraic sets. In this paper, we show that, for convex polynomial optimization, the Lasserre hierarchy with a slightly extended quadratic module always converges asymptotically even in the face of non-compact semi-algebraic feasible sets. We do this by exploiting a coercivity property of convex polynomials that are bounded below. We further establish that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point (rather than the objective function at each minimizer) guarantees finite convergence of the hierarchy. We obtain finite convergence by first establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets under a saddle-point condition. We finally prove that the existence of a saddle-point of the Lagrangian for a convex polynomial program is also necessary for the hierarchy to have finite convergence.Comment: 17 page

Chiral Anomaly Effects and the BaBar Measurements of the γγ∗→π0\gamma\gamma^{*}\to \pi^{0} Transition Form Factor

The recent BaBar measurements of the $\gamma\gamma^{*}\to \pi^{0}$ transition form factor show spectacular deviation from perturbative QCD prediction for large space-like $Q^{2}$ up to $34\,\rm GeV^{2}$. When plotted against $Q^{2}$, $Q^{2}F(Q^{2})$ shows steady increase with $Q^{2}$ in contrast with the flat $Q^{2}$ behavior predicted by perturbative QCD, and at $34\,\rm GeV^{2}$ is more than 50% larger than the QCD prediction. Stimulated by the BaBar measurements, we revisit our previous paper on the cancellation of anomaly effects in high energy processes $Z^{0}\to \pi^{0}\gamma$, $e^{+}e^{-}\to \pi^{0}\gamma$ and apply our results to the $\gamma^{*}\gamma\to \pi^{0}$ transition form factor measured in the $e^{+}e^{-}\to e^{+}e^{-}\pi^{0}$ process with one highly virtual photon. We find that, the transition form factor $F(Q^{2})$ behaves as $(\frac{m^{2}}{Q^{2}})\times (\ln(Q^{2}/m^{2}))^{2}$ and produces a striking agreement with the BaBar data for $Q^{2}F(Q^{2})$ with $m=132\,\rm MeV$ which also reproduces very well the CLEO data at lower $Q^{2}$.Comment: v4, LaTeX, 8 pages, one figure, minor changes(references), to appear in Int. J. Mod. Phys.

Charmless Final State Interaction in B-> pi pi decays

We estimate effects of the final state interactions in B -> pi pi decays coming from rescattering of pi pi via exchange of rho, sigma, f_0 mesons. Then we include the rho rho rescattering via exchange of pi, omega, a_1 mesons and finally we consider contributions of the a_1 pi rescattering via exchange of rho. The absorptive parts of amplitudes for these processes are determined. In the case of pi^+ pi^- decay mode, due to model uncertainties, the calculated contribution is |M_A| =< 1.7 x 10^-8 GeV. This produces a small relative strong phase for the tree and color-suppressed B -> pi pi amplitudes consistent with the result of a recent phenomenological analysis based on the BaBar and Belle results for the B -> pi pi branching ratios and CP asymmetries.Comment: 10 pages, 2 figure

Urine adulteration: Can bleach be used to mask MDMA use?

Concerns regarding specimen integrity have long been a major issue of urine drug testing due to acts of urine adulteration. At a high concentration, in vitro urine adulteration using sodium hypochlorite (bleach) produced false-negative results for 3,4-methylenedioxymethamphetamine (MDMA) in CEDIA® immunoassay screening with strong negative readings. However, these strong negative readings may act as a warning sign for further investigation of the sample where the detection of a unique marker in the form of N-chloroMDMA will suggest urine adulteration via bleach. Liquid chromatography-tandem mass spectrometry (LC-MS/MS) identified N-chloroMDMA is a major product formed between hypochlorite and MDMA in urine. N-ChloroMDMA was found stable at 4°C for at least 10 h, but decomposed over time at room temperature (20°C) with MDMA being identified as one of its main decomposition products. © 2013 The Royal Society of Chemistry

Long-term stability studies of a semiconductor photoelectrode in three-electrode configuration

Improving the stability of semiconductor materials is one of the major challenges for sustainable and economic photoelectrochemical water splitting. N-terminated GaN nanostructures have emerged as a practical protective layer for conventional high efficiency but unstable Si and III-V photoelectrodes due to their near-perfect conduction band-alignment, which enables efficient extraction of photo-generated electrons, and N-terminated surfaces, which protects against chemical and photo-corrosion. Here, we demonstrate that Pt-decorated GaN nanostructures on an n+-p Si photocathode can exhibit an ultrahigh stability of 3000 h (i.e., over 500 days for usable sunlight ∼5.5 h per day) at a large photocurrent density (&gt;35 mA cm-2) in three-electrode configuration under AM 1.5G one-sun illumination. The measured applied bias photon-to-current efficiency of 11.9%, with an excellent onset potential of ∼0.56 V vs. RHE, is one of the highest values reported for a Si photocathode under AM 1.5G one-sun illumination. This study provides a paradigm shift for the design and development of semiconductor photoelectrodes for PEC water splitting: stability is no longer limited by the light absorber, but rather by co-catalyst particles

Optimized FRP Wrapping Schemes for Circular Concrete Columns under Axial Compression

This study investigates the behavior and failure modes of fiber-reinforced polymer (FRP) confined concrete wrapped with different FRP schemes, including fully wrapped, partially wrapped, and nonuniformly-wrapped concrete cylinders. By using the same amount of FRP, this study proposes a new wrapping scheme that provides a higher compressive strength and strain for FRP-confined concrete, in comparison with conventional fully wrapping schemes. A total of 33 specimens were cast and tested, with three of these specimens acting as reference specimens and the remaining specimens wrapped with different types of FRP (CFRP and GFRP) by different wrapping schemes. For specimens that belong to the descending branch type, the partially-wrapped specimens had a lower compressive strength but a higher axial strain as compared to the corresponding fully-wrapped specimens. In addition, the nonuniformly-wrapped specimens achieved both a higher compressive strength and axial strain in comparison with the fully-wrapped specimens. Furthermore, the partially-wrapping scheme changes the failure modes of the specimens and the angle of the failure surface. A new equation that can be used to predict the axial strain of concrete cylinders wrapped partially with FRP is proposed