Search Results (18)

Some classical texts on the Sturm–Liouville equation ${(p(x)y^{\prime })}^{\prime }-q(x)y+\lambda \rho (x)y=0$ are revised to highlight further properties of its solutions. Often, in the treatment of the ensuing integral equations, $\rho =const$ is assumed (and, further, $\rho =1$). Instead, here we preserve $\rho (x)$ and make a simple change only of the independent variable that reduces the Sturm–Liouville equation to $y^{″}-q(x)y+\lambda \rho (x)y=0$. We show that many results are identical with those with $\lambda \rho -q=const$. This is true in particular for the mean value of the oscillations and for the analog of the Riemann–Lebesgue Theorem. From a mechanical point of view, what is now the total energy is not a constant of the motion, and nevertheless, the equipartition of the energy is still verified and, at least approximately, it does so also for a class of complex $\lambda$. We provide here many detailed properties of the solutions of the above equation, with $\rho =\rho (x)$. The conclusion, as we may easily infer, is that, for large enough $\lambda$, locally, the solutions are trigonometric functions. We give the proof for the closure of the set of solutions through the Phragmén–Lindelöf Theorem, and show the separate dependence of the solutions from the real and imaginary components of $\lambda$. The particular case of $q(x)=\alpha \rho (x)$ is also considered. A direct proof of the uniform convergence of the Fourier series is given, with a statement identical to the classical theorem. Finally, the proof of J. von Neumann of the completeness of the Laguerre and Hermite polynomials in non-compact sets is revisited, without referring to generating functions and to the Weierstrass Theorem for compact sets. The possibility of the existence of a general integral transform is then investigated. Full article

The clumping index (CI) is a key structural parameter that quantifies the nonrandomness of the spatial distribution of vegetation canopy leaves. Investigating seasonal variations in the CI is crucial, especially for estimating the leaf area index (LAI) and studying global carbon and water cycles. However, accurate estimations of the seasonal CI have substantial challenges, e.g., from the need for accurate hot spot measurements, i.e., the typical feature of the bidirectional reflectance distribution function (BRDF) shape in the current CI algorithm framework. Therefore, deriving a phenologically simplified stable CI product from a high-frequency CI product (e.g., 8 days) to reduce the uncertainty of CI seasonality and simplify CI applications remains important. In this study, we applied the discrete Fourier transform and an improved dynamic threshold method to estimate the start of season (SOS) and end of season (EOS) from the CI time series and indicated that the CI exhibits significant seasonal variation characteristics that are generally consistent with the MODIS land surface phenology (LSP) product (MCD12Q2), although seasonal differences between them probably exist. Second, we divided the vegetation cycle into two phenological stages based on the MODIS LSP product, ignoring the differences mentioned above, i.e., the leaf-on season (LOS, from greenup to dormancy) and the leaf-off season (LFS, after dormancy and before greenup of the next vegetation cycle), and developed the phenologically simplified two-stage CI product for the years 2001–2020 using the MODIS 8-day CI product suite. Finally, we assessed the accuracy of this CI product (RMSE = 0.06, bias = 0.01) via 95 datasets from 14 field-measured sites globally. This study revealed that the CI exhibited an approximately inverse trend in terms of phenological variation compared with the NDVI. Globally, based on the phenologically simplified two-stage CI product, the CI_LOS is smaller than the CI_LFS across all land cover types. Compared with the LFS stage, the quality for this CI product is better in the LOS stage, where the QA is basically identified as 0 and 1, accounting for more than ~90% of the total quality flag, which is significantly higher than that in the LFS stage (~60%). This study provides relatively reliable CI datasets that capture the general trend of seasonal CI variations and simplify potential applications in modeling ecological, meteorological, and other surface processes at both global and regional scales. Therefore, this study provides both new perspectives and datasets for future research in relation to CI and other biophysical parameters, e.g., the LAI. Full article

The Sentinel-2 NDVI time series information content from 2017 to 2023 at a 10 m spatial resolution was evaluated based on the NDVI temporal dependency in five scenarios in central Spain. First, time series were interpolated and then filtered using the Savitzky–Golay, Fast Fourier Transform, Whittaker, and Maximum Value filters. Temporal dependency was assessed using the Q-Ljung-Box and Fisher’s Kappa tests, and similarity between raw and filtered time series was assessed using Correlation Coefficient and Root Mean Square Error. An Interpolating Efficiency Indicator (IEI) was proposed to summarize the number and temporal distribution of low-quality observations. Type of climate, atmospheric disturbances, land cover dynamics, and management were the main sources of variability in five scenarios: (1) rainfed wheat and barley presented high short-term variability due to clouds (lower IEI in winter and spring) during the growing cycle and high interannual variability due to precipitation; (2) maize showed stable summer cycles (high IEI) and low interannual variability due to irrigation; (3) irrigated alfalfa was cut five to six times during summer, resulting in specific intra-annual variability; (4) beech forest showed a strong and stable summer cycle, despite the short-term variability due to clouds (low IEI); and (5) evergreen pine forest had a highly variable growing cycle due to fast responses to temperature and precipitation through the year and medium IEI values. Interpolation after removing non-valid observations resulted in an increase in temporal dependency (Q-test), particularly a short term in areas with low IEI values. The information improvement made it possible to identify hidden periodicities and trends using the Fisher’s Kappa test. The SG filter showed high similarity values and weak influence on dynamics, while the MVF showed an overestimation of the NDVI values. Full article

Nonextensive statistical mechanics has developed into an important framework for modeling the thermodynamics of complex systems and the information of complex signals. To mark the 80th birthday of the field’s founder, Constantino Tsallis, a review of open problems that can stimulate future research is provided. Over the thirty-year development of NSM, a variety of criticisms have been published ranging from questions about the justification for generalizing the entropy function to the interpretation of the generalizing parameter q. While these criticisms have been addressed in the past and the breadth of applications has demonstrated the utility of the NSM methodologies, this review provides insights into how the field can continue to improve the understanding and application of complex system models. The review starts by grounding q-statistics within scale-shape distributions and then frames a series of open problems for investigation. The open problems include using the degrees of freedom to quantify the difference between entropy and its generalization, clarifying the physical interpretation of the parameter q, improving the definition of the generalized product using multidimensional analysis, defining a generalized Fourier transform applicable to signal processing applications, and re-examining the normalization of nonextensive entropy. This review concludes with a proposal that the shape parameter is a candidate for defining the statistical complexity of a system. Full article

This study examined the ability of the green microalgae Chlorella vulgaris to remove arsenic from aqueous solutions. A series of studies was conducted to determine the optimal conditions for biological arsenic elimination, including biomass amount, incubation time, initial arsenic level, and pH values. At 76 min, pH 6, 50 mgL⁻¹ metal concentration, and 1 gL⁻¹ bio-adsorbent dosage, the maximum removal of arsenic from an aqueous solution was 93%. The uptake of As (III) ions by C. vulgaris reached an equilibrium at 76 min of bio-adsorption. The maximum adsorptive rate of arsenic (III) by C. vulgaris was 55 mg/gm. The Langmuir, Freundlich, and Dubinin–Radushkevich equations were used to fit the experimental data. The best theoretical isotherm of Langmuir, Freundlich, or/and Dubinin–Radushkevich for arsenic bio-adsorption by Chlorella vulgaris was determined. To choose the best theoretical isotherm, the coefficient of correlation was used. The data on absorption appeared to be linearly consistent with the Langmuir (q_max = 45 mgg⁻¹; R² = 0.9894), Freundlich (k_f = 1.44; R² = 0.7227), and Dubinin–Radushkevich (q_D–R = 8.7 mg/g; R² = 0.951) isotherms. The Langmuir and Dubinin–Radushkevich isotherms were both good two-parameter isotherms. In general, Langmuir was demonstrated to be the most accurate model for As (III) bio-adsorption on the bio-adsorbent. Maximum bio-adsorption values and a good correlation coefficient were observed for the first-order kinetic model, indicating that it was the best fitting model and significant in describing the arsenic (III) adsorption process. SEM micrographs of treated and untreated algal cells revealed that ions adsorbed on the algal cell’s surface. A Fourier-transform infrared spectrophotometer (FTIR) was used to analyze the functional groups in algal cells, such as the carboxyl group, hydroxyl, amines, and amides, which aided in the bio-adsorption process. Thus, C. vulgaris has great potential and can be found in eco-friendly biomaterials capable of adsorbing arsenic contaminants from water sources. Full article

In the field of corrosion protection coatings, layered double hydroxide (LDH) has gained wide attention as a novel controlled-release nanocontainer. In this paper, by using a co-precipitation to store corrosion inhibitors in layered double hydroxide with barrier properties, an environmentally friendly gallic acid (GA) intercalated layered double hydroxide corrosion protection filler (GA-LDH) was prepared. The epoxy coating was then modified with GA-LDH to improve its corrosion protection performance. The structure, composition, and release behavior of GA-LDH were investigated by a series of characterizations, such as field emission scanning electron microscopy (FE-SEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR) and ultraviolet-visible spectrophotometry (UV-vis). Electrochemical impedance spectroscopy (EIS) and a neutral salt spray test (NSS) were performed to evaluate the effect of EP coating containing GA-LDH on corrosion protection for Q235 steel. The results show that GA-LDH added to an epoxy coating can achieve excellent corrosion protection performance and is expected to be widely used in marine corrosion protection contexts. Full article

In this work, two series of chemically reactive polymers, silane coupling agents (SCAs) and water-soluble polymers, were specifically designed as an additive to improve the ductility of slag geopolymer paste by vibration pressure technique. The influences of organic polymers on the fluidity, rheological behavior, mechanical property, porosity, and toughening mechanism of slag geopolymer were investigated. The polycondensation and bonding characteristics of organic–inorganic products were calculated by ¹H liquid nuclear magnetic resonance (NMR) technology and Fourier transform infrared (FT-IR). The polymerization degree of composite geopolymer was evaluated by ²⁹Si NMR and X-ray photoelectron spectroscopy (XPS). The microscopic morphology of the geopolymer matrix was analyzed using scanning electron microscopy (SEM). The results showed that the dosage of the KH570 and PAA-Na with 5 wt% behaved best in improving the flexural strength and the compressive strength of geopolymer in their corresponding organic series, respectively. The addition of polymers decreased the fluidity and the fluidity loss ratio of geopolymer slurry but reduced the harmful pores of hardened geopolymer. The organic polymers acting as bridge-fixed water molecules weakened the repulsion force, and formed a three-dimensional network through molecular interweaving in a geopolymer matrix. Methacryloxy in silane coupling agents and carboxyl group in water-soluble polymers may contribute to the improvement of hydration product structure through strong bonding with C-A-S-H. Microscopic measurements indicated that the addition of KH570 and PAA-Na in geopolymer could form 73.55% and 72.48% Si-O-Si with C-A-S-H gel, higher than the reference, and increase the polycondensation degree of C-A-S-H phase, reflected by the increased generation of Q² and Q²(1Al) and the longer chain length, leading to a higher densified geopolymer matrix with high ductility. Full article

In this paper, we present the q-Lidstone polynomials which are q-Bernoulli polynomials generated by the third Jackson q-Bessel function, based on the Green’s function of a certain q-difference equation. Also, we provide the q-Fourier series expansions of these polynomials and derive some results related to them. Full article

Classifying fluctuating operating wireless environments can be crucial for successfully delivering authentic and confidential packets and for identifying legitimate signals. This study utilizes raw in-phase (I) and quadrature-phase (Q) samples, exclusively, to develop a low-order statistical feature set for wireless signal classification. Edge devices making decentralized decisions from I/Q sample analysis is beneficial. Implementing appropriate security and transmitting mechanisms, reducing retransmissions and increasing energy efficiency are examples. Wireless sensor networks (WSNs) and their Internet of Things (IoT) utilization emphasize the significance of this time series classification problem. Here, I/Q samples of typical WSN and industrial, scientific and medical band transmissions are collected in a live operating environment. Analog Pluto software-defined radios and Raspberry Pi devices are utilized to achieve a low-cost yet high-performance testbed. Features are extracted from Matlab-based statistical analysis of the I/Q samples across time, frequency (fast Fourier transform) and space (probability density function). Noise, ZigBee, continuous wave jamming, WiFi and Bluetooth signal data are examined. Supervised machine learning approaches, including support vector machines, Random Forest, XGBoost, k nearest neighbors and a deep neural network (DNN), evaluate the developed feature set. The optimal approach is determined as an XGBoost/SVM classifier. This classifier achieves similar accuracy and generalization results, on unseen data, to the DNN, but for a fraction of time and computation requirements. Compared to existing approaches, this study’s principal contribution is the developed low-order feature set that achieves signal classification without prior network knowledge or channel assumptions and is validated in a real-world wireless operating environment. The feature set can extend the development of resource-constrained edge devices as it is widely deployable due to only requiring received I/Q samples and these features are warranted as IoT devices become widely used in various modern applications. Full article

In the design of a building envelope, there is the issue of heat flow through the partitions. In the heat flow process, we distinguish steady and dynamic states in which heat fluxes need to be obtained as part of building physics calculations. This article describes the issue of determining the size of those heat fluxes. The search for the temperature field in a two-dimensional problem is common in building physics and heat exchange in general. Both numerical and analytical methods can be used to obtain a solution. Two methods were dealt with, the first of which was used to obtain the solution in the steady state and the other in the transient. In the steady state a method of initial functions, the basics of which were given by W.Z. Vlasov and A.Y. Lur’e was adopted. Originally MIF was used for analysis of the loads of a flat elastic medium. Since then it was used for solving concrete beams, plates and composite materials problems. Polynomial half-reverse solutions are used in the theory of a continuous medium. Here solutions were obtained by the direct method. As a result, polynomial forms of the considered temperature field were obtained. A Cartesian coordinate system and rectangular shape of the plate were assumed. The problem is governed by the Laplace equation in the steady state and Poisson in the transient state. Boundary conditions in the form of temperature (τ(x), t(y)) or/and flux (p(x), q(y)) can be provided. In the steady state the solution T(x, y) was assumed in the form of an infinite power series developed in relation to the variable y with coefficients C_n depending on x. The assumed solution was substituted into the Fourier equation and after expanding into the Taylor series the boundary condition for y = 0 and y = h was taken into account. From this condition the coefficient C_n can be calculated and, therefore, a closed solution for the temperature field in the plate. Full article

The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic solutions, the so-called inner and outer solutions, are considered. Each of them holds a particular asymptotic relation with the formal ones in terms of asymptotic expansions in the perturbation parameter. The growth rate in the asymptotics leans on the $-1$ -branch of Lambert W function, which turns out to be crucial. Full article

The purpose of this study was to characterize the polysaccharides from Athyrium multidentatum (Doll.) Ching (AMC) rhizome and explore the protective mechanism against d-galactose-induced oxidative stress in aging mice. Methods: A series of experiments, including molecular weight, monosaccharide composition, Fourier transform infrared (FT-IR) spectroscopy, and ¹H nuclear magnetic resonance (¹H NMR) spectroscopy were carried out to characterize AMC polysaccharides. The mechanism was investigated exploring d-galactose-induced aging mouse model. Quantitative real-time reverse transcription polymerase chain reaction (RT-qPCR) and western blotting assays were performed to assess the gene and protein expression in liver. Key findings: Our results showed that AMC polysaccharides were mainly composed of mannose (Man), rhamnose (Rha), glucuronic acid (Glc A), glucose (Glc), galactose (Gal), arabinose (Ara), and fucose (Fuc) in a molar ratio of 0.077:0.088:0.09:1:0.375:0.354:0.04 with a molecular weight of 33203 Da (Mw). AMC polysaccharides strikingly reversed d-galactose-induced changes in mice, including upregulated phosphatidylinositol 3-kinase (PI3K), Akt, nuclear factor-erythroid 2-related factor 2 (Nrf2), forkhead box O3a (FOXO3a), and hemeoxygenase-1 (HO-1) mRNA expression, raised Bcl-2/Bax ratio, downregulated caspase-3 mRNA expression, enhanced Akt, phosphorylation of Akt (p-Akt), Nrf2 and HO-1 protein expression, decreased caspase-3, and Bax protein expression. Conclusion: AMC polysaccharides attenuated d-galactose-induced oxidative stress and cell apoptosis by activating the PI3K/AKT pathway, which might in part contributed to their anti-aging activity. Full article

The polycyclic aromatic hydrocarbon (PAH)-degrading strain Q8 was isolated from oilfield produced water. According to the analysis of a biochemical test, 16S rRNA gene, house-keeping genes and DNA–DNA hybridization, strain Q8 was assigned to a novel species of the genus Gordonia. The strain could not only grow in mineral salt medium (MM) and utilize naphthalene and pyrene as its sole carbon source, but also degraded mixed naphthalene, phenanthrene, anthracene and pyrene. The degradation ratio of these four PAHs reached 100%, 95.4%, 73.8% and 53.4% respectively after being degraded by Q8 for seven days. A comparative experiment found that the PAHs degradation efficiency of Q8 is higher than that of Gordonia alkaliphila and Gordonia paraffinivorans, which have the capacities to remove PAHs. Fourier transform infrared spectra, saturate, aromatic, resin and asphaltene (SARA) and gas chromatography–mass spectrometry (GC–MS) analysis of crude oil degraded by Q8 were also studied. The results showed that Q8 could utilize n-alkanes and PAHs in crude oil. The relative proportions of the naphthalene series, phenanthrene series, thiophene series, fluorene series, chrysene series, C21-triaromatic steroid, pyrene, and benz(a)pyrene were reduced after being degraded by Q8. Gordonia sp. nov. Q8 had the capacity to remediate water and soil environments contaminated by PAHs or crude oil, and provided a feasible way for the bioremediation of PAHs and oil pollution. Full article

Acceleration effects of heat flow are included in the law of heat conduction by eliminating the acceleration term between the equation of motion for a spinless electron and the Boltzmann equipartition energy theorem differentiated with respect to time. The resulting law of heat conduction is a capite ad calcem in temperature as given in Equations (17), (19) and (20). (q_z/k)_z = -(δT/δz) - 1/v_h(δT/δt). Evaluation of use of this equation using the entropy production term reveals that as long as the flux, q, and the temperature accumulation both have the same signs, the law does not violate the second law of thermodynamics. For systems that obey the first law of thermodynamics, this is the case. σ == q/T²(q/k + 1/v_h • q(δT/δt)). In the chemical potential Stokes-Einstein formulation, when acceleration of the molecule is accounted for, a law of diffusion a capite ad calcem concentration results. In cartesian one-dimensional heat conduction in semi-infinite coordinates, the governing equation for temperature or concentration was solved for by the method of Laplace transforms. The results are in terms of the modified Bessel composite function in space and time of the first order and first kind. This is when τ > X. X > τ the solution is in terms of the Bessel composite function in space and time of the first order and first kind. The wave temperature is a decaying exponential in time when X = τ. An approximate expression for dimensionless temperature was obtained by expanding the binomial series in the exponent in the Laplace domain and after neglecting fourth- and higher-order terms before inversion from the Laplace domain. The Fourier model, the damped wave model and the a capite ad calcem in temperature/concentration model solutions are compared side by side in the form of a graph. The a capite ad calcem model solution is seen to undergo the convex to concave transition sooner than the damped wave model. The results of the a capite ad calcem temperature model for distances further from the surface are closer to the Fourier model solution. Full article