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The decay J/ψ → ωpp has been studied, using 225.3 × 10 6 J/ψ events accumulated at BESIII. No significant enhancement near the pp invariant-mass threshold (denoted as X(pp)) is observed. The upper limit of the branching fraction B(J/ψ → ωX(pp) → ωpp) is determined to be 3.9 × 10 −6 at the 95% confidence level. The branching fraction of J/ψ → ωpp is measured to be B(J/ψ → ωpp) = (9.0 ± 0.2 (stat.) ± 0.9 (syst.)) × 10 −4 . 124The investigation of the near-threshold pp invariant 125 mass spectrum in other J/ψ decay modes will be helpful 126 in understanding the nature of the observed structure. 127The decay J/ψ → ωpp restricts the isospin of the pp 128 system, and it is helpful to clarify the role of the pp in the return iron yoke of the superconducting magnet. 174The position resolution is about 2 cm. 175The optimization of the event selection and the es- 247The branching fraction of J/ψ → ωpp is calculated 248 according to :(1) where N obs is the number of signal events determined Breit-Wigner function :Here, q is the momentum of the proton in the pp rest where N obs is the number of signal events, and L is the Author's Copy where σ sys. is the total systematic uncertainty which will 299 be described in the next section. The upper limit on the 300 product of branching fractions is B(J/ψ → ωX(pp) → 301 ωpp) < 3.9 × 10 −6 at the 95% C.L.. 302An alternative fit with a Breit-Wigner function includ-for X(pp) is performed. Here, f FSI is the Jülich FSI cor- between data and MC simulation is 2% per charged track. 323The systematic uncertainty from PID is 2% per proton 324(anti-proton). 325The photon detection systematic uncertainty is studied efficiency difference is about 1% for each photon [32, 33]. 329Author's Copy Near-threshold pp invariant-mass spectrum. The signal J/ψ → ωX(pp) → ωpp is described by an acceptanceweighted Breit-Wigner function, and and signal yield is consistent with zero. The dotted line is the shape of the signal which is normalized to five times the estimated upper limit. The dashed line is the non-resonant contribution described by the function f (δ) and the dashed-dotted line is the non ωpp contribution which is estimated from ω sidebands. The solid line is the total contribution of the two components. The hatched area is from the sideband region.Here, 3% is taken as the systematic error for the efficien- ciency between data and MC is 3%, and is taken as the 338 systematic uncertainty caused by the kinematic fit. 339As described above, the yield of J/ψ → ωpp is de- The signal J/ψ → ωX(pp) → ωpp is described by an acceptanceweighted Breit-Wigner function, and and signal yield is consistent with zero. The dashed line is the non-resonant contribution fixed to a phase space MC simulation of J/ψ → ωpp and the dashed-dotted line is the non ωpp contribution which is estimated from ω sidebands. The solid line is the total contribution of the two components. The hatched area is from a phase space MC simulation of J/ψ → ωpp.sented by Figure.

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PrefaceThis book provides an introduction to a newly developed bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering. The first two chapters of the book contain a brief introduction to the standard bifurcation theory for nonlinear PDEs. The treatment of the classical theorems is unified by the Lyapunov-Schmidt reduction and the center manifold reduction procedures.The next four chapters introduce a new bifurcation theory developed recently by the authors. This theory is centered at a new notion of bifurcation, called attractor bifurcation for nonlinear evolution equations. The main ingredients of the theory include a) the attractor bifurcation theory, b) steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and c) new strategies for the Lyapunov-Schmidt reduction and the center manifold reduction procedures.With the bifurcation theory, many long standing bifurcation problems in science and engineering are becoming accessible, and are treated in the last four chapters of the book. In particular, applications are made for variety of PDEs from science and engineering, including, in particular, the Kuramoto-Sivashinshy equation, the Cahn-Hillard equation, the GinzburgLandau equation, Reaction-Diffusion equations in Biology and Chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other hand, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is hoped that the book will be helpful in advancing the study

Enzymatic reactions in living cells are highly dynamic but simultaneously tightly regulated. Enzyme engineers seek to construct multienzyme complexes to prevent intermediate diffusion, to improve product yield, and to control the flux of metabolites. Here we choose a pair of short peptide tags (RIAD and RIDD) to create scaffold-free enzyme assemblies to achieve these goals. In vitro, assembling enzymes in the menaquinone biosynthetic pathway through RIAD–RIDD interaction yields protein nanoparticles with varying stoichiometries, sizes, geometries, and catalytic efficiency. In Escherichia coli, assembling the last enzyme of the upstream mevalonate pathway with the first enzyme of the downstream carotenoid pathway leads to the formation of a pathway node, which increases carotenoid production by 5.7 folds. The same strategy results in a 58% increase in lycopene production in engineered Saccharomyces cerevisiae. This work presents a simple strategy to impose metabolic control in biosynthetic microbe factories.