Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model

This paper studies the asymptotic behavior of coexistence steady-states of the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. In the case when either one of two cross-diffusion coefficients tends to infinity, Lou and Ni [18] derived a couple of limiting systems, which characterize the asymptotic behavior of coexistence steady-states. Recently, a formal observation by Kan-on [10] implied the existence of a limiting system including the nonstationary problem as both cross-diffusion coefficients tend to infinity at the same rate. This paper gives a rigorous proof of his observation as far as the stationary problem. As a key ingredient of the proof, we establish a uniform $L^{\infty }$ estimate for all steady-states. Thanks to this a priori estimate, we show that the asymptotic profile of coexistence steady-states can be characterized by a solution of the limiting system.     

Davey-Stewartson系统粗糙爆破解的极限行为

研究了Davey-Stewartson系统(简记为D-S系统)粗糙爆破解的动力学性质.所谓粗糙爆破解即为正则性为H~s(s1)的爆破解,此时D-S系统粗糙解不再满足能量守恒率.利用I-方法与Profile分解理论,得到了D-S系统粗糙爆破解在H~s(R~2)(其中ss_0,且s_0≤(1+11~(1/2))/5≈0.8633)中的极限行为,包括L~2强极限的不存在性与L~2集中性质以及极限图景.     

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.     

Effect of mobile phase anionic additives on selectivity,efficiency, and sample loading capacity of cationic drugs in reversed-phase liquid chromatography

In the present work, we study the effect of mobile phase anionic additive type and concentration on the selectivity, efficiency, and sample loading capacity of cationic drugs in reversed-phase liquid chromatography (RPLC). The type and concentration of an anionic additive are known to have a strong effect on the absolute retention of cations in RPLC; in contrast they have only a small effect on the selectivity of one cation relative to a second as seen here. This is mainly due to the similarity of the ion pair formation constants between the selected cations. The limiting retention factors of cations (i.e. the retention factor of the fully ion-paired analyte at very high additive concentration) are roughly proportional to their inherent hydrophobicities (i.e. the retention factor of the analyte in the absence of the anionic additive). With a given anion, differences in ion pairing strength between the solutes are required for effective selectivity adjustment. Based on the Wade–Lucy–Carr (W–L–C) kinetic model of overload peaks, the approach we developed in our previous work was used to study the effect of mobile phase anionic additives type and concentration on the limiting plate count (N₀) and sample loading capacity (ω_0.5) of various cationic drugs. Under linear chromatographic conditions, where the analyte exhibits its smallest peak width and thus maximum apparent plate count, the type and concentration of anionic additives have almost no effect on peak width. In comparison to neutral analytes the sorption isotherms of cationic species are very easily overloaded even when many fewer moles of cations as compared to neutrals are injected. We showed that different anionic additives profoundly affect the cations’ “overload profiles” (i.e. plots of plate count versus amount injected) by changing the sample loading capacities. The increase in sample loading capacities with different anions show the same order as the extent of ion pairing between the anions and the basic analytes. The detrimental effect of sample overloading on peak width can be greatly diminished by using either a stronger ion pairing agent or a higher concentration of a given ion pairing agent. Both effects operate by increasing the sample loading capacity, thereby allowing more solute to be injected. We believe that the increase in sample loading capacity described above is due in part to the increase in the number of ion-exchange sites as more anions sorb to the stationary phase. At the same time, the formation of a neutral ion-paired analyte also increases the amount of cation which can be loaded onto the stationary phase by allowing a greater fraction of the analyte to be present in the stationary phase as an electrically neutral (i.e. ion-paired) species.     

Transition distributions of young diagrams under periodically weighted plancherel measures

Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.     

On Chebyshev functions and Klee functions

Associated to a lower semicontinuous function, one can define its proximal mapping and farthest mapping. The function is called Chebyshev (Klee) if its proximal mapping (farthest mapping) is single-valued everywhere. We show that the function f is 1/λ-hypoconvex if its proximal mapping Pλf is single-valued. When the function f is bounded below, and Pλf is single-valued for every λ>0, the function must be convex. Similarly, we show that the function f is 1/μ-strongly convex if the farthest mapping Qμf is single-valued. When the function is the indicator function of a set, this recovers the well-known Chebyshev problem and Klee problem in Rn. We also give an example illustrating that a continuous proximal mapping (farthest mapping) needs not be locally Lipschitz, which answers one open question by Hare and Poliquin.     

Self-consistency in non-extensive thermodynamics of highly excited hadronic states

The self-consistency of a thermodynamical theory for hadronic systems based on the non-extensive statistics is investigated. We show that it is possible to obtain a self-consistent theory according to the asymptotic bootstrap principle if the mass spectrum and the energy density increase q-exponentially. A direct consequence is the existence of a limiting effective temperature for the hadronic system. We show that this result is in agreement with experiments.     

Thermal degradation and flame retardance in copolymers of methyl methacrylate with diethyl(methacryloyloxymethyl)phosphonate

Methyl methacrylate (MMA) has been free radically copolymerized, both in bulk and in solution, with diethyl(methacryloyloxymethyl)phosphonate (DEMMP), to give polymers which are significantly flame retarded when compared with PMMA, as indicated by the results of limiting oxygen index (LOI) measurements, UL 94 tests, and the results of cone calorimetric experiments. The physical and mechanical properties of the copolymers are similar to those of PMMA, except that the bulk copolymers are slightly crosslinked, and are better than those of PMMA flame retarded to a similar extent by some phosphate and phosphonate additives. Examination of the some of the gaseous products of pyrolysis and combustion, and of chars produced on burning, show that flame retardation occurs in the copolymers by both a condensed-phase and a vapour-phase mechanism. The condensed-phase mechanism is shown to involve generation of phosphorus acid species followed by reaction of these with MMA units giving rise to methacrylic acid units. The methacrylic acid units subsequently form anhydride links, which probably impede depolymerization of the remaining MMA sequences, resulting in evolution of less MMA (the major fuel when MMA-based polymers burn). By undergoing decarboxylation, leading to interchain cyclisation and, eventually, to aromaticisation, the anhydride units are probably also the principal precursors to char.     

Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications

We consider a class of optimization problems that is called a mathematical program with vanishing constraints (MPVC for short). This class has some similarities to mathematical programs with equilibrium constraints (MPECs for short), and typically violates standard constraint qualifications, hence the well-known Karush-Kuhn-Tucker conditions do not provide necessary optimality criteria. In order to obtain reasonable first order conditions under very weak assumptions, we introduce several MPVC-tailored constraint qualifications, discuss their relation, and prove an optimality condition which may be viewed as the counterpart of what is called M-stationarity in the MPEC-field.     

倾斜煤柱稳定性的弹塑性分析

考虑煤体的塑性软化性质,通过极限平衡法分析了煤层倾角对煤柱稳定性的影响,并通过产例验证了该法的合理性。