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A stationary boundary-value problem for the Boltzmann equation in a half space is considered for a binary mixture of gases when the indata on the boundary are given for the both species. Under the assumption that one of the species is dominant and close to equilibrium but the density of the other is small, the problem is decomposed into two half-space problems: the so-called Milne problem for the linearized Boltzmann equation with a source term for the dominant species and that for the linear Boltzmann equation for the low-density species. The two problems are coupled in such a way that the source term in the former is specified by the solution of the latter. The existence and uniqueness of the solutions to the two problems are proved, and their accurate asymptotic behavior in the far field is obtained. In particular, the precise rate of approach of the solution to the state at infinity is expressed in terms of the decay rate in the molecular velocity of the boundary data for both species.

In this paper, we get the quantitative space-time behavior of the full Boltzmann equation with soft potentials ($-2

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad’s angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543–1608, 2004), (Bull Inst Math Acad Sin 1:1–78, 2006), (Bull Inst Math Acad Sin 6:151–243, 2011) and Lee et al. (Commun Math Phys 269:17–37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

We study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption on the initial data, it is shown that the solution becomes smooth instantaneously in both the space and momentum variables. Moreover, the large time behavior of the solution is also obtained.

This paper studies the use of simulated recordings to perform audio identification experiments. In contrast to use actual recordings in the experiments, we use the measured room impulse response to generate simulated recordings. Doing so greatly reduces the burden of manually recording audio items for experiments. By comparing the correlations between actual and simulated recordings, we conclude that this approach is highly possible. The audio identification experiments are conducted based on the moving picture expert group audio signature descriptors to represent the simulated recordings. We also add environmental noises, provided by European Telecommunications Standards Institute, to the simulated recordings to study the performance degradation. Finally, we study if performing filtering in the descriptor domain can improve the accuracy. The experimental results show that filtering in the frequency direction yields higher accuracy for signal to noise ratio of 10 dB items.

We study the pointwise (in the space and time variables) behavior of the Fokker-Planck Equation with flat confinement. The solution has very clear description in the $xt-$plane, including large time behavior, initial layer and asymptotic behavior. Moreover, the structure of the solution highly depends on the potential function.

We study the contraction of a convex immersed plane curve with speed (1/{\alpha})k^{{\alpha}}, where {\alpha}in(0,1] is a constant and show that, if the blow-up rate of the curvature is of type one, it will converge to a homothetic self-similar solution. We also discuss a special symmetric case of type two blow-up and show that it converges to a translational self-similar solution. In the case of curve shortening flow (i.e., when {\alpha}=1), this translational self-similar solution is the familiar "Grim Reaper" (a terminology due to M. Grayson [GR])., Comment: 24 pages, 3 figures

We use the Aleksandrov reflection result of Chow and Gulliver to show that the center of expansion in expanding a given convex embedded closed curve γ 0 C ℝ 2 lies on a certain convex plane region interior to γ 0 .

For a class of general quasilinear equations on S 1 , we show that, by a very simple maximum principle technique, as long as the solution stays finite, all of its derivatives also remain finite. Some specific examples are given. Under suitable assumptions, we also derive exponential decay of the derivatives of the solution.

We examined three questions. First, do reading difficulties increase children’s risk of behavior difficulties? Second, do behavioral difficulties increase children’s risk of reading difficulties? Third, do mathematics difficulties increase children’s risk of reading or behavioral difficulties? We investigated these questions using a sample of 9,324 children followed from third to fifth grade as they participated in a nationally representative dataset, conducting multilevel logistic regression modeling and including statistical control for many potential confounds. Results indicated that poor readers in third grade were significantly more likely to display poor task management, poor self-control, poor interpersonal skills, internalizing behavior problems, and externalizing behavior problems in fifth grade (odds ratio [OR] range = 1.30 – 1.57). Statistically controlling for a prior history of reading difficulties, children with poor mathematics skills in third grade were also significantly more likely to display poor task management, poor interpersonal skills, internalizing behavior problems, and reading difficulties in fifth grade (OR range = 1.38 – 5.14). In contrast, only those children exhibiting poor task management, but not other types of problem behaviors, in third grade were more likely to be poor readers in fifth grade (OR = 1.49).

Motivated by a recent curvature flow introduced by Professor S.-T. Yau [S.-T. Yau, Private communication on his “Curvature Difference Flow”, 2007], we use a simple curvature flow to evolve a convex closed curve to another one (under the assumption that both curves have the same length). We show that, under the evolution, the length is preserved and if the curvature is bounded above during the evolution, then an initial convex closed curve can be evolved to another given one.

We examined three questions. First, do reading difficulties increase children's risk of behavioral difficulties? Second, do behavioral difficulties increase children's risk of reading difficulties? Third, do mathematics difficulties increase children's risk of reading or behavioral difficulties? We investigated these questions using (a) a sample of 9,324 children followed from third to fifth grade as they participated in a nationally representative dataset, (b) multilevel logistic regression modeling, and (c) statistical control for many potential confounds. Results indicated that poor readers in third grade were significantly more likely to display poor task management, poor self-control, poor interpersonal skills, internalizing behavior problems, and externalizing behavior problems in fifth grade (odds ratio [OR] range = 1.30–1.57). Statistically controlling for a prior history of reading difficulties, children with poor mathematics skills in third grade were also significantly more likely to display poor task management, poor interpersonal skills, internalizing behavior problems, and reading difficulties in fifth grade (OR range = 1.38–5.14). In contrast, only those children exhibiting poor task management, but not other types of problem behaviors, in third grade were more likely to be poor readers in fifth grade (OR = 1.49). Poor readers in third grade were extremely likely to still be poor readers in fifth grade (OR = 19.69).

Infectious antigens may be triggers for the exacerbation of systemic lupus erythematosus. The underlying mechanism causing acceleration and exacerbation of lupus nephritis (LN) is largely unknown. Bacterial lipopolysaccharide (LPS) is capable of inducing an accelerated model of LN in NZB/W mice, featuring diffuse proliferation of glomerular resident cells. We hypothesized that mesangial cells (MCs) from LN subjects are more responsive to LPS than normal subjects. Cultured primary NZB/W and DBA/W (nonautoimmune disease-prone strain with MHC class II molecules identical to those of NZB/W) MCs were used. Monocyte chemoattractant protein-1 (MCP-1) and osteopontin (OPN) expressions either in the baseline (normal culture) condition or in the presence of LPS were evaluated by real-time PCR, ELISA, or western blot analysis. NF-kappaB was detected by ELISA, electrophoresis mobility-shift assay, and immunofluorescence. First, either in the baseline condition or in the presence of LPS, NZB/W MCs produced significantly higher levels of MCP-1 and OPN than the DBA/W MC controls. Second, NZB/W MCs expressed significantly higher levels of Toll-like receptor 4, myeloid differentiation factor 88, and NF-kappaB than the DBA/W MC controls, both receiving exactly the same LPS treatment. In conclusion, NZB/W MCs are significantly more sensitive than their normal control DBA/W MCs in producing both MCP-1 and OPN. With LPS treatment, the significantly elevated levels of both chemokines produced by NZB/W MCs are more likely due to a significantly greater activation of the Toll-like receptor 4-myeloid differentiation factor 88-associated NF-kappaB pathway. The observed abnormal molecular events provide an intrarenal pathogenic pathway involved in an accelerated type of LN, which is potentially infection triggered.