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A boundary value problem for the stationary Boltzmann equation with hard sphere in a half-space is considered for a binary mixture of gases, imposing slightly perturbed reflection boundary conditio...

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 deal with the relativistic Boltzmann equation in the whole space ${\mathbb{R}}_{x}^{3}$ under the closed to equilibrium setting. We obtain the existence, uniqueness, and large tim...

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.

Enterovirus 71 (EV71) is considered one of the most virulent pathogens in the family Picornaviridae. However, there have been no effective treatments for the severe complications caused by EV71. Development of new drugs against targets that are essential for viral replication often requires screening large collections of compounds, for which a high-throughput screening platform is needed. In this study, a drug-screening platform was developed based on a genetically engineered cell line that displays fluorescence resonance energy transfer (FRET) and shows a real-time and quantifiable impairment of FRET upon EV71 infection. A library of small molecules consisting of 1280 compounds with defined bioactivities was used for screening drugs with anti-EV71 activity; accurate, rapid, and robust results were obtained from this screening procedure. Ten drugs were identified in the primary screening, and their antiviral activities were indicated by dose-dependent elevation of FRET. Among these, AC-93253, mitoxantrone and N-bromoacetamide had not been reported as enterovirus inhibitors, and it was confirmed that they were able to suppress viral yields in a dose-dependent manner. Taken together, these studies demonstrate the feasibility of this FRET-based platform for efficient screening and identification of novel compounds with activity against EV71 infection.

We discuss several examples of non-parabolic curve flows in the plane. In these flows, the speed functions do not involve the curvature at all. Although elementary in nature, there are some interesting properties. In particular, certain non-parabolic flows can be employed to evolve a convex closed curve to become circular or to evolve a non-convex curve to become convex eventually, like what we have seen in the classical curve shortening flow (parabolic flow) by Gage and Hamilton (J Differ Geom 23:69–96, 1986), Grayson (J Differ Geom 26:285–314, 1987).

The main goal is to understand the quantitative spatial decay of the solution to the linearized Boltzmann equation for hard potentials with cutoff. We obtain the quantitative space-time behavior of the linearized Boltzmann equation under some slow velocity decay assumption but without any regularity assumption on the initial data. This result extends the classical results of Liu and Yu [Commun. Pure Appl. Math. 57, 1543–1608 (2004); Bull. Inst. Math. Acad. Sin. 1, 1–78 (2006); and ibid. 6, 151–243 (2011)] from hard sphere to hard potential under the same assumption on the initial condition [compactly support in the space variable and polynomial decay in the velocity variable with power β = (3/2)+].

This article reports on a large scale randomized controlled trial to study the efficacy of a web-based intelligent tutoring system for the structure strategy designed to improve content area reading comprehension. The research was conducted with 128 fifth-grade classrooms within 12 school districts in rural and suburban settings. Classrooms within each school were randomly assigned to intervention or control groups. The intervention group used the intelligent web-based tutoring system for the structure strategy (ITSS) for 30 to 45 min each week as a partial substitute for the language arts curriculum for the entire school year. The structure strategy teaches students how to read and comprehend expository texts by identifying the text structure and creating strategic mental representations of the text. The web-based tutoring system delivered the structure strategy training with modeling, practice tasks, assessment, and feedback. The control classrooms used the school's language arts curriculum for ...

Display Omitted We propose a simple and cost-effective method of immersion interference lithography.It allows close contact with the solid coupling medium without index matching liquid.The photoresist is kept free from the contamination of liquid.The solid coupling medium improves the resolution by a factor of its refractive index.We obtained a 58-nm half-pitch grating, which corresponds to a feature size of 0.18λ. This study proposes a simple and cost-effective method of solid immersion interference lithography that uses a conformable phase mask. Perfluoropolyether based polymer was used as the material of the elastomeric phase mask. The proposed method requires no liquid layer to function as the coupling medium or the index matching layer and keeps the photoresist free from the contamination of liquid. The solid coupling medium improves the resolution of interference fringes by a factor of its refractive index. This study presents an exposed interference fringe with a half-pitch of 58nm using a He-Cd laser with λ=325nm, which corresponds to a feature size of λ/5.6.

We consider the expansion of a convex closed plane curve C0 along its outward normal direction with speed G(1/k), where k is the curvature and \({G \left(z \right) :\left(0, \infty \right) \rightarrow \left( 0, \infty \right)}\) is a strictly increasing function. We show that if \({{\rm lim}_{z \rightarrow \infty} G \left(z \right) = \infty}\), then the isoperimetric deficit \({D \left(t \right) : = L^{2}\left(t \right) -4 \pi A \left(t \right)}\) of the flow converges to zero. On the other hand, if \({{\rm lim}_{z \rightarrow \infty}G \left(z \right) = \lambda \in (0,\infty)}\), then for any number d ≥ 0 and \({\varepsilon > 0}\), one can choose an initial curve C0 so that its isoperimetric deficit \({D \left(t \right)}\) satisfies \({\left \vert D \left(t \right) -d \right \vert < \varepsilon}\) for all \({t \in [0, \infty)}\). Hence, without rescaling, the expanding curve Ct will not become circular. It is close to some expanding curve Pt, where each Pt is parallel to P0. The asymptotic speed of Pt is given by the constant \({\lambda}\).

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.

A short version of the Counseling Center Assessment of Psychological Symptoms–62 (CCAPS-62) was created via three studies. The final short version (CCAPS-34), which contains 34 items and 7 subscale...

We shall apply certain inequalities by Andrews and Green-Osher to area-preserving and length-preserving flows of convex plane curves and show that, if we have bound on the curvature, the evolving curves will converge to a round circle.

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

Design and fabrication of transparent and superhydrophilic self-cleaning thin films on glass substrate by 7 nm TiO 2 /22 nm SiO 2 all-nanoparticle coatings via aqueous electrostatic layer-by-layer assembly processing were demonstrated in this work. Stable and conformal structure of multibilayer (TiO 2 /SiO 2 ) x with x up to 120 was shown to exhibit antireflective, superhydrophilic, and self-cleaning multifunctional properties. This was achieved by using appropriate periodic calcinations rather than only once calcination of the assembled nanoparticulate thin films. Average refractive index of 1.30 ± 0.03 at 633 nm and average bilayer thickness of 20.18 nm were determined for the as-fabricated nanoparticulate thin films. Furthermore, average transmittance values higher than 93.5% were exhibited by all the nanoparticulate thin films and the experimental results were only at the very most of 2% lower than those predicted by the theory. The self-cleaning properties of the nanoparticulate thin films were revealed by the decomposition of two model contaminants under UV illumination. The experimental results showed that the photocatalytic decomposition rates are increased with the increase of bilayer number of the nanoparticulate thin film.

In the study, we investigated effects of 2 different versions of a web-based tutoring system to provide 5th-grade students with strategy instruction about text structure, which was an intervention to improve reading comprehension. The design feature assessed varied in individualization of instruction (individualized or standard). The more individually tailored version was developed to provide remediation or enrichment lessons matched to the individual needs of each student. Stratified random assignment was used to compare the effects of 2 versions of the 6-month web-based intervention. Students in the individualized condition made greater improvements from pretest to posttest on a standardized reading comprehension test (d 0.55) than did students in the standard condition (d 0.30). Students receiving more individualized instruction demonstrated higher mastery achievement goals when working in the lessons than did students receiving the standard instruction (d 0.53). Students receiving more individualized instruction showed greater improvement in using signaling, better work in lessons, and more positive posttest attitudes toward computers than did students receiving standard instruction. Students in both conditions improved their recall of ideas from texts and their use of the text structure strategy and comparison signaling words.

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 .

A retrograde orbit of the planar three-body problem is a relative periodic solution with two adjacent masses revolving around each other in one direction while their mass center revolves around the third mass in the other direction. The orbit is said to be prograde or direct if both revolutions follow the same direction. Let T > 0 and \({\phi\in[0,2\pi)}\) be fixed, and consider the rotating frame which rotates the inertia frame about the origin with angular velocity \({\frac{\phi}{T}}\) . In a recent work of K.-C.Chen [5], the existence of action-minimizing retrograde orbits which are T-periodic on this rotation frame were proved to exist for a large class of masses and a continuum of \({\phi}\) . In this paper we generalize the main result in [5], provide some quantitative estimates for admissible masses and mutual distances, and show miscellaneous examples of action-minimizing retrograde orbits. We also show the existence of some prograde and retrograde solutions with additional symmetries.

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).

Wireless Sensor Networks is dispersed by a group composed of sensors and Base Stations. It can be used in various applications of remote monitoring system. Sensor nodes route the collected data to the Base Station via multi-hop wireless links. These sensors typically use batteries to operate, the battery cannot be replaced when the depletion of energy resources. Therefore, how to use energy-saving sensor networks to extend the overall working time efficiently is an important subject. Our research is based on "A Power Control Mechanism based on Sleep Scheduling for Wireless Sensor Networks". We proposed a refined mechanism of routing protocol for wireless sensor networks with sleep scheduling. In wireless sensor network with sleep scheduling, active node adjusts its working time and each step in sleeping state earlier. In the multi-hop transmission mode, each node broadcasts the packet to confirm the receiving node. Therefore, we use routing information to reduce the number of broadcasting during transmission. When route node with low rest power cannot transfer, in order to remain completed route, we can execute interrupt handler procedure to reduce the package loss. Finally, to achieve power efficiency, we will simulate if the proposed algorithm can reduce energy consumption effectively in the data transmission procedure.

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.