EXISTENCE FOR CALCULUS OF VARIATIONS AND OPTIMAL CONTROL PROBLEMS ON TIME SCALES

1. Introduction. Continuous-time modelling and discrete-time modelling are two main approaches which dominate the methodology of mathematical modelling. System dynamics can be analyzed by using either approach. For example, both continuous-time recurrent neural networks and their discrete-time analogue have been studied in the literature (see, for example, [1] and the references therein). However, in practice, some processes consist of both continuous and discrete elements. A simple example of this kind of hybrid continuous-discrete time system is seasonally breeding population whose generations do not overlap. Temperate zone insects (including many economically important crop and orchid pests) are of this kind. These insects lay their eggs just before the generation dies out at the end of the season, with the eggs laying dormant, hatching at the start of the next season, and giving rise to a new, nonoverlapping generation. During each generation the population varies continuously (due to mortality, resource consumption, predation, interaction, etc.), while the population varies in a discrete fashion between the end of one generation and the beginning of the nex

The Effects of Pepper (<i>Zanthoxylum bungeanum</i>) from Different Production Areas on the Volatile Flavor Compounds of Fried Pepper Oils Based on HS-SPME–GC–MS and Multivariate Statistical Method

Fried pepper oil retains the overall flavor outline of pepper, and its unique rich and spicy flavor is deeply loved by consumers. In order to study the effect of different production areas of pepper on the flavor compounds of fried pepper oil, taking dried pepper from seven different production areas as raw materials, and taking rapeseed oil as a carrier oil as well as a constant frying temperature to prepare pepper oil, the present study analyzed the volatile flavor components of pepper oil qualitatively and quantitatively by employing headspace solid phase microextraction (HS-SPME) and gas chromatography–mass spectrometry (GC–MS). The principal component analysis (PCA) method was used to construct the correlation analysis model of volatile flavor substances among different samples of pepper oil. Applying the hierarchical cluster analysis (HCA), the main volatile substances causing the flavor differences of pepper oil from different production areas were identified. The results showed that a total of 81 chemical components were identified, including 15 alcohols, 10 aldehydes, 5 ketones, 34 hydrocarbons, 11 esters, 6 acids, and others. Terpinen-4-ol, linalool, 2,4-decadienal, trans-2-heptenal, sabinene, linalyl acetate, bornyl acetate, myrcene, 1-caryophyllene, trans-α-ocimene, and limonene were selected as the main substances leading to the flavor differences among the pepper oil samples. These 11 chemical components played a decisive role in the construction of the overall aroma of the pepper oil. Using a descriptive sensory analysis, it was concluded that pepper oil from different production areas holds different aroma intensities. Compared with the other six samples, S4 Hanyuan Pepper Oil (HYPO) shows a relatively strong trend toward a spicy fragrance, fresh grassy fragrance, floral and fruity fragrance, fresh sweet fragrance, and fatty aroma

Impedance spectroscopy dependent water content detection in dynamic oil-water emulsions

The water content in static crude emulsions has been extensively studied. However, the dynamic emulsions under shear conditions have a higher stability of the water content, primarily affecting the characteristics of the oil–water two-phase flow in the gathering lines. In this study, a dynamic apparatus was fabricated to investigate the impedance characteristics of water content in oil–water emulsions under the influence of the shear force. The characteristic frequency was proposed to describe the water content in a cubic function. The equivalent circuit model of emulsion has provided an explanation for the variation of the characteristic frequency is mainly caused by the capacitance with the increasing water content. The dynamic conditions have an effect on the electrical properties, which is related to the measurement of water content of the emulsion system. The characteristic function of water content can contribute to a quantitative characterization of the water content of dynamic crude oil, and promote the efficiency and safety of crude oil exploitation

Existence for calculus of variations and optimal control problems on time scales

In this paper we prove the existence for optimal control problems with terminal constraints on time scales. A definition of the solution of semi-linear control systems involving Sobolev space W1;2T is proposed and new existence and uniqueness results of this kind of dynamic systems on time scales are presented under a weaker assumption. According to L2T strong-weak lower semi-continuity of integral functionals, we establish the existence of optimal controls. In particular, the existence for calculus of variations on time scales is derived

Advances in the Formation and Control Methods of Undesirable Flavors in Fish

Undesirable flavor formation in fish is a dynamic biological process, decreasing the overall flavor quality of fish products and impeding the sale of fresh fish. This review extensively summarizes chemical compounds contributing to undesirable flavors and their sources or formation. Specifically, hexanal, heptanal, nonanal, 1−octen−3−ol, 1−penten−3−ol, (E,E)−2,4−heptadienal, (E,E)−2,4−decadienal, trimethylamine, dimethyl sulfide, 2−methyl−butanol, etc., are characteristic compounds causing off−odors. These volatile compounds are mainly generated via enzymatic reactions, lipid autoxidation, environmentally derived reactions, and microbial actions. A brief description of progress in existing deodorization methods for controlling undesirable flavors in fish, e.g., proper fermenting, defatting, appropriate use of food additives, and packaging, is also presented. Lastly, we propose a developmental method regarding the multifunctional natural active substances made available during fish processing or packaging, which hold great potential in controlling undesirable flavors in fish due to their safety and efficiency in deodorization

Design of a Ka-Band Five-Bit MEMS Delay with a Coplanar Waveguide Loaded U-Shaped Slit

This paper designs a five-bit microelectromechanical system (MEMS) time delay consisting of a single-pole six-throw (SP6T) RF switch and a coplanar waveguide (CPW) microstrip line. The focus is on the switch upper electrode design, power divider design, transmission line corner compensation structure design, CPW loading U-shaped slit structure design, and system simulation. The switch adopts a triangular upper electrode structure to reduce the cantilever beam equivalent elastic coefficient and the closed contact area to achieve low drive voltage and high isolation. The SP6T RF MEMS switch uses a disc-type power divider to achieve consistent RF performance across the output ports. When designed by loading U-shaped slit on transmission lines and step-compensated tangents at corners, the system loss is reduced, and the delay amount is improved. In addition, the overall size of the device is 2.1 mm × 2.4 mm × 0.5 mm, simulation results show that the device has a delay amount of 0–60 ps in the frequency range of 26.5–40 GHz, the delay accuracy at the center frequency is better than 0.63 ps, the delay error in the whole frequency band is less than 22.2%, the maximum insertion loss is 3.69 dB, and the input–output return rejection is better than 21.54 dB

Quality Control of Mutton by Using Volatile Compound Fingerprinting Techniques and Chemometric Methods

A method for chromatographic fingerprinting of flavor was established for the quality control of mutton. Twenty-five mutton samples that were chosen from twelve batches were investigated by gas chromatography-mass spectroscopy (GC-MS) and gas chromatography-olfactometry (GC-O). Spectral correlative chromatograms combined with GC-O assessment were employed, and 32 common odor-active compounds that characterize mutton flavor fingerprint were obtained. Based on the flavor chromatographic fingerprint data, principal component analysis (PCA) and partial least squares-discriminant analysis (PLS-DA) were designed and employed as chromatographic fingerprint methods. Defined categories were perfectly discriminated after PLS-DA was conducted on the fused matrix, demonstrating a 100% accurate classification. Fourteen constituents were further screened with PLS-DA to be the main chemical markers, and they were used to develop similar approaches for the determination of mutton quality and traceability. The flavor fingerprint of mutton established using SPME-GC-MS/O coupled with PLS-DA is appropriate for differentiating and identifying samples, and the procedure would be used in quality control

Gradual Optimization of Headspace Solid-Phase Microextraction Conditions of Volatiles in Pepper Chicken Soup Combined with Gas Chromatography-Mass Spectrometry and Principal Component Analysis

A single-factor gradual optimization method was developed in this experiment in order to improve the headspace solid-phase microextraction (HS-SPME) effect of volatile compounds in pepper chicken soup. The different extraction conditions included fibers with different coating materials, sample volume, extraction temperature, and extraction time. The total peak areas and the numbers of valid peaks were compared and analyzed as the indicators of condition optimization. Gas chromatography-mass spectrometry (GC-MS) results showed that the four factors all have significant impact on the extraction effect of volatiles in pepper chicken soup. Using the principal component analysis (PCA), the optimal conditions of HS-SPME were inferred below: an extraction fiber of 50/30μm DVB/CAR/PDMS, a sample volume of 7 g, an extraction temperature of 65°C, and an extraction time of 30 min. Compared to the original extraction conditions, the optimized conditions were especially advantageous for the comprehensive analysis of volatiles, which could be potentially used in further study of soup

Correlation of Volatile Compounds and Sensory Attributes of Chinese Traditional Sweet Fermented Flour Pastes Using Hierarchical Cluster Analysis and Partial Least Squares-Discriminant Analysis

The aroma compositions, sensory attributes, and their correlations of various traditional Chinese sweet fermented flour pastes (SFFPs) were investigated. SFFPs, including LEEJ, LEEH, and XH6, showed high overall acceptance scores of 8.00, 8.21, and 7.50, respectively. Ninety-six volatile compounds were detected using solid-phase microextraction gas chromatography mass spectrometry. Hierarchical cluster analysis grouped SFFPs into three clusters according to their concentrations and compositions of volatile components. Partial least squares-discriminant analysis showed that volatile compounds, including ethyl phenylacetate, 5-methyl furfural, amyl cinnamal, ethyl myristate, decyl aldehyde, 1-phenylethyl acetate, 1-octen-3-ol, 3-buten-2-ol, butanoic acid, and caproaldehyde, were highly negatively correlated with saltiness, sourness, and bitterness, while they were positively correlated with sweetness, umami, richness, and acceptance. The obvious correlation between flavor profiles and sensory attributes could help online monitoring of SFFPs’ flavor quality during production