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In this paper, we consider a container leasing firm that has elementary and premium containers, which are downward substitutable and for use by elementary contract customers (ECCs), premium contract customers (PCCs), as well as walk-in customers (WICs). ECCs can be satisfied by elementary containers or premium ones at discounted prices while PCCs only accept premium containers. WICs can be satisfied by any type of container at different prices. The objective is to maximise the expected total rental revenue by managing its limited capacity. We formulate this problem as a discrete-time Markov Decision Process and show the submodularity and concavity of the value function. Based on this, we show that the optimal policy can be characterised by a series of rationing thresholds, a series of substitution thresholds and a priority threshold, all of which depend on the system states. We further give conditions under which the optimal policy can be simplified. Numerical experiments are conducted to show the impact of the substitution of two items on the revenue, to compare the performance of the optimal policy with those of the commonly used policies and to investigate the influence of arrival rates on the optimal policy. Last, we extend the basic model to consider different rental durations, ECCs’ acceptance behaviour and endogenous prices for WICs. This paper was accepted by Jayashankar Swaminathan, operations management. Funding: This work was supported by National Natural Science Foundation of China/Research Grants Council of Hong Kong Joint Research Scheme [Grant 71661167009, N_PolyU531/16], National Natural Science Foundation of China [Grants 72171016, 71831001], and British Academy\Leverhulme Small Research [Grant SRG19\190059]. This work was also supported by Zhejiang Shuren University Research [Grant KXJ0121605] and Beijing Logistics Informatics Research Base. Supplemental Material: The e-companion and data files are available at https://doi.org/10.1287/mnsc.2022.4425 .

There is an urgent demand for non-invasive and high compliance delivery systems of macromolecules for long-term therapy. However, oral administration of macromolecules is hindered by low permeability and instability in the gastrointestinal (GI) tract. Therefore, we developed a novel aptamer-modified liposomes (Apt-Lip) with M cell targeting for oral delivery of exenatide (EXT). Firstly, we optimized aptamers to M cells by Cell-SELEX and aptamer truncations. The selected aptamer T-M3 (Apt-T-M3) with high binding affinity (K

Profust reliability analysis, in which the failure state of a load-bearing structure is assumed to be fuzzy, is investigated in this paper. A novel active learning method based on the Kriging model is proposed to minimize the number of function evaluations. The new method is termed ALK-Pfst. The sign of performance function at a given random threshold determines the profust failure probability. Therefore, the expected risk function at an arbitrary threshold is derived as the learning function of ALK-Pfst. By making full use of the prediction information of Kriging model, the prediction error of profust failure probability is carefully derived into a closed-form expression. Aided by the prediction error, the accuracy of Kriging model during the learning process can be monitored in real time. As a result, the learning process can be timely terminated with little loss of accuracy. Four examples are provided to demonstrate the advantages of the proposed method.

A novel domino reaction from benzaldehydes and 2-acetylfuran/2-acetylthiophene with sodium sulfide was developed to synthesize a series of tetrahydrothiopyran (THTP) derivatives. The reaction proceeded well to construct a tetrahydrothiopyran ring and five new bonds in one step. A mechanism is proposed, involving a stepwise Aldol/double Michael addition/Aldol (AMMA) reaction cascade. In this transformation, sodium sulfide acts as a nucleophile and base. This method is characterized by transition-metal-free, commercially available starting materials and mild reaction conditions.

In this study, we investigated the relaxation effect and mechanisms of patchouli alcohol (PA) on rat corpus cavernosum. Corpus cavernosum strips were used in organ baths for isometric tension studies. The results showed that PA demonstrated concentration-dependent relaxation effect on rat corpus cavernosum. The relaxant response to PA was not influenced by tetrodotoxin and atropine while it was significantly inhibited by removal of endothelium. L-NG-nitroarginine methyl ester (L-NAME, a nitric oxide synthase inhibitor) or 1H-[1,2,4]oxadiazolo[4,3-a]quinoxalin-1-one (ODQ, a soluble guanylate cyclase inhibitor) significantly inhibited relaxation response to PA, whereas indomethacin (COX inhibitor) had no effect on PA-induced relaxation. The treatment of endothelium-deprived corpus cavernosum with several potassium channel blockers including tetraethylammonium (TEA), 4-aminopyridine (4-AP), and glibenclamide had no effect on PA-induced relaxation. Endothelium-deprived corpus cavernosal contractions induced by cumulative addition of Ca2+ to high KCl solution without CaCl2 were significantly inhibited by PA. Also, PA improved relaxant capacity of sildenafil in rat corpus cavernosum. In addition, the perfusion with PA significantly increased the levels of cGMP and expression of mRNA and protein of neuronal nitric oxide synthase (nNOS) and endothelial nitric oxide synthase (eNOS). Furthermore, intracavernous injection of PA enhanced the rise in intracavernous pressure in rats during cavernosal nerve electric stimulation. In conclusion, PA relaxed the rat corpus cavernosum attributed to both endothelium-dependent and -independent properties. While the former component was mostly involved in nitric oxide signaling pathway, the endothelium-independent mechanism involved in PA-induced relaxation was probably linked to calcium antagonism.

The rapid selection of salinity-tolerant crops to increase food production in salinized lands is important for sustainable agriculture. Recently, high-throughput plant phenotyping technologies have been adopted that use plant morphological and physiological measurements in a non-destructive manner to accelerate plant breeding processes. Here, a hyperspectral imaging (HSI) technique was implemented to monitor the plant phenotypes of 13 okra (Abelmoschus esculentus L.) genotypes after 2 and 7 days of salt treatment. Physiological and biochemical traits, such as fresh weight, SPAD, elemental contents and photosynthesis-related parameters, which require laborious, time-consuming measurements, were also investigated. Traditional laboratory-based methods indicated the diverse performance levels of different okra genotypes in response to salinity stress. We introduced improved plant and leaf segmentation approaches to RGB images extracted from HSI imaging based on deep learning. The state-of-the-art performance of the deep-learning approach for segmentation resulted in an intersection over union score of 0.94 for plant segmentation and a symmetric best dice score of 85.4 for leaf segmentation. Moreover, deleterious effects of salinity affected the physiological and biochemical processes of okra, which resulted in substantial changes in the spectral information. Four sample predictions were constructed based on the spectral data, with correlation coefficients of 0.835, 0.704, 0.609 and 0.588 for SPAD, sodium concentration, photosynthetic rate and transpiration rate, respectively. The results confirmed the usefulness of high-throughput phenotyping for studying plant salinity stress using a combination of HSI and deep-learning approaches.

Pomelo is rich in bioactive compounds (carotenoids, phenolics and essential oil) in the early stage of fruit development, but it is often wasted in the cultivation and management process. To gain an insight into the carotenoid metabolism pathway in pomelo, the carotenoid profiles and the expression patterns of carotenogenic genes were investigated in two genotypes of pomelo during early fruit development. The results showed that a higher carotenoid content was observed in honey pomelo as compared with golden pomelo, which may be related to different gene regulation mechanisms. Lutein, α-carotene, and β-carotene were the main carotenoids in pomelo young fruit, and lutein was the highest one. The accumulation of carotenoids during fruit early development in honey pomelo is related to the transcriptional regulation of ZISO and LUT5. In golden pomelo, the rate-limiting gene for carotenoids is PDS and ZDS. In addition, the expression of seven genes except CRTISO in honey pomelo was higher than that in golden pomelo. The results are helpful to further clarify the regulatory mechanism of carotenoid accumulation during early fruit development and provide a direction for the high-value utilization of young fruits in pomelo.

Background Acute pancreatitis (AP), one of the most common clinical emergencies, is characterized by variable clinical features and inadequate diagnostic methods. At present, the commonly used indicators do not have high specificity and do not necessarily reflect disease severity. We therefore aimed to investigate diagnostic and prognostic value of plasma procalcitonin, heparin‐binding protein, and interleukin‐6 for acute pancreatitis by separate detection and joint detection. Methods The study involved 451 participants, including 343 AP patients and 108 healthy controls. We analyzed the association of the three biomarkers with the severity and prognosis of AP. Results A statistically significant increase in the mean plasma analyte levels was detected in the study group compared to the control group. Multivariate comparison showed that plasma levels of PCT, HBP, and IL‐6 were all significantly different among the three groups at different sampling times (1st, 3rd, 7th, and 10th day of admission) (p, For a single biomarker, the order of the AUC value was IL‐6 ˃ PCT ˃ HBP > 0.78, and each had a certain predictability. Surprisingly, the AUC of any pairwise combination was not higher than those of isolated individual biomarkers, that is, the combined use of any two markers was no more advantageous than single use in the prediction of SAP. When the three combined, the AUC, sensitivity, and specificity were 0.96, 90%, and 98%, respectively, showed 93% overall accuracy. Comparing various combinations, we found that the combination of the three biomarkers showed better predictive capability than any of the individual biomarkers or two biomarker combinations.

Aim Diabetic bladder dysfunction (DBD) is one of the most common and bothersome complications of diabetes mellitus (DM). This study aimed to investigate the functional, structural, and molecular changes of the bladder at 0, 3, 6, 9, and 12 weeks after DM induction by streptozotocin (STZ) in male C57BL/6 mice. Methods Male C57BL/6J mice were injected with STZ (130 mg/kg). Then, diabetic general characteristics, cystometry test, histomorphometry, and contractile responses to α, β‐methylene ATP, KCl, electrical‐field stimulation, carbachol were performed at 0, 3, 6, 9, and 12 weeks after induction. Finally, protein and messenger RNA (mRNA) expressions of myosin Va and SLC17A9 were quantified. Results DM mice exhibited lower body weight, voiding efficiency and higher water intake, urine production, fasting blood glucose, oral glucose tolerance test, bladder wall thickness, maximum bladder capacity, residual volume, bladder compliance. In particular, nonvoiding contractions has increased more than five times at 6 weeks. And the amplitudes of spontaneous activity, contractile responses to all stimulus was about two times higher at 6 weeks but cut almost in half at 12 weeks. The protein and mRNA expressions of myosin Va and SLC17A9 were about two times higher at 6 weeks, but myosin Va was reverted nearly 40% while SLC17A9 is still higher at 12 weeks. Conclusions DBD transitioned from a compensated state to a decompensated state in STZ‐induced DM mice at 9 to 12 weeks after DM induction. Our molecular data suggest that the transition may be closely related to the alterations of myosin Va and SLC17A9 expression levels in the bladder with time.

To reduce loss and damage caused by gas explosions in ducts, the effect of side vent size on explosion characteristics was studied in a 1000 × 100 × 100 mm end-vented duct containing an obstacle. Explosion characteristics including the flame propagation process, propagation velocity and overpressure were analyzed. The experimental results showed that when a side vent with length of 60 mm is located in front of an obstacle, the existence of the obstacle promotes the flame to be released through the side vent, thus causing a better deceleration effect on flame propagation than that of the configuration without an obstacle. Whereas for a side vent with length of 100 mm, the influence of the obstacle on flame propagation is relatively small. Furthermore, the discharge effects of side vents with different vent sizes are obviously affected by the relative positions of the obstacle and the side vent. For a side vent in front of an obstacle, the side vent has a perfect effect on flame propagation deceleration and overpressure discharging, and the discharging effect is less sensitive to vent size. However, for a side vent behind an obstacle, only a side vent with length of 100 mm has a considerable discharging effect, and the discharging effect is very sensitive to vent size. The experimental results strongly suggest that in practical applications, the side vent should be placed near the flammable point and set up in front of potential obstacles to play an ideal role of safety relief.

Objective: Diabetic bladder dysfunction (DBD) is one of the most common and bothersome complications of diabetes mellitus (DM). The purpose of the present study is to investigate DBD in KK-Ay mice, and to identify the expression of relative genes. Method: Totally twenty-seven KK-Ay mice and thirty C57BL/6 J mice, respectively, were randomly divided into 12-, 18-, and 25-week old groups. The weight, water intake, voided volume, the frequency of micturition, fasting blood glucose (FBG), oral glucose tolerance test (OGTT) were measured at varying time points. Maximum bladder volume (MBC), residual volume (RV), bladder compliance (BC), micturition efficiency (VE) and maximum micturition pressure (MVP) were assessed by urodynamic test, and contractile responses to α, β‐methylene ATP, KCl, electrical‐field stimulation, carbachol were performed by detrusor smooth muscle strips contractility test. The bladders were stained with hematoxylin and eosin (H&E) and Masson’s trichrome to determine bladder wall thickness. Additionally, the mRNA expression of Myosin Va, SLC17A9, P2X1, M3 and M2 were then verified by qRT-PCR. Result: The weight, water intake, voided volumes, micturition frequency, FBG, the blood glucose AUC0-2h of KK-Ay mice were significantly increased at three time points. MBC, RV and BC were significantly increased; VE was significantly lower at the age of 18 and 25 weeks in KK-Ay mice; MVP was significantly increased at the age of 25 weeks in KK-Ay mice. In DSM strips contractility test, the amplitude of the spontaneous activity in KK-Ay mice significant increased at 12 weeks and 18 weeks, while both the amplitude and frequency were significantly decreased at the age of 25 weeks. The level of Myosin Va, SLC17A9 and M3 receptor significantly decreased in KK-Ay mice at 12 weeks, while Myosin Va markedly increased at 18 weeks; P2X1 and M2 receptors of KK-Ay mice was significantly increased at all three time points. Conclusion: Taken together, this study demonstrates that KK-Ay mice can be a proper model to investigate DBD whose transformation from compensatory state to decompensated state may ascribe to the time-dependent alternations of Myosin Va, SLC17A9, P2X1, M3 and M2 expression levels.

The purpose of this paper is to investigate the performance of laser shock peening (LSP) subjected to fretting fatigue with TC11 titanium alloy specimens and pads. Three laser power densities (3.2 GW/cm2, 4.8 GW/cm2 and 6.4 GW/cm2) of LSP were chosen and tested using manufactured fretting fatigue apparatus. The experimental results show that the LSP surface treatment significantly improves the fretting fatigue lives of the fretting specimens, and the fretting fatigue life increases most when the laser power density is 4.8 GW/cm2. It is also found that with the increase of the laser power density, the fatigue crack initiation location tends to move from the surface to the interior of the specimen.

Coastal waters usually have intense and complicated biogeochemical processes, the interaction of which makes a challenge to identify the dominant factor of pH natural variations such as seasonal signals. In this study, we report seasonal variation and controls of sea surface pH in the highly urbanized Jiaozhou Bay (JZB) based on four cruises conducted in March, July, October 2014 and January 2015. With sea surface temperature increasing, surface pH on the NBS (NIST) scale decreased from 8.16 ± 0.03 in early spring and 8.19 ± 0.02 in winter to 7.96 ± 0.05 in summer and 7.98 ± 0.01 in autumn. The correlation analyses between pH and temperature shows that temperature seems to be a dominant factor of pH seasonal variation. But the mass balance model indicates that biological effect is the most important for the seasonal variation of pH in the JZB. These two apparently different conclusions are due to the fact that the biological effect on pH is greatly weakened (offset by 73%) by the effect of air-sea CO2 exchange. This study highlights the importance of deciphering pH controlling processes in a quantitative manner particularly in shallow and human activities strongly influenced coastal waters, where these processes usually interact each other and readily obscure the dominant factor.

Metformin (Met) is a widely used antidiabetic drug and has demonstrated interesting anticancer effects in various cancer models, alone or in combination with chemotherapeutic drugs. The aim of the present study is to investigate the synergistic effect of Met with cisplatin (Cis) on the tumor growth inhibition of gallbladder cancer cells (GBC-SD and SGC-996) and explore the underlying mechanism. Cells were treated with Met and/or Cis and subjected to cell viability, colony formation, apoptosis, cell cycle, western blotting, xenograft tumorigenicity assay and immunohistochemistry. The results demonstrated that Met and Cis inhibited the proliferation of gallbladder cancer cells, and combination treatment with Met and Cis resulted in a combination index

Objective. To investigate the effectiveness of a new individualized contrast medium injection protocol for enhanced liver CT scan. Methods. 324 patients who underwent plain and dual phase enhanced liver CT were randomly assigned to 2 groups: G1 (n=224, individualized contrast medium injection protocol); G2 (n=100, standard contrast medium injection with a dose of 1.5 ml/kg). CT values and ΔHU (CT values difference between plain and enhanced CT) of liver parenchyma and tumor-liver contrast (TLC) during hepatic arterial phase (HAP) and portal venous phase (PVP) and contrast medium dose were measured. The tumor conspicuity of hepatocellular carcinoma (HCC) between two groups was independently evaluated by two radiologists. Results. The mean contrast medium dose of G1 was statistically lower than that of G2. There were no significantly statistical differences in CT values and ΔHU of liver parenchyma during HAP, TLC values during HAP, and PVP between two groups. The CT values and ΔHU of liver parenchyma during PVP of G2 were significantly higher than those of G1. Two independent radiologists were both in substantial conformity in grading tumor conspicuity. Conclusion. Using the individually optimized injection protocol might reduce contrast medium dose without impacting on the imaging quality in enhanced liver CT.

The feasibility of using the fourier transform infrared (FTIR) spectroscopic technique with a stacked sparse auto-encoder (SSAE) to identify orchid varieties was studied. Spectral data of 13 orchids varieties covering the spectral range of 4000&ndash, 550 cm&minus, 1 were acquired to establish discriminant models and to select optimal spectral variables. K nearest neighbors (KNN), support vector machine (SVM), and SSAE models were built using full spectra. The SSAE model performed better than the KNN and SVM models and obtained a classification accuracy 99.4% in the calibration set and 97.9% in the prediction set. Then, three algorithms, principal component analysis loading (PCA-loading), competitive adaptive reweighted sampling (CARS), and stacked sparse auto-encoder guided backward (SSAE-GB), were used to select 39, 300, and 38 optimal wavenumbers, respectively. The KNN and SVM models were built based on optimal wavenumbers. Most of the optimal wavenumbers-based models performed slightly better than the all wavenumbers-based models. The performance of the SSAE-GB was better than the other two from the perspective of the accuracy of the discriminant models and the number of optimal wavenumbers. The results of this study showed that the FTIR spectroscopic technique combined with the SSAE algorithm could be adopted in the identification of the orchid varieties.

Laser quenching hardening is one of the most used surface treated technologies. In order to study the effect of laser quenching on the fretting fatigue life, fretting fatigue experiments of TC11 (Ti-6.5Al-1.5Zr-3.5Mo-0.3Si) titanium alloy specimens with different surface conditions were carried out on a special hydraulic servo fatigue test system. The experimental results showed that laser quenching hardening has a good performance in increasing the fretting fatigue lives of the TC11 alloy. However, the effects of laser quenching on fretting fatigue are more obviously at low stress level than at high stress level, the fretting fatigue life was increased by 110.78% at low stress level and 17.56% at high stress level, respectively. Based on the critical plane approach, the traditional SWT (Smith&ndash, Watson&ndash, Topper) parameter was modified and used to describe the fretting fatigue life of the TC11 alloy after hardening by the consideration of the variations of the hardening layer&rsquo, s elastic modulus. Compared with the experimental results, all the errors of the predicted results lied in the error band of two.

Original recordings of the detrusor strips contraction to stimulus. (DOCX 595 kb)

To balance the conflict between low cost and high quality of 3D woven composites (3DWC), we develop a multi-objective optimization methodology. A multiscale process simulation model is proposed to calculate microscopic residual stresses in 3DWC, and the model is validated by experimental measurement using fiber Bragg grating sensors. To address the enormous computational amount, a surrogate model is constructed through three sequential sampling algorithms called Monte Carlo based space reduction, cross-validation Voronoi and greedy algorithm. An interface is developed to integrate the process simulation, sequential sampling and optimization. The multi-objective optimization is conducted to minimize residual stresses and process time utilizing a genetic algorithm, and the Pareto front is obtained. The global sensitivity analysis is conducted based on the surrogate model, and the key parameters are identified. The results show that the effects of process parameters on objectives are coupled. The overall cure cycle should be considered in process optimization.

A physics-based numerical model for prediction and compensation of the process-induced distortion of 3D woven composite (3DWC) is presented. A new tool-part interaction modelling method for the Resin Transfer Molding process is developed, in which the nonlinear material properties and non-thermoelastic distortion are taken into account. Flat and L-shaped 3DWC parts were fabricated and the process-induced distortions were evaluated. Adopting the input values determined by the warpages of flat parts, the spring-in of L-shaped parts predicted by the model is consistent with the experimental measurements. Based on the model, it is found that taking the warpage/spring-in of the uncompensated parts as the compensation value will result in a deviation between the manufactured parts and the nominal shape. An improved comprehensive compensation procedure is proposed and applied to an L-shaped 3DWC part. The result shows that the dimensional precision of the part can be significantly improved by the compensation process.

The reliability analysis of fatigue strength of rail vehicle wheels is studied in this paper. On the basis of deterministic analysis, a basic model for reliability analysis of wheel fatigue strength is established by comprehensively considering many uncertain factors. A reliability analysis method based on active learning Kriging (ALK) model is introduced to solve the fatigue strength failure probability of wheels. The results of reliability analysis are verified, and the results show that the reliability analysis based on ALK model can significantly improve the efficiency on condition the accuracy is guaranteed.

The process-induced residual strain and stress have a significant impact on the forming quality and service performance of 3D woven composites (3DWC). A multiscale model of 3DWC is developed to predict the residual strain and stress after the manufacturing process. Representative volume element at fiber scale and yarn scale are developed according to the geometric characteristics of 3DWC, and the modulus-development model is developed with respect to finite element based micromechanics method. An equivalent temperature load method is proposed to develop the cure shrinkage strain model. A thermal-chemical-mechanical coupling analysis of 3DWC curing process is carried out by integrating the abovementioned models, and the evolutions of temperature, degree of cure and residual strain/stress are obtained. Fiber Bragg Grating sensors are hybridized into the fabrics before Resin Transfer Molding (RTM) processing. The signal from sensors during RTM shows that the residual strain evolution is in good agreement with our modeling prediction.

Probability and convex set hybrid reliability analysis (HRA) is investigated in this paper. It is figured out that a surrogate model only rightly predicting the sign of the performance function can meet the demand of HRA in accuracy. According to this idea, a methodology based on active learning Kriging model called ALK-HRA is proposed. When constructing the Kriging model, the proposed method only approximates the performance function in some region of interest, i.e., the region where the sign of response tends to be wrongly predicted. Then Monte Carlo Simulation (MCS) is performed based on the Kriging model. ALK-HRA is very accurate for HRA with calling the performance function as few times as possible. Three numerical examples are investigated to demonstrate the efficiency and accuracy of the presented method, which include two simple problems and one complicated engineering application.

Hybrid reliability analysis (HRA) with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described by random variables, and the epistemic uncertainties are described by a probability-box (p-box) model. Although tremendous efforts have been devoted to propagating random or p-box uncertainties, much less attention has been paid to analyzing the hybrid reliability with both of them. For HRA, optimization-based Interval Monte Carlo Simulation (OIMCS) is available to estimate the bounds of failure probability, but it requires enormous computational performance. A new method combining the Kriging model with OIMCS is proposed in this paper. When constructing the Kriging model, we only locally approximate the performance function in the region where the sign is prone to be wrongly predicted. It is based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA. Then OIMCS can be effectively performed based on the Kriging model. Three numerical examples and an engineering application are investigated to demonstrate the performance of the proposed method.

The objective of this study was to develop once-daily metformin hydrochloride sustained-release tablets (MHSRT) and evaluate their in vitro release behavior. MHSRT were prepared by the film coating method. The in vitro drug release rate of MHSRT and the commercial tablets Fortamet? made in the United States of America in water was fitted with zero order kinetic equation, and Ritger-Peppas kinetic equation in 0.1 M HCl and pH 6.8-phosphate buffer, respectively. The similarity factor f2 values of MHSRT in three different dissolution medium were 82, 80 and 74, respectively in comparison with imported Fortamet?, which were all greater than 50. The results of storage-stability showed that MHSRT were stable for at least 6 months under stress condition (40℃ ± 2℃, RH 75% ± 5%). Therefore, in this study, MHSRT were successfully prepared using optimized formulation technologies that meet mass produce. The in vitro release behavior of MHSRT was almost similar to that of imported Fortamet?.

The moment-independent importance measure (IM) on the failure probability is important in system reliability engineering, and it is always influenced by the distribution parameters of inputs. For the purpose of identifying the influential distribution parameters, the parametric sensitivity of IM on the failure probability based on local and global sensitivity analysis technology is proposed. Then the definitions of the parametric sensitivities of IM on the failure probability are given, and their computational formulae are derived. The parametric sensitivity finds out how the IM can be changed by varying the distribution parameters, which provides an important reference to improve or modify the reliability properties. When the sensitivity indicator is larger, the basic distribution parameter becomes more important to the IM. Meanwhile, for the issue that the computational effort of the IM and its parametric sensitivity is usually too expensive, an active learning Kriging (ALK) solution is established in this study. Two numerical examples and two engineering examples are examined to demonstrate the significance of the proposed parametric sensitivity index, as well as the efficiency and precision of the calculation method.

We present here a surface plasmon interference lithography method with double-layer planar silver lens. This kind of lithography method provides interference patterns with sufficient contrast for lithography process and simple structure for the convenience of fabrication. Rigorous coupled wave analysis method has been performed with practical parameters to testify this lithography scheme. Furthermore, some key factors influencing the pattern quality have been discussed. It is pointed out that three factors mainly determine the resolution of the interference patterns, and therefore we give a theoretical resolution limit of about 1/12 wavelength to the surface plasmon interference lithography method.