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We investigate the well-posedness of $α$-SQG equations in the half-plane, where $α=0$ and $α=1$ correspond to the 2D Euler and SQG equations respectively. For $0, 20 pages, 1 figure

We study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on $\mathbb{S}$. We show that this system is locally well-posed in $L^p, p\geq 1$ as well as for atomic measures, that is logarithmic spiral vortex sheets. In particular, we realize the dynamics of logarithmic vortex sheets as the well-defined limit of logarithmic solutions which could be smooth in the angle. Furthermore, our formulation not only allows for a simple proof of existence and bifurcation for non-symmetric multi branched logarithmic spiral vortex sheets but also provides a framework for studying asymptotic stability of self-similar dynamics. We give a complete characterization of the long time behavior of logarithmic spirals. We prove global well-posedness for bounded logarithmic spirals as well as data that admit at most logarithmic singularities. This is due to the observation that the local circulation of the vorticity around the origin is a strictly monotone quantity of time. We are then able to show a dichotomy in the long time behavior, solutions either blow up (either in finite or infinite time) or completely homogenize. In particular, bounded logarithmic spirals should converge to constant steady states. For logarithmic spiral sheets, the dichotomy is shown to be even more drastic where only finite time blow up or complete homogenization of the fluid can and does occur., Comment: 21 pages, 2 figures

We perform asymptotic analysis for the Euler--Riesz system posed in either $\mathbb{T}^d$ or $\mathbb{R}^d$ in the high-force regime and establish a quantified relaxation limit result from the Euler--Riesz system to the fractional porous medium equation. We provide a unified approach for asymptotic analysis regardless of the presence of pressure, based on the modulated energy estimates, the Wasserstein distance of order $2$, and the bounded Lipschitz distance., Comment: 19 pages

We provide a simple proof that the Cauchy problem for the incompressible Euler equations in $\mathbb{R}^{d}$ with any $d\ge3$ is ill-posed in critical Sobolev spaces, extending an earlier work of Bourgain and Li in the case $d = 3$. The ill-posedness is shown for certain critical Lorentz spaces as well., Comment: To appear in J. Funct. Anal

We show that the log-H��lder coefficients of a solution to the transport equation is preserved in time., 8 pages

We consider axisymmetric incompressible inviscid flows without swirl in $\mathbb{R}^3$, under the assumption that the axial vorticity is non-positive in the upper half space and odd in the last coordinate, which corresponds to the flow setup for head-on collision of anti-parallel vortex rings. For any such data, we establish monotonicity and infinite growth of the vorticity impulse on the upper half-space. As an application, we achieve infinite growth of Sobolev norms for certain classical/smooth and compactly supported vorticity solutions in $\mathbb{R}^{3}$., Comment: 33 pages, 1 figure; several results have been improved from the previous version

For the axisymmetric incompressible Euler equations, we prove linear in time filamentation near Hill's vortex: there exists an arbitrary small outward perturbation growing linearly for all times. This is based on combining the recent nonlinear orbital stability obtained in [13] with a dynamical bootstrapping scheme for particle trajectories. These results rigorously confirm numerical simulations by Pozrikidis [45] in 1986., Comment: 32 pages, 1 figure, minor corrections

We consider the 3D incompressible Navier-Stokes equations under the following $2+\frac{1}{2}$-dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove anomalous dissipation induced by such vortex-stretching., Comment: To appear in Math. Annal

We consider vortex patch solutions of the incompressible Euler equations in the plane. It is shown that the winding number around the origin for most particles in the patch grows linearly in time when the initial patch is close to a disk enough., Comment: 11 pages, the condition for the origin to be fixed was removed

In this paper and the companion paper [EJE2], we establish finite-time singularity formation for finite-energy strong solutions to the axi-symmetric $3D$ Euler equations in the domain $\{(x,y,z)\in\mathbb{R}^3:z^2\leq c(x^2+y^2)\}$ for some $c>0$. In the spirit of our previous works, [EJSI] and [EJB], we do this by first studying scale-invariant solutions which satisfy a one dimensional PDE system and proving that they may become singular in finite time for properly chosen initial data. We then prove local well-posedness for the $3D$ Euler equations in a natural regularity class which includes scale-invariant solutions. While these solutions have uniformly bounded vorticity from time zero until right before the blow-up time, they do not have finite energy. To remedy this, we cut off the scale-invariant data to ensure finite energy and prove that the corresponding local solution must also become singular in finite time. This paper focuses only on the analysis of the scale-invariant solutions themselves and the proof that they can become singular in finite time. The local well-posedness theorem and the cut-off argument are very close to those in [JSI] and [EJB] and are left for the companion paper [EJE2]. It is important to remark that while the fluid domain is the exterior of a cone, we prove global regularity for the axi-symmetric $3D$ Euler equations without swirl in the exact same regularity classes and in the same domain. It is quite possible that the methods we use can be adapted to establish finite-time singularity formation for $C^\infty$ finite-energy solutions to the $3D$ Euler equations on $\mathbb{R}^3_+$., There was a sign error in the version of the axi-symmetric Euler equations that we have adopted. While Theorems A and D remain valid as stated, it is unclear whether finite-time singularity formation results hold for the systems with correct signs

This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 + x_2^2) \}$ for $\mathfrak{c}$ sufficiently small in a scale of critical spaces. Second, we will prove that if the vorticity at $t=0$ can be decomposed into a scale-invariant part and a smoother part vanishing at $x=0$, then this decomposition remains valid for $t>0$ so long as the solution exists. This will then immediately imply singularity formation for finite-energy solutions in those critical spaces using that there are scale-invariant solutions which break down in finite time (this was proved in the companion paper [EJE1]). Third, we establish global regularity in the same domain and in the same scale of critical spaces for $0-$swirl solutions to the system. This implies that the finite-time singularity is not coming from the domain or the critical regularity of the data (though, these are important for the present construction), they are coming from a genuine vorticity growth mechanism due to the presence of the swirl. This work and the companion work seem to be the first case when this mechanism has been effectively used to establish finite-time singularity formation for the actual $3D$ Euler system., There was a sign error in the version of the axi-symmetric Euler equations that we have adopted, and therefore there are corresponding sign errors in the 1D system that we have derived

This paper shows a reinforced construction scheme of training data for improvement of text classification by automatic search of boundary category. The documents laid on boundary area are usually misclassified as they are including multiple topics and features. which is the main factor that we focus on. In this paper, we propose an automated exploring methodology of optimal boundary category based on previous research. We consider the boundary area among target categories to new category to be required training, which are then added to the target category sementically. In experiments, we applied our method to complex documents by intentionally making errors in training process. The experimental results show that our system has high accuracy and reliability in noisy environment.

For the $2D$ Euler equation in vorticity formulation, we construct localized smooth solutions whose critical Sobolev norms become large in a short period of time, and solutions which initially belong to $L^\infty \cap H^1$ but escapes $H^1$ immediately for $t>0$. Our main observation is that a localized chunk of vorticity bounded in $L^\infty \cap H^1$ with odd-odd symmetry is able to generate a hyperbolic flow with large velocity gradient at least for a short period of time, which stretches the vorticity gradient., 16 pages, 2 figures

A parametric study was carried out to improve the cyclic performance of the three-bed pressure−vacuum swing adsorption (PVSA) process, which consisted of two zeolite 10X beds for equilibrium separa...

To produce O2 with a high purity of 99+% and a high productivity from various oxygen-rich feeds, a parametric study was done on a six-step pressure swing adsorption (PSA) purifier using carbon molecular sieve (CMS). The cyclic performances of the PSA process such as purity, recovery, and productivity were compared under nonisothermal conditions. To study the effects of N2 amount on the PSA purifier, various feeds with 90% O2 or more were experimentally and theoretically applied for the PSA process. Since N2 plays a key role in product purity, the maximum purity of the PSA was 99% O2 with 51.5% recovery from a higher nitrogen feed (O2:Ar:N2; 90:4:6 vol %) and 99.8% O2 with 56.9% recovery from a lower nitrogen feed (O2:Ar:N2; 95:4:1 vol %) within the experimental range. The adsorption step time and feed flow rate served as key operating variables in the purification of the oxygen-rich feeds because the concentration wave fronts of minor impurities such as N2 and Ar were controlled by kinetic selectivity. To...

The adsorption dynamics of N2, O2, and Ar in kinetic separation bed with CMS and equilibrium separation bed with zeolite 13X were investigated by using dried air as a feed. In the CMS bed initially saturated with He, Ar was the first breakthrough component showing a small roll-up and N2 followed at a very close interval. Then, the breakthrough of O2 occurred with a broad roll-up due to its fast diffusion rate and the relatively slow diffusion rate of N2. In the zeolite 13X bed initially saturated with O2, the breakthrough of Ar first occurred with roll-up owing to the strong adsorption of N2, then the breakthrough of N2 followed after a very short interval. Based upon these results, the cyclic adsorption dynamics of the zeolite 13X VSA for air bulk separation and CMS PSA for oxygen purification were studied. The five-step two-bed O2 VSA with zeolite 13X produced O2 of over 90% purity with high recovery. The MTZ variation of N2 during the adsorption and vacuum steps was described in detail. In the case of the six-step two-bed PSA process for O2 purification, O2 of 99.8+% purity could be produced from the binary mixture (O2/Ar—95:5 vol.%). The dynamic adsorption behaviors were investigated by using a concentration-dependent rate model incorporated with mass, energy, and momentum balances. The model reasonably predicted the adsorption dynamics at the equilibrium and kinetic separation beds.

Four different pressure swing adsorption (PSA) cycles using CMS for oxygen purification were developed to produce high-purity oxygen of over 99% with a high level of productivity. The cyclic performances such as purity, recovery, and productivity of the four different PSA cycles were experimentally and theoretically compared under non-isothermal conditions. In addition, one binary (O 2 /Ar; 95:5 vol%) and two ternary (O 2 /Ar/N 2 ; 95:4:1 and 90:4:6 vol%) mixtures were used to study the effects of feed composition. The PSA cycles with two consecutive blowdown steps produced oxygen with 98.0–99.9% purity and 56–66% recovery. The PSA cycle with oxygen generation in the second blowdown step produced oxygen with a higher level of purity and productivity. Also, the cycle introducing a pressure equalization step instead of a pure step produced oxygen with about 99.8% purity and 78% recovery. The period for the cyclic steady state of the ternary feed with 1% N 2 was slightly longer than that of the binary feed, while the PSA performance of the ternary feed was similar to that of the binary feed without nitrogen. However, in the ternary feed with 6% N 2 , the purity of the O 2 in the purification cycles decreased by up to 97.3%. Therefore, nitrogen played a key role in producing high-purity oxygen in the CMS PSA instead of argon.

A three-bed PVSA (pressure vacuum swing adsorption) process, combining equilibrium separation with kinetic separation, was developed to overcome the 94% O2 purity restriction inherent to air separation in the adsorption process. To produce 97+% and/or 99+% purity O2 directly from air, the PVSA process with two zeolite 10X beds and one CMS bed was executed at 33.44–45.60 to 253.31 kPa. In addition, the effluent gas from the CMS bed to be used for O2 purification was backfilled to the zeolite 10X bed to improve its purity, recovery, and productivity in bulk separation of the air. PVSA I, which made use of a single blowdown/backfill step, produced an O2 product with a purity of 95.4–97.4% and a recovery of 43.4–84.8%, whereas PVSA II, which used two consecutive blowdown/backfill steps, produced O2 with a purity of 98.2–99.2% and a recovery of 47.2–63.6%. Because the primary impurity in the O2 product was Ar, the amounts of N2 contained in the product were in the range of 4000–5000 ppm at PVSA I and several tens of ppm at PVSA II. A nonisothermal dynamic model incorporating mass, energy, and momentum balances was applied to predict the process dynamics. Using the linear driving force (LDF) model with constant diffusivity for the equilibrium separation bed and a modified LDF model with concentration dependency of the diffusion rate for the kinetic separation bed, the dynamic model was able to accurately predict the results of the experiment. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Adsorption and desorption in zeolite 5A and CMS beds were compared by using a ternary mixture (N 2/ O2/Ar; 78 : 21 : 1 vol%). Because the breakthrough curves for both beds show a tail by temperature variance, a non- isothermal mathematical model was applied to the simulation of adsorption dynamics. The LDF model with a constant rate parameter was enough to predict the experimental brea kthrough and temperature curves of an equilibrium separa- tion bed, while the modified LDF model with a concentrati on-dependent parameter should be applied to a kinetic sep- aration bed. In the CMS bed initially saturated with He, Ar was the first breakthrough component with N 2 following after a short interval. Then, after a long interval, the breakthrough of O 2 occurred with a broad roll-up due to its fast diffusion rate and the relative ly slow diffusion rate of N 2. In the CMS bed initially saturated with O 2, the breakthrough curves of O2 and N2 showed a very broad shape because of the slow diffusion of N 2 into CMS. In the zeolite 5A bed, the breakthrough time sequence was Ar, O2, and N2 at very close time intervals. After the sharp roll-ups of O 2 and Ar, the variation of the breakthrough curves was negligible. The in flection of the temperature profile in the zeolite 5A bed was caused by the crossover of the O 2 and N2 MTZs, while in the CMS bed it was caused by the difference in the diffu- sion rates of O2 and N2.

Object tracking in a real time image is one of Interesting subjects in computer vision and many practical application fields past couple of years. But sometimes existing systems cannot find object by recognize background noise as object. This paper proposes a method of object detection and tracking using adaptive background image in real time. To detect object which does not influenced by illumination and remove noise in background image, this system generates adaptive background image by real time background image updating. This system detects object using the difference between background image and input image from camera. After setting up MBR(minimum bounding rectangle) using the internal point of detected object, the system tracks object through this MBR. In addition, this paper evaluates the test result about performance of proposed method as compared with existing tracking algorithm.

Adsorption and desorption experiments for the binary mixture (N2/O2; 79:21 vol%) on zeolite 5A, 10X, and 13X beds were performed to study the dynamic characteristics of air separation adsorption processes. Because the breakthrough and desorption curves showed a tail by temperature variance in the beds, a nonisothermal dynamic model incorporating mass and energy balances was applied to the simulation of adsorption dynamics using the Langmuir–Freundlich model and the LDF approximation. The breakthrough and desorption results were compared among three different beds with respect to the breakthrough and desorption times, tailing effect, and temperature variation with the effects of pressure and flow rate. On the basis of the similar bed density, the order of breakthrough time and desorption time was zeolite 10X, 13X, and 5A beds. Also, the O2 MTZ of the zeolite 10X bed was slightly sharper than those of the zeolite 5A and 13X beds due to more favorable N2 isotherm of zeolite 10X. Furthermore, the breakthrough...

Adsorption characteristics in a layered bed packed with activated carbon and zeolite 5A were studied experimentally and theoretically through the breakthrough experiments of binary (H2/CO, H2/CH4, H2/CO2), ternary (H2/CH4/CO), and five-component (H2/CH4/CO/N2/CO2) systems. The effects of adsorption pressure, feed flow rate, and carbon-to-zeolite ratio on the breakthrough curve in a layered bed were observed. Breakthrough curves in all of the mixtures showed tailing due to temperature variance in the bed by the heat of adsorption. In the layered bed, each mixture showed the specific characteristics of concentration and temperature wave fronts in each layer. Although the amount of impurity in a ternary mixture is larger than that in a binary mixture, the breakthrough time and elongation depending on the adsorption pressure and flow rate showed an intermediate value between the results of the H2/CO and H2/CH4 mixtures, and the tailing was not much different from those in these binary systems. Also, the roll-...

Objective Many dental patients take bisphosphonates to reduce the risk of hip and vertebral fractures. In vivo micro–computed tomography (micro-CT) was used to examine the longitudinal inhibitory effect of alendronate on the healing of extraction sockets in ovariectomized rats. Study design Twenty 5-week-old Sprague-Dawley rats were assigned randomly to 1 of 3 groups: sham-operated (n = 5), and 2 ovariectomized (OVX) groups: saline treated (0.1 mL/100 g/d, n = 7) and alendronate treated (1 mg/kg/d, n = 8). Before micro-CT scanning, the left maxillary first molars of the rats were extracted. In vivo micro-CT (spatial resolution 50 × 50 μm) of the jaw was performed at baseline and at 2-week intervals for 6 weeks. Alveolar-bone radiographic densities and dimensions were analyzed with repeated measures analysis of variance. The bony healing patterns of the extraction sockets were also evaluated in each group. Result The radiographic socket densities of the sham-treated and OVX-alendronate groups significantly increased during the first 4 weeks after extraction (P < .05). At 2 weeks, the radiographic densities of the sockets in the OVX-saline group increased, but the increase was significantly lower than for the other groups at 4 weeks (P < .05). Newly formed bone was identified in the extraction sockets in all groups 2 to 6 weeks after extraction. There was a significant loss of alveolar ridge height at the second week postextraction compared with baseline, and at the fourth week compared with the second week (P < .05) except in the alendronate group. Conclusion Alendronate appears to promote the healing of extraction sockets in estrogen-deficient rats and helps resist the loss of alveolar bone adjacent to extraction sockets.

This paper develop the complexity reduction schemes of real root method that is mainly used in the CELP (Code Excited Linear Prediction) vocoder. The real root method is that if polynomial equations have the real roots, it is able to find those and transform them into LSP (Line Spectrum Pairs). Proposed algorithm is developed by using Mel scale and is to reduce the LSP complexity That is, the searching interval is arranged by using Mel scale but not it is uniform. In experimental results, complexity of the developed algorithm is reduced about 46% in average, but the transformed LSP parameters of the proposed method were the same as those of real root method. Hence, in case of applying proposed algorithm in G.723.1 (6.3kbps MP-MLQ), the speech quality is no distortion compared to original speech quality.

This paper proposes more various key generation algorithms than conventional encryption method, and more secure encryption method that does not keep each symmetric key of key generation algorithm in server. After implementing proposed system, we verify the system using various sizes of video data. We get the fact that proposed system can reduce the delay time of encryption and decryption at the replay of video data.

Objective: To evaluate the therapeutic effects of a preformed assembly of nickel-titanium (NiTi) and stainless steel (SS) archwires (preformed C-wire) combined with temporary skeletal anchorage devices (TSADs) as the sole source of anchorage and to compare these effects with those of a SS version of C-wire (conventional C-wire) for en-masse retraction. Methods: Thirty-one adult female patients with skeletal Class I or II dentoalveolar protrusion, mild-to-moderate anterior crowding (3.0?6.0 mm), and stable Class I posterior occlusion were divided into conventional (n = 15) and preformed (n = 16) C-wire groups. All subjects underwent first premolar extractions and en-masse retraction with pre-adjusted edgewise anterior brackets, the assigned C-wire, and maxillary C-tubes or C-implants; bonded mesh-tube appliances were used in the mandibular dentition. Differences in pretreatment and post-retraction measurements of skeletal, dental, and soft-tissue cephalometric variables were statistically analyzed. Results: Both groups showed full retraction of the maxillary anterior teeth by controlled tipping and space closure without altered posterior occlusion. However, the preformed C-wire group had a shorter retraction period (by 3.2 months). Furthermore, the maxillary molars in this group showed no significant mesialization, mesial tipping, or extrusion; some mesialization and mesial tipping occurred in the conventional C-wire group. Conclusions: Preformed C-wires combined with maxillary TSADs enable simultaneous leveling and space closure from the beginning of the treatment without maxillary posterior bonding. This allows for faster treatment of dentoalveolar protrusion without unwanted side effects, when compared with conventional C-wire, evidencing its clinical expediency.