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Summary: The existence, solution structure, and equivalence of sparse control for linear time‐varying systems are investigated. We proved the existence of the optimal solution of sparse control for the linear time‐varying systems. By using the non‐smooth maximum principle, we are given the necessary conditions for the sparse control optimality for linear time‐varying systems. We proved that the optimal solution of sparse control taking values of ±1$$ \pm 1 $$ and 0. Under the normality of the linear time‐varying systems, we proved an equivalence theorem between the sparse control and L1$$ {L}^1 $$ optimal control. Numerical examples are included to illustrate the effectiveness of the sparse control for linear time‐varying systems. [ABSTRACT FROM AUTHOR]

In this paper, for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get the uniqueness of the conservative solution in the original variables. [ABSTRACT FROM AUTHOR]

A coplanar energetic salt (3) was designed and synthesized by protonation and hydrogen bonding assembly. X-ray single crystal diffraction data and theoretical calculations indicate that the incorporation of protons and robust hydrogen bonding is crucial to the planarization of the twisted molecule (1). The planarized energetic salt 3 with layer-by-layer stacking is more insensitive compared to its analogue compound 1. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the Cauchy problem of a weakly dissipative Camassa-Holm equation. We first establish the local well-posedness of equation in Besov spaces B p , r s with s > 1 + 1 p and s = 1 + 1 p , r = 1 , p ∈ [ 1 , ∞). Then, we prove the global existence for small data, and present two blow-up criteria. Finally, we get two blow-up results, which can be used in the proof of the ill-posedness in critical Besov spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the existence and uniqueness of globally weak solutions to the Cauchy problem for the weakly dissipative Camassa–Holm equation in time weighted H1 space. First, we derive an equivalent semi-linear system by introducing some new variables, and present the globally conservative solutions of this equation in time weighted H1 space. Second, given a globally conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system has a unique solution. In turn, we get the uniqueness of the conservative solutions in the original variables. Finally, we show that the peakon solutions are conservative weak solutions in H1. [ABSTRACT FROM AUTHOR]

For the famous Camassa-Holm equation, the well-posedness in C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 1 ≤ p ≤ 2 and the ill-posedness in C ([ 0 , T ] ; B ∞ , 1 1 (R)) had been studied in [15,16,23]. That is to say, it left an open problem in the critical case C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 2 < p < + ∞ proposed by Danchin in [15,16]. In this paper, we solve this problem and obtain the local well-posedness for the Camassa-Holm equation in critical Besov spaces C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 1 ≤ p < + ∞. It is worth mentioning that our method is suitable for many Camassa-Holm type equations, such as the Novikov equation and the two-component Camassa-Holm system, and can also improve their index of the local well-posedness. [ABSTRACT FROM AUTHOR]

Pursuing the structural planarization of energetic materials is an efficient method for achieving improved performance. Although many planar energetic molecules have been prepared so far, the innovation of advanced planar explosives still relies on the scientific intuition, experience and trial-and-error of researchers. Now, a triazole-induced planarization strategy is proposed based on the regulation of aromaticity, charge distribution, and hydrogen bonds. The incorporation of a triazole ring into the non-planar molecule 5-amino-1-nitriminotetrazole (VII) results in a planar energetic material named N-[5-amino-1-(1H-tetrazol-5-yl)-1H-1,2,4-triazol-3-yl]nitramide (3). Compared with VII (Td = 85 °C; IS < 0.25 J; FS < 5 N), 3 shows remarkably improved thermal stability (Td = 145 °C) and reduced sensitivities (IS = 20 J; FS > 360 N). The variation of thermal stability and mechanical sensitivity from VII to 3 reflects the effectiveness and superiority of the planarization strategy. Benefiting from the properties of 3, its energetic salt 5 exhibits excellent overall performance (Dv = 9342 m s−1; P = 31.6 GPa; Td = 201 °C; IS = 20 J; FS = 360 N), which is comparable to that of HMX. Moreover, the triazole-induced planarization strategy may serve as a guide for exploring advanced energetic materials. [ABSTRACT FROM AUTHOR]

This paper is devoted to the global conservative solutions of a dissipative Camassa-Holm type equation with cubic and quartic nonlinearities. We first transform the equation into an equivalent semilinear system by introducing a new set of variables. Using the standard ordinary differential equation theory, we then obtain the global solutions of the semilinear system. Returning to the original variables, we get the global conservative solution of the equation. Finally, we show that the peakon solutions of the equation still conserve in H 1 . [ABSTRACT FROM AUTHOR]

Periprosthetic osteolysis (PPO) along with aseptic loosening (AL) caused by wear particles after artificial joint replacement is the key factor in surgical failure and subsequent revision surgery, however, the precise molecular mechanism underlying PPO remains unclear. Aseptic inflammation triggered by metal particles, resulting in the imbalance between bone formation by osteoblasts and bone resorption by osteoclasts may be the decisive factor. Pyroptosis is a new pro-inflammatory pattern of regulated cell death (RCD), mainly mediated by gasdermins (GSDMs) family, among which GSDMD is the best characterized. Recent evidence indicates that activation of NLRP3 inflammasomes and pyroptosis play a pivotal role in the pathological process of PPO. Here, we review the pathological process of PPO, the molecular mechanism of pyroptosis and the interventions to inhibit the inflammation and pyroptosis of different cells during the PPO. Conclusively, this review provides theoretical support for the search for new strategies and new targets for the treatment of PPO by inhibiting pyroptosis and inflammation. [ABSTRACT FROM AUTHOR]

A new readout architecture for single-bit quanta image sensor (QIS) consisting of a capacitive transimpedance amplifier (CTIA) before a 1-bit quantizer to improve the threshold uniformity of the readout cluster is proposed in this paper. The 1-bit quantizer in the previous single-bit QIS had significant threshold non-uniformity likely caused by the fluctuation of the common-mode voltage of the jot output. To guarantee the stability of the common-mode voltage of input signals fed to the 1-bit quantizer, the CTIA is added before the 1-bit quantizer. A pipeline operation mode is also proposed so the CTIA and 1-bit ADC can work at the same time, thereby reducing the CTIA power consumption. A 2048 × 1024 high-speed test chip was implemented with 45 nm/65 nm stacked backside illuminated (BSI) CMOS image sensor (CIS) process and tested. According to the measured D-log-H results, a good threshold uniformity in the range of 0.3 to 0.8 e− for all readout clusters is demonstrated at 500 frame per second (fps) equivalent timing with 68 mW power consumption. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the Cauchy problem of a generalized Camassa–Holm equation. We prove the existence of global weak solutions for this generalized Camassa–Holm equation by the viscous approximation method. [ABSTRACT FROM AUTHOR]

In this paper we mainly investigate the Cauchy problem of the Doi-Edwards polymer model with dimension d ≥ 2. The model was derived in the late 1970s to describe the dynamics of polymers in melts. The system contains a Navier-Stokes equation with an additional stress tensor which depend on the deformation gradient tensor and the memory function. The deformation gradient tensor satisfies a transport equation and the memory function satisfies a degenerate parabolic equation. We first proved the local well-posedness for the Doi-Edwards polymer model in Besov spaces by using the Littlewood-Paley theory. Moreover, if the initial velocity and the initial memory is small enough, we obtain a global existence result. [ABSTRACT FROM AUTHOR]

Sarcopenia is an age-related condition that causes loss of skeletal muscle mass and disability. Sarcopenia is closely related to the prognosis of patients suffering osteoporotic thoraco-lumbar compression fractures (OTLCF). The purpose of this study was to investigate the effect of sarcopenia on the efficacy of percutaneous kyphoplasty (PKP) in the treatment of older adults with OTLCF surgery and postoperative mortality. From February 2016 to June 2019, 101 patients who met the inclusion and exclusion criteria were included in this study. The grip strength of the dominant hand was measured using an electronic grip tester. The diagnostic cutoff value of grip strength for sarcopenia was <27 kg for males and <16 kg for females. The cross-sectional area (cm2) of the musculature at the level of the pedicle of the thoracic 12th vertebra (T12) was measured by chest CT. The skeletal muscle index (SMI) was calculated by dividing the muscle cross-sectional area at the T12 pedicle level by the square of the height. The diagnostic cut-off value of SMI at T12 level is 42.6 cm2/m2 for males and 30.6 cm2/m2 for females. Sarcopenia was diagnosed when the grip strength and SMI values were both lower than the diagnostic cut-off value. All included patients received PKP treatment for OTLCF. The age, gender, operation time, bleeding volume, time to ground, length of hospital stay, visual analog scale (VAS) score before operation and one month after operation, Oswestry Disability Index (ODI) one month after operation and the incidence of refracture within 36 months after operation were compared between the two groups. The survival curves of the two groups were analyzed by Kaplan Meier. Chi-square test was used to compare the differences in survival rates between the two groups at 12, 24, and 36 months after operation. Univariate and multivariate Cox regression analysis compared multivariate factors on OTLCF postoperative mortality. There was no significant difference in gender, operation time, blood loss and preoperative VAS score between the two groups (χ 2 = 1.750, p = 0.186; t = 1.195, p = 0.235; t = −0.582, p = 0.562; t = −1.513, p = 0.133), respectively. The patients in the sarcopenia group were older (t = 3.708, p = 0.000), and had longer postoperative grounding time and hospitalization time (t = 4.360, p = 0.000; t = 6.458, p = 0.000). The VAS scores and ODI scores one month postoperatively were also higher in sarcopenia group (t = 5.900, p = 0.000; t = 7.294, p = 0.000), and there was a statistical difference between the two groups. Interestingly, there was no significant difference in the incidence of spinal refracture within 36 months between the two groups (χ 2 = 1.510, p = 0.219). The sarcopenia group had a higher mortality rate at 36 months after operation, and the difference was statistically significant (p = 0.002). Sarcopenia is an independent risk factor for long-term mortality in OTLCF patients received PKP surgery. Patients with sarcopenia combined with OTLCF have poor postoperative recovery of limb function and a high risk of death in the long-term (36 months) after surgery. Active and effective intervention for sarcopenia is required during treatment. • Patients with sarcopenia combined with OTLCF have poor postoperative recovery of limb function. • Patients with sarcopenia combined with OTLCF have a high risk of death in the long-term (36 months) after surgery. • Active and effective intervention for sarcopenia is required during treatment. [ABSTRACT FROM AUTHOR]

A novel alternating-frequency ultrasonic melt treatment (AUMT) technology is used to refine the grain and improve the strength of AS41 magnesium alloy. The AUMT exhibits better grain refinement efficiency than the traditional 20 kHz single-frequency ultrasonic melt treatment method, showing the grain refinement efficiency up to 82.7%. The improvement of cavitation is suspected to be the reason for better grain refinement. The faster alternating time is beneficial to improve grain refinement efficiency. The AUMT also refines the Mg17Al12 and eliminates the agglomeration of Mg2Si. Such microstructure evolution helps improve the tensile strength and elongation of AS41. [ABSTRACT FROM AUTHOR]

In this paper, we first establish the local well-posedness and the rotational speed limit for the rotation Camassa–Holm equation modelling the equatorial water waves with the weak Coriolis effect in nonhomogeneous Besov spaces B p , r s with s > max (1 + 1 p , 3 2) or s = 1 + 1 p , r = 1. Then, we prove the local ill-posedness of the rotation Camassa–Holm equation in B p , r 1 + 1 p , p ∈ [ 1 , + ∞ ] , r ∈ (1 , + ∞ ]. Finally, we show the existence of global weak solutions for the rotation Camassa–Holm equation. [ABSTRACT FROM AUTHOR]

Three energetic salts (2, 3, and 5) based on (Z)-1,1-diamino-2-nitro-2-(1H-tetrazol-5-yl)ethene (1) were designed and prepared. All of them were fully characterized by NMR spectroscopy, IR spectroscopy, and elemental analysis. Their structures were further supported by single-crystal X-ray diffraction analysis. The detonation performances were calculated by using EXPLO5 software (Dv: ranging from 8580 m s−1 to 8810 m s−1, P: ranging from 24.1 GPa to 26.1 GPa). Additionally, these energetic salts showed good thermal stabilities ranging from 197 °C to 240 °C. Their mechanical sensitivities toward friction (FS) and impact (IS) were measured, which exhibited relatively insensitive characteristics. These properties make them promising energetic materials for future applications. [ABSTRACT FROM AUTHOR]

Aim: Oxytocin plays an important role in social recognition in rodents, which is mediated predominantly by the olfactory system. Although oxytocin modulates neural activity in the olfactory bulb, the underlying mechanism is largely unknown. Here, we studied how direct infusion of oxytocin into the olfactory bulb affect social interactions in mice and modulate the neural activity of mitral/tufted cells in the olfactory bulb. Methods: A three‐chamber social interaction test was used in the behavioural test. For in vivo studies, single unit recordings, local field potential recordings and fibre photometry recordings were used to record the neural activity of olfactory bulb. For in vitro studies, we performed patch clamp recordings in the slice of the olfactory bulb. Results: Behaviourally, direct oxytocin infusion in olfactory bulb increased performance in a social interaction task. Moreover, odour‐evoked responses of mitral/tufted cells and neural discrimination of odours were both enhanced by oxytocin, whereas the spontaneous firing rate of mitral/tufted cells was reduced. At the neural network level, oxytocin decreased the amplitude of odour‐evoked high gamma responses. At the cell population level, oxytocin decreased odour‐evoked calcium responses (reflecting neural activity) specifically in granule cells. Moreover, in vitro slice recordings revealed that the inhibitory effect of oxytocin on mitral cell activity is mediated mainly by modulation of ATP‐sensitive potassium channels and involves the oxytocin receptor–Gq–PLC–IP3 signalling pathway. Conclusion: Oxytocin modulates social interaction, likely by increasing the signal‐to‐noise ratio of odour responses in mitral cells which is partly through ATP‐sensitive potassium channel. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with global well-posedness and optimal decay rate for strong solutions of the compressible finite extensible nonlinear elastic (FENE) dumbbell model. For d ≥ 2 , we firstly prove that the compressible FENE dumbbell model admits the unique global strong solutions provided initial data are close to equilibrium state. Then, by the Littlewood-Paley decomposition theory and the Fourier splitting method, we show optimal L 2 decay rate of global strong solutions for d ≥ 3. Finally, we mainly study optimal decay rate to the 2-D FENE dumbbell model. The improved Fourier splitting method yields that the L 2 decay rate is ln − l ⁡ (e + t) for any l ∈ N. By virtue of the time weighted energy estimate, we can improve the decay rate to (1 + t) − 1 4 . Under the low-frequency condition and by the Littlewood-Paley theory, we show that the solutions belong to some Besov spaces with negative index and obtain optimal L 2 decay rate without the smallness restriction of low frequencies. [ABSTRACT FROM AUTHOR]

We first establish the local well-posedness for a generalized Degasperis-Procesi equation in nonhomogeneous Besov spaces. Then we present a global existence result for the equation. Moreover, we obtain a blow-up criteria and provide a sufficient condition for strong solutions to blow up in finite time. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Cauchy problem for the incompressible inhomogeneous nematic liquid crystal flows in R n with initial data in some critical Besov spaces. Under the assumptions that initial density is close to the equilibrium state and the smallness on the initial direction field and nonlinear smallness on the linearized velocity, we obtain the global existence of solutions by fully using the Fourier localization technique and the advantage of weighted function generated by heat kernel. The meanings of this kind of initial data are that we can provide an example of large highly oscillating data satisfying that nonlinear smallness assumption, despite each component of the initial data could be arbitrarily large. [ABSTRACT FROM AUTHOR]

In this paper we mainly investigate the initial value problem of the periodic Euler-Poincaré equations. We first present a new blow-up result to the system for a special class of smooth initial data by using the rotational invariant properties of the system. Then, we prove that the periodic Euler-Poincaré equations are ill-posed in critical Besov spaces by a contradiction argument. Finally, we verify the system possesses a class of peakon solutions in the sense of distributions. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the Cauchy problem of the Euler–Nernst–Planck–Poisson (ENPP) system. We first establish local well-posedness for the Cauchy problem of the ENPP system in Besov spaces. Then we present a blow-up criterion of solutions to the ENPP system. Moreover, we prove that the solutions of the Navier–Stokes–Nernst–Planck–Poisson system converge to the solutions of the ENPP system as the viscosity ν goes to zero, and the convergence rate is at least of order ν 1 / 2 . [ABSTRACT FROM AUTHOR]

Spinal cord ischemia and reperfusion (SCIR) injury can induce autophagy, which is involved in the survival of neurons. However, whether autophagy plays a neuroprotective or a detrimental role in SCIR injury remains controversial. Angiopoietin-1 (Ang-1), an endothelial growth factor, has been shown to have neuroprotective effects. The present study aimed to explore the neuroprotective mechanisms of Ang-1 in neuronal cells in a rat model of SCIR injury in vivo. Ang-1 protein and rapamycin were injected intrathecally. Basso Beattie Bresnahan (BBB) scoring and hematoxylin and eosin staining were used to assess the degree of SCIR injury. Proteins that reflected the level of autophagy expression, such as Beclin-1 and LC3, were evaluated by western blotting. The results indicated that SCIR injury resulted in loss in lower limb motor function. Ang-1 protein inhibited the expression of Beclin-1 and LC3, which improved the BBB score and alleviated spinal cord injury. In contrast, rapamycin, an autophagy activator, caused the opposite effect. This study provides evidence that Ang-1 plays a neuroprotective role by inhibiting of autophagy expression in SCIR injury. Overall, findings could be useful for the treatment of SCIR injury. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate global solutions and blow-up phenomena for the Cauchy problem of a generalized Degasperis–Procesi equation. We develop a new approach to consider the equation for (1 − ∂ x) u instead of (1 − ∂ x 2) u. We first prove a new conserved quantity ‖ (1 − ∂ x) u ‖ L 1 and give the local characterization of this conserved quantity. These properties then allow us to improve considerably a previous global existence result in [38] , and establish two new blow-up results for strong solutions to the equation. In the end, based on vanishing viscosity method and using the conserved quantity we deduce the existence of global weak solutions to the equation for any initial data belonging to L 1 ∩ B V. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the Gevrey regularity and analyticity of the solution to a generalized two-component shallow water wave system with higher-order inertia operators, namely, m = (1 − ∂ x 2) s u with s > 1. Firstly, we obtain the Gevrey regularity and analyticity for a short time. Secondly, we show the continuity of the data-to-solution map. Finally, we prove the global Gevrey regularity and analyticity in time. [ABSTRACT FROM AUTHOR]

In this paper, we establish the continuous dependence for the non-resistive MHD equations in Sobolev spaces. Our obtained result fills considerably the recent result [5] for the continuous dependence on initial data. We also show that this result is optimal. More precisely, we proved that the data-to-solution map is not uniform continuous dependence in Sobolev spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Cauchy problem of the generalized short-pulse equation in periodic domain. We first establish the local well-posedness of the equation in H s (S) , s ≥ 2 by taking advantage of the Kato method and present some useful conservation laws. Then, we obtain the boundedness of the solution by virtue of the conservation laws. Finally, we give a precise blow-up criterion for α > 0 (or α < 0) and get several blow-up results provided the initial data satisfies some certain conditions. [ABSTRACT FROM AUTHOR]

Abstract In this paper we mainly study the long time behavior of solutions to the finite extensible nonlinear elastic (FENE) dumbbell model with dimension two in the co-rotation case. Firstly, we obtain the L 2 decay rate of the velocity of the 2D co-rotation FENE model is (1 + t) − 1 2 with small data. Then, by virtue of the Littlewood–Paley theory, we can remove the small condition. Our obtained sharp result improves considerably the recent results in [8,14]. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem for a viscous shallow water system with Korteweg type in Sobolev spaces. We first establish the local well-posedness of the solution by using the Friedrich method and compactness arguments. Then, we prove the global existence of the solution to the system for the small initial data. [ABSTRACT FROM AUTHOR]

In this paper we mainly investigate the Cauchy problem of a generalized Camassa–Holm equation. We first derive two global existence results and two blow‐up results from the relationship between the Degasperis–Procesi equation and the generalized Camassa–Holm equation. We then prove the existence and uniqueness of global weak solutions under some certain sign conditions on the initial data. [ABSTRACT FROM AUTHOR]

The aim of this study was to assess the risk factors associated with the behavioral development among 24-month-old children in rural northwestern China. A total of 657 children whose mothers had participated in a double-blinded, randomized, controlled trial of antenatal micronutrient supplementation in western China were followed until 24 months of age. Their mental, psychomotor, and behavioral development were assessed by the Bayley Scales of Infant Development. Multivariate logistic regression models were used to examine the factors associated with infant behavioral development. Six behavioral factors of infants were presented: activity, social adaptability, reactivity, endurance, concentration, and motor coordination. Further analysis demonstrated that maternal malnutrition, exposure to risk factors during pregnancy, and adverse birth outcomes negatively affected the behavioral development of children at 24 months, which is a common co-occurrence with cognitive and emotional problems. These results suggest that strategies to improve infant behavioral development should consider the maternal pregnancy status. [ABSTRACT FROM AUTHOR]

In the paper, by the approximation of smooth solutions and a regularization technique, we show the existence and uniqueness of global weak solutions for a two-component Camassa-Holm system with an arbitrary smooth function provided the initial data satisfy some certain sign condition. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a generalized Camassa–Holm equation whose solutions are velocity potentials of the classical Camassa–Holm equation. By exploiting the connection between these two equations, we first establish the local well-posedness of the new equation in the Besov spaces and deduce several blow-up criteria and blow-up results. Then, we investigate the existence of global strong solutions and present a class of cuspon weak solutions for the new equation. [ABSTRACT FROM PUBLISHER]

In this paper, we mainly study the well-posedness for the 3-D inhomogeneous incompressible Navier–Stokes equations with variable viscosity. With some smallness assumption on the BMO-norm of the initial density, we first get the local well-posedness of (1.1) in the critical Besov spaces. Moreover, if the viscosity coefficient is a constant, we can extend this local solution to be a global one. Our theorem implies that we have successfully extended the integrability index p of the initial velocity which has been obtained by Abidi, Gui and Zhang in [3] , Burtea in [8] and Zhai and Yin in [32] to approach the ideal one i.e. 1 < p < 6 . The main novelty of this work is to apply the CRW theorem obtained by Coifman, Rochberg, Weiss in [11] to get a new a priori estimate for an elliptic equation with variable coefficients. The uniqueness of the solution also relies on a Lagrangian approach as in [16–18] . [ABSTRACT FROM AUTHOR]

In this paper we mainly investigate the Cauchy problem of the finite extensible nonlinear elastic (FENE) dumbbell model with dimension d ≥ 2 . We first proved the local well-posedness for the FENE model in Besov spaces by using the Littlewood–Paley theory. Then by an accurate estimate we get a blow-up criterion. Moreover, if the initial data is a small perturbation around equilibrium, we obtain a global existence result. Our obtained results generalize and cover recent results in Masmoudi (2008). [ABSTRACT FROM AUTHOR]

Large-aperture optical components have a wide application in high-power laser facilities. Surface flaws such as damages and contaminants generated under high-power laser irradiation can greatly affect the optical or mechanical performance of optics, so the optical components must be carefully inspected to evaluate optics damage and cleanliness. However, it is of great challenge to achieve rapid and accurate positioning, classification, and measurement of micron-level flaws on the surface of large-aperture optics. This paper proposes a novel surface flaw detection technology based on machine vision and machine learning. To balance efficiency and accuracy, a dark-field imaging system based on progressive scanning is designed to obtain the image of optics surface. A set of surface flaw detection algorithms based on machine learning including object segmentation, flaw feature extraction, and classification and size calibration of flaw are proposed to accurately assess the state of surface flaws. The experiments show that the system can complete the detection of an optical component (430 mm × 430 mm) within 6 min. The minimum detectable size of the flaws can reach 20 μm, and the position accuracy of the flaws is better than 50 μm. The classification accuracy of flaw is 98.59 %, and the average relative errors of the size measurement of damages and contaminants are 3.23 % and 6.58 %, respectively. The experimental results demonstrate the effectiveness of the method in detecting surface flaws of large-aperture optics. [ABSTRACT FROM AUTHOR]

We study global weak solutions to the Novikov equation by vanishing viscosity method. We prove that global weak solutions can be obtained as weak limits of viscous approximations for a class of initial data. The proof relies on a space–time higher integrability estimate and the method of renormalization. In addition, we analyze the interaction of peakon and antipeakon and prove that wave breaking leads to energy concentration. By different continuations beyond the wave breaking, we obtain conservative solutions and dissipative solutions respectively. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the global strong solutions to a micro-macro model for compressible polymeric fluids with small initial data and their long-time decay rates of all order spatial derivatives. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck equation. We first present that the micro-macro model admits a unique global strong solution provided the initial data are close to equilibrium state for d ≥ 2. Moreover, for d ≥ 3 , we show a new critical Fourier estimation that allows us to derive the long-time decay rates of the L 2 norm for all order spatial derivatives. [ABSTRACT FROM AUTHOR]

In the paper, we mainly investigate blow-up phenomena and global existence of strong solutions to a two-component Camassa–Holm systems with an arbitrary smooth function H . For three types of smooth functions H , by using a conservation law and the sign-preserving property of strong solutions, we obtain two new blow-up results and a new global existence result for the two-component system. Our obtained results generalize and cover the recent results in Yan et al. (2015), Zhang and Yin (2015, 2016). [ABSTRACT FROM AUTHOR]

In this paper we mainly study the finite extensible nonlinear elastic (FENE) dumbbell model with dimension $${d \geqq 2}$$ in the whole space. We first prove that there is only the trivial solution for the steady-state FENE model under some integrable condition. The obtained results generalize and cover the classical results for the stationary Navier-Stokes equations. We then obtain that the L decay rate of the velocity of the co-rotation FENE model is $${(1+t)^{-\frac{d}{4}}}$$ when $${d \geqq 3}$$ , and $${\ln^{-k}{(e+t)}, k\in \mathbb{N}^{+}}$$ when d = 2. This result improves considerably the recent result of Schonbek (SIAM J Math Anal 41:564-587, 2009). Moreover, we investigate the L decay of solutions to the general FENE model. [ABSTRACT FROM AUTHOR]

In this paper, we consider a generalized Camassa–Holm equation with the flow generated by the vector field and its gradient. We first establish the local well-posedness of equation in the sense of Hadamard in both critical Besov spaces and supercritical Besov spaces. Then we gain a blow-up criterion. Under a sign condition we reach the sign-preserved property and a precise blow-up criterion. Applying this precise criterion we finally present two blow-up results and the precise blow-up rate for strong solutions to equation. [ABSTRACT FROM AUTHOR]

In this paper we consider the Cauchy problem for a generalized Camassa–Holm equation with cubic nonlinearity in Besov spaces. We first establish the local well-posedness of the equation in the Besov space B p , r s by using the Littlewood–Paley theory. Then, under a sign condition we reach the sign-preserved property and a precise blow-up criterion. Applying this precise criterion we present a blow-up result and the precise blow-up rate for strong solutions to the equation. [ABSTRACT FROM AUTHOR]

The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier–Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (2012) [2] , and (2013) [3] to a lower regularity index about the initial velocity. The key to that improvement is a new a priori estimate for an elliptic equation with nonconstant coefficients in Besov spaces which have the same degree as L 2 in R 3 . Finally, we also generalize our well-posedness result to the inhomogeneous incompressible MHD equations. [ABSTRACT FROM AUTHOR]

A fast multiple correlated sampling technique based on successive approximation register analog-to-digital converter (SAR ADC) for low-noise CMOS image sensors is proposed in this paper. During the whole operation of the fast multiple correlated sampling, m -times samplings and conversions are achieved. The SAR ADC completes a full conversion in the first conversion and only converts lower M bits in the following conversions to decrease the total conversion time. The influences of three factors, the number of samplings, the number of bits converted in the repeated conversions and the resolution of ADC, on the fast multiple correlated sampling are analyzed in detail. A 12-bit SAR ADC with digital calibration based one bit redundancy to relieve the requirement of the capacitor mismatch is designed in the fast correlated multiple sampling technique. The proposed correlated multiple sampling technique is implemented and simulated through standard 180 nm CMOS process. The SAR ADC achieves 72.55 dB signal-to-noise-and-distortion ratio after digital calibration. The simulation results match the analysis well. Readout noise in CMOS image sensors can be reduced by the factor of m effectively with appropriate M based on the fast correlated multiple sampling technique. The total conversion time is decreased effectively, and it is only 10.9 μs for 16 times fast correlated multiple sampling. The fast multiple correlated sampling technique based on SAR ADC is suitable for low-noise and high-speed CMOS image sensor. [ABSTRACT FROM AUTHOR]

In this paper, we prove the solution map of the Cauchy problem of Camassa–Holm type equations depends continuously on the initial data in nonhomogeneous Besov spaces in the sense of Hadamard by using the Littlewood–Paley theory and the method introduced by Kato [37] and Danchin [21] . [ABSTRACT FROM AUTHOR]

In this paper, we study the global well-posed problem for the three dimensional incompressible anisotropic Navier–Stokes system (ANS) with initial data in the scaling invariant Besov–Sobolev type spaces. We prove that (ANS) has a unique global solution provided that the initial vertical velocity is large while initial horizontal data are sufficiently small compared with the horizontal viscosity. In particular, our result implies the global well-posedness of (ANS) with highly oscillating initial data. [ABSTRACT FROM AUTHOR]

This paper is concerned with a new integrable multi-component Camassa–Holm system, which has been proven to be integrable and has peakon solutions. This system includes many one-component and two-component Camassa–Holm type systems as special cases. In this paper, we first establish the local well-posedness and a continuation criterion for the system, then we present several global existence and blow-up results for two important integrable two-component subsystems. Our obtained results cover and improve considerably recent results in Gui et al. (2013), Yan et al. (2015). [ABSTRACT FROM AUTHOR]

In this paper, we first use the energy method to establish the local well-posedness for a family of generalized Camassa–Holm equations in Sobolev spaces. Next, we give a precise blow-up criterion for the Cauchy problem on the family of equations. Then, we show the global existence of strong solutions to the family of equations under some certain sign conditions. Finally, we prove that the family of equations possesses some wave-breaking phenomena. [ABSTRACT FROM AUTHOR]

In this paper we consider the Cauchy problem for the 2D viscous shallow water system in H s ( R 2 ) , s > 1 . We first prove the local well-posedness of this problem by using the Littlewood–Paley theory, the Bony decomposition, and the theories of transport equations and transport diffusion equations. Then, we get the global existence of the system with small initial data in H s ( R 2 ) , s > 1 . Our obtained result improves considerably the recent result in [14] . [ABSTRACT FROM AUTHOR]

We first establish the local existence and uniqueness of strong solutions for the Cauchy problem of a generalized Degasperis–Procesi equation in nonhomogeneous Besov spaces by using the Littlewood–Paley theory. Then, we prove the solution depends continuously on the initial data. Finally, we derive a blow-up criterion and present a global existence result for the equation. [ABSTRACT FROM AUTHOR]