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Fried Mugil cephalus was investigated under optimal vacuum and atmospheric conditions. The water distribution, texture, and color properties of vacuum-fried samples were enhanced compared with atmospheric-fried samples. Meanwhile, vacuum frying (VF) reduced the total oil content, protein oxidation, and degradation. The molecular weight and amino acid content suggested that protein was well-preserved during VF. In addition, the total carbonyl, free thiol groups, thiobarbituric acid reactive substances (TBARS), and Schiff base values were all significantly improved by the VF method compared to atmospheric frying (AF). VF inhibited the shift of amide bands to a higher frequency and the disordering of protein secondary structure. The sample surface morphology shrank under vacuum conditions, likely resulting in the lower fat content of vacuum-fried M. cephalus. Thus, VF improved the quality, water distribution, and microstructure and decreased the protein oxidation and degradation of M. cephalus and was considered a potential method for frying processing.

With the major education model as the dominant model, general education is squeezed in quality and quantity, and implementing the concept of general education is challenging. There are several problems in undergraduate education with “strong majors and weak general education” that need to be addressed in order to integrate major education with general education. Therefore, we selected three levels of universities: nine first-class research universities, seven key provincial teaching–research universities, and seven teaching universities from China. One-way ANOVA, principal component analysis (PCA), and cluster analysis were used to analyze the differences in three kinds of universities based on the total undergrad credits and “big category” majors. One-way ANOVA results showed that “total undergrad credits” and “big category” majors are significantly different between research universities, teaching–research universities, and teaching universities, but there are no significant differences in minor course credits, general course credits, disciplinary and major basic course credits, and elective course credits. Based on cluster analysis, the first cluster G1 showed that all the research universities had similarities in the total undergrad credits, minor course credits, general course credits, disciplinary and major basic course credits, elective course credits, and “big category” majors. PCA results confirmed that research universities are significantly separated from teaching universities and teaching–research universities at the PC1 axis, which has a higher number of “big category” majors. There are three key issues with strong majors and weak general education: (1) the difficulties in popularizing the progressive minor training model; (2) the low percentage of elective courses, general elective courses, and individualized courses; and (3) major transfer system restrictions. Based on their own student characteristics and school resources, teaching universities, research universities, and teaching–research universities are encouraged to enhance the cultivation of students’ compound knowledge and skills at the three levels of micro-major, double degree (minor degree), and minor-major (double majors or second majors), respectively. The universities should adhere to the diversified combination of general and major education, the integration-oriented undergraduate education, the reform concept of reducing burden and improving quality, appropriately increase students’ freedom of choice in undergraduate instructional management for an effective combination of “general education and major education”, and then bring the undergraduate education to a characteristic and high level.

In this paper, we formulate two different network-based epidemic models to investigate the effect of partly effective treatment on disease dynamics. The first network model represents the individuals with heterogeneous number of contacts in a population as choosing a new partner at each moment, whereas the second one assumes the individuals have fixed or stable neighbors. The basic reproduction number [Formula: see text] is computed for each model, using the next generation matrix method. In particular, the critical treatment rate is defined for the model, above which the disease can be eliminated through the treatment. The final epidemic size relations are derived, and the solvability of these implicit equations is studied. In particular, a unique solution of the implicit equation for the final epidemic size is determined, and by rewriting the implicit equation as a suitable fixed point problem, it is proved that the iteration of the fixed point problem converges to the unique solution. Stochastic simulations and numerical simulations, including in comparison with the model outputs and the joint influence of network topology and treatment on the final epidemic size, are conducted to illustrate the theoretical results.

Background Acerola cherry is a famous functional fruit containing plentiful antioxidants and other nutrients. However, studies on the variations among nutrients during the ripening process of acerola fruit are scare. Results Comparative metabolomic and transcriptomic analyses were performed and identified 31 331 unigenes and 1896 annotated metabolite features in acerola cherry fruit. K Kyoto Encyclopedia of Genes and Genomes enrichment analysis showed that several antioxidant and nutrient-related metabolic pathways, such as the flavonoids, vitamins, carotenoids, amino acids, and fatty acids metabolic pathways, were significantly changed during the ripening process. The metabolites related to the vitamin, carotenoid, and fatty acid metabolic pathways were downregulated during the ripening process. Several flavonoid biosynthesis-related genes (including dihydroflavonol 4-reductase, chalcone synthase, flavanone 3-hydroxylase, and anthocyanidin synthase), were significantly upregulated, suggesting their essential functions in the accumulation of flavonoids in mature fruit. Conclusion Most of the vitamin and carotenoid metabolism-related metabolites significantly accumulated in immature fruit, suggesting that immature acerola fruit is a good material for the extraction of vitamins and carotenoids. For macronutrients, most of the amino acids accumulated in mature fruit and most of the fatty acids greatly accumulated in immature fruit. Our data revealed the differential accumulation of antioxidants and nutrients during the ripening process of acerola cherry fruit. © 2021 Society of Chemical Industry.

This paper is devoted to adaptive neural network control issue for a class of nonstrict-feedback uncertain systems with input delay and asymmetric time-varying state constraints. State-related external disturbances are involved into the system, and the upper bounds of disturbances are assumed as functions of state variables instead of constants. Additionally, during the approximations of unknown functions by neural networks, the online computation burdens are declined sharply, since the norms of neural network weight vectors are only estimated. In the process of dealing with input delay, an auxiliary function is applied such that the conditions for time delay are more general than the ones in existing literature. A novel adaptive neural network controller is designed by constructing the asymmetric barrier Lyapunov function, which guarantees that the output of system has a good tracking performance and the state variables never violate the asymmetric time-varying constraints. Finally, numerical simulations are presented to verify the proposed adaptive control scheme.

In this paper, a distributed filter is designed for time-varying systems corrupted by dynamic bias and packet disorders over sensor networks, where the plant under consideration includes stochastic bias which is governed by a dynamical equation. Moreover, the transmission delays are present in all sensor-to-filter communication channels, and such delays are described by using random variables that have known probability distributions. We focus on constructing a distributed yet recursive filter under the corruption of dynamic bias plus packet disorders. By means of the inductive method, upper bounds (on attained error covariances of the distributed filter) are first given and later minimized by properly parameterizing filter gains. Subsequently, a sufficient condition is presented to rigorously ensure the mean-square boundedness with respect to attained filtering errors. Finally, an example is given for effectiveness validation. This work was supported by National Natural Science Foundation of China under Grants 61933007, 62103359, 62173292 and 12071409, the Natural Science Foundation of Universities in Jiangsu Province of China under Grant 21KJB120011, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany.

Non-suicidal self-injury (NSSI) can be defined as the deliberate destruction of body tissues to generate harm. College students have a higher incidence of NSSI. With the deepening of research on college students’ NSSI, the connection between their self-consistency congruence and NSSI has drawn the attention of many scholars. The current study examined the association between self-concordance and NSSI, the mediating function of negative emotions, and the moderating role of gender. We surveyed 1020 college students from three universities in Jiangxi Province using a self-concordant scale, a NSSI questionnaire, and a negative emotion questionnaire. The results showed that self-concordance was negatively correlated with NSSI. There is an obvious negative connection between self-consistency congruence and negative emotions. There was a significant positive correlation between negative emotions and the NSSI scores. Negative emotions could mediate the association between self-consistency congruence and NSSI. Compared to males, females’ self-concordant effects on negative emotions are easier to moderate.

In this article, we elaborated on the problem of fixed time stability (FxTS) of nonlinear impulsive systems. For handing this problem, we propose a new concept of fixed-time stable function set (FT...

This paper addresses the nonstationary quantized control problem for the discrete-time Markov jump singularly perturbed systems (MJSPSs) subject to deception attacks (DAs). The control inputs are characterized by randomly occurring DAs and nonstationary quantization simultaneously, where the DAs are depicted by means of a Bernoulli distributed sequence. By applying a multi-layer structure methodology (MLSM), the nonstationary controllers are devised for MJSPSs. Meanwhile, the correlation among system mode, controller mode, and quantizer mode are portrayed via the nonstationary Markov process. Based on a mode-dependent Lyapunov functional, sufficient criteria are established such that the resulting closed-loop system (CLS) is stochastic mean square exponential ultimately bounded (SMSEUB), and the desired controller is designed. Ultimately, two simulation examples are offered to elaborate on the validity and superiority of the proposed theoretical results.

For Markov switched stochastic functional differential systems (SFDSs), asymptotic property is one of the most desired issues. Recently, a new class of delay-dependent asymptotic stability for non-linear Markov switched SFDSs was investigated. However, the existing references do not take the convergent speed and non-autonomous factor into consideration. Therefore, by means of multiple Lyapunov–Krasovskii functionals, this study is devoted to examine the exponential stability for highly non-linear autonomous Markov switched SFDSs and the exponential stability, polynomial stability and polynomial growth at most for highly non-linear non-autonomous systems, where all the criteria rely on the intervals lengths of continuous delays. In addition, the properties of boundedness and asymptotic stability are as well explored.

Sea urchin Mesocentrotus nudus, Glyptocidaris crenularis, and Strongylocentrotus intermedius gonad protein isolates (mnGPIs, gcGPIs, and siGPIs) were extracted by isoelectric solubilization/precipitation (ISP) from the defatted gonads, and their functional properties were compared. Sodium dodecyl sulfate polyacrylamide gel electrophoresis results showed the similar protein pattern between each protein isolate and defatted gonad, indicating the high efficiency of ISP processing for protein recovery. Amino acid profileconfirmed that the mnGPIs and siGPIs could be potential sources of essential amino acid in nature. As regard to functional properties, mnGPIs showed higher water- and oil- holding capacities followed bysiGPIs and gcGPIs and all protein isolates presented great foaming property. As for emulsifying activity index (EAI), mnGPIs, gcGPIs, and siGPIs showed the minimum solubility and EAI at pH 5, 3, and 4, respectively, and behaved a pH-dependent manner. The gcGPIs revealed the highest EAI from pH 6 to 8 among the samples. In addition, circular dichroism showed increased content of β-sheet at the expense of α-helix and β-turn, suggesting the structure denaturation of the protein isolates. Indeed, no statistical difference was observed between secondary structure of mnGPIs and siGPIs. Moreover, ISP processing increased free sulfhydryl content of sea urchin protein isolates, but no difference was observed among the samples. Furthermore, siGPIs revealed the highest amount of total sulfhydryl and disulfide bonds, whereas both defatted gonads and protein isolates from G. crenularis presented the maximum surface hydrophobicity. These results suggest that gonad protein isolates from three species of sea urchin possess various functionalities and therefore can be potentially applied in food system. PRACTICAL APPLICATION: Sea urchin M. nudus, G. crenularis, and S. intermedius gonads are edible, whereas the functional properties of protein isolates from sea urchin gonad remain unknown. In this case, the extraction and comparison of three species of sea urchin gonad protein isolates will not only confirm functional properties but also screen food ingredients with suitable functions. In this study, functionalities of protein isolates derived from M. nudus, G. crenularis, and S. intermedius gonads would provide potential application in bakery food and meat products or as emulsifier candidates in food system.

In this study, surimi products rich in lipids were prepared by using myofibril protein (MP) emulsion gel as carriers. The MP emulsion gel (MP concentration, c = 1.5%, oil fraction, ø = 0.68) was prepared by one-step homogenization. The emulsion gel maintained a high elastic modulus (G') after heating and freezing treatment. Confocal laser scanning microscopy revealed that the structure of the emulsion gel was a hybrid network consisting of polymers of cross-linked MP and aggregated protein-stabilized emulsion (W/O/W multiple structures) droplets. The double emulsification of the emulsion gel and MP stabilized the oil droplets in the surimi product, preventing water and oil from leaching out. The microstructure also showed smaller gaps between MPs with increased porosity, while oil droplets were stably embedded in the surimi gel matrix. Moreover, adding MP emulsion gel significantly reduced the surimi gel strength compared to adding oil directly (p 0.05).

With the chub frozen surimi as experimental material, low-field nuclear magnetic resonance spectroscopy was used to study the effect of vacuum (0.05, 0.07, and 0.09 Mpa) and temperature (35, 40, 45 °C) interaction on the changes in water distribution, state, and content during the process of surimi gel. The results showed that the gel strength and water state of the surimi were similar to those of the two-stage heating at a vacuum degree of 0.09 MPa and 45 °C for 60 min. From the angle of water migration during the transverse relaxation time T2, it can be seen that under the interaction between the vacuum degree and the temperature, the surimi gel process has a similar tendency of change as the two-stage heated water state. The surimi gel water has two states, T21 and T22, when the vacuum degree is 0.05 Mpa at 35 °C; when it is 35 °C, the vacuum degree is 0.07 MPa, the water has one state of T223; and when the vacuum degree is 0.09 Mpa at 45 °C, there are three states of water: T21, T22, and T23. To sum up, the vacuum treatment conditions have a significant effect on the water state of the surimi gel process, which provides basic data for elucidation of the theory of induced surimi gel under vacuum treatment.

In order to study the heat dissipation characteristics of lithium batteries, a staggered bi-directional flow cooling method is designed and numerical simulations are established using computational fluid dynamics in this paper with a circular battery as the research object. Since the optimal operating range of Li-ion battery is 293.15-313.15K and the maximum temperature difference is not higher than 5K, the maximum temperature and maximum temperature difference are selected as the optimized design objectives. Firstly, the temperature field of the round lithium battery with discharge multiplier 3C working at ambient temperature 308.15K is studied, and an orthogonal test design is carried out for three factors: battery pack embedding distance, coolant flow rate and coolant temperature, and the best combination of orthogonal test is selected by extreme difference analysis and analysis of variance. Secondly, in order to further verify the heat dissipation efficiency of the battery pack, a back propagation neural network with multi-objective optimization algorithm is proposed, and the optimal heat dissipation method of the numerical simulation is obtained by parameter solution and simulation analysis using the parameter range of the orthogonal test as the constraints of the multi-objective optimization. The results show that this optimized way of battery pack heat dissipation has a significant improvement for the maximum temperature, and none of them will exceed its working range; compared with the 3.39K obtained from the orthogonal test design, the maximum temperature difference of the battery pack calculated by the multi-objective optimization is 3.15K, which is reduced by 7.08%.

The large yellow croakers (Larimichthys crocea) are mainly present in the Chinese coast and near seas with high economic importance, but vulnerable to many diseases, especially in the breeding and aquaculture. The purpose of this research was to boost the innate immune system of the large yellow croaker by administering bitter peptides into their peritoneal cavity. Total 120 Juvenile of large yellow croakers in very even weight of 60 g were divided into 4 different groups in 200/300 L of water tank, respectively. Fish growth were observed for 3 months before and after different treatments. The bitter peptides from pepsin hydrolysis were applied because they possess the highest bitter sensory scores. The blood of fish from the different groups was collected and tested for different immune parameters to evaluate the effectiveness of bitter peptides as immune stimulants after administration for 8 weeks. The average ratio of leukocytes/total blood cells (%) for control was found at 14.6%, for the low dose of bitter peptides 0.6 mg/fish was at 29.3%, for middle dose of 1.2 mg/fish was at 35%, and high dose of 2.4 mg/fish was at 30%. The lysozyme assay showed that the OD (optical density) units of relative progress lysis activity at 60 min were 0.17, 0.101, 0.307 and 0.198, respectively. Similarly in the same order as in phagocyte assay, most importantly the middle dose (1.2mg/fish) gave the highest survival rate throughout the assay. The results showed that bitter peptides can be used as immune boosters for the yellow croakers and the optimum dose was 1.2 mg/fish due to both leukocytes and lysozyme activity in the treated samples increased significantly compared with the control group. According to the results obtained, we suggest that the incorporation of middle dose of bitter peptides into fish feeds may reduce the fish diseases in aquaculture, at least for large yellow croakers.

In this paper, we obtain the existence of global entropy solutions for the Cauchy problem of the nonstrictly hyperbolic systems modelling polymer flooding in enhanced oil recovery, under a more flexible condition on the function β ( T ) , which models the adsorption of the polymer on rock. This work improves the previous results in the paper Lu (2013), where β ( T ) is limited to meas { T : β ′ ′ ( T ) = 0 } = 0 or β ( T ) = b T for a nonnegative constant b .

Charges inside a dielectric object embedded in a dissimilar dielectric medium polarize the surrounding medium, which in turn makes a contribution, called the reaction field, to the electric field inside the object. In this work, we develop complete image systems for the reaction field inside a prolate or oblate spheroidal dielectric object embedded in an infinite dissimilar dielectric medium. In either case, an image system consists of a point image and a symmetric surface image over an exterior confocal spheroid that passes through the point image. As an application, the point image is applied into the generalized image charge solvation model (GICSM) and is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulation as references. The results indicate that, for both the prolate and oblate cases, the single point image charge approximation for the reaction field inside the dielectric cavity of the model is good enough for the GICSM to faithfully reproduce typical static and dynamic properties of the liquid water at least when the spheroidal cavity has relatively small eccentricity.

Green’s functions for Poisson’s equation in inhomogeneous media with material interfaces have many practical applications. In the present work, we focus on Green’s functions for Poisson’s equation in inhomogeneous media with diffuse material interfaces where a gradual and continuous transition in the material constant is assumed in a small region around the interfaces between different materials. We present a unified general framework for calculating Green’s functions for Poisson’s equation in such inhomogeneous media and the framework can apply to all eleven orthogonal coordinate systems in which the three-dimensional Laplace equation is separable. Within this framework, the idea on how to design the so-called quasi-harmonic diffuse interface is discussed, formulations for building Green’s function for Poisson’s equation in an inhomogeneous medium with such a diffuse interface is elaborated, and a robust numerical method for calculating Green’s functions for Poisson’s equation in inhomogeneous media with general diffuse interfaces is developed. Several practically relevant separable coordinate systems are briefly surveyed at the level of definition and basic facts relevant for implementing the unified framework in these coordinate systems.

Two-step algorithms for the stationary incompressible Navier–Stokes equations with friction boundary conditions are considered in this paper. Our algorithms consist of solving one Navier–Stokes variational inequality problem used the linear equal-order finite element pair (i.e., P 1 – P 1 ) and then solving a linearization variational inequality problem used the quadratic equal-order finite element pair (i.e., P 2 – P 2 ). Moreover, the stability and convergence of our two-step algorithms are derived. Finally, numerical tests are presented to check theoretical results.

Spheroidal harmonics and modified Bessel functions have wide applications in scientific and engineering computing. Recursive methods are developed to compute the logarithmic derivatives, ratios, and products of the prolate spheroidal harmonics ( $$P_n^m(x)$$ , $$Q_n^m(x)$$ , $$n\ge m\ge 0$$ , $$x>1$$ ), the oblate spheroidal harmonics ( $$P_n^m(ix)$$ , $$Q_n^m(ix)$$ , $$n\ge m\ge 0$$ , $$x>0$$ ), and the modified Bessel functions ( $$I_n(x)$$ , $$K_n(x)$$ , $$n\ge 0$$ , $$x>0$$ ) in order to avoid direct evaluation of these functions that may easily cause overflow/underflow for high degree/order and for extreme argument. Stability analysis shows the proposed recursive methods are stable for realistic degree/order and argument values. Physical examples in electrostatics are given to validate the recursive methods.

In this note, we point out two errors in the article “On the Neumann function and the method of images in spherical and ellipsoidal geometry” by Dassios and Sten. Two corrections are then proposed.

Acerola cherry (Malpighia emarginata D.C.) is a tropical fruit of great economic and nutritional value due to its high content of vitamin C. However, there is little information available about which ripening stage of Acerola cherry can provide the best nutrients. In the current study, the chemical variation at two developmental stages (immature and mature) were investigated by metabolic profiling, and the biological properties of Acerola cherry and its antioxidant assays at four developmental stages were measured, respectively. Through comprehensive metabolites analysis via ultra-high-performance liquid chromatography coupled with quadrupole-time-of-flight mass spectrometry system (UPLC-QTOF), 1896 annotated metabolite features were obtained, and 133 metabolites were finally identified according to the MS/MS fragments compared with these standards in in-house database. Statistically differences in the levels of amino acids, flavonoids, lipids, terpenoids and ascorbic acids were found between mature and immature fruits. Interestingly, most of differential accumulated amino acids, flavonoids, lipids, and terpenoids predominantly accumulated in the mature fruits and ascorbic acid predominantly accumulated in the immature fruits. On the other hand, their antioxidant activities were compared. The alcoholic extract of immature acerola fruit possessed better scavenging ability of DPPH and ABTS than the mature one. The well correlations were found between the antioxidant potential with its content of ascorbic acid (r = 0.9803 and 0.9897, respectively). In conclusion, Acerola cherry showed very different metabolite profile and antioxidant activities during the fruit ripening development. The maturity of Acerola cherry has to be considered when it is being used for health food products.

To investigate the variation in the condition factor of the sea urchin Strongylocentrotus nudus (S. nudus), gonads were collected in May (MAY), June (JUN), and July (JUL), at the beginning (AUG-b) and end of August (AUG-e). Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) detection of the gonads revealed an obvious enhancement of the band at about 37 kDa from July, which was identified as transforming growth factor-beta-induced protein ig-h3 (TGFBI) by nanoLC-ESI-MS/MS. Gonadal proteins were identified by isobaric tagging for relative and absolute quantitation (iTRAQ), and regulation of the identified proteins in pairs of the collected groups was observed. A total of 174 differentially expressed proteins (DEPs) were identified. Seven of the DEPs showed significant correlations with both the gonad index (GI) and protein content. These correlations included 6-phosphogluconate dehydrogenase, decarboxylating isoform X2 (6PGD), CAD protein, myoferlin isoform X8, ribosomal protein L36 (RL36), isocitrate dehydrogenase [NADP], mitochondrial isoform X2 (IDH), multifunctional protein ADE2 isoform X3, sperm-activating peptides (SAPs) and aldehyde dehydrogenase, and mitochondrial (ALDH). However, TGFBI had no correlation with gonad index (GI) or protein content. 6PGD, IDH, multifunctional protein ADE2 isoform X3, and ALDH were shown to interact with each other and might play key roles in changing the condition factor of S. nudus gonads.

A discrete-time fractional-order quaternion-valued memristive system is considered in this note. By utilizing contraction mapping theory, a sufficient condition for the existence and uniqueness of the equilibrium point for the considered system is derived. Via the comparison principle of linear fractional difference system, the quasi-stability condition of the given system is obtained, subsequently, the quasi-synchronization conclusion is derived through Lyapunov method and a proper controller, which can well handle the quasi-synchronization problem in the process of implementing the controller. Applying the lexicographical order method to the quaternion-valued memristive neural networks, the closed convex hull consisted by the connection weights is meaningful. One example is given to substantiate the obtained conclusions.

In a preceding paper [Comput. Phys. Commun. 184 (1): 51–59, 2013], we revisited the problem of calculating Coulomb Green’s function and image potential near a planar diffuse interface within which the dielectric permittivity of the inhomogeneous medium changes continuously along one Cartesian direction in a transition layer between two dissimilar dielectric materials. In the present paper, we consider a cylindrical diffuse interface within which the dielectric permittivity changes continuously along the radial direction instead. First we propose a specific cylindrical diffuse interface model, termed the quasi-harmonic diffuse interface model, that can admit analytical solution for the Green’s function in terms of the modified Bessel functions. Then and more importantly we develop a robust numerical method for building Green’s functions for any cylindrical diffuse interface models. The main idea of the numerical method is, after dividing a diffuse interface into multiple sublayers, to approximate the dielectric permittivity profile in each one of the sublayers by one of the quasi-harmonic functional form rather than simply by a constant value as one would normally do. Next we describe how to efficiently compute well-behaved ratios, products, and logarithmic derivatives of the modified Bessel functions so as to avoid direct evaluations of individual modified Bessel functions in our formulations. Finally we conduct numerical experiments to show the effectiveness of the quasi-harmonic diffuse interface model in overcoming the divergence of the image potential, to validate the numerical method in terms of its accuracy and convergence, and to demonstrate its capability for computing Green’s functions for any cylindrical diffuse interface models.

In this paper, we remove the bounded total variation condition on the initial data and the restriction of the concentration of a fixed background charge being a constant in the paper “Relaxation of the Isothermal Euler–Poisson System to the Drift-Diffusion Equations,” (Quart. Appl. Math., 58 (2000), 511–521), and obtain the zero relaxation time limits to isothermal hydrodynamic model for semiconductor by using the varying viscosity method.

Interior and exterior Neumann functions for the Laplace operator are derived in terms of prolate spheroidal harmonics with the homogeneous, constant, and nonconstant inhomogeneous boundary conditions. For the interior Neumann functions, an image system is developed to consist of a point image, a line image extending from the point image to infinity along the radial coordinate curve, and a symmetric surface image on the confocal prolate spheroid that passes through the point image. On the other hand, for the exterior Neumann functions, an image system is developed to consist of a point image, a focal line image of uniform density, another line image extending from the point image to the focal line along the radial coordinate curve, and also a symmetric surface image on the confocal prolate spheroid that passes through the point image.

A strongly damped and driven nonlinear wave equation describing nonlinear vibrations of axially moving beams is investigated. We establish the existence of an approximate inertial manifold and obtain the amplitude frequency response of the reduced system on this manifold by using multiscale method. The numerical calculations show that, as forcing frequency and damping coefficient are varied, the saddle-node bifurcations can be detected in the two-parameter plane. Thus, an arbitrary small perturbation may lead to a sudden amplitude jump corresponding to a relatively large amplitude response for the primary resonance.

Background: Different saponins from herbs have been used as tonic or functional foods, and for treatment of various diseases including cancers. Although clinical data has supported the function of these saponins, their underlying molecular mechanisms have not been well defined. Methods: With the simulated hypoxia created by 8 hours of Cu++ exposure and following 24 hour incubation with different concentration of saponins in HepG2 cells for MTT assay, migration and invasion assays, and for RT-PCR, and with each group of cells for immunofluorescence observation by confocal microscopy. Results： ZC-4 had the highest rate of inhibition of cell proliferation by MTT assay, and the highest inhibition of migration rate by in vitro scratch assay, while ZC-3 had the highest inhibition of invasion ratio by transwell assay. Under the same simulated hypoxia, the molecular mechanism of saponin function was conducted by measuring the gene expression of Hypoxia Inducible Factor (HIF)-1α through RT-PCR, in which ZC-3 showed a potent inhibition of gene HIF-1α. For the protein expression by immunofluorescence staining with confocal microscopy, HIF-1α was also inhibited by saponins, with the most potent one being ZC-4 after eight hours’ relatively hypoxia incubation. Conclusion: Saponins ZC-4 and ZC-3 have the potential to reduce HepG2 cell proliferation, migration and invasion caused by hypoxia through effectively inhibiting the gene and protein expression of HIF-1α directly and as antioxidant indirectly

This paper extends the image charge solvation model (ICSM) [J. Chem. Phys. 131, 154103 (2009)], a hybrid explicit/implicit method to treat electrostatic interactions in computer simulations of biomolecules formulated for spherical cavities, to prolate spheroidal and triaxial ellipsoidal cavities, designed to better accommodate non-spherical solutes in molecular dynamics (MD) simulations. In addition to the utilization of a general truncated octahedron as the MD simulation box, central to the proposed extension is an image approximation method to compute the reaction field for a point charge placed inside such a non-spherical cavity by using a single image charge located outside the cavity. The resulting generalized image charge solvation model (GICSM) is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulations as a reference. We find that, for improved computational efficiency due to smaller simulation cells and consequently a less number of explicit solvent molecules, the generalized model can still faithfully reproduce known static and dynamic properties of liquid water at least for systems considered in the present paper, indicating its great potential to become an accurate but more efficient alternative to the ICSM when bio-macromolecules of irregular shapes are to be simulated.