Comparative Study on the Policy of Multiplicity Issues in Clinical Trials at Home and Abroad

Objective To study the content of China’s guiding principles on multiplicity issues in clinical trials,and to provide reference for the revision of China’s relevant guiding principles.Methods Based on ICH E9,the similarities and differences of the guiding principles of US Food and Drug Administration(FDA),European Medicines Agency(EMA),and National Medical Products Administration(NMPA)on the multiplicity issues in clinical trials were compared one by one.Results and Conclusion In general,NMPA guidelines are based on ICH E9,but in detail,the guidelines of FDA and EMA focus differently on the multiplicity issues.Therefore,NMPA guidelines need to be detailed and comprehensive.NMPA guidelines can be refined by referring to foreign guidelines to improve the practical guiding significance for clinical research and promote the level of domestic clinical trials in line with international standards.

THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM

In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.

Cycle Multiplicity of Total Graph of Complete Bipartite Graph

Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].

The Method on Deducing Multiplicity Measurement Equations of Neutron/γ

Based on some important domestic and international references,the third γ multiplicity measurement equation is derived,but it is different from the results given in current researches.The neutron multiplicity equation is deduced in this paper,especially the fourth fast-neutron multiplicity equation based on the liquid scintillation detectors,which is more complex than the other multiplicity equations up to the fourth order.The equations given in this paper can be used to verify the validity and availability of principles for the multiplicity measurement up to the fourth order,and extend the application scopes of the neutron multiplicity measurement,such as correcting the additional measurement value to eliminate influences for dead times.It will be the foundation of nuclear researches,if the higher order multiplicity measurement is important for nuclear materials’control and accountability.

Multiplicity in Continuous Adiabatic MSMPR Reactive Precipitators

The possibility of both concentration and temperature multiplicities has bcen studied for the case of acontinuous adiabatic mixed suspension mixed product removal(MSMPR)reactive precipitaior.A Process in-volving homogeneous chemical reaction in first order reaction kinetics with respect to each of the reactive compo-nents and subsequent crystallization described by conventional power law growth and power law magma depen-dent nucleation models is considered.The temperature dependency of each of these kinetics is described by Ar-rhenius relations.Parameter regions are determined in which multiple steady states exist.The linear stability ofthese steady states is analyzed by using the Routh criterion approach.

Multiplicity of solutions to geophysical inversion reflected by rupture slip distribution of the 2015 Nepal earthquake

The equivalence of geophysical fields, the finiteness of measurements and the measurement errors make the result of geophysical inversion non-unique. For example, the measurements and inversion method used, the priori rupture model determined and the slip distribution smoothing factor selected will have significant influences on the earthquake rupture slip distribution. Using different data and methods, different authors have given different rupture slip distribution models of the 2015 Mw7.9 Nepal earth- quake, with the maximum slip ranging from 3.0 m to 6.8 m. In this paper, geometry parameters of the single rectangular fault model in elastic half-space were inferred constraining with the Global Posi- tioning System （GPS） and Interferometric Synthetic Aperture Radar （InSAR） coseismic deformations and bounding the slip with approximate average value; and then, the single rectangular fault was divided into multiple sub-faults, and the final slip smoothing factor, the final slip distribution and the maximum slip were determined with the misfit-roughness tradeoff curve, the cross-validation sum of squares （CVSS） and the third-party observation data or indexes being comprehensively taken into account. The results show that, the rupture of the Nepal earthquake extended by over 100 km east by south. The maximum slip of the earthquake was about 6.5-6.7 m, and most of the slip is confined at depths of 8 -20 kin, consistent with the depth distribution of aftershocks. The method for reducing the multiplicity of solutions to rupture slip distribution in this paper was ever used in inversion of rupture slip distri- bution for the 2008 Wenchuan and 2013 Lushan earthquakes, and the third-party measurement - surface dislocation has very large effect on reducing the multiplicity of solutions to inversion of the Wenchuan earthquake. Other priori information or indicators, such as fault strike, dip, earthquake magnitude, seismic activity, Coulomb stress, and seismic period, can be used for beneficial validation of and comparison with inversion results.

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL

By the fixed point theorem on a cone and monotone iterativc technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f（t, u） increases in u.

Analysis of prompt fission neutron spectrum and multiplicity for ^(237)Np(n, f) in the frame of multi-modal Los Alamos model

The improved version of Los Alamos model with the multi-modal fission approach is used to analyse the prompt fission neutron spectrum and multiplicity for the neutron-induced fission of 237Np. The spectra of neutrons emitted from fragments for the three most dominant fission modes （standard Ⅰ, standard Ⅱ and superlong） are calculated separately and the total spectrum is synthesized. The multi-modal parameters contained in the spectrum model are determined on the basis of experimental data of fission fragment mass distributions. The calculated total prompt fission neutron spectrum and multiplicity are better agreement with the experimental data than those obtained from the conventional treatment of the Los Alamos model.

Hadron Multiplicity in Pb+Pb Collisions at√s=2.76 TeV from Color Glass Condensate

The pseudo-rapidity distribution of charged hadron multiplicity in Pb+Pb collisions at√s=2.76 TeV is studied by using Color Glass Condensate dynamics in the fixed coupling case.We fit the HERA experimental data with heavy parton mass effect to obtain saturation exponentλ=0.22.It is found that the charged hadron multiplicity can only describe after including heavy parton mass effect due to a large amount of heavy partons produced at large hadron collider(LHC)energy.The pomeron loop effect contribution to hadron production is also investigated.It shows that charged hadron multiplicity is underestimated by including the pomeron loop effect,which indicates that the pomeron loop effect may not exist at LHC energy.

MULTIPLICITY RESULTS FOR AN INHOMOGENEOUS NONLINEAR ELLIPTIC PROBLEM

The author proves that there exist three solutions u(0), u(1) and u(2) in the following problem [GRAPHICS] where some conditions are imposed on Q and f. Here, 0 < u(0) < u(1), u(2) changes sign.

A Remarkable Chord Iterative Method for Roots of Uncertain Multiplicity

In this note we at first briefly review iterative methods for effectively approaching a root of an unknown multiplicity. We describe a first order, then a second order estimate for the multiplicity index m of the approached root. Next we present a second order, two-step method for iteratively nearing a root of an unknown multiplicity. Subsequently, we introduce a novel chord, or a two- step method, not requiring beforehand knowledge of the multiplicity index m of the sought root, nor requiring higher order derivatives of the equilibrium function, which is quadratically convergent for any , and then reverts to superlinear.

STEADY STATE MULTIPLICITY FEATURES OF ETHYLENE OXIDATION ON PLATINUM FOIL

The catalytic oxidation of ethylene to carbon dioxide in excess air has been studied atsteady state.The catalyst temperature was measured for various feed temperature and concentration.The bifurcation diagrams Which describe the dependence of the catalyst temperature on the feed gastemperature were obtained for different ethylene concentrations in the feed gas.The ignition and ex-tinction temperatures were found out and the unique and multiple steady state regions could bedetermined from these diagrams.The experimental results can be satisfactorily explained by thecatastrophe theory and singularity theory.According to the steady state multiplicity features an at-tempt to discriminate the competitive kinetic models was made for the reaction.

Existence and multiplicity of positive solutions for an elastic beam equation

This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.

MULTIPLICITY OF PERIODIC SOLUTIONS FOR SECOND ORDER HAMILTONIAN SYSTEMS WITH MIXED NONLINEARITIES

The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.

MULTIPLICITY OF SOLUTIONS OF WEIGHTED(p, q)-LAPLACIAN WITH SMALL SOURCE

In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system -div（h1（x）｜△u｜p-2△u）=d（x）｜u｜r-2u＋Gu（x,u,v） in Ω -div（h2（x）｜△u｜q-2△v）=f（x）｜v｜s-2v＋Gv（x,u,v） in Ω, u=v=0 on δΩ where Ω is a bounded domain in RN with smooth boundary δΩ, N ≥ 2, 1 〈 r 〈 p ∞, 1〈 s 〈 q 〈 ∞; h1（x） and h2（x） are allowed to have ＂essential＂ zeroes at some points in Ω; d（x）｜u｜r-2u and f（x）｜v｜s-2v are small sources with Gu（x,u,v）, Gv（x,u,v） being their high-order perturbations with respect to （u, v） near the origin, respectively.

e^(+)e^(-)→JETS FOR MULTIPLICITY DISTRIBUTION

The black-body radiation model used in the present work is a statistical model of e^(+)e^(-) jets for hadron multiplicity particle creation.It shows that in terms of Bose-Einstein statistics,kT_(0)∝s^(1/4).The average number,<nch>_(Q),of the charged hadrons is given by statistical theory and SU(3) group calculation.

SOME MULTIPLICITY RESULTS FOR AN ELASTIC BEAM EQUATION AT RESONANCE

This paper deals with multiplicity results for nonlinear elastic equations of the typewheregi[0,1] X R R satisfies Caratheodory condition L2[0,1]. The solvability of this problem has been studied by several authors, but there isn't any multiplicity result until now to the author's knowledge. By combining the Lyapunov-Schmidt procedure with the technique of connected set, we establish several multiplicity results under suitable condition.

Predidtion of the Multiplicity Distributions at Tevatron/LHC Energies and the Approach to Asymptotic KNO Scaling

The multiplicity distributions at Tevatron/large hadron collider(LHC)energies are predicted.The approximate Koba,Neilsen,Olesen(KNO)scaling at lower energies and its violation at above intersectin6 storage ring energy are discussed by using three fire ball model.It is predicted that there will appear a new KNO scaling in multiplicity distributions at asymptotic energy region after LHC.

Analysis of Multiplicity Fluctuations in pp Collisions at 400 GeV/c by Bunching Parameters

The multiplicity fluctuations of charged particles produced in pp collisions at 400 GeV/c have been studied by means of the bunching parameters(BPs).The results show that the values of BPsŋ2(M)andŋ3(M)depend not only on the width of multiplicity distribution,but also on the phase space correlations.The BPs:ŋ2(M)andŋ3(M)follow the same power-law behavior,which indicates that the multifractal structure in pp collisions at 400 GeV/c is observed.