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This study extended the electromechanical impedance (EMI) technique to monitor the 28‐day age of strength gain in mass concrete, although it has been validated in strength monitoring of a lab‐scaled concrete specimen. Embedded piezoelectric (PZT) transducer, namely, aluminum embedded PZT (AEP), that was wrapped by two sandwich aluminum pastes was proposed for EMI monitoring. The workability of the AEP was first verified via finite element analysis, where the effect of hydration heat on the EMI signature of the AEP was evaluated via numerical modeling and prior thermal test. In the experiment, totally four AEP transducers arranged at different loci were applied to monitor strength gain in a mass concrete specimen. As a comparison, the maturity method was also performed to estimate the strength of the specimen. Characteristics of EMI signature and its statistical indices including root mean square deviation (RMSD) and mean absolute percentage deviation (MAPD) were analyzed and correlated to strength development in mass concrete. Monitoring results indicated that the AEP transducers were capable of identifying the strength gain of mass concrete. The logarithmic function between the RMSD/MAPD index values and compressive strength perfectly predicted the strength development, which could be further employed for real‐life and in situ applications. [ABSTRACT FROM AUTHOR]

To investigate the mechanical and energy dissipation characteristics of gray sandstone at critical failure, dynamic impact compression tests were conducted under different axial pressure and confining pressure levels. The critical energy dissipation density of gray sandstone under different dynamic-static combination loading conditions was determined, and an empirical model for predicting the critical energy dissipation density was established. The conclusions of the current research are: (1) the dynamic peak stress increases and then decreases with increasing axial pressure and increases with increasing confining pressure. The axial pressure turning points of dynamic peak stress from strong to poor under 4 MPa, 8 MPa, and 12 MPa confining pressure conditions were 22.54 MPa, 22.05 MPa, and 23.64 MPa, respectively. (2) The second type of cut line modulus increases and then decreases with the increase of axial pressure, showing a quadratic law of change. (3) When there is no axial pressure, the critical energy dissipation density increases and then decreases with the increase of confining pressure, showing an exponential function change rule. Under the condition of axial pressure, the critical energy dissipation density increases with the increase of confining pressure, showing the change rule of logarithmic function, and increases with the increase of axial pressure and then decreases, showing the change rule of quadratic function. (4) Under the conditions of confining pressure of 4 MPa, 8 MPa, 12 MPa, and axial pressure of 25.00 MPa, 28.33 MPa, and 20.00 MPa, the critical dissipation densities reached the maximum values of 7.01 J cm−3, 7.38 J cm−3, and 8.40 J cm−3, respectively. The empirical model can better predict the critical absorbed energy density of gray sandstone under different dynamic and static combinations loading conditions. [ABSTRACT FROM AUTHOR]

Owing to the remarkable success of the hypergeometric functions of one variable, the authors present a study of some families of hypergeometric functions of two or more variables. These functions include (for example) the Kampé de Fériet-type hypergeometric functions in two variables and Srivastava's general hypergeometric function in three variables. The main aim of this paper is to provide several (presumably new) transformation and summation formulas for appropriately specified members of each of these families of hypergeometric functions in two and three variables. The methodology and techniques, which are used in this paper, are based upon the evaluation of some definite integrals involving logarithmic functions in terms of Riemann's zeta function, Catalan's constant, polylogarithm functions, and so on. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain \Omega \subset \mathbb {R}^{d}, where d=2,3, in terms of the maximum radius of \Omega. We first provide these estimations in the particular case of a ball and a disc. Then we extend them to general shapes using a, derived, monotonicity property of the eigenvalues of the Newtonian operator. The derivation of the lower bounds is quite tedious for the 2D-Logarithmic potential operator. Such upper/lower bounds appear naturally while estimating the electric/acoustic fields propagating in \mathbb {R}^{d} in the presence of small scaled and highly heterogeneous particles. [ABSTRACT FROM AUTHOR]

We investigate the rational solitons of the Kraenkel–Manna–Merle (KMM) system in ferrites via symbolic computation with the ansatz functions technique and logarithmic transformation. The KMM system describes the propagations of the ferromagnetic particles in ferrite materials. Multiwave solitons are reported by using the three-wave technique. Homocentric breathers (HBs) approach is also applied to build new forms of exact solutions. We construct M-shaped solitons and their dynamics are shown via the appropriate values of parameters. Two types of interactions for rational soliton with kink wave are investigated. Additionally, kink cross-rational solitons (KCRSs) and periodic cross-rational solitons (PCRSs) are examined via suitable transformation. [ABSTRACT FROM AUTHOR]

Background: The prevalence of frailty and activities of daily living (ADL) disability may be higher in high-altitude Andean regions, due to chronic hypoxia, malnutrition, and physical challenges. and their association is relevant. This study aimed to evaluate the association between frailty and ADL disability among older adults residing in the Totos district in Peru during the year 2022. Methods: A cross-sectional study was conducted in Totos district (mean altitude: 3286 m above sea level), located in Ayacucho, Peru, during 2022. A complete census was employed including residents aged 60 and above. The exposure variable was frailty, defined by fulfilling 3 or more criteria of the Fried phenotype. The outcome variable was ADL disability, defined as a score below 95 on the Barthel index. Generalized linear models with a Poisson family, logarithmic link function, and robust variances were employed to estimate crude prevalence ratios and adjusted prevalence ratios (aPRs), along with their corresponding 95% confidence intervals (CIs). Results: We evaluated 272 older adults with a mean age of 74 years, of whom 59.9% were female, 62.1% were cohabiting or married and 83.1% had not completed primary education. We found that 19.5% were frail, while 51.1% had ADL disability. In the adjusted regression model, we found frailty increased the prevalence of ADL disability (aPR = 1.77; 95%CI: 1.44–2.16; p < 0.001). Conclusion: Frailty was associated with an increased prevalence of ADL disability. These findings could contribute to establishing government intervention plans to manage disability and frailty within the high-risk group comprising older adults living at high altitudes. [ABSTRACT FROM AUTHOR]

Sustainable development is crucial for conserving resources and ensuring smooth supply chain operations. In the context of the complex task of supplier selection, the traditional assumptions of attribute independencies are frequently found to be inadequate. The effective interaction between attributes and their weights plays a crucial role in navigating the decision outcomes. This paper presents a Choquet integral-based hybrid interactive decision-making approach to address the two important issues regarding the weights and interaction of criteria. To achieve this aim, first a hybrid weight determination method is proposed, combining the merits of multi-objective optimization and clustering techniques. To comprehensively assess the interactions among attributes, a non-additive measure determination method is introduced, leveraging concepts such as standard deviation and correlation. This approach effectively captures the interdependencies among attributes, leading to a more accurate decision-making process. Then, the Choquet integral incorporates a logarithmic function, which serves to enhance the modeling of uncertainty and effectively address the complexities present in intricate decision-making situations. Furthermore, a comprehensive interactive MCDM model is constructed, serving as a framework for supplier selection. Finally, experimental and sensitivity analysis demonstrate the effectiveness and stability of the proposed approach. [ABSTRACT FROM AUTHOR]

Background: Gait speed is associated with a higher prevalence of balance disorders in older adults residing at high altitudes. This study investigated this association in older adults from 12 high-altitude Andean Peruvian communities. Methods: We performed a secondary data analysis from an analytical cross-sectional study of adults >60 years of age, residing in 12 high-altitude Andean Peruvian communities, enrolled between 2013 and 2019. The exposure and outcome variables were gait speed (categorized in tertiles), and balance disorders (defined as a functional reach value of ≤20.32 cm), respectively. We built generalized linear models of the Poisson family with a logarithmic link function and robust variances, and estimated crude prevalence ratios (cPR) and adjusted prevalence ratios (aPR) with 95% confidence intervals (CIs). Results: We analyzed 418 older adults; 38.8% (n=162) were male, and the mean age was 73.2±6.9 years. The mean gait speed and functional reach were 0.66±0.24 m/s and 19.9±6.48 cm, respectively. In the adjusted regression model, the intermediate (aPR=1.88; 95% CI, 1.39–2.55; p<0.001) and low (aPR=2.04; 95% CI, 1.51–2.76; p<0.001) tertiles of gait speed were associated with a higher prevalence of balance disorders. Conclusion: The intermediate and low tertiles of gait speed were associated with a higher prevalence of balance disorders among older adult residents of 12 high-altitude Andean communities. We recommend further research on the behavior of this association to propose interventions for these vulnerable groups and reduce the impact of geriatric conditions. [ABSTRACT FROM AUTHOR]

Heterogeneity of shale pores at nano-scale and micrometer-scale is of great significance to gas transport properties. In this study, the pore structure of shale samples from lower Silurian Longmaxi Formation in the Sichuan basin is investigated by field emission-scanning electron microscopy (FE-SEM) and x-ray micro-computed tomography (Xμ-CT) technology. Based on fractal theory, the lacunarity is introduced to describe the clustering degree of pores in shale matrix, which can compensate for the limitations of fractal dimension. Combining lacunarity with fractal dimension allows for quantification of subtle differences in pore spatial distribution. For FE-SEM images at nano-scales, the fractal dimension changes in a "U" shape, while lacunarity changes in a "∩" shape. For Xμ-CT images at micrometer-scale, both the fractal dimension and lacunarity change in a logarithmic function. Lacunarity at both nano-scale and micrometer-scale linearly decreases with the increase in fractal dimension. By three-dimensional (3D) pore network modeling analysis, the structure properties of the connected pores, such as the number of pores and throats, pore diameter, pore volume, pore surface, throat length, and coordination number, are quantitatively calculated, and these structure parameters show strong heterogeneity. The average coordination number of the connected pores ranges in 2.92–4.36. This indicates that these pores in shale matrix have poor connectivity. The permeability varies from 0.06 to 0.17 μm2 in two-dimensional (2D) Xμ-CT images but from 3.20 to 34.99 μm2 in a 3D structure. The permeability in the 3D structure is about two order higher in magnitude than that in the 2D Xμ-CT images. [ABSTRACT FROM AUTHOR]

Seawater with different salt concentration and different infiltration frequency were simulated to carry out seawatererosion test on standard formed concrete specimens and determine chloride ion content. The determination of internal freechloride ion content, fitting of surface chloride ion content curve, and study on the surface chloride ion concentration time rulewere conducted under different salinity. The content of free chloride ions at different depths under different infiltrationfrequency was determined, and the relationship between surface chloride ion concentration and different infiltration frequencywas analyzed and studied. The results show that the content of free chloride in concrete increases with the increase of salinityand erosion time. The temporal evolution of chloride ion concentration on concrete surface meets the power index model, andthe power index parameter varies with the change of infiltration frequency. Within a certain age, the law of the influence ofsalinity on the chloride ion concentration on the concrete surface meets the logarithmic function model. When the infiltrationfrequency is low, the chloride ion penetration of concrete increases with the increase of the frequency. When the infiltrationfrequency is increased to 12 times/d the infiltration rate of chloride ions slows down and the content of free chloride ions inconcrete decreases. [ABSTRACT FROM AUTHOR]

Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev's estimates, etc.) particularly valuable. These methods also offer avenues for number-theoretic exploration through analytical manipulation. In this work, we introduce a novel approximation function, ϕ(n), which adds to the existing repertoire of approximation methods and provides a fresh perspective for number-theoretic studies. Deeper analytical investigation of ϕ(n) reveals modified representations of the Chebyshev function, prime number theorem, and Riemann zeta function. Computational studies indicate that the difference between ϕ(n) and the logarithmic integral at magnitudes greater than 10100 is less than 1%. [ABSTRACT FROM AUTHOR]

Introduction: Investigations of responses of animals and humans to changes of plasma volume are usually reported as average responses of groups of individuals. This ignores considerable quantitative variation between individuals. We examined the hypothesis that individual responses follow a common temporal pattern with variations reflecting different parameters describing that pattern. Methods: We illustrate this approach using data of Hahn, Lindahl and Drobin (Acta Anaesthesiol Scand.2011, 55:987‐94) who measured urine volume and haemoglobin dilution of 10 female subjects during intravenous Ringer infusions for 30 min and subsequent 3.5 h. The published time courses were digitised and analysed to determine if a family of mathematical functions accounted for the variation in individual responses. Results: Urine excretion was characterised by a time delay (Td) before urine flow increased and a time course of cumulative urine excretion described by a logarithmic function. This logarithmic relation forms the theoretical basis of a family of linear relations describing urine excretion as a function of Td. Measurement of Td enables estimation of subsequent values of urine excretion and thereby the fraction of infused fluid retained in the body. Conclusion: The approach might be useful for physiologists and clinical investigators to compare the response to infusion protocols when both test and control responses can be described by linear relations between cumulative urine volume at specific times and Td. The approach may also be useful for clinicians by complementing strategies to guide fluid therapy by enabling the later responses of an individual to be predicted from their earlier response. [ABSTRACT FROM AUTHOR]

Some Cauchy-type mean-value theorems for Chebychev's inequality, Steffensen's inequality, midpoint rule, and Simpson's rule are presented. Furthermore, we give some applications for the obtained results using the exponential and logarithmic functions, their Taylor polynomials, and some trigonometric functions. Further, we obtain some exponential, logarithmic, and trigonometric equations and give two inequalities for midpoint and Simpson's rules. [ABSTRACT FROM AUTHOR]

Distance decay of urban park visitation (e.g., visitation number and visitation frequency) has been widely acknowledged and is increasingly integrated into urban park planning and management considering spatial accessibility and service equity. However, thorough understandings especially concerning the variations among visitors with different personal characteristics and visitation patterns are still scarce. Taking Changsha, China as an example, we collected data on visitation distance (i.e., the distance between urban parks and visitor's homes) and visitation frequency of 2535 urban park visitors, modeled the distance decay of visitation density and visitation frequency, and investigated their variations among visitors with different personal characteristics and visitation patterns. The results show that: (1) The median visitation distance was 1.3 km and the median visitation frequency was 24 times per season. (2) Both visitation density and visitation frequency showed clear spatial patterns of distance decay and can be effectively modeled using common distance decay functions (e.g., power function, exponential function, and logarithmic function). (3) Visitors' characteristics (e.g., gender and age) and visitation patterns (e.g., duration time, transportation modes, and visitation purposes) significantly impact visitation distance, visitation frequency, and the characteristics of distance decay (i.e., the rate of distance decay). These findings extend our understanding of the distance decay of urban park visitation which can help better urban park planning and management. [ABSTRACT FROM AUTHOR]

To reveal the influence of cement proportion (P) and curing age (T) on the anti-cracking ability of cement soil, notched semi-circular bending specimens were used in this study. Tensile strength tests and mode I fracture tests were performed on cement soils with different P and T. The evolutionary characteristics of the tensile strength σt and mode I fracture toughness KIC were obtained. The test results showed that σt and KIC gradually increased with increasing cement proportion P and curing age T, with both exhibiting a logarithmic function relationship. Predictive models for σt and KIC, which were developed using regression analysis, can be used to evaluate the anti-cracking ability of cement soils. Therefore, the correlation between KIC and σt of cement soils was theoretically analyzed. The variability of the correlation coefficients was discussed in the context of existing research on soil materials, and the differences in the critical dimensions were analyzed based on the correlation coefficients. [ABSTRACT FROM AUTHOR]

In 1956, J.L. Kelly provided the formula for the optimal portion f of one's capital to bet on a coin toss with favorable odds. We show that when the bet can be repeated a fixed number of times, but the game has a maximum payout M, the optimal portion f becomes a function of both k, the number of games remaining, and B, the current bankroll. We describe this function f k (B) and quantify the advantages gained over the fixed Kelly criterion. We also discuss the impact of changing the underlying utility function from a logarithmic utility to a more linear utility, and thereby optimizing a risk-reward ratio. [ABSTRACT FROM AUTHOR]

Malicious attack is a potential threat to collision‐free and connectivity‐preserving formation. In this article, a predictor‐based collision‐free and connectivity‐preserving resilient formation control strategy is proposed for a class of multi‐agent systems under sensor deception attacks. The predictor states are constructed to replace original states in the control strategy, and a novel attack compensator is constructed to suppress sensor deception attacks. Prediction errors, instead of compromised errors, are introduced to update weights of radial basis function neural networks (RBFNNs). To achieve collision avoidance and connectivity preservation, a transformation function in logarithmic form is introduced. To avoid static and dynamic obstacles, an improved artificial potential function (APF) combined with their velocity information is constructed. Furthermore, to solve the local minimum problem in the combining of transformation function and APF, a virtual force is added. Based on the Lyapunov function, all closed‐loop signals are bounded and collision‐free and connectivity‐preserving formation is achieved. The simulation related to a group of quadrotors verifies the effectiveness of the proposed resilient control strategy. [ABSTRACT FROM AUTHOR]

This article considers the adaptive tracking control problem of a class of strict feedback nonlinear systems with unknown time‐varying parameters. Note that the recent adaptive method, that is, congelation of variables, is built upon the assumption that the known basis functions are zeros as zero states. To remove this assumption, a novel monotonically increasing function is designed to transform the output tracking error and the backstepping tracking errors into increasing forms, which is integrated into the congelation of variables to design the σ$$ \sigma $$‐modification adaptive tracking control law. It is noted that the proposed form of monotonically increasing function is general, which includes positive proportional functions, exponential functions, and logarithmic functions and so on. To yield the boundedness of increasing tracking errors, a barrier Lyapunov function is designed. The asymptotic convergence of the resulting adaptive tracking system is analyzed in detail. Simulations demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study explores various wave phenomena related to the concatenation model, which is characterized by the inclusion of the Kerr law of nonlinearity in birefringent fibers. Several distinct auxiliary functions and logarithmic transformation are utilized to formulate various analytical solutions, including multi-wave solutions, two solitary wave solutions, breather waves, periodic cross kink solutions, Peregrine-like rational solutions, and three-wave solutions. To demonstrate the influence of different parameters on the interaction of the obtained solutions, some figures are provided to vividly display these transmission and interaction characteristics. [ABSTRACT FROM AUTHOR]

This paper studies the attitude consensus for nonlinear multi-spacecraft systems with disturbances and limited communication bandwidth and computing resources. A dynamic event-based attitude controller is developed to conserve communication resources, where a positive constant term is introduced to improve resource conservation efficiency. The developed event-driven controller is updated according to the constructed triggering mechanism, which greatly reduces the number of computations for the control algorithm. The triggering mechanism does not require continuous state information of neighboring spacecraft, which indicates that continuous communication is not needed for the operation of the formation system. Then, a self-triggered mechanism using the current triggering information is designed to further avoid continuous computation, and the avoidance of logarithmic functions enables the trigger interval to be close to that of the dynamic event-driven algorithm. The formation system is Zeno-free and uniformly ultimately bounded stable under the proposed event-based consensus control framework with the triggering strategies. Finally, simulations exhibit that the dynamic event-triggered protocol can reduce the communication frequency by 88%, and the self-triggered protocol can reduce the communication and computation frequency by 83% and have higher control accuracy than the dynamic event-triggered protocol. [ABSTRACT FROM AUTHOR]

The Loess Plateau is an important source of particulate matter pollution in North China. In order to establish and repair shelterbelts and improve their function of inhibiting wind erosion and dust, four typical shelterbelts (Populus simonii, Pinus tabulaeformis Carr., Pinus tabulaeformis Carr. × Populus simonii and Caragana korshinskii Kom.) were selected to investigate the inhibition rate of soil wind-erosion and the reduction rates of PM1, PM2.5 and PM10 by stand type, stand structure and soil properties. A sample plot survey and semi-fixed observation method were used to measure wind speed and particulate matter concentration and to calculate wind protection effect, sand transport rate, vertical flux of particulate matter, wind-erosion inhibition rate and particulate matter reduction rate. The results showed that the Pinus tabulaeformis Carr. forest and Caragana korshinskii Kom. forest had the best windproofing effect, at 2 m (82.9% ± 23.8%) and 0.5 m (54.4% ± 21.5%), respectively. The distribution curve of the sediment flux of shelterbelts is a logarithmic function. The wind-erosion inhibition rate and PM1 reduction rate of the Pinus tabulaeformis Carr. forest were significantly greater than those of other stand types (p < 0.05). The generalized linear mixed model (GLMM) shows that the DBH variation coefficient (CV) can effectively explain the reduction rate of PM1. It is suggested that policies be enacted to add or replace Pinus tabulaeformis Carr. forest in polluted areas to prevent wind erosion and dust. [ABSTRACT FROM AUTHOR]

Geogrid is a horizontal reinforcement material that is used in geosynthetic-reinforced pile-supported (GRPS) embankments in freeways with soft soil. Nevertheless, the long-term deformation mechanics of geogrid in the GRPS embankment under cyclic loading is not clear enough. This paper presents a laboratory model study of a GRPS embankment to study the long-term geogrid strain under cyclic loading. The effects of parameters such as number of load cycles, load frequency, geogrid layer numbers, and length of supporting piles on the long-term strain of geogrid were investigated. The results showed that geogrid strain increased with the number of load cycles, mainly developed in the first 10 000 load cycles and increased slowly in the later period. When the frequency was increased from 1 to 5 Hz, geogrid strain increased dramatically. When compared with the condition of a single geogrid layer, the upper layer of two geogrid layers caused a less geogrid strain. Compared with long piles and short piles GRPS embankments, a sufficient membrane effect of geogrid was found for long-short piles GRPS embankments. Finally, the 95% prediction interval proposed in this paper could be expressed using a logarithmic function, providing a theoretical foundation for future engineering applications. [ABSTRACT FROM AUTHOR]

In the recent years, the study of the Hankel determinant problems have been widely investigated by many researchers. We were essentially motivated by the recent research going on with the Hankel determinant and other coefficient bounds problems. In this research article, we first considered the subclass of analytic starlike functions connected with the domain of the tangent function. We then derived the initial four sharp coeffcient bounds, the sharp Fekete-Szegö inequality, and the sharp second and third order Hankel determinant for the defined class. Also, we derived sharp estimates like sharp coefficient bounds, Fekete-Szegö estimate, and sharp second order Hankel determinant for the functions having logarithmic coefficient and for the inverse coefficient, respectively, for the defined functions class. [ABSTRACT FROM AUTHOR]

In the convolutional retinex approach to image lightness processing, an image is filtered by a centre/surround operator that is designed to mitigate the effects of shading (illumination gradients), which in turn compresses the dynamic range. Typically, the parameters that define the shape and extent of the filter are tuned to provide visually pleasing results, and a mapping function such as a logarithm is included for further image enhancement. In contrast, a statistical approach to convolutional retinex has recently been introduced, which is based upon known or estimated autocorrelation statistics of the image albedo and shading components. By introducing models for the autocorrelation matrices and solving a linear regression, the optimal filter is obtained in closed form. Unlike existing methods, the aim is simply to objectively mitigate shading, and so image enhancement components such as a logarithmic mapping function are not included. Here, the full mathematical details of the method are provided, along with implementation details. Significantly, it is shown that the shapes of the autocorrelation matrices directly impact the shape of the optimal filter. To investigate the performance of the method, we address the problem of shading removal from text documents. Further experiments on a challenging image dataset validate the method. [ABSTRACT FROM AUTHOR]

The frost deterioration and deformation of porous rock are commonly investigated under uniform freeze-thaw (FT) conditions. However, the unidirectional FT condition, which is also prevalent in engineering practice, has received limited attention. Therefore, a comparative study on frost deformation and microstructure evolution of porous rock under both uniform and unidirectional FT conditions was performed. Firstly, frost deformation experiments of rock were conducted under cyclic uniform and unidirectional FT action, respectively. Results illustrate that frost deformation of saturated rock exhibits isotropic characteristics under uniform FT cycles, while it shows anisotropic characteristics under unidirectional FT condition with both the frost heaving strain and residual strain along FT direction much higher than those perpendicular to FT direction. Moreover, the peak value and residual value of cumulative frost strain vary as logarithmic functions with cycle number under both uniform and unidirectional FT conditions. Subsequently, the microstructure evolution of rock suffered cyclic uniform and unidirectional FT action were measured. Under uniform FT cycles, newly generated pores uniformly distribute in rock and pore structure of rock remains isotropic in micro scale, and thus the frost deformation shows isotropic characteristics in macro scale. Under unidirectional FT cycles, micro-cracks or pore belts generate with their orientation nearly perpendicular to the FT direction, and rock structure gradually becomes anisotropic in micro scale, resulting in the anisotropic characteristics of frost deformation in macro scale. [ABSTRACT FROM AUTHOR]

Aiming to solve the problems of unclear pore structure, unknown fluid storage and seepage pattern, and inaccurate fluid recoverability evaluation under in situ high pressure of thermal storage, a new method based on in situ high pressure nuclear magnetic resonance displacement test is proposed for evaluating the seepage capacity and recoverability of geothermal fluid under in situ stress. Based on the study of in situ pore structure and movable water content under different displacement pressures, a new prediction method for the recoverable heat of geothermal reservoir fluids is established. This study finds that significant changes in the pore structure of the samples are observed in the in situ test environment. The pore volumes of macropores and mesopores decrease significantly, while the influence of stress on transition pores and micropores is relatively small. Movable water content increases as a logarithmic function with increase in displacement pressure. Considering in situ stress and fluid mobility, the recoverable heat of geothermal fluids predicted under the new assessment methodology is 27.26% of the static predicted resource. Through the establishment of the above model, accurate prediction of recoverable resources can be realized under different in situ stress. [ABSTRACT FROM AUTHOR]

The Heimaguan Tunnel in China serves as a case study to exemplify the variation laws related to surface settlement, deformation, and stress characteristics in a shallow-buried soft-rock tunnel, while emphasizing in the tunnel support requirements. The first stage of this study begins with monitoring the time-varying characteristics of surface settlement, vault subsidence, and the horizontal convergence of Grade V rock. In the second stage, Peck theory is used to calculate the distribution characteristics of surface settlement. The results of both stages are compared to create a vault settlement model, thus establishing the horizontal convergence based on exponential function, logarithmic function and hyperbolic function, and determining the optimal time of secondary lining construction. On this basis, the time-dependent variation laws and characteristics of vertical and horizontal displacement and principal stress of surrounding rock are studied. After this, using simulation and analysis, the proper support is recommended. The study reveals that the surface settlement, vault subsidence, and horizontal convergence of the shallow-buried soft-rock tunnel stabilize within 25–30 days. Peck theory closely aligns with predictions based on exponential functions, with only a 0.72% difference. The recommended time for secondary lining application is 26–27 days. [ABSTRACT FROM AUTHOR]

To simultaneously solve the problems of the state-of-charge (SOC) equalization and accurate current distribution among distributed energy storage units (DESUs) with different capacities in isolated DC microgrids, a multi-storage DC microgrid energy equalization strategy based on the hierarchical cooperative control is proposed. In the primary control layer, the link between the droop coefficient and SOC is established through a logarithmic function, and the droop coefficient is adaptively adjusted according to the SOC value in order to achieve fast SOC equalization. In the secondary control layer, by designing a coordinated state factor, only one PI controller is required to eliminate the influence of the line impedance on the accurate distribution of the output current and the DC bus voltage drop. In the communication layer, local nodes only need to communicate with neighboring nodes without the need for a central controller, and the dynamic consistency algorithm is used to obtain the average value information about the energy storage system (ESS). Finally, the feasibility and effectiveness of the proposed control strategy are verified by experimental analysis on the DC microgrid hardware-in-the-loop experimental platform. [ABSTRACT FROM AUTHOR]

This paper focuses on finding the upper bounds of the second Hankel and Toeplitz determinants, whose entries are logarithmic coefficients of inverse functions for a new subclass of starlike functions with respect to symmetric conjugate points associated with the exponential function defined by subordination. Results on initial Taylor coefficients and logarithmic coefficients of inverse functions for a new subclass are also presented. This study may inspire others to focus further to the coefficient functional problems associated with the inverse functions of various classes of univalent functions. [ABSTRACT FROM AUTHOR]

The study presents results on the dependence of changes in the rheological characteristics (density and viscosity) of the products of phosphogypsum conversion with sodium carbonate on various factors, including temperature, concentration, sodium carbonate rate, stirring duration, and the temperature of the components mixture. Density was determined using the pycnometric method, and viscosity was measured with a VPJ-2 capillary viscometer. An increase in the concentration of sodium carbonate from 5 to 30%, maintaining it at a constant 105% of the stoichiometric rate, leads to an increase in the density and viscosity of the suspension from 1.0813 to 1.3922 g/cm3 and from 0.78 to 3.30 cP at 20°C, and from 1.0514 to 1.3091 g/cm3 and from 0.31 to 1.86 cP at 80°C, respectively. It was shown that increasing the stirring time from 15 to 120 minutes resulted in an average increase in the density and viscosity of the suspension by 1.02 to 1.08 times and 2.20 to 3.07 times, respectively, at 20°C and 80°C. The study revealed that the temperature of the mixture of phosphogypsum and sodium carbonate in the range of 20-90°C significantly increases the density and viscosity from 1.1922 to 1.2381 g/cm3 and from 1.35 to 2.75 cP, respectively, and from 1.1650 to 1.2033 g/cm3 and from 0.50 to 1.77 cP. With a 30-min conversion of phosphogypsum at varying rates (100–110%) and concentrations (10-30%) of sodium carbonate, the degree of phosphogypsum conversion increased from 84.09 to 97.07%. The optimal degree of phosphogypsum conversion (93.94%) was achieved at a sodium carbonate rate of 105% and a concentration of 20%. Experimental data on the rheological properties of the suspension obtained at various rates and concentrations of sodium carbonate showed the possibility of describing these properties using a linear and logarithmic function, with high correlation coefficient values (R2 = 0.95–0.99). The results provide an assessment of the feasibility of easily pumping the suspension in existing industrial equipment. [ABSTRACT FROM AUTHOR]

The Lombok earthquake in August 2018 triggered a sequential rupture with doublet earthquake up to Mw 6.9. This tectonic activity occurred near the main earthquake due to the decay of residual energy from one event to another. This activity is suspected to be a post-seismic deformation process such as afterslip and viscoelastic. In this paper, we conducted a study to determine the deformation pattern. Each of these processes can be investigated by extracting InSAR observational data. Time series from Sentinel-1 SAR is processed using LiCSBAS as data observation and then compare with the model based on exponential and logarithmic functions. The results of combined logarithmic and exponential fitting suggest the Lombok multi-event earthquakes were influenced by seismic activity from dual-releasing residual energy comprises of afterslip and viscoelastic as a dual mechanism with long duration rather than single mechanism. [ABSTRACT FROM AUTHOR]

This study proposes a three-dimensional spray calculation model for a rotary sprinkler to evaluate the characteristics of water droplets under different rotation speeds. The water droplet trajectories are calculated using ballistic trajectory equations, and the secondary breakup of droplets is computed based on the WAVE breakup model. A water superposition model is proposed to calculate the water application rate within the spraying wetted area, and the accuracy of the model is verified through experiments at a rotation speed of 2 rpm. The characteristics of the sprayed droplets are analyzed and compared for five different rotation speeds. The results show that the relationship between droplet velocity and diameter follows an exponential function, while the droplet diameter and distance from the sprinkler follow a logarithmic function. As the rotation speed increases, the diameter of droplets decreases, the velocity and the peak value of specific power increase, and the area of the radially wet region expands. At the pressures of 200 and 300 kPa, the model has average standard deviations of 0.46 and 0.35, respectively, for predicting the water application rate. The prediction errors of the irrigation peak are 8.69% and 2.78%, respectively, confirming the good accuracy of the model. The results of this research can support the water-saving irrigation industry and provide an effective theoretical basis for the arrangement and application of sprinklers in sprinkler irrigation systems. [ABSTRACT FROM AUTHOR]

This study utilized the developmental research design to identify the least taught topics in basic calculus and design and investigate the effectiveness of a Moodle-based courseware package. Data were collected from seven basic calculus teachers and five academic administrators through survey questionnaires, interviews, and validation sheets. The quasi-experimental phase of the study used a pre-/post-test control group design with a sample of 69 students, 34 students in the experimental group and 35 students in the control group. The experimental group received instruction using an asynchronous Moodle-based courseware package, while the control group received instruction through lecture notes. Results showed that the least taught topics include infinite limits, limits at infinity, and limits of trigonometric, exponential, and logarithmic functions. These topics were least taught due to time constraints, students' capacity, scheduling, complexity, and relatability. Validation of the courseware package showed a very high validity. It was found that the use of Moodle-based courseware package and lecture notes effectively increased the students' performance. However, one-way analysis of covariance results showed that the experimental group gained considerably greater than those in the control group. It was recommended that teachers continue to update their knowledge of different teaching methodologies to develop an encouraging and dynamic learning environment. [ABSTRACT FROM AUTHOR]

The paper mainly investigates the initial coefficients for the subclasses of starlike functions defined by using the Sine function involving a (0 = a < 1). We obtain upper bounds for the second and third Toeplitz determinants whose elements are the initial coefficients. Also, we obtain upper bounds of initial logarithmic coefficients for the subclass of starlike functions of order a which are connected with the sine function. Parts of the results we obtained generalized and improved previous work. [ABSTRACT FROM AUTHOR]

Two new assertions characterizing analytically disks in the Euclidean plane ℝ² are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a novel type of analytic bi-univalent functions by utilizing specialized q-Salagean differential operators. Then, we use the q-analogue of the logarithmic function to introduce definition and provide properties of a class of bi-univalent functions. Further, we use the subordination principle to estimate the initial Taylor and Maclaurin coefficients for these given univalent functions. Additionally, we introduce new operators to demonstrate practical applications of the existing theory and establish Fakte-Szego results for each function in the defined sets. Further, we discuss certain coefficient inequalities in detail. [ABSTRACT FROM AUTHOR]

The filled function method is a deterministic algorithm for finding a global minimizer of global optimization problems, and its effectiveness is closely related to the form of the constructed filled function. Currently, the filled functions mainly have three drawbacks in form, namely, parameter adjustment and control (if any), inclusion of exponential or logarithmic functions, and properties that are discontinuous and non-differentiable. In order to overcome these limitations, this paper proposed a parameter-free filled function that does not include exponential or logarithmic functions and is continuous and differentiable. Based on the new filled function, a filled function method for solving unconstrained global optimization problems was designed. The algorithm selected points in the feasible domain that were far from the global minimum point as initial points, and improved the setting of the step size in the stage of minimizing the filled function to enhance the algorithm’s global optimization capability. In addition, tests were conducted on 14 benchmark functions and compared with existing filled function algorithms. The numerical experimental results showed that the new algorithm proposed in this paper was feasible and effective. [ABSTRACT FROM AUTHOR]

Construction activities such as road projects modify original land uses and intensify soil erosion. Understanding the sediment contributed by these projects and its spatial variation throughout a watershed is critical in terms of guiding conservation. Based on field sampling in a road construction-disturbed watershed in southeastern Tibet, a composite fingerprint analysis was conducted to explore the contributions of different sources to the deposited sediment. The results showed that 10 factors, including Al2O3, TFe2O3, Sn, total phosphorous (TP), Cr, Na2O, Mn, W, SiO2, and Sr, formed an optimum composite fingerprint combination. The multivariate mixed model revealed that the average contribution percentage rates of sediment deposited along the main channel were as follows: bank material (52.52%) > roads (33.02%) > forest and grassland (14.46%). The contribution percentage of road-related sediment fluctuated from the beginning point along the channel and was significantly correlated with factors such as the flow length to the channel (R = −0.6), road segment slope (R = 0.66), and ratio of the road length to the channel length (R = 0.65). The flow length to the channel was the most important factor affecting the road sediment contribution and a decreasing logarithmic function was established to describe the effect. These results have clarified how road construction spatially affects sediment at the watershed scale. They can therefore offer guidance for evaluating the environmental impact of human activities and supporting efforts in watershed soil and water conservation. [ABSTRACT FROM AUTHOR]

In order to improve the performance of high-pressure abrasive water jet cutting extremely hard rock, research on the cutting effect and mechanism of abrasive water jet was carried out. The research focused on cutting depth, and one-factor tests were devised to cut hard rock using key parameters of high-pressure abrasive water jets. The cutting performance of the process parameters was assessed using both the cutability index and the energy-consumption index. The mechanism of abrasive water jet cutting hard rocks was examined using a stereomicroscope. The governing relationships of key parameters influencing the effectiveness of abrasive waterjet in breaking extremely hard rocks were investigated. The results indicate a linear correlation between the cutting depth of the abrasive water jet and pump pressure. Additionally, there is a power function relationship with traverse speed and target distance, a quadratic function relationship with abrasive flow, an exponential function relationship with nozzle diameter, and a logarithmic function relationship with cutting times. Under high traverse speed conditions, the removal mechanism of the abrasive water jet on hard rock involves brittle fracture and plastic shear, while on extremely hard rock, it encompasses plastic shear and a minimal amount of brittle fracture. These research findings can serve as a valuable reference for choosing construction parameters for abrasive water jet-assisted TBM cutting of hard rock. [ABSTRACT FROM AUTHOR]

Copyright of Food & Machinery is the property of Food & Machinery Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Guangdong University of Technology is the property of Journal of Guangdong University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this investigation, we study a class of analytic functions of type Carathéodory style in the open unit disk connected with some fractal domains. This class of analytic functions is formulated based on a kind of Langevin differential equations (LDEs). We aim to study the analytic solvability of LDEs in the advantage of geometric function theory consuming the geometric properties of the Julia fractal (JF) and other fractal connected with the logarithmic function. The analytic solutions of the LDEs are obtainable by employing the subordination theory. [ABSTRACT FROM AUTHOR]

The study aimed to develop a quantitative colorimetric loop-mediated isothermal amplification technique using the phenol red indicator (QLAMP-PhR) for detecting Fusobacterium nucleatum (Fn) levels in colorectal cancer (CRC) patients and healthy individuals. QLAMP-PhR assays were conducted on 251 stool samples specific for the Fn FadA gene. Six primers were synthesized and utilized with master mix reagents, and a phenol red indicator was employed to enhance the QLAMP-PhR technique. A standard quantitative analysis curve was generated using a logarithmic function (absorbance vs. concentration) by serially diluting the copy number of genomic DNA templates (Fn ATCC25586). The CRC group exhibited a significantly higher abundance of Fn compared to the healthy control group (P < 0.001). These findings suggest that the QLAMP-PhR technique effectively identifies Fn specifically by its gene for the key virulence factor FadA. Additionally, ideas for developing a real-time QLAMP-PhR test were presented. Compared to the traditional polymerase chain reaction (PCR) technique, QLAMP-PhR offers several advantages including rapidity, simplicity, specificity, sensitivity, and cost-effectiveness method that can quantitatively screen for Fn presence in normal populations. The QLAMP-PhR method represents a sensitive and specific amplification assay for the rapid detection of the Fn pathogen. To the best of our knowledge, this study is the first to report the application of QLAMP-PhR for detecting FadA in Fn. [ABSTRACT FROM AUTHOR]

By employing the bisection series approach, two classes of nonterminating 3 F 2 (1) -series are examined. Several new summation formulae are established in closed form through the summation formulae of Gauss and Kummer for the 2 F 1 (± 1) -series. They are expressed in terms of well-known functions such as π , Euler–Gamma, and logarithmic functions, which can be used in physics and applied sciences for numerical and theoretical analysis. [ABSTRACT FROM AUTHOR]

Ventilation problems are critical in tunnel engineering, and the loss of air volume in ventilation ducts is generally estimated using empirical methods. The air volume calculation makes it difficult to meet the accuracy requirements, resulting in resource waste or insufficient air supply. In this study, the forced ventilation system of the tunnel under construction was investigated based on the computational fluid dynamics method. The mechanism of air leakage on airflow distribution and pollutant transport in the tunnel is determined. Air leakage reduces the distribution peak of pollutants and effectively accelerates the emission of harmful gases. However, this effect decreases with distance from the air duct inlet. Through the calculation results of nearly one hundred models, it is found that the air leakage of the duct can be fitted by logarithmic function and verified by empirical equation. The matching degree between the fitting function of the model and the empirical equation depends on the length of the tunnel. On this basis, the calculation formula of effective air volume near the working face is derived. This study can be applied to the ventilation engineering of the tunnel under construction and provide a theoretical basis for the calculation of the effective air supply. [ABSTRACT FROM AUTHOR]

Exponential DNA amplification techniques are fundamental in ultrasensitive molecular diagnostics. These systems offer a wide dynamic range, but the quantification requires real‐time monitoring of the amplification reaction. Linear amplification schemes, despite their limited sensitivity, can achieve quantitative measurement from a single end‐point readout, suitable for low‐cost, point‐of‐care, or massive testing. Reconciling the sensitivity of exponential amplification with the simplicity of end‐point readout would thus break through a major design dilemma and open a route to a new generation of massively scalable quantitative bioassays. Here a hybrid nucleic acid‐based circuit design is introduced to compute a logarithmic function, therefore providing a wide dynamic range based on a single end‐point measurement. CELIA (Coupling Exponential amplification reaction to LInear Amplification) exploits a versatile biochemical circuit architecture to couple a tunable linear amplification stage – optionally embedding an inverter function – downstream of an exponential module in a one‐pot format. Applied to the detection of microRNAs, CELIA provides a limit of detection in the femtomolar range and a dynamic range of six decades. This isothermal approach bypasses thermocyclers without compromising sensitivity, thereby opening the way to applications in various diagnostic assays, and providing a simplified, cost‐efficient, and high throughput solution for quantitative nucleic acid analysis. [ABSTRACT FROM AUTHOR]

Medical images, especially mammogram images, have low contrast and brightness so mammogram image enhancement is very much necessary in diagnosing breast cancer or tumor at an early stage. Further, enhancement is a crucial step to increase efficiency of computer assisted hardware. This paper proposes a novel image enhancement method using neutrosophic set (NS). A variety of image enhancement algorithms are in literature, but accuracy is still a crucial problem. NS has an ability to handle indeterminant information, thus reducing the uncertainty in the images. The image is initially converted into neutrosophic domain, where an image is represented using three membership degrees—truth membership (T), indeterminacy membership (I), and false membership (F). Indeterminate degree is computed from two information, and these are combined using fuzzy Lukaseiwics t norm. Then a novel neutrosophic divergence score (NDS) is suggested, and computed from fuzzy divergence that measures the degree with respect to an ideal image. This is done to improve the brightness of the image and also highlights fine structures. Then, a modified histogram hyperbolization is used that uses a new logarithmic function to obtain a final enhanced image. Performance of the proposed method is evaluated and compared both qualitatively and quantitatively with recent methods. Experiment has been performed on different types of mammogram images to evaluate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

The functional equation f (x + y) = g (x y) is investigated with unknown functions f : A + A → Y , g : A · A → Y in the following cases: A : = α , β ⊆ F + where F is an Archimedean ordered field; A is the set of all positive integers; A is the set of all positive dyadic rational numbers. The set Y is an arbitrarily fixed (infinite) set. The main result of the paper shows that there exists a set A ⊆ R + that is closed under addition and multiplication and there exist functions f, g : A → Y which satisfy the equation f (x + y) = g (x y) for all x , y ∈ A such that the range of the function f is infinite. Finally, some application of the above results is also given. [ABSTRACT FROM AUTHOR]

In this research article, we introduce new family R G of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for the functions belonging to this newly defined family, demonstrating their sharpness. Furthermore, we find the third Hankel determinant for functions in the class R G . Moreover, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the under-considered class R G are estimated. [ABSTRACT FROM AUTHOR]

In this paper, we create a new subclass of convex functions given with tangent functions applying the combination of Babalola operators and Binomial series. Moreover, we obtain several important geometric results, including sharp coefficient bounds, sharp Fekete–Szego inequality, Kruskal inequality, and growth and distortion estimates. Furthermore, for functions with logarithmic coefficients, we compute sharp Fekete–Szego inequality and sharp coefficient bounds. [ABSTRACT FROM AUTHOR]