Potential of mucilage-based hydrogel for passive cooling technology: Mucilage extraction techniques and elucidation of thermal, mechanical and physiochemical properties of mucilage-based hydrogel

Mercy Ogbonnaya; Abimbola P.I Popoola; Mercy Ogbonnaya; Abimbola P.I Popoola

doi:10.3934/matersci.2023056

AIMS Materials Science

2023, Volume 10, Issue 6: 1045-1076. doi: 10.3934/matersci.2023056

Previous Article Next Article

Review

Potential of mucilage-based hydrogel for passive cooling technology: Mucilage extraction techniques and elucidation of thermal, mechanical and physiochemical properties of mucilage-based hydrogel

Department of Chemical, Metallurgical and Materials Engineering, Tshwane University of Technology, Pretoria, South Africa

Received: 21 September 2023 Revised: 10 November 2023 Accepted: 15 November 2023 Published: 29 November 2023

Current air-conditioning and refrigeration systems utilize active cooling technology, which consumes a lot of energy from fossil fuels, thereby increasing global warming and depletion of the ozone layer. Passive cooling is considered an alternative to active cooling because it is effective and less expensive and does not require the use of electricity, so cooling can be achieved in locations where there is no electricity. Hydrogels are flexible and soft 3-dimensional networks with high water content and evaporative and radiative cooling properties that make them suitable for use in passive cooling technology. Natural hydrogels are considered alternatives to synthetic hydrogels because they are biodegradable, biocompatible, sensitive to external environments and mostly sourced from plant-based sources. There are limited studies on the application of mucilage-based hydrogel for passive cooling, despite its excellent thermal, mechanical and physiochemical properties. Therefore, this study evaluates the properties of mucilage-based hydrogel as a plausible alternative to synthetic hydrogel for passive cooling. The possibility of using mucilage-based hydrogel in passive cooling technology depends on the mucilage biomass feedstock, mucilage extraction techniques, polymerization techniques and additives introduced into the hydrogel matrix. Different mucilage extraction techniques; mucilage percentage yield; the effects of crosslinkers, polymers and nanoparticle additives on the properties of mucilage-based hydrogel; and the potential of using mucilage-based hydrogel for passive cooling technology are examined in this review.

Keywords:

Citation: Mercy Ogbonnaya, Abimbola P.I Popoola. Potential of mucilage-based hydrogel for passive cooling technology: Mucilage extraction techniques and elucidation of thermal, mechanical and physiochemical properties of mucilage-based hydrogel[J]. AIMS Materials Science, 2023, 10(6): 1045-1076. doi: 10.3934/matersci.2023056

Related Papers:

[1]	Vanya Ivanova . COVID-19 and return intentions among mobile Bulgarian citizens living abroad. AIMS Geosciences, 2023, 9(2): 382-391. doi: 10.3934/geosci.2023020
[2]	Diana I Bakalova, Ekaterina E Dimitrova . Optimistic expectations and life satisfaction as antecedents of emigration attitudes among Bulgarian Millennials and Zoomers. AIMS Geosciences, 2023, 9(2): 285-310. doi: 10.3934/geosci.2023016
[3]	Jama Mohamed, Dahir Abdi Ali, Abdimalik Ali Warsame, Mukhtar Jibril Abdi, Eid Ibrahim Daud, Mohamed Mohamoud Abdilleh . Bayesian extreme value modelling of annual maximum monthly rainfall in Somalia from 1901 to 2022. AIMS Geosciences, 2024, 10(3): 598-622. doi: 10.3934/geosci.2024031
[4]	Elisabetta Genovese . University student perception of sustainability and environmental issues. AIMS Geosciences, 2022, 8(4): 645-657. doi: 10.3934/geosci.2022035
[5]	Leonardo Mercatanti, Gaetano Sabato . Digital education, geography and multidisciplinarity: Themes, methods and critical issues¹. AIMS Geosciences, 2023, 9(1): 184-190. doi: 10.3934/geosci.2023010
[6]	Corey A. Palmer, Katherine P. Markstein, Lawrence H. Tanner . Experimental test of temperature and moisture controls on the rate of microbial decomposition of soil organic matter: preliminary results. AIMS Geosciences, 2019, 5(4): 886-898. doi: 10.3934/geosci.2019.4.886
[7]	Eric Ariel L. Salas, Geoffrey M. Henebry . Canopy Height Estimation by Characterizing Waveform LiDAR Geometry Based on Shape-Distance Metric. AIMS Geosciences, 2016, 2(4): 366-390. doi: 10.3934/geosci.2016.4.366
[8]	Margherita Bufalini, Farabollini Piero, Fuffa Emy, Materazzi Marco, Pambianchi Gilberto, Tromboni Michele . The significance of recent and short pluviometric time series for the assessment of flood hazard in the context of climate change: examples from some sample basins of the Adriatic Central Italy. AIMS Geosciences, 2019, 5(3): 568-590. doi: 10.3934/geosci.2019.3.568
[9]	Shahid Latif, Firuza Mustafa . Trivariate distribution modelling of flood characteristics using copula function—A case study for Kelantan River basin in Malaysia. AIMS Geosciences, 2020, 6(1): 92-130. doi: 10.3934/geosci.2020007
[10]	Shahid Latif, Firuza Mustafa . A nonparametric copula distribution framework for bivariate joint distribution analysis of flood characteristics for the Kelantan River basin in Malaysia. AIMS Geosciences, 2020, 6(2): 171-198. doi: 10.3934/geosci.2020012

Abstract

1. Introduction

In practical applications, due to the interference of various factors, collected data is often incomplete. Missing data is common in public opinion polls, medical research, experimental science, and other application fields. Missing data will not only result in the reduction of effective information, the deviation of the estimation result, but also affect the statistical decision-making and distort the analysis result to some extent. One approach to deal with missing data is complete-case analysis, which deletes all incomplete data. However, Little and Rubin ^[1] pointed out that this will cause biased estimation when the occurrence of missing data is not completely at random. Yates ^[2] introduced an imputation method which is widely used to handle missing responses. The purpose of this method is to find suitable values for the missing data to impute. Then, the data of the filled values are regarded as the complete observation data, which can be analyzed by the classical method. Inverse probability weighting (IPW), which was proposed by Horvitz and Thompson ^[3], is another method to deal with missing data. The inverse of the selection probability is chosen to be the weight assigned to the fully observed data. The missing at random (MAR) assumption, in the sense of Rubin et al. ^[4], is a common assumption for statistical analysis with missing data.

In the case of missing data, the missing mechanism is usually unknown, and parameter methods and nonparametric methods are commonly used to estimate. For the parameter method, there may be a model misspecification problem. Imai and Ratkovic ^[5] proposed the covariate balanced propensity score (CBPS), which improves the parameter method. Based on the CBPS method, Guo et al. ^[6] applied the CBPS method to mean regression to obtain the estimators of the regression parameters $\beta$ and the mean $\mu$ in the case of missing data.

Expectile regression, which was proposed by Newey and Powell ^[7], can be regarded as a generalization of mean regression. Expectile regression uses the sum of asymmetric residual squares as the loss function, and since the loss function is convex and differentiable, expectile regression has computational advantages over quantile regression. Recently, people have carried out a lot of specific research on expectile regression. Sobotka et al. ^[8] established the asymptotic properties of a semi-parametric expectile regression estimator and introduced confidence intervals for expectiles. Waltrup et al. ^[9] observed that expectile regression tends to have less crossing and more robustness against heavy tailed distributions than quantile regression. Ziegel ^[10] concluded that expectile shares coherence and elicitability. Pan et al. ^[11] considered fitting a linear expectile regression model for estimating conditional expectiles based on a large quantity of data with covariates missing at random. Recently, Pan et al. ^[12] developed a weighted expectile regression approach for estimating the conditional expectile when covariates are missing at random (MAR). They only considered a single expectile, and the missing mechanism was assumed to be logistic regression. However, the missing mechanism model may be misspecified. In addition, it is known that making full use of multiple target information can improve the efficiency of parameter estimation. In summary, when the model may be misspecified, we use the idea of covariate balance to study the weighted expectile average estimation of unknown parameters based on CBPS by using multiple expected information. Our estimators can improve performance of the usual weighted expectile average estimator in terms of standard deviation (SD) and mean squared error (MSE).

The rest of this paper is organized as follows. In Section 2, we propose a CBPS-based estimator for the propensity score. In Section 3, we estimate the expected quantile weighted average of the regression parameters based on CBPS. Moreover, we establish the asymptotic normality of the weighted estimator in Section 4. In Section 5, a simulation study is carried out to assess the performance of the proposed method. The proofs of those theoretical results are deferred to the Appendix.

2. CBPS-based estimator for the propensity score

Consider the following linear regression model:

$\begin{equation} Y_i = X_i^T\beta+\varepsilon_i, \quad i = 1, 2, \dots, n, \end{equation}$

(2.1)

where $Y_i$ is response, $X_i$ is covariate, $\beta$ is the $p$ -dimensional vector of unknown parameters, and $\varepsilon_i$ is the random error. Assuming that the response variable $Y_i$ is missing at random, the covariate $X_i$ can be fully observed. For the $i^{th}$ individual, let $\delta_i$ denote the observing indicator, i.e., $\delta_i = 1$ if $Y_i$ is observed and $0$ otherwise. In our paper, we only consider the missing mechanism of missing at random (MAR), that is,

$\begin{equation} P(\delta_i = 1|X_i, Y_i) = \pi(X_i)\triangleq\pi_i, \end{equation}$

(2.2)

where $\pi_i$ is called the selection probability function or the propensity score.

The most popular choice of $\pi(X_i)$ is a logistic regression function (Peng et al. ^[13]). We make the same choice and posit a logistic regression model for $\pi(X_i)$ ,

$\begin{equation} \pi{(X_i, \gamma)} = \frac{\exp(\gamma_0+X_i^T\gamma_1)}{1+\exp(\gamma_0+X_i^T\gamma_1)}, \end{equation}$

(2.3)

and $\gamma = (\gamma_0, \gamma_1^T)^T\in\Theta$ is the unknown parameter vector with the parameter space $\Theta\subseteq {R^{q+1}}$ . Here, $\gamma$ can be estimated by maximizing the log-likelihood function

$L(\gamma) = \sum\limits_{i = 1}^{n}\{\delta_i\log\pi(X_i, \gamma)+(1-\delta_i)\log(1-\pi(X_i, \gamma)\}.$

Assuming that $\pi(X_i, \gamma)$ is twice continuously differentiable with respect to $\gamma$ , maximizing $L(\gamma)$ implies the first-order condition

$\begin{equation} \frac{1}{n}\sum\limits_{i = 1}^{n}s(\delta_i, X_i, \gamma) = 0, \quad s(\delta_i, X_i, \gamma) = \frac{\delta_i\pi'(X_i, \gamma)}{\pi(X_i, \gamma)}-\frac{(1-\delta_i)\pi'(X_i, \gamma)}{1-\pi(X_i, \gamma)}, \end{equation}$

(2.4)

where $\pi'(X_i, \gamma) = \partial \pi(X_i, \gamma)/\partial \gamma^T.$ The maximum likelihood method is a commonly used and simple parameter estimation method. However, when the selection probability model (2.3) is assumed to be wrong, the estimator based on this method will have a large deviation. In order to make the parameter method more robust, we use the covariate balanced propensity score method proposed by Imai and Ratkovic ^[5] to estimate the unknown parameter $\gamma$ , that is,

$\begin{equation} E\left\{\frac{\delta_i \tilde{X_i}}{\pi(X_i, \gamma)}-\frac{(1-\delta_i)\tilde{X_i}}{1-\pi(X_i, \gamma)} \right\} = 0. \end{equation}$

(2.5)

$\tilde{X_i} = f(X_i)$ is an M-dimensional vector-valued measurable function of $X_i$ . For any covariate function, as long as the expectation exists, Eq (2.5) must hold. If the propensity score model is incorrectly specified, then the maximum likelihood may not be able to balance the covariates. Following Imai and Ratkovic ^[5], we can set $\tilde{X_i} = X_i$ to ensure that the first moment of each covariate is balanced even when the model is misspecified. $\pi(X_i, \gamma)$ satisfies the condition

$\begin{equation} E\left\{\frac{\delta_iX_i}{\pi(X_i, \gamma)}-\frac{(1-\delta_i)X_i}{1-\pi(X_i, \gamma)} \right\} = 0. \end{equation}$

(2.6)

The sample form of the covariate equilibrium condition obtained from (2.6) is

$\begin{equation} \frac{1}{n}\sum\limits_{i = 1}^{n}z(\delta_i, X_i, \gamma)X_i = 0, \end{equation}$

(2.7)

where

$z(\delta_i, X_i, \gamma) = \frac{\delta_i-\pi(X_i, \gamma)}{\pi(X_i, \gamma)(1-\pi(X_i, \gamma))}.$

According to Imai and Ratkovic ^[5], if we only use the condition of the $\pi'(X_i, \gamma)$ equilibrium, i.e., (2.4), at this time, the number of equations is equal to the number of parameters. Then, the covariate equilibrium propensity score is just-identified. If we combine Eq (2.4) with the score condition given in Eq (2.7),

$\begin{equation} \bar{U}(\gamma) = \frac{1}{n}\sum\limits_{i = 1}^{n}U(\delta_i, X_i, \gamma), \end{equation}$

(2.8)

where

$U(\delta_i, X_i, \gamma) = \binom{s(\delta_i, X_i, \gamma)}{z(\delta_i, X_i, \gamma)X_i} ,$

then the covariate equilibrium propensity score is over-identified because the number of moment conditions exceeds that of parameters. For over-identified CBPS, the estimation of $\gamma$ can be obtained by using the generalized moment method (GMM) (Hansen ^[14]). For a positive semidefinite symmetric weight matrix $W$ , the GMM estimator $\hat{\gamma}$ can be obtained by minimizing the following objective function for $\gamma$ :

$\begin{equation} Q(\gamma) = \bar{U}^T(\gamma)W\bar{U}(\gamma). \end{equation}$

(2.9)

The above method is also applicable to the case where the covariate balanced propensity score is just-identified.

3. Estimator for the regression parameter

Pan et al. ^[12] introduced the weighted expectile regression estimation of a linear model in detail. According to the idea of inverse probability weighting, when the selection probability function $(\pi_1\dots, \pi_n)^T$ is known, the expectile estimator of $\beta$ under missing responses is defined as

$\begin{equation} (\hat{\beta}_{\tau_k, T}, \hat{b}_{\tau_k}) = \mathop{\arg\min}\limits_{\beta, b_{\tau_k}}\sum\limits_{i = 1}^{n}\frac{\delta_i}{\pi(X_i, \gamma)}\Phi_{\tau_k}(Y_i-X_i^T\beta-b_{\tau_k}), \end{equation}$

(3.1)

where $\tau_k\in (0, 1)$ is expectile level, and $\Phi_{\tau_k}(v) = \left|\tau_k-I(v\le0) \right|v^2$ . $b_{\tau_k}$ represents the ${\tau_k}$ -expectile of the error term $\varepsilon_i$ . Then, according to Zhao et al.^[15], let $K$ be the number of expectiles, and consider the equally spaced expectiles $\tau_k = \frac{k}{K+1}$ , $k = 1, 2, \dots, K$ . The weighted expectile average estimator of the linear model parameter $\beta$ when the missing mechanism is known is defined as

$\hat{\beta} = \sum\limits_{k = 1}^{K}\omega_k\hat{\beta}_{\tau_{k, T}},$

where the weight vector $(\omega_1, \dots, \omega_K)^T$ satisfies $\sum_{k = 1}^{K}\omega_k = 1$ .

When the selection probability function is unknown, we use the method proposed in the second section to estimate the parameter $\gamma$ based on CBPS, so as to obtain $\pi(X_i, \hat{\gamma})$ . The loss function of the $\tau_k$ -expectile can be defined as

$L_n(\beta_{{\tau_k}}, b_{\tau_k}) = \sum\limits_{i = 1}^{n}\frac{\delta_i}{\pi(X_i, \hat{\gamma})}\Phi_{\tau_k}(Y_i-X_i^T\beta-b_{\tau_k}).$

By minimizing the loss function, we can obtain the expectile estimation of the unknown parameter $\beta$ ,

$\begin{equation} (\hat{\beta}_{\tau_k}, \hat{b}_{\tau_k}) = \mathop{\arg\min}\limits_{\beta, b_{\tau_k}}L_n(\beta_{{\tau_k}}, b_{\tau_k}). \end{equation}$

(3.2)

Therefore, the weighted expectile average estimation of the linear model parameter $\beta$ when the missing mechanism is unknown under the missing responses is defined as

$\begin{equation} \hat{\beta}_w = \sum\limits_{k = 1}^{K}\omega_k\hat{\beta}_{\tau_{k}}. \end{equation}$

(3.3)

The weight vector $(\omega_1, \dots, \omega_K)^T$ satisfies $\sum_{k = 1}^{K}\omega_k = 1$ .

4. Asymptotic property

Let $\gamma_0$ and $\beta_0$ represent the true values of $\gamma$ and $\beta$ respectively, and $U(\gamma) = \begin{pmatrix} s(\delta, X, \gamma)\\z(\delta, X, \gamma)X\end{pmatrix}$ . In addition, with reference to Pan et al. ^[12] and Guo ^[16], the following regularity conditions are required.

C1: $\gamma_0$ is the interior point of $\Theta$ .

C2: $U(\gamma)$ is differentiable in the neighborhood $\triangle$ of $\gamma_0$ .

C3: $E[U(\gamma_0)] = 0$ , $E[{\left \| U(\gamma_0) \right\|}^2] < \infty$ .

C4: $E[\sup_{\gamma\in \triangle }\left \| \nabla_\gamma U(\gamma) \right \|] < \infty$ , where $\nabla_{\gamma}$ is the first-order partial derivative of the function to $\gamma$ .

C5: $\Gamma = E[\nabla_\gamma U(\gamma)]$ exists.

C6: For any $i$ , there exists a compact set $\mathcal{X}$ , such that $X_i\in\mathcal{X}\subset\mathbb{R}^p$ , and $X_i$ and $\varepsilon_i$ are independent.

C7: The regression errors $\left\{\varepsilon_i\right\}_{i = 1}^n$ are independent and identically distributed with common cumulative distribution function $F(\cdot)$ , satisfying $E[\varepsilon_i^2] < \infty$ .

C8: There exists $a > 0$ such that $\pi(V_i, \gamma) > a$ for any $i$ .

C9: The symmetric matrix $\Sigma_1$ is positive definite.

The following theorem presents the asymptotic distribution of $\hat{\beta}_w$ .

Theorem 4.1 (Asymptotic Normality of $\hat{\beta}_w$ ) Under the assumptions C1–C9, we have

$\sqrt{n}(\hat{\beta}_{\omega}-\beta_0)\stackrel{d}{\rightarrow }N(0, \Sigma_1^{-1}\Lambda\Sigma_1^{-1}),$

where $\Sigma_1 = E[X_iX_i^T]$ , $\Lambda = E[\lambda\lambda^T], \lambda = \mu-E[\partial \mu/\partial \gamma^T]\{E[\partial U(\gamma)/\partial \gamma^T]\}^{-1}U(\gamma)$ , $\mu = \frac{\delta}{\pi(X, \gamma)}X\sum_{k = 1}^{K}\frac{\omega_k\Psi_{\tau_k}(\varepsilon-b_{0k})}{g(\tau_k)}$ .

5. Simulation

In the following, the expectile weighted average estimation based on covariate balancing propensity score proposed in this paper is analyzed by numerical simulation, and the method is compared with the usual parameter estimation method in the case of correct and wrong model assumptions. Consider the following linear model:

$\begin{equation} Y = \beta_1X_1+\beta_2X_2+\beta_3X_3+\varepsilon, \end{equation}$

(5.1)

where $\beta_1 = 0.5$ , $\beta_2 = 1$ , $\beta_3 = 1$ , and $(X_1, X_2, X_3)$ obeys the joint normal distribution with mean of $0$ , covariance of $0.5$ , and variance of $1$ . The error term $\varepsilon$ obeys the standard normal distribution. In our simulation, we take $K = 10$ , $\tau_{k} = k/11$ for $k = 1, 2, \dots, 10$ , and consider the real choice probability model as

$\begin{equation} \pi(X_1, X_2, X_3) = \exp(0.3X_1+0.25X_2+0.25X_3)/[1+\exp(0.3X_1+0.25X_2+0.25X_3)]. \end{equation}$

(5.2)

Under the assumption of random missing, in order to illustrate the effect when the model is misspecified, we assume that the covariates

$X^* = (X_1^*, X_2^*, X_3^*)\triangleq \{ \exp(X_1/2), (X_2)/\{1+\exp(X_1)\}+10, (X_1X_3/25+0.6)^3 \}.$

If the model (5.2) is represented by $\pi(X^*)$ , the model will be specified incorrectly. In the simulation study of the expectile regression of the unknown parameter $\beta$ , we consider the following two cases: (1) Propensity score model is correctly specified. (2) Propensity score model is misspecified. Zhao ^[15] proposed the weighted composite expectile regression method for a varying-coefficient partially linear model. For a given scenario, referring to Zhao ^[15], we compare the weighted expectile average estimation based on CBPS, denoted as CBPS-WEAE, with weighted composite expectile regression, denoted as WCER, and weighted composite quantile regression, denoted as WCQR, to examine the performance of the estimator, where the weights of WCER and WCQR are estimated by the generalized linear model.

In the simulation, samples of size $n = 500,800, 1000, 1200$ are generated independently. For each scenario, we conduct $1000$ simulations and calculate the average mean squared error (MSE) for estimator of $\beta$ and the average bias (Bias) and standard deviation (SD) for estimator of $\beta_1$ , $\beta_2$ , and $\beta_3$ . In order to examine the influence of the error distribution on the performance of the proposed method, two different distributions of the model error $\varepsilon$ are considered: standard normal distribution $N(0, 1)$ and centralized $\chi^2$ distribution with 4 degrees of freedom. The results of our simulations are presented in Tables 1 and 2.

Table 1. Simulation results

$(\times 100)$ under the error

$\varepsilon\sim N(0, 1)$ .

n	Model	Method	MSE	$\beta_1$		$\beta_2$		$\beta_3$
n	Model	Method	MSE	Bias	SD	Bias	SD	Bias	SD
500	correct	WCQR	2.437	-0.100	9.038	-0.221	9.041	2.498	8.966
		WCER	2.155	-0.172	8.533	-0.303	8.384	0.366	8.512
		CBPS-WEAE	2.139	0.023	8.490	-0.433	8.355	-0.218	8.488
	incorrect	WCQR	2.371	0.731	8.908	-0.616	8.866	2.498	8.855
		WCER	2.256	0.518	8.642	-0.471	8.698	0.366	8.658
		CBPS-WEAE	2.122	0.348	8.382	-0.680	8.547	-0.104	8.280
800	correct	WCQR	1.490	-0.033	6.944	0.105	7.190	2.498	7.011
		WCER	1.380	-0.012	6.616	-0.036	6.886	0.366	6.844
		CBPS-WEAE	1.356	0.311	6.569	-0.219	6.931	0.076	6.663
	incorrect	WCQR	1.392	0.474	6.729	-0.176	6.689	2.498	6.997
		WCER	1.357	0.266	6.980	0.291	6.455	0.366	6.732
		CBPS-WEAE	1.310	-0.262	6.676	0.098	6.536	-0.285	6.609
1000	correct	WCQR	1.491	0.123	6.156	-0.143	6.427	2.498	6.375
		WCER	1.107	0.067	6.008	0.003	6.182	0.366	6.044
		CBPS-WEAE	1.098	3.303	6.094	-0.296	5.973	-0.260	6.069
	incorrect	WCQR	1.202	0.037	6.497	-0.307	6.477	2.498	6.000
		WCER	1.172	-0.155	6.252	0.213	6.452	0.366	6.042
		CBPS-WEAE	1.122	-0.483	6.137	-0.070	6.209	-0.279	5.985
1200	correct	WCQR	1.033	0.021	5.819	0.136	5.967	2.498	5.824
		WCER	0.902	0.132	5.513	0.027	5.470	0.366	5.472
		CBPS-WEAE	0.898	0.403	5.486	-0.115	5.487	-0.267	5.421
	incorrect	WCQR	1.005	0.401	5.968	-0.347	5.687	2.498	5.681
		WCER	0.960	0.117	5.682	-0.027	5.578	0.366	5.712
		CBPS-WEAE	0.923	-0.118	5.611	-0.290	5.451	-0.119	5.571

| Show Table

DownLoad: CSV

Table 2. Simulation results

$(\times 100)$ under the error

$\varepsilon\sim \chi^2(4)$ .

n	Model	Method	MSE	$\beta_1$		$\beta_2$		$\beta_3$
n	Model	Method	MSE	Bias	SD	Bias	SD	Bias	SD
500	correct	WCQR	42.007	1.385	36.000	1.970	37.445	2.498	38.742
		WCER	19.889	0.282	25.231	0.767	26.285	0.366	25.743
		CBPS-WEAE	18.424	-3.970	24.657	10.138	24.950	-0.236	24.431
	incorrect	WCQR	37.935	4.173	36.241	0.443	35.828	2.498	34.384
		WCER	19.472	1.481	25.942	-0.235	25.159	0.366	25.316
		CBPS-WEAE	19.078	-3.454	25.124	-3.294	24.263	-4.148	25.491
800	correct	WCQR	33.040	1.769	33.706	1.452	32.203	2.498	33.593
		WCER	12.696	1.142	21.067	0.887	20.695	0.366	19.901
		CBPS-WEAE	12.471	-4.204	21.122	1.985	19.963	-0.534	19.540
	incorrect	WCQR	32.691	2.495	34.420	1.215	32.328	2.498	32.158
		WCER	13.098	-0.743	21.348	0.776	20.046	0.366	21.269
		CBPS-WEAE	12.594	-4.931	20.047	-2.309	20.593	-3.187	19.872
1000	correct	WCQR	31.334	2.961	32.292	-1.051	32.338	2.498	32.208
		WCER	12.647	1.554	21.038	0.214	19.026	0.366	21.370
		CBPS-WEAE	9.456	-3.280	18.555	0.380	16.798	0.746	17.568
	incorrect	WCQR	31.671	4.760	33.762	0.512	31.422	2.498	31.931
		WCER	11.049	0.102	18.822	-0.729	17.908	0.366	20.694
		CBPS-WEAE	9.811	-2.869	18.456	-3.676	17.077	-2.495	17.939
1200	correct	WCQR	29.885	-0.103	31.443	2.665	30.750	2.498	32.389
		WCER	11.241	-0.516	18.673	1.694	18.976	0.366	20.328
		CBPS-WEAE	8.751	-5.023	17.754	1.652	16.251	-0.198	16.391
	incorrect	WCQR	31.091	1.617	33.886	3.476	30.736	2.498	31.688
		WCER	10.297	0.207	18.428	0.508	18.222	0.366	18.942
		CBPS-WEAE	9.455	-4.175	17.484	-2.462	16.866	-3.193	17.961

| Show Table

DownLoad: CSV

From and we observe that, as expected, all three estimators are unbiased. In terms of MSE, as a convenient measure of average error, we observe that when model error $\varepsilon$ follows the standard normal distribution $N(0, 1)$ , CBPS-WEAE performs best among the three estimators considered, followed immediately by WCER, while WCQR performs worst. When $\varepsilon$ follows a centralized $\chi^2$ distribution with 4 degrees of freedom, CBPS-WEAE is superior to the other two methods. When sample size is large, it can be seen that the performance of the three estimators is significantly improved compared with that when the sample size is small. In general, our proposed improved estimator is effective.

6. Conclusions

In this paper, in order to improve the estimation efficiency of weighted expectile average estimation, we estimate the selection probability function based on CBPS and propose a weighted expectile average estimator based on CBPS when the response variables are missing at random. The asymptotic normality of the proposed method is proved, and the estimation effect of the method is further illustrated by numerical simulation. The numerical simulation results show that the method is effective.

Author contributions

Qiang Zhao: Conceptualization, methodology, supervision, writing-review and editing; Zhaodi Wang: Validation, software, writing-original draft; Jingjing Wu: Funding acquisition, formal analysis, writing-original draft; Xiuli Wang: Funding acquisition, investigation, resources, writing-review and editing. All authors have read and approved the final version of the manuscript for publication.

Use of AI tools declaration

The authors declare they have not used artificial intelligence (AI) tools in the creation of this article.

Acknowledgments

The research is supported by Natural Science Foundation of Shandong Province (Grant Nos. ZR2021MA077 and ZR2021MA048).

Conflict of interest

All authors declare that there is no conflict of interest.

Appendix: Assumptions and proofs

Define the following symbols:

$\eta_i = \frac{\delta_i}{\pi(X_i, \gamma)}X_i\Psi_{\tau_k}(\varepsilon_i)$ ,

$\hat{\eta_i} = \frac{\delta_i}{\pi(X_i, \hat{\gamma})}X_i\Psi_{\tau_k}(\varepsilon_i)$ ,

$F_n = -\frac{1}{\sqrt{n}}\sum_{i = 1}^{n}\hat{\eta}_i$ ,

$\varepsilon_i = Y_i-X_i^T\beta_0$ ,

$\omega = (\omega_1, \omega_2, ...\omega_n)^T$ ,

$\Sigma_1 = E[X_iX_i^T]$ ,

$\Psi_{\tau_k} = 2\left|\tau_k-I(v\le0) \right|v$ ,

$u = (u_1, u_2, ..., u_n)^T$ ,

$G_n(u) = \sum_{i = 1}^{n}\frac{\delta_i}{\pi(X_i, \hat{\gamma})}\left[\Psi_{\tau_k}(\varepsilon_i-\frac{X_i^Tu}{\sqrt{n}})-\Psi_{\tau_k}(\varepsilon_i)\right]$ .

Lemma 1. Assume that C1–C5 hold. Then, when $n\to \infty$ ,

$\sqrt{n}(\hat\gamma-\gamma_0)\stackrel{d}{\rightarrow }N(0, (\Gamma^T\Sigma^{-1}\Gamma)^{-1}),$

where $\Gamma = E[\nabla_{\gamma}U(\gamma)]$ , $\Sigma = E[U(\gamma)U^T(\gamma)]$ .

The proof of Lemma 1 can refer to Theorem 2.2.1 in Guo ^[16].

Lemma 2. If the conditions C1–C4 are satisfied, then

$F_n\stackrel{d}{\rightarrow }N(0, \Omega),$

where $\Omega = E[QQ^T], Q = \eta-E[\partial \eta/\partial \gamma^T]\{E[\partial U(\gamma)/\partial \gamma^T]\}^{-1}U(\gamma)$ .

Proof. By expanding $\frac{1}{\sqrt{n}}\sum_{i = 1}^{n}\hat{\eta}_i$ at $\gamma$ and the proof process of Lemma 1, we can get

$\begin{equation} \begin{aligned} \frac{1}{\sqrt{n}}\sum\limits_{i = 1}^{n}\hat{\eta}_i& = \frac{1}{\sqrt{n}}\sum\limits_{i = 1}^{n}\eta_i+\left[\frac{1}{n}\sum\limits_{i = 1}^{n}\frac{\partial \eta_i}{\partial \gamma}\right]_{\gamma^\ast}\sqrt{n}(\hat{\gamma}-\gamma)\\& = \frac{1}{\sqrt{n}}\sum\limits_{i = 1}^{n}\eta_i-\left[\frac{1}{n}\sum\limits_{i = 1}^{n}\frac{\partial \eta_i}{\partial \gamma} \right] _{\gamma^\ast}\left[\frac{1}{n}\sum\limits_{i = 1}^{n}\frac{\partial U_i(\gamma)}{\partial \gamma}\right]^{-1}_{\gamma^\ast}\left[\frac{1}{\sqrt{n}}\sum\limits_{i = 1}^{n}U_i(\gamma)\right]\\ & = \frac{1}{\sqrt{n}}\sum\limits_{i = 1}^{n}\left[\eta_i-D_nB_n^{-1}U_i(\gamma)\right], \end{aligned} \end{equation}$

(A.1)

where $D_n = \left[\frac{1}{n}\sum_{i = 1}^{n}\frac{\partial \eta_i}{\partial \gamma} \right]_{\gamma^\ast}, B_n = \left[\frac{1}{n}\sum_{i = 1}^{n}\frac{\partial U_i(\gamma)}{\partial \gamma}\right]_{\gamma^\ast}$ , and $\gamma^\ast$ lies between $\gamma$ and $\hat{\gamma}$ .

According to the central limit theorem,

$\frac{1}{\sqrt{n}}\sum\limits_{i = 1}^{n}(\eta_i-D_nB_n^{-1}U_i(\gamma))\stackrel{d}{\rightarrow }N(0, \Omega),$

where $\Omega = E[QQ^T], Q = \eta-E[\partial \eta/\partial \gamma^T]\{E[\partial U(\gamma)/\partial \gamma^T]\}^{-1}U(\gamma)$ .

Therefore, Lemma 2 is proved.

Lemma 3. If the conditions C1–C4 are satisfied, then

$\sqrt{n}(\hat{\beta}_{\tau_k}-\beta_0)\stackrel{d}{\rightarrow }N(0, \frac{1}{4g^2(\tau)}\Sigma_1^{-1}\Omega\Sigma_1^{-1}).$

Proof. If the conditions C1–C4 are satisfied, it can be known from Pan et al. ^[12] that

$\begin{equation} G_n(u) = g(\tau)u^T\Sigma_1u+F_n^Tu+o_p(1), \end{equation}$

(A.2)

where $g(\tau) = (1-\tau)F(0)+\tau(1-F(0))$ .

Known by Hjort and Pollard ^[17], if

$D_n(u) = \frac{1}{2}u^TAu+B^Tu+o_p(1),$

where $D_n(u)$ is a convex objective function with minimum point $\hat{u}_n$ , $A$ is a symmetric and positive definite matrix, and $B$ is a random variable, then

$\hat{u}_n\stackrel{d}{\longrightarrow}-A^{-1}B.$

Therefore, if we define $\hat{u}_n = \sqrt{n}(\hat{\beta}_{\tau_k}-\beta_0)$ , then $\hat{\beta}_{\tau_k} = \beta_0+\frac{\hat{u}_n}{\sqrt{n}}$ . By some simple calculations and (A.2), we have

$\begin{equation} \begin{aligned} \hat{u}_n& = \mathop{\arg\min}\limits_{u}\sum\limits_{i = 1}^{n}\frac{\delta_i}{\pi(V_i, \hat{\gamma})}\left[\Psi_{\tau_k}(\varepsilon_i-\frac{X_i^Tu}{\sqrt{n}})-\Psi_{\tau_k}(\varepsilon_i)\right] = \mathop{\arg\min}\limits_{u}G_n(u)\\ & = \mathop{\arg\min}\limits_{u}\left[g(\tau)u^T\Sigma_1u+F_n^Tu+o_p(1)\right]. \end{aligned} \end{equation}$

(A.3)

According to condition C4, $\Sigma_1$ is a symmetric positive definite matrix. Lemma 3 is proved by Lemma 1 and Slutsky's theorem.

Proof of Theorem 4.1. By Lemma 3 we know that

$\sqrt{n}(\hat{\beta}_{\tau_k}-\beta_0) = \Sigma_1^{-1}\frac{\frac{1}{\sqrt{n}}\sum\limits_{i = 1}^{n}\frac{\delta_i}{\pi(X_i, \hat{\gamma})}X_i\Psi_{\tau_k}(\varepsilon_i-b_{0k})}{2g(\tau_k)}+o_p(1).$

From $\hat{\beta}_w = \sum_{k = 1}^{K}\omega_k\hat{\beta}_{\tau_{k} }$ , $\sum_{k = 1}^{K}\omega_k = 1$ , we can get

$\begin{equation} \begin{aligned} \sqrt{n}(\hat{\beta}_w-\beta_0)& = \sqrt{n}(\sum\limits_{k = 1}^{K}\omega_k\hat{\beta}_{\tau_k}-\beta_0)\\ & = \sqrt{n}\sum\limits_{k = 1}^{K}\omega_k(\hat{\beta}_{\tau_k}-\beta_0)\\ & = \frac{1}{\sqrt{n}}\Sigma_1^{-1}\sum\limits_{i = 1}^{n}\frac{\delta_i}{\pi(X_i, \hat{\gamma})}X_i\left\{\sum\limits_{k = 1}^{K}\frac{\omega_k\Psi_{\tau_k}(\varepsilon_i-b_{0k})}{2g(\tau_k)}\right\}+o_p(1). \end{aligned} \end{equation}$

(A.4)

According to the proof of Lemma 2, we can obtain that

$\sum\limits_{i = 1}^{n}\hat{\eta}_i = \sum\limits_{i = 1}^{n}\frac{\delta_i}{\pi(X_i, \hat{\gamma})}X_i\Psi_{\tau_k}(\varepsilon_i) = \sum\limits_{i = 1}^{n}\left[\eta_i-D_nB_n^{-1}U_i(\gamma)\right].$

Let $\mu_i = \frac{\delta_i}{\pi(X_i, \gamma)}X_i\sum_{k = 1}^{K}\frac{\omega_k\Psi_{\tau_k}(\varepsilon_i-b_{0k})}{g(\tau_k)}, \hat{\mu}_i = \frac{\delta_i}{\pi(X_i, \hat{\gamma})}X_i\sum_{k = 1}^{K}\frac{\omega_k\Psi_{\tau_k}(\varepsilon_i-b_{0k})}{g(\tau_k)}$ , and then

$\sum\limits_{i = 1}^{n}\hat{\mu}_i = \sum\limits_{i = 1}^{n}\left[\mu_i-H_nB_n^{-1}U_i(\gamma)\right],$

where $H_n = \left[\frac{1}{n}\sum_{i = 1}^{n}\frac{\partial \mu_i}{\partial \gamma} \right]_{\gamma^\ast}$ . Therefore, Eq (A.4) is equivalent to

$\begin{equation} \sqrt{n}(\hat{\beta}_w-\beta_0) = \frac{1}{\sqrt{n}}\Sigma_1^{-1}\sum\limits_{i = 1}^{n}\{\left[\mu_i-H_nB_n^{-1}U_i(\gamma)\right]\}+o_p(1). \end{equation}$

(A.5)

Therefore,

$\sqrt{n}(\hat{\beta}_{\omega}-\beta_0)\stackrel{d}{\rightarrow }N(0, \Sigma_1^{-1}\Lambda\Sigma_1^{-1}),$

where $\Lambda = E[\lambda\lambda^T]$ , $\lambda = \mu-E[\partial \mu/\partial \gamma^T]\{E[\partial U(\gamma)/\partial \gamma^T]\}^{-1}U(\gamma)$ , $\mu = \frac{\delta}{\pi(X, \gamma)}X\sum_{k = 1}^{K}\frac{\omega_k\Psi_{\tau_k}(\varepsilon-b_{0k})}{g(\tau_k)}$ .

References

[1]	Lickley M, Solomon S, Fletcher S, et al. (2020) Quantifying contributions of chlorofluorocarbon banks to emissions and impacts on the ozone layer and climate. Nat Commun 11: 1380. https://doi.org/10.1038/s41467-020-15162-7 doi: 10.1038/s41467-020-15162-7
[2]	Madduma-Bandarage USK, Madihally SV (2021) Synthetic hydrogels: Synthesis, novel trends, and applications. J Appl Polym Sci 138: e50376. https://doi.org/10.1002/app.50376 doi: 10.1002/app.50376
[3]	Zhao W, Jin X, Cong Y, et al. (2013) Degradable natural polymer hydrogels for articular cartilage tissue engineering. J Chem Technol Biotechnol 88: 327–339. https://doi.org/10.1002/jctb.3970 doi: 10.1002/jctb.3970
[4]	Rehman WU, Asim M, Hussain S, et al. (2020) Hydrogel: A promising material in pharmaceutics. Curr Pharm Des 26: 5892–5908. https://doi.org/10.2174/1381612826666201118095523 doi: 10.2174/1381612826666201118095523
[5]	Rajendran JV, Thomas S, Jafari Z, et al. (2022) Recent advances on large-scale manufacture of curcumin and its nanoformulation for cancer therapeutic application. Biointerface Res Appl Chem 12: 7863–7885. https://doi.org/10.33263/BRIAC126.78637885 doi: 10.33263/BRIAC126.78637885
[6]	Loo HL, Goh BH, Lee LH, et al. (2022) Application of chitosan-based nanoparticles in skin wound healing. Asian J Pharm Sci 17: 299–332. https://doi.org/10.1016/j.ajps.2022.04.001 doi: 10.1016/j.ajps.2022.04.001
[7]	Liu RR, Shi QQ, Meng YF, et al. (2023) Biomimetic chitin hydrogel via chemical transformation. Nano Res 4: 1–7. https://doi.org/10.1007/s12274-023-5886-5 doi: 10.1007/s12274-023-5886-5
[8]	Michelini L, Probo L, Farè S, et al. (2020) Characterization of gelatin hydrogels derived from different animal sources. Mater Lett 272: 127865. https://doi.org/10.1016/j.matlet.2020.127865 doi: 10.1016/j.matlet.2020.127865
[9]	Tosif MM, Najda A, Bains A, et al. (2021) A comprehensive review on plant-derived mucilage: Characterization, functional properties, applications, and its utilization for nanocarrier fabrication. Polymers 13: 1066. https://doi.org/10.3390/polym13071066 doi: 10.3390/polym13071066
[10]	Cakmak H, Ilyasoglu-Buyukkestelli H, Sogut E, et al. (2023) A review on recent advances of plant mucilages and their applications in food industry: Extraction, functional properties and health benefits. Food Hydrocolloids Health 3: 100131. https://doi.org/10.1016/j.fhfh.2023.100131 doi: 10.1016/j.fhfh.2023.100131
[11]	Beikzadeh S, Khezerlou A, Jafari SM, et al. (2020) Seed mucilages as the functional ingredients for biodegradable films and edible coatings in the food industry. Adv Colloid Interfac 280: 102164. https://doi.org/10.1016/j.cis.2020.102164 doi: 10.1016/j.cis.2020.102164
[12]	Chiang JH, Ong DSM, Ng FSK, et al. (2021) Application of chia (Salvia hispanica) mucilage as an ingredient replacer in foods. Trends Food Sci Tech 115: 105–116. https://doi.org/10.1016/j.tifs.2021.06.039 doi: 10.1016/j.tifs.2021.06.039
[13]	Timilsena YP, Adhikari R, Kasapis S, et al. (2016) Molecular and functional characteristics of purified gum from Australian chia seeds. Carbohyd Polym 136: 128–136. https://doi.org/10.1016/j.carbpol.2015.09.035 doi: 10.1016/j.carbpol.2015.09.035
[14]	Rostamabadi MM, Falsafi SR, Nishinari K, et al. (2023) Seed gum-based delivery systems and their application in encapsulation of bioactive molecules. Crit Rev Food Sci 63: 9937–9960. https://doi.org/10.1080/10408398.2022.2076065 doi: 10.1080/10408398.2022.2076065
[15]	Hesarinejad MA, Sami Jokandan M, Mohammadifar MA, et al. (2018) The effects of concentration and heating-cooling rate on rheological properties of Plantago lanceolata seed mucilage. Int J Biol Macromol 115: 1260–1266. https://doi.org/10.1016/j.ijbiomac.2017.10.102 doi: 10.1016/j.ijbiomac.2017.10.102
[16]	Olawuyi IF, Kim SR, Lee WY (2021) Application of plant mucilage polysaccharides and their techno-functional properties' modification for fresh produce preservation. Carbohyd Polym 272: 118371. https://doi.org/10.1016/j.carbpol.2021.118371 doi: 10.1016/j.carbpol.2021.118371
[17]	Sacco P, Lipari S, Cok M, et al. (2021) Insights into mechanical behavior and biological properties of chia seed mucilage hydrogels. Gels 7: 47. https://doi.org/10.3390/gels7020047 doi: 10.3390/gels7020047
[18]	Liu Y, Liu Z, Zhu X, et al. (2021) Seed coat mucilages: Structural, functional/bioactive properties, and genetic information. Compr Rev Food Sci Food Saf 20: 11–26. https://doi.org/10.1111/1541-4337.12742 doi: 10.1111/1541-4337.12742
[19]	Halász K, Tóth A, Börcsök Z, et al. (2022) Edible antioxidant films from ultrasonically extracted Plantago psyllium seed husk flour mucilage. J Polym Environ 30: 2685–2694. https://doi.org/10.1007/s10924-022-02409-1 doi: 10.1007/s10924-022-02409-1
[20]	Safdar B, Zhihua P, Xinqi L, et al. (2020) Influence of different extraction techniques on recovery, purity, antioxidant activities, and microstructure of flaxseed gum. J Food Sci 85: 3168–3182. https://doi.org/10.1111/1750-3841.15426 doi: 10.1111/1750-3841.15426
[21]	Niknam R, Ghanbarzadeh B, Ayaseh A, et al. (2020) Barhang (Plantago major L.) seed gum: Ultrasound-assisted extraction optimization, characterization, and biological activities. J Food Process Preserv 44: e14750. https://doi.org/10.1111/jfpp.14750 doi: 10.1111/jfpp.14750
[22]	Dybka-Stępień K, Otlewska A, Góźdź P, et al. (2021) The renaissance of plant mucilage in health promotion and industrial applications: A review. Nutrients 13: 3354. https://doi.org/10.3390/nu13103354 doi: 10.3390/nu13103354
[23]	Ang AMG, Raman IC (2019) Characterization of mucilages from abelmoschus manihot linn., amaranthus spinosus linn. and talinum triangulare (jacq.) willd. leaves for pharmaceutical excipient application. Asian J Biol Life Sci 8: 16–24. https://doi.org/10.5530/ajbls.2019.8.3 doi: 10.5530/ajbls.2019.8.3
[24]	Ma F, Wang R, Li X, et al. (2020) Physical properties of mucilage polysaccharides from Dioscorea opposita Thunb. Food Chem 311: 126039. https://doi.org/10.1016/j.foodchem.2019.126039 doi: 10.1016/j.foodchem.2019.126039
[25]	Nazir S, Wani IA, Masoodi FA (2017) Extraction optimization of mucilage from Basil (Ocimum basilicum L.) seeds using response surface methodology. J Adv Res 8: 235–244. https://doi.org/10.1016/j.jare.2017.01.003 doi: 10.1016/j.jare.2017.01.003
[26]	Tosif MM, Najda A, Klepacka J, et al. (2022) Concise review on taro mucilage: Extraction techniques, chemical composition, characterization, applications, and health attributes. Polymers 14: 1163. https://doi.org/10.3390/polym14061163 doi: 10.3390/polym14061163
[27]	Estévez AM, Saenz C, Hurtado ML, et al. (2004) Extraction methods and some physical properties of mesquite (Prosopis chilensis (Mol) Stuntz) seed gum. J Sci Food Agric 84: 1487–1492. https://doi.org/10.1002/jsfa.1795 doi: 10.1002/jsfa.1795
[28]	Quintero-García M, Gutiérrez-Cortez E, Bah M, et al. (2021) Comparative analysis of the chemical composition and physicochemical properties of the mucilage extracted from fresh and dehydrated opuntia ficus indica cladodes. Foods 10: 2137. https://doi.org/10.3390/foods10092137 doi: 10.3390/foods10092137
[29]	Rodríguez-González S, Martínez-Flores HE, Chávez-Moreno CK, et al. (2014) Extraction and characterization of mucilage from wild species of opuntia. J Food Process Eng 37: 285–292. https://doi.org/10.1111/jfpe.12084 doi: 10.1111/jfpe.12084
[30]	Kassem IAA, Joshua Ashaolu T, Kamel R, et al. (2021) Mucilage as a functional food hydrocolloid: Ongoing and potential applications in prebiotics and nutraceuticals. Food Funct 12: 4738–4748. https://doi.org/10.1039/d1fo00438g doi: 10.1039/d1fo00438g
[31]	Waghmare R, Preethi R, Moses JA, et al. (2022) Mucilages: Sources, extraction methods, and characteristics for their use as encapsulation agents. Crit Rev Food Sci Nutr 62: 4186–4207. https://doi.org/10.1080/10408398.2021.1873730 doi: 10.1080/10408398.2021.1873730
[32]	Capello C, Fischer U, Hungerbuhler K (2007) What is a green solvent? A comprehensive framework for the environmental assessment of solvents. Green Chem 9: 927–934. https://doi.org/10.1039/b617536h doi: 10.1039/b617536h
[33]	Tian S, Hao C, Xu G, et al. (2017) Optimization conditions for extracting polysaccharide from Angelica sinensis and its antioxidant activities. J Food and Drug Anal 25: 766–775. https://doi.org/10.1016/j.jfda.2016.08.012 doi: 10.1016/j.jfda.2016.08.012
[34]	Cong Q, Chen H, Liao W, et al. (2016) Structural characterization, and effect on anti-angiogenic activity of a fucoidan from Sargassum fusiforme. Carbohyd Polym 136: 899–907. https://doi.org/10.1016/j.carbpol.2015.09.087 doi: 10.1016/j.carbpol.2015.09.087
[35]	Saifullah Md, McCullum R, Vuong QV (2021) Optimization of microwave–assisted extraction of polyphenols from lemon myrtle: Comparison of modern and conventional extraction techniques based on bioactivity and total polyphenols in dry extracts. Processes 9: 2212. https://doi.org/10.3390/pr9122212 doi: 10.3390/pr9122212
[36]	Desai M, Parikh J, Parikh PA (2010) Extraction of natural products using microwaves as a heat source. Sep Purif Rev 39: 1–32. https://doi.org/10.1080/15422111003662320 doi: 10.1080/15422111003662320
[37]	Chen C, Zhang B, Huang Q, et al. (2017) Microwave-assisted extraction of polysaccharides from Moringa oleifera Lam. leaves: Characterization and hypoglycemic activity. Ind Crop Prod 100: 1–11. https://doi.org/10.1016/j.indcrop.2017.01.042 doi: 10.1016/j.indcrop.2017.01.042
[38]	Shiehnezhad M, Zarringhalami S, Malekjani N (2023) Optimization of microwave-assisted extraction of mucilage from ocimum basilicum var. album (l.) seed. J Food Process 2023: 552462. https://doi.org/10.1155/2023/5524621 doi: 10.1155/2023/5524621
[39]	Al-Dhabi NA, Ponmurugan K (2020) Microwave assisted extraction and characterization of polysaccharide from waste jamun fruit seeds. Int J Biol Macromol 152: 1157–1163. https://doi.org/10.1016/j.ijbiomac.2019.10.204 doi: 10.1016/j.ijbiomac.2019.10.204
[40]	Han YL, Gao J, Yin YY, et al. (2016) Extraction optimization by response surface methodology of mucilage polysaccharide from the peel of Opuntia dillenii haw. fruits and their physicochemical properties. Carbohyd Polym 151: 381–391. https://doi.org/10.1016/j.carbpol.2016.05.085 doi: 10.1016/j.carbpol.2016.05.085
[41]	Felkai-Haddache L, Dahmoune F, Remini H, et al. (2016) Microwave optimization of mucilage extraction from Opuntia ficus indica Cladodes. Int J Biol Macromol 84: 24–30. https://doi.org/10.1016/j.ijbiomac.2015.11.090 doi: 10.1016/j.ijbiomac.2015.11.090
[42]	Zhao JL, Zhang M, Zhou HL (2019) Microwave-assisted extraction, purification, partial characterization, and bioactivity of polysaccharides from panax ginseng. Molecules 24: 1605. https://doi.org/10.3390/molecules24081605 doi: 10.3390/molecules24081605
[43]	Wei E, Yang R, Zhao H, et al. (2019) Microwave-assisted extraction releases the antioxidant polysaccharides from seabuckthorn (Hippophae rhamnoides L.) berries. Int J Biol Macromol 123: 280–290. https://doi.org/10.1016/j.ijbiomac.2018.11.074 doi: 10.1016/j.ijbiomac.2018.11.074
[44]	Castejón N, Luna P, Señoráns FJ (2017) Ultrasonic removal of mucilage for pressurized liquid extraction of omega-3 rich oil from chia seeds (Salvia hispanica L.). J Agric Food Chem 65: 2572–2579. https://doi.org/10.1021/acs.jafc.6b05726 doi: 10.1021/acs.jafc.6b05726
[45]	Huang S, Ning Z (2010) Extraction of polysaccharide from Ganoderma lucidum and its immune enhancement activity. Int J Biol Macromol 47: 336–341. https://doi.org/10.1016/j.ijbiomac.2010.03.019 doi: 10.1016/j.ijbiomac.2010.03.019
[46]	Hedayati S, Niakousari M, Babajafari S, et al. (2021) Ultrasound-assisted extraction of mucilaginous seed hydrocolloids: Physicochemical properties and food applications. Trends Food Sci Tech 118: 356–361. https://doi.org/10.1016/j.tifs.2021.10.022 doi: 10.1016/j.tifs.2021.10.022
[47]	Wang W, Ma X, Xu Y, et al. (2015) Ultrasound-assisted heating extraction of pectin from grapefruit peel: Optimization and comparison with the conventional method. Food Chem 178: 106–114. https://doi.org/10.1016/j.foodchem.2015.01.080 doi: 10.1016/j.foodchem.2015.01.080
[48]	Majzoobi M, Hedayati S, Farahnaky A (2015) Functional properties of microporous wheat starch produced by α-amylase and sonication. Food Biosci 11: 79–84. https://doi.org/10.1016/j.fbio.2015.05.001 doi: 10.1016/j.fbio.2015.05.001
[49]	Pereira GA, Silva EK, Peixoto Araujo NM, et al. (2019) Obtaining a novel mucilage from mutamba seeds exploring different high-intensity ultrasound process conditions. Ultrasonics Sonochem 55: 332–340. https://doi.org/10.1016/j.ultsonch.2019.01.010 doi: 10.1016/j.ultsonch.2019.01.010
[50]	Zhao X, Qiao L, Wu AM (2017) Effective extraction of Arabidopsis adherent seed mucilage by ultrasonic treatment. Sci Rep 7: 40672. https://doi.org/10.1038/srep40672 doi: 10.1038/srep40672
[51]	Akhtar MN, Mushtaq Z, Ahmad N, et al. (2019) Optimal ultrasound-assisted process extraction, characterization, and functional product development from flaxseed meal derived polysaccharide gum. Processes 7: 189. https://doi.org/10.3390/pr7040189 doi: 10.3390/pr7040189
[52]	Souza GS, de Cassia Bergamasco R, Stafussa AP, et al. (2020) Ultrasound-assisted extraction of Psyllium mucilage: Evaluation of functional and technological properties. Emir J Food Agr 32: 238–244. https://doi.org/10.9755/ejfa.2020.v32.i4.2089 doi: 10.9755/ejfa.2020.v32.i4.2089
[53]	Silva LA, Sinnecker P, Cavalari AA, et al. (2022) Extraction of chia seed mucilage: Effect of ultrasound application. Food Chem Adv 1: 100024. https://doi.org/10.1016/j.focha.2022.100024 doi: 10.1016/j.focha.2022.100024
[54]	Zhu C, Zhai X, Li L, et al. (2015) Response surface optimization of ultrasound-assisted polysaccharides extraction from pomegranate peel. Food Chem 177: 139–146. https://doi.org/10.1016/j.foodchem.2015.01.022 doi: 10.1016/j.foodchem.2015.01.022
[55]	Yeh YC, Lai LS (2022) Effect of extraction procedures with ultrasound and cellulolytic enzymes on the structural and functional properties of Citrus grandis Osbeck seed mucilage. Molecules 27: 612. https://doi.org/10.3390/molecules27030612 doi: 10.3390/molecules27030612
[56]	Kim JH, Lee HJ, Park Y, et al. (2013) Mucilage removal from cactus cladodes (Opuntia humifusa Raf.) by enzymatic treatment to improve extraction efficiency and radical scavenging activity. Lwt-Food Sci Technol 51: 337–342. https://doi.org/10.1016/j.lwt.2012.10.009 doi: 10.1016/j.lwt.2012.10.009
[57]	Chiang CF, Lai LS (2019) Effect of enzyme-assisted extraction on the physicochemical properties of mucilage from the fronds of Asplenium australasicum (J. Sm.) Hook. Int J Biol Macromol 124: 346–353. https://doi.org/10.1016/j.ijbiomac.2018.11.181 doi: 10.1016/j.ijbiomac.2018.11.181
[58]	Zeng W, Lai L (2016) Characterization of the mucilage extracted from the edible fronds of bird's nest fern (Asplenium australasicum) with enzymatic modifications. Food Hydrocolloid 53: 84–92. https://doi.org/10.1016/j.foodhyd.2015.03.02 doi: 10.1016/j.foodhyd.2015.03.02
[59]	Tavares LS, Junqueira LA, Guimarães ICO, et al. (2018) Cold extraction method of chia seed mucilage (Salvia hispanica L.): Effect on yield and rheological behavior. J Food Sci Technol 55: 457–466. https://doi.org/10.1007/s13197-017-2954-4 doi: 10.1007/s13197-017-2954-4
[60]	Mutlu S, Kopuk B, Palabiyik I (2023) Effect of cold atmospheric pressure argon plasma jet treatment on the freeze-dried mucilage of chia seeds (salvia hispanica l.). Foods 12: 1563. https://doi.org/10.3390/foods12081563 doi: 10.3390/foods12081563
[61]	Li X, Zhang ZH, Qi X, et al. (2021) Application of nonthermal processing technologies in extracting and modifying polysaccharides: A critical review. Compr Rev Food Sci Food Saf 20: 4367–4389. https://doi.org/10.1111/1541-4337.12820 doi: 10.1111/1541-4337.12820
[62]	Ramazzina I, Berardinelli A, Rizzi F, et al. (2015) Effect of cold plasma treatment on physicochemical parameters and antioxidant activity of minimally processed kiwifruit. Postharvest Biol Technol 107: 55–65. https://doi.org/10.1016/j.postharvbio.2015.04.008 doi: 10.1016/j.postharvbio.2015.04.008
[63]	Mehta D, Purohit A, Bajarh P, et al. (2022) Cold plasma processing improved the extraction of xylooligosaccharides from dietary fibers of rice and corn bran with enhanced in-vitro digestibility and anti-inflammatory responses. Innov Food Sci Emerg Technol 78: 103027. https://doi.org/10.1016/j.ifset.2022.103027 doi: 10.1016/j.ifset.2022.103027
[64]	Brasoveanu M, Nemtanu MR (2020) Pasting properties modelling and comparative analysis of starch exposed to ionizing radiation. Radiat Phys Chem 168: 108492. https://doi.org/10.1016/j.radphyschem.2019:108492 doi: 10.1016/j.radphyschem.2019.108492
[65]	Zielinska S, Cybulska J, Pieczywek P, et al. (2022) Structural morphology and rheological properties of pectin fractions extracted from okra pods subjected to cold plasma treatment. Food Bioprocess Technol 15: 1168–1181. https://doi.org/10.1007/s11947-022-02798-0 doi: 10.1007/s11947-022-02798-0
[66]	Muñoz LA, Cobos A, Diaz O, et al. (2012) Chia seeds: Microstructure, mucilage extraction and hydration. J Food Eng 108: 216–224. https://doi.org/10.1016/j.jfoodeng.2011.06.037 doi: 10.1016/j.jfoodeng.2011.06.037
[67]	Wang WH, Lu CP, Kuo MI (2022) Combination of ultrasound and heat in the extraction of chia seed (salvia hispanica l.) mucilage: Impact on yield and technological properties. Processes 10: 519. https://doi.org/10.3390/pr10030519 doi: 10.3390/pr10030519
[68]	Xue X, Hu Y, Wang S, et al. (2022) Fabrication of physical and chemical crosslinked hydrogels for bone tissue engineering. Bioact Mater 12: 327–339. https://doi.org/10.1016/j.bioactmat.2021.10.029 doi: 10.1016/j.bioactmat.2021.10.029
[69]	Hu W, Wang Z, Xiao Y, et al. (2019) Advances in crosslinking strategies of biomedical hydrogels. Biomater Sci 7: 843–855. https://doi.org/10.1039/C8BM01246F doi: 10.1039/C8BM01246F
[70]	Parhi R (2017) Cross-linked hydrogel for pharmaceutical applications: A review. Adv Pharm Bull 7: 515–530. https://doi.org/10.15171/apb.2017.064 doi: 10.15171/apb.2017.064
[71]	Palencia M, Lerma TA, Garcés V, et al. (2021) Eco-friendly hydrogels, In: Palencia M, Lerma TA, Garcés V, et al. Eco-friendly Functional Polymers, Amsterdam: Elsevier, 141–153. https://doi.org/10.1016/B978-0-12-821842-6.00015-4
[72]	Samateh M, Pottackal N, Manafirasi S, et al. (2018) Unravelling the secret of seed-based gels in water: The nanoscale 3D network formation. Sci Rep 8: 7315. https://doi.org/10.1038/s41598-018-25691-3 doi: 10.1038/s41598-018-25691-3
[73]	Sharma G, Kumar A, Devi K, et al. (2018) Guar gum-crosslinked-Soya lecithin nanohydrogel sheets as effective adsorbent for the removal of thiophanate methyl fungicide. Int J Biol Macromol 114: 295–305. https://doi.org/10.1016/j.ijbiomac.2018.03.093 doi: 10.1016/j.ijbiomac.2018.03.093
[74]	Deore UV, Mahajan HS (2022) Hydrogel for topical drug delivery based on Mimosa pudica seed mucilage: Development and characterization. Sustain Chem Pharm 27: 100701. https://doi.org/10.1016/j.scp.2022.100701 doi: 10.1016/j.scp.2022.100701
[75]	Sharma R, Gupta RK, Rani A (2023) Hydrogels based on mucilage of underutilized cereals: Synthesis and characterization. Indian J Chem Techn 30: 524–533. https://doi.org/10.56042/ijct.v30i4.70238 doi: 10.56042/ijct.v30i4.70238
[76]	Mahmood A, Erum A, Mumtaz S, et al. (2022) Preliminary investigation of linum usitatissimum mucilage-based hydrogel as possible substitute to synthetic polymer-based hydrogels for sustained release oral drug delivery. Gels 8: 170. https://doi.org/10.3390/gels8030170 doi: 10.3390/gels8030170
[77]	Choudhary V, Sharma S, Shukla PK, et al. (2023) Biocompatible stimuli responsive hydrogels of okra mucilage with acrylic acid for controlled release phytochemicals of Calendula officinalis: In vitro assay. Mater Today Proc (in press). https://doi.org/10.1016/j.matpr.2023.03.701
[78]	Rodríguez-Loredo NA, Ovando-Medina VM, Pérez E, et al. (2023) Preparation of poly(acrylic acid)/linseed mucilage/chitosan hydrogel for ketorolac release. J Vinyl Addit Technol 29: 890–900. https://doi.org/10.1002/vnl.22023 doi: 10.1002/vnl.22023
[79]	Hosseini MS, Hemmati K, Ghaemy M (2016) Synthesis of nanohydrogels based on tragacanth gum biopolymer and investigation of swelling and drug delivery. Int J Biol Macromol 82: 806–815. https://doi.org/10.1016/j.ijbiomac.2015.09.067 doi: 10.1016/j.ijbiomac.2015.09.067
[80]	Moya-Ortega MD, Alvarez-Lorenzo C, Sigurdsson HH, et al. (2012) Cross-linked hydroxypropyl-β-cyclodextrin and γ-cyclodextrin nanogels for drug delivery: Physicochemical and loading/release properties. Carbohyd Polym 87: 2344–2351. https://doi.org/10.1016/j.carbpol.2011.11.005 doi: 10.1016/j.carbpol.2011.11.005
[81]	Pathania D, Verma C, Negi P, et al. (2018) Novel nanohydrogel based on itaconic acid grafted tragacanth gum for controlled release of ampicillin. Carbohyd Polym 196: 262–271. https://doi.org/10.1016/j.carbpol.2018.05.040 doi: 10.1016/j.carbpol.2018.05.040
[82]	Dalwadi C, Patel G (2015) Application of nanohydrogels in drug delivery systems: Recent patents review. Recent Pat Nanotechnol 9: 17–25. https://doi.org/10.2174/1872210509666150101151521 doi: 10.2174/1872210509666150101151521
[83]	Sabzevar SM, Mehrshad ZM, Naimipour M (2021) A biological magnetic nano-hydrogel based on basil seed mucilage: Study of swelling ratio and drug delivery. Iran Polym J 30: 485–493. https://doi.org/10.1007/s13726-021-00905-0 doi: 10.1007/s13726-021-00905-0
[84]	Archana, Suman A, Singh V (2022) An inclusive review on mucilage: Extraction methods, characterization, and its utilization for nanocarriers manufacturing. J Drug Delivery Ther 12: 171–179. https://doi.org/10.22270/jddt.v12i1-S.5210 doi: 10.22270/jddt.v12i1-S.5210
[85]	Sen S, Bal T, Rajora AD (2022) Green nanofiber mat from HLM–PVA–Pectin (Hibiscus leaves mucilage–polyvinyl alcohol–pectin) polymeric blend using electrospinning technique as a novel material in wound-healing process. Appl Nanosci 12: 237–250. https://doi.org/10.1007/s13204-021-02295-4 doi: 10.1007/s13204-021-02295-4
[86]	Emadzadeh MK, Aarabi A, Aarabi Najvani F, et al. (2022) The effect of extraction method on physicochemical properties of mucilage extracted from yellow and brown flaxseeds. Jundishapur J Nat Pharm Prod 17: e123952. https://doi.org/10.5812/jjnpp-123952 doi: 10.5812/jjnpp-123952
[87]	Wang X, Wu Y, Chen G, et al. (2013) Optimisation of ultrasound assisted extraction of phenolic compounds from Sparganii rhizoma with response surface methodology. Ultrason Sonochem 20: 846–854. https://doi.org/10.1016/j.ultsonch.2012.11.007 doi: 10.1016/j.ultsonch.2012.11.007
[88]	Guo Y, Bae J, Fang Z, et al. (2020) Hydrogels and hydrogel-derived materials for energy and water sustainability. Chem Rev 120: 7642–7707. https://doi.org/10.1021/acs.chemrev.0c00345 doi: 10.1021/acs.chemrev.0c00345
[89]	Chai Q, Jiao Y, Yu X (2017) Hydrogels for biomedical applications: Their characteristics and the mechanisms behind them. Gels 3: 6. https://doi.org/10.3390/gels3010006 doi: 10.3390/gels3010006
[90]	Ganji F, Vasheghani FS, Vasheghani FE (2010) Theoretical description of hydrogel swelling: A review. Iran Polym J 19: 375–398.
[91]	Nerkar PP, Gattani S (2011) In vivo, in vitro evaluation of linseed mucilage based buccal mucoadhesive microspheres of venlafaxine. Drug Deliv 18: 111–121. https://doi.org/10.3109/10717544.2010.520351 doi: 10.3109/10717544.2010.520351
[92]	Sumaira, Ume RT, Alia E, et al. (2021) Fabrication, characterization, and toxicity evaluation of chemically cross-linked polymeric network for sustained delivery of metoprolol tartrate. Des Monomers Polym 24: 351–361. https://doi.org/10.1080/15685551.2021.2003995 doi: 10.1080/15685551.2021.2003995
[93]	Xu L, Sun DW, Tian Y, et al. (2022) Combined effects of radiative and evaporative cooling on fruit preservation under solar radiation: Sunburn resistance and temperature stabilization. ACS Appl Mater Interfaces 14: 45788–45799. https://doi.org/10.1021/acsami.2c11349 doi: 10.1021/acsami.2c11349
[94]	Ninan N, Muthiah M, Park IK, et al. (2013) Pectin/carboxymethyl cellulose/microfibrillated cellulose composite scaffolds for tissue engineering. Carbohyd Polym 98: 877–885. https://doi.org/10.1016/j.carbpol.2013.06.067 doi: 10.1016/j.carbpol.2013.06.067
[95]	Zhou Z, Qian C, Yuan W (2021) Self-healing, anti-freezing, adhesive and remoldable hydrogel sensor with ion-liquid metal dual conductivity for biomimetic skin. Compos Sci Technol 203: 108608. https://doi.org/10.1016/j.compscitech.2020.108608 doi: 10.1016/j.compscitech.2020.108608
[96]	Quinzio CM, Ayunta CA, Alancay MM, et al. (2018) Physicochemical and rheological properties of mucilage extracted from Opuntia ficus indica (L. Miller). Comparative study with guar gum and xanthan gum. Food Measure 12: 459–470. https://doi.org/10.1007/s11694-017-9659-2 doi: 10.1007/s11694-017-9659-2
[97]	Martin AA, de Freitas RA, Sassaki GL, et al. (2017) Chemical structure and physical-chemical properties of mucilage from the leaves of Pereskia aculeata. Food Hydrocoll 70: 20–28. https://doi.org/10.1016/j.foodhyd.2017.03.020 doi: 10.1016/j.foodhyd.2017.03.020
[98]	Singh S, Bothara SB (2014) Physico-chemical and structural characterization of mucilage isolated from seeds of Diospyros melonoxylon Roxb. Braz J Pharm Sci 50: 713–726. http://dx.doi.org/10.1590/S1984-82502014000400006 doi: 10.1590/S1984-82502014000400006
[99]	Sriamornsak P (2003) Chemistry of pectin and its pharmaceutical uses: A review. Silpakorn Univ Int J 3: 206–228.
[100]	Glaue ÖŞ, Akcan T, Tavman Ş (2023) Thermal properties of ultrasound-extracted okra mucilage. Appl Sci 13: 6762. https://doi.org/10.3390/app13116762 doi: 10.3390/app13116762
[101]	Santos FSD, de Figueirêdo RMF, Queiroz AJM, et al. (2023) Physical, chemical, and thermal properties of chia and okra mucilages. J Therm Anal Calorim 148: 7463–7475. https://doi.org/10.1007/s10973-023-12179-0 doi: 10.1007/s10973-023-12179-0
[102]	Xin F, Lyu Q (2023) A review on thermal properties of hydrogels for electronic devices applications. Gels 9: 7. https://doi.org/10.3390/gels9010007 doi: 10.3390/gels9010007
[103]	Guo H, Ge J, Li L, et al. (2022) New insights and experimental investigation of high-temperature gel reinforced by nano-SiO₂. Gels 8: 362. https://doi.org/10.3390/gels8060362 doi: 10.3390/gels8060362
[104]	Pardeshi S, Damiri F, Zehravi M, et al. (2022) Thermoresponsiveness hydrogel molecule. Encyclopedia https://encyclopedia.pub/entry/25914
[105]	Matsumoto K, Sakikawa N, Miyata T (2018) Thermo-responsive gels that absorb moisture and ooze water. Nat Commun 9: 2315. https://doi.org/10.1038/s41467-018-04810-8 doi: 10.1038/s41467-018-04810-8
[106]	Miranda ND, Renaldi R, Khosla R, et al. (2021) Bibliometric analysis and landscape of actors in passive cooling research. Renew Sust Energ Rev 149: 111406. https://doi.org/10.1016/j.rser.2021.111406 doi: 10.1016/j.rser.2021.111406
[107]	Yang Y, Cui G, Lan CQ (2019) Developments in evaporative cooling and enhanced evaporative cooling–A review. Renew Sust Energ Rev 113: 109230. https://doi.org/10.1016/j.rser.2019.06.037 doi: 10.1016/j.rser.2019.06.037
[108]	Zeyghami M, Goswami DY, Stefanakos E (2018) A review of clear sky radiative cooling developments and applications in renewable power systems and passive building cooling. Sol Energ Mat Sol C 178: 115–128. https://doi.org/10.1016/j.solmat.2018.01.015 doi: 10.1016/j.solmat.2018.01.015
[109]	Zhao B, Wang C, Hu M, et al. (2022) Light and thermal management of the semi-transparent radiative cooling glass for buildings. Energy 238: 121761. https://doi.org/10.1016/j.energy.2021.121761 doi: 10.1016/j.energy.2021.121761
[110]	Cai L, Song AY, Li W, et al. (2018) Spectrally selective nanocomposite textile for outdoor personal cooling. Adv Mater 30: 1–7. https://doi.org/10.1002/adma.201802152 doi: 10.1002/adma.201802152
[111]	Zhao B, Xuan Q, Zhang W, et al. (2023) Low-emissivity interior wall strategy for suppressing overcooling in radiatively cooled buildings in cold environments. Sustain Cities 99: 104912. https://doi.org/10.1016/j.scs.2023.104912 doi: 10.1016/j.scs.2023.104912
[112]	Zhao B, Xu C, Jin C, et al. (2023) Superhydrophobic bilayer coating for passive daytime radiative cooling. Nanophotonics https://doi.org/10.1515/nanoph-2023-0511 doi: 10.1515/nanoph-2023-0511
[113]	Zhao B, Xuan Q, Xu C, et al. (2023) Considerations of passive radiative cooling. Renew Energ 219: 119486. https://doi.org/10.1016/j.renene.2023.119486 doi: 10.1016/j.renene.2023.119486
[114]	Feng C, Yang P, Liu H, et al. (2021) Bilayer porous polymer for efficient passive building cooling. Nano Energy 85: 105971. https://doi.org/10.1016/j.nanoen.2021.105971 doi: 10.1016/j.nanoen.2021.105971
[115]	Lu Z, Strobach E, Chen N, et al. (2020) Passive sub-ambient cooling from a transparent evaporation–insulation bilayer. Joule 4: 2693–2701. https://doi.org/10.1016/j.joule.2020.10.005 doi: 10.1016/j.joule.2020.10.005
[116]	Xu L, Sun D, Tian Y, et al. (2023) Nanocomposite hydrogel for daytime passive cooling enabled by combined effects of radiative and evaporative cooling. Chem Eng J 457: 141231. https://doi.org/10.1016/j.cej.2022.141231 doi: 10.1016/j.cej.2022.141231
[117]	Tu Y, Wang R, Zhang Y, et al. (2018) Progress and expectation of atmospheric water harvesting. Joule 2: 1452–1475. https://doi.org/10.1016/j.joule.2018.07.015 doi: 10.1016/j.joule.2018.07.015
[118]	Pollard J (2023) Hydrogel-coated heat sinks enhance passive CPU cooling efficiency. Available from: https://www.electropages.com.
[119]	Mu X, Shi X, Zhou J, et al. (2023) Self-hygroscopic and smart color-changing hydrogels as coolers for improving energy conversion efficiency of electronics. Nano Energy 10: 108177. https://doi.org/10.1016/j.nanoen.2023.108177 doi: 10.1016/j.nanoen.2023.108177
[120]	Abdo S, Saidani-Scott H, Benedi J, et al. (2020) Hydrogels beads for cooling solar panels: Experimental study. Renew Energ 153: 777–786. https://doi.org/10.1016/j.renene.2020.02.057 doi: 10.1016/j.renene.2020.02.057
[121]	Amith MG, Joshi VV (2022) Cooling enhancement using acacia gum based hydrogel in roof ponds: Model room experimental analysis. Res Square https://doi.org/10.21203/rs.3.rs-1560597/v1 doi: 10.21203/rs.3.rs-1560597/v1
[122]	Future Market Insight. Hydrogel market. Accessed 9 November 2023. Available from: www.futuremarketinsights.com/report/hydrogel-market.

This article has been cited by:

László Zoltán Zöldi, Anna Sára Ligeti, Zoltán Csányi, The migratory impact of COVID‐19: The role of time and distances in the migration decisions of Hungarians during the COVID‐19 pandemic, 2024, 1544-8444, 10.1002/psp.2804

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)