A method to calculate numerically the multiplicity of a solution to a system of algebraic equations is presented. The method is an application of Zeuthen’s rule which gives the multiplicity of a solution as the multiplicity of a united point of an algebraic correspondence defined naturally by the system. The numerical calculation is applicable to a large scale system of algebraic equations whic...

mulas §1.5. Multiplicity-free representations — definition §2. Multiplicity-free theorem — general framework §2.1. Holomorphic bundles and anti-holomorphic maps §2.2. Multiplicity-free theorem — line bundle case §2.3. Geometry on the base space D §2.4. Multiplicity-free theorem — vector bundle case §3. Visible actions on complex manifolds §3.1. Previsible and visible actions on complex manifold...

Semi-inclusive transverse momentum spectra observed in proton-proton and proton-lead nuclear collisions at LHC energies obey a geometric scaling with variable using multiplicity-dependent saturation momentum. The extracted from the experimental data is proportional to 1/6 power of hadron multiplicity final state. However, system's size 1/3 multiplicity, system are strongly correlated Since aver...

The production of $\chi_{c1}(3872)$ and $\psi(2S)$ hadrons is studied as a function charged particle multiplicity in $pp$ collisions at center-of-mass energy 8 TeV, corresponding to an integrated luminosity 2 fb$^{-1}$. For both states, the fraction that produced promptly collision vertex found decrease increases. ratio cross-sections for particles also with multiplicity, while no significant d...

The production of $\chi_{c1}(3872)$ and $\psi(2S)$ hadrons is studied as a function charged particle multiplicity in $pp$ collisions at center-of-mass energy 8 TeV, corresponding to an integrated luminosity 2 fb$^{-1}$. For both states, the fraction that produced promptly collision vertex found decrease increases. ratio cross-sections for particles also with multiplicity, while no significant d...

In order to reduce the current ripple and improve power density of system, multiple structure design is generally adopted by traditional bidirectional DC/DC converter. However, fixed multiplicity can’t make converter always output smallest under different duty ratios. Through this research, it found that related cycle parallel multiplicity, then a variable proposed. Firstly, relationship betwee...

In this paper, we extend the MURM (Modified Universe Reaction Model) of a CSTR to a tubular reactor with axial dispersion. Furthermore, we use this mixing model to study the effort of the micromixing on the steady state multiplicity for an autocatalytical reaction of tubular reactor.

We analyze the Hamiltonian of the compactified D = 11 supermembrane with non-trivial central charge in terms of the matrix model constructed in [1]. Our main result provides a rigorous proof that the quantum Hamiltonian of the supersymmetric model has compact resolvent and thus its spectrum consists of a discrete set of eigenvalues with finite multiplicity.

We show that soft color rearrangement of final states can account for the appearance of rapidity gaps between jets. In the color evaporation model the probability to form a gap is simply determined by the color multiplicity of the final state. This model has no free parameters and reproduces all data obtained by the ZEUS, H1, DØ, and CDF collaborations.

Monte-Carlo simulations to calculate the number of prompt particles emitted during fission were performed using Fifrelin code and compared recent experimental data. We show that we are able reproduce both neutron ?-ray multiplicity distributions as a function pre-neutron mass fragments single consistent set parameters. This result was made possible by an energy-dependent spin cut-off model, dri...