Auxiliary Functions Research Articles

Artificial intelligent housekeeper based on consumer purchase decision: a case study of online E-commerce

PurposeThe rise of artificial intelligence (AI) and machine learning has largely promoted the emergence of “autonomous decision-making” (ADM). This paper aims to establish a personalized artificial intelligent housekeeper (AIH) that knows more about our hobbies, habits, personality traits, and shopping needs than ourselves and can replace us to do some habitual purchasing behavior.Design/methodology/approachWe propose an AI decision-making method based on machine learning algorithm, a novel framework for personalized customer preference and purchase. First, the method uses interactive big data to predict a potential consumer’s decision possibility. Then, the method mines the correlation between consumer decision possibility and various factors affecting consumer behavior. Finally, the machine learning algorithm is used to estimate the consumer’s purchase decision according to the comprehensive influencing factors data of the target consumer.FindingsThe experimental results show that the method can predict the regular consumption behavior of consumers in advance and make accurate decision-making behavior. It can find correlations from a large amount of data to help predict many simple purchase decisions in our life, and become our AIH.Originality/valueThis study introduces a new approach that not only has the auxiliary decision-making function but also has the decision-making function. These findings contribute to the research on automated decision-making process of AI and on human–technology interaction by investigating how data attributes consumer purchase decision to AI.

Dimensionless resolutions for heat flux decrement factor and time lag of the wall during cyclic variations in outdoor air temperature

The heat flux decrement factor (DF) and time lag (TL) are two vital indicators for assessing wall dynamic thermal performance. However, computing these indicators involves complex variables such as material thermal properties, wall thickness, and others. Therefore, exploring the inherent relation between these two indicators and the influencing parameters is an urgent problem for reducing building energy consumption. To this end, an analytical method based on the auxiliary function was employed to calculate the heat flux DF and TL of a single-layer wall. Then, the impact of the influencing factors on heat flux DF and TL were evaluated. The results showed that heat flux DF and TL are only determined by two dimensionless parameters: diffusion length and thermal efficiency coefficient. The heat flux DF decreases by at least 5 times as the diffusion length varies from 0 to 2. Besides, it is also affected by the diffusion length when the thermal efficiency coefficient (ε) is less than 5, and the smaller the ε, the smaller the heat flux DF. On the other hand, the heat flux TL increases linearly with the diffusion length initially but declines precipitously as the diffusion length approaches 6–7. When the diffusion length is the same, the heat flux TL slightly decreases as the thermal efficiency coefficient increases.

Optimizing wall structure for enhanced thermal performance: A layer-specific dimensionless parameter analysis in multi-layer walls

Enhancing building energy efficiency and thermal comfort crucially involves optimizing the phase shift (PS) and decrement factor (DF) of exterior walls. Using the auxiliary function method, this paper presents analytical solutions for the DF and PS in double-layer walls, subsequently extending these to multi-layer walls. Insulation and structural material properties (density, thermal conductivity, specific heat capacity), thickness, internal and external convective heat transfer coefficients, outdoor temperature fluctuations, and insulation layering in multi-layered walls were taken into consideration in acquiring analytical solutions. Our findings in double-layer walls and analogous structures show that the DF and PS are largely governed by two dimensionless parameters per layer: thermal diffusivity index and Biot number. Regardless of Biot numbers (ε1 and ε2), an increase in thermal diffusivity indexes (δ1 and δ2) consistently reduces the DF and enhances the PS. Moreover, a larger ε1 with a smaller ε2 generally associates with a lower DF, but their impact on PS is less significant compared to thermal diffusivity index. In multi-layer walls, especially with mirror symmetry, we observe a dual extremum phenomenon, marked by prolonged PS and reduced DF. This underlines the importance of structural configuration in wall thermal performance. Thus, in double-layer structures, while the DF decreases and PS increases with increasing thermal diffusivity index, the influence of Biot numbers is comparatively minimal, highlighting the paramount role of thermal diffusivity index in optimizing thermal behavior. This discovery provides valuable guidance for identifying wall structures with minimal DF and maximal PS during the architectural design phase.

Projective synchronization in fixed/predefined-time for quaternion-valued BAM neural networks under event-triggered aperiodic intermittent control

This study aims to solve the fixed/predefined-time projective synchronization (FTPS/PTPS) of quaternion-valued BAM neural networks (BAMNNs) through event-triggered aperiodic intermittent control (ETAIC). Firstly, a novel quaternion-valued BAMNN model is established by integrating discontinuous activations, parameter uncertainties and time-varying delays. Subsequently, under the framework of the non-separation method several concise ETAIC schemes are designed by utilizing an exponential term instead of a sign function and two power-law terms. Different from the previous time-triggered intermittent controllers, the control and rest intervals of the ETAIC strategies are determined according to the dynamics of the network rather than being pre-specified. Furthermore, several adequate conditions are acquired to guarantee the FTPS and PTPS of the considered networks by constructing auxiliary functions and applying Taylor expansion Ultimately, three simulation examples are presented to confirm the validity and usefulness of the theoretical findings.

Lattice eigenfunction equations of KdV-type *

We develop lattice eigenfunction equations of the lattice KdV equation, which are equations obeyed by auxiliary functions, or eigenfunctions, of the Lax pair of the lattice KdV equation. These equations are three-dimensionally consistent quad-equations, that are closely related to lattice equations in the Adler-Bobenko-Suris (ABS) classification. The connection between the H3(δ), Q1(δ), Q2 and Q3(δ) equations in the ABS classification and the lattice eigenfunction equations is explicitly showed. In particular, we provide a natural interpretation of the δ term in those equations. This can be understood as ‘interactions’ between the eigenfunctions. Other integrable properties of the eigenfunction equations, such as exact solutions, discrete zero curvature conditions are also provided. We believe that the approach presented in this paper can be used as a means to search for integrable lattice equations.>

Relation-Preserving Functional Contractions Involving a Triplet of Auxiliary Functions with an Application to Integral Equations

This article addresses certain fixed-point results in a metric space equipped with a locally transitive binary relation under a functional contraction containing three auxiliary functions. The findings proved herein enrich and improve a number of existing results. In order to prove the credibility of our findings, an illustrative example is provided. Making use of our findings, we study the genuineness of the unique solution to a Fredholm integral equation.

Free and Forced Vibration Analysis of Carbon/Glass Hybrid Composite Laminated Plates Under Arbitrary Boundary Conditions

This paper presents the theoretical investigations on the free and forced vibration behaviours of carbon/glass hybrid composite laminated plates with arbitrary boundary conditions. The unknown allowable displacement functions of the physical middle surface are expressed in terms of standard cosine Fourier series and sinusoidal auxiliary functions to ensure the continuity of the displacement functions and their derivatives at the structural boundaries. Arbitrary boundary conditions are achieved through the introduction of an artificial spring technique. The first shear deformation theory and Lagrange equations are utilized to derive the energy expression, and the eigenvalue equations associated with free and forced vibration are obtained by Rayleigh-Ritz variational operations. Subsequently, these equations are then solved to determine the natural frequency, mode of vibration, and the steady-state displacement response under forced excitation. The new results are compared with those from references and finite element methods to verify the convergence, accuracy and efficiency of the analytical method. The effects of hybrid ratios, stacking sequences, lamination schemes, fibre orientation, boundary conditions and excitation force on the free and forced vibration behaviours of the carbon/glass hybrid composite laminated plates are analyzed in detail.

Refined batch of Estimators for Estimating Population Mean with the help of known Auxiliary Parameters

In the presented work, we have instituted a batch of ratio type estimators for estimating the population mean under simple random sampling with the help of known auxiliary variables or function of auxiliary variables, for more refined result. The expression of bias and mean square error of the instituted class are induced up to the first order of approximation. The strength of the proposed batch of estimators is compared with some existing estimators in terms of MSEs, first theoretically and then a numerical study is also carried out by using real data set to support the findings. It is concluded that the proposed class outperforms the various prevailing estimators in terms of minimum MSE and higher percentage relative efficiency.. KEYWORDS :Estimator, Mean, Bias, Mean square error, Percentage relative efficiency, Auxiliary information.

Pioneering Dermatological Disease Detection with CNNs

Abstract: Skin cancer poses a significant public health concern globally, with its incidence steadily rising. Early and accurate detection plays a pivotal role in improving patient outcomes and survival rates. With leveraging advancements in deep learning, this project explores the efficacy of Convolutional Neural Networks (CNNs) in automating the classification and detection of skin cancer from dermatoscopic images. The methodology employed in this project involves the development and optimization of a CNN architecture tailored for skin cancer analysis. The proposed model harnesses the hierarchical feature learning capabilities of CNN to automatically extract intricate patterns and discriminative features from dermatoscopic images, enabling accurate differentiation among various skin lesion types, including melanoma, basal cell carcinoma, and benign nevi. In addition to classification, the developed CNN architecture integrates a lesion detection mechanism. This auxiliary functionality enables the identification and delineation of potentially cancerous regions within skin lesions. The proposed model’s detection capabilities are evaluated through bounding box prediction and segmentation masks, exhibit notable performance in localizing suspicious areas, aiding dermatologists in targeted examinations. With the help of this project, we can prevent the cause of damage to skin at an early stage.

Application of the Auxiliary Function Method to the Search for the Global Minimum of Functions of Many Variables

Application of the Auxiliary Function Method to the Search for the Global Minimum of Functions of Many Variables

Extension of optimal auxiliary function method to nonlinear Sine Gordon differential equations

In this paper, the new semi-analytical method called optimal auxiliary function method has been extended for finding the approximate solution of the non-linear Sine Gordon and Burger equations. The parameters of the auxiliary function’s optimum values control convergence, and they were determined using the well-known collocation approach. The Modified Adomian Decomposition Technique, Variational Homotopy Perturbation Method, Variational Iteration Method, and the Adomian Decomposition Method are used to compare the results produced by the suggested technique. It has been demonstrated that the suggested approach is straightforward, quickly convergent, effective, and consistent. The proposed method can also be made more accurate when making higher-order approximations.

Fractional view analytical analysis of generalized regularized long wave equation

Abstract In this research study, we focus on the generalized regularized long wave equation and the modified regularized long wave equation, which play pivotal roles in characterizing plasma waves in oceans and ion acoustic waves in shallow water, a domain deeply rooted in physical phenomena. Employing two computational techniques, namely, the optimal auxiliary function method and the Laplace iterative transform method, we approximate these equations. These formulas are used to characterize plasma waves in oceans and ion acoustic waves in shallow water. The results discovered have important ramifications for our comprehension of many physical events. Our results show that both methods are robust, easy to use, and successful. Both methods yield results that are satisfactory to each other. With the use of tables and graphs, we compared the two suggested approaches. The findings suggest that the suggested methods can be widely applied to explore other real-world problems.

Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

In this article, we explore the utilization of the Caputo derivative and the Riemann–Liouville (R–L) fractional integral to analyze the optimal auxiliary function method for approximating fractional nonlinear long waves. Approximate long wave equation with a distinct dispersion relation offers the most accurate description of shallow water wave properties. Various methods, including the Adomian decomposition technique, the variational iteration method, the optimum homotopy asymptotic method, and the new iterative technique, have been employed and compared to those obtained using the fractional-order approximate long wave equation. The results of our study indicate that the optimal auxiliary function method is highly successful and practically simple, achieving better and more rapid convergence after just one repetition. This method is recognized as an efficient approach, demonstrating high precision in solving intriguing and intricate problems. Furthermore, it proves to be more time and resource efficient than other relevant analytical techniques, leading to significant savings in both volume and time. Compared to the Adomian decomposition technique, the new iterative technique, the variational iteration method, and the optimum homotopy asymptotic method, the suggested technique is extremely accurate computationally. It is also easy to analyze and solve fractionally linked nonlinear complex phenomena that arise in science and technology. We present the numerical and graphical findings that support these conclusions.

Nano-engineered versatile Janus natural-skin with sandwich structure for wearable all-season personal thermal management

Thermal management wearables hold significant promise for various applications, such as bio-integrated electronics, multifunctional fabrics, thermoelectric devices, etc. Given the complex and volatile external environmental conditions they may encounter, thermal management wearables should possess versatile and comprehensive auxiliary functions to enable cutting-edge advanced applications. Herein, we present a multifunctional nano-engineered Janus-type natural-skin (SHRC-skin) offering dual-modes of solar heating and radiative cooling. Additionally, the SHRC-skin integrated functionalities like flammability resistance, electromagnetic interference (EMI) shielding, and physiological signal monitoring achieved through the integration of traditional spray techniques and a phase-conversion pathway on natural-skin as a substrate, SHRC-skin enabled all-season thermal management. The radiative cooling side of the SHRC-skin incorporates a CA/Mg11(HPO3)8(OH)6 composite coating with an irregular porous structure, while the solar heating side consists of multi-walled carbon nanotubes (MWCNT) with a rough structure. The radiative cooling layer exhibited a solar reflectance of ∼90.13 % and a mid-infrared emittance of ∼87.6 %, whereas the heating layer demonstrated a solar absorptance of ∼89 %. These attributes translated to excellent thermal management performance in outdoor-tests. Furthermore, SHRC-skin offered extensive additional functionalities, including exceptional asymmetric wetting, flame retardancy, electrical conductivity, Joule heating, electromagnetic shielding, and physiological signal monitoring. This versatility significantly enhances SHRC-skin's adaptability to complex and diverse environments. In summary, the multifunctional SHRC-skin seamlessly transitions between cooling and heating modes without additional energy input. This innovation holds great promise for all-season wearable thermal management, environmentally friendly travel, and energy-efficient building furnishings, and opens new possibilities for the development of wearable materials across various scenarios.

Non-singular control strategies for a class of strict-feedback nonlinear time-delay systems

This paper focuses on the non-singular control for strict-feedback nonlinear time-delay systems. The boundedness of all the signals of the closed-loop system is rigorously proved by introducing a class of Lyapunov-Krasovskii functionals, including exponential functions. Besides, novel auxiliary functions with continuous derivatives are proposed to construct the control law to avoid the discontinuity of the virtual controllers. Besides, the amount of computation is reduced by applying the new auxiliary functions when the other control methods require loads of calculations for handling singular problems. In the end, numerical examples are given to validate the effectiveness of the proposed control scheme.

Symbiotic virus-bacteria interactions in biological treatment of coking wastewater manipulating bacterial physiological activities

Biological treatment is commonly used in coking wastewater (CWW) treatment. Prokaryotic microbial communities in CWW treatment have been comprehensively studied. However, viruses, as the critical microorganisms affecting microbial processes and thus engineering parameters, still remain poorly understood in CWW treatment context. Employing viromics sequencing, the composition and function of the viral community in CWW treatment were discovered, revealing novel viral communities and key auxiliary metabolic functions. Caudovirales appeared to be the predominant viral order in the oxic-hydrolytic-oxic (OHO) CWW treatment combination, showing relative abundances of 62.47 %, 56.64 % and 92.20 % in bioreactors O1, H and O2, respectively. At the family level, Myoviridae, Podoviridae and Siphoviridae mainly prevailed in bioreactors O1 and H while Phycodnaviridae dominated in O2. A total of 56.23–92.24% of novel viral contigs defied family-level characterization in this distinct CWW habitat. The virus-host prediction results revealed most viruses infecting the specific functional taxa Pseudomonas, Acidovorax and Thauera in the entire OHO combination, demonstrating the viruses affecting bacterial physiology and pollutants removal from CWW. Viral auxiliary metabolic genes (AMGs) were screened, revealing their involvement in the metabolism of contaminants and toxicity tolerance. In the bioreactor O1, AMGs were enriched in detoxification and phosphorus ingestion, where glutathione S-transferase (GSTs) and beta-ketoadipyl CoA thiolase (fadA) participated in biodegradation of polycyclic aromatic hydrocarbons and phenols, respectively. In the bioreactors H and O2, the AMGs focused on cell division and epicyte formation of the hosts, where GDPmannose 4,6-dehydratase (gmd) related to lipopolysaccharides biosynthesis was considered to play an important role in the growth of nitrifiers. The diversities of viruses and AMGs decreased along the CWW treatment process, pointing to a reinforced virus-host adaptive strategy in stressful operation environments. In this study, the symbiotic virus-bacteria interaction patterns were proposed with a theoretical basis for promoting CWW biological treatment efficiency. The findings filled the gaps in the virus-bacteria interactions at the full-scale CWW treatment and provided great value for understanding the mechanism of biological toxicity and sludge activity in industrial wastewater treatment.

Analysis of nonlinear fractional-order Fisher equation using two reliable techniques

Abstract In this article, the solution to the time-fractional Fisher equation is determined using two well-known analytical techniques. The suggested approaches are the new iterative method and the optimal auxiliary function method, with the fractional derivative handled in the Caputo sense. The obtained results demonstrate that the suggested approaches are efficient and simple to use for solving fractional-order differential equations. The approximate and exact solutions of the partial fractional differential equations for integer order were compared. Additionally, the fractional-order and integer-order results are contrasted using simple tables. It has been confirmed that the solution produced using the provided methods converges to the exact solution at the appropriate rate. The primary advantage of the suggested method is the small number of computations needed. Moreover, it may be used to address fractional-order physical problems in a number of fields.

Modified optimal auxiliary functions method for approximate-analytical solutions in fractional order nonlinear Foam Drainage equations

The study aims to obtain new approximate analytical solutions for the fractional order nonlinear Foam Drainage equation through a novel modification of the well-known Optimal Auxiliary Functions Method (OAFM). This method systematically constructs auxiliary functions, and by optimizing their parameters, it provides approximate solutions closely mirroring the original behavior of the problem. Numerical simulations, presented in tabular form, demonstrate the effectiveness of the proposed approach. Graphical representations of the solutions are utilized to further validate the applicability and accuracy of the suggested technique. Additionally, the results affirm that the modified OAFM stands out as one of the most effective tools for addressing nonlinear problems in the field of science and technology, thereby contributing valuable addition to the field.

Quantitative Analysis of Phagocytosis in Whole Blood Using Double Staining and Visualization.

Phagocytosis is an essential innate immunity function in humans and animals. A decrease in the ability to phagocytize is associated with many diseases and aging of the immune system. Assessment of phagocytosis dynamics requires quantification of bacteria inside and outside the phagocyte. Although flow cytometry is the most common method for assessing phagocytosis, it does not include visualization and direct quantification of location of bacteria. Here, we used double-labeled Escherichia coli cells to evaluate phagocytosis by flow cytometry (cell sorting) and confocal microscopy, as well as employed image cytometry to provide high-throughput quantitative and spatial recognition of the double-labeled E. coli associated with the phagocytes. Retention of pathogens on the surface of myeloid and lymphoid cells without their internalization was suggested to be an auxiliary function of innate immunity in the fight against infections. The developed method of bacterial labeling significantly increased the accuracy of spatial and quantitative measurement of phagocytosis in whole blood and can be recommended as a tool for phagocytosis assessment by image cytometry.

Pressure characteristics of a nonspherical underwater explosion bubble in a compressible fluid

The pressures produced by underwater explosions present serious threats to ships, submarines, and other marine structures. A significant part of underwater explosion pressure comes from the explosion bubble. Most computational studies on bubble pressure have considered the case of an incompressible fluid or have confined calculations to the time before the formation of a toroidal bubble, because of the complexity and strong nonlinearity of a compressible flow field with a doubly connected geometry. The few compressible models that are capable of calculating the pressure after jet impact suffer from computational difficulties. In this paper, we calculate the bubble pressure by constructing a new form for solving an auxiliary function based on a boundary integral method that takes account of the compressibility of the flow field. We verify out numerical algorithm by comparison with a classical theoretical model and a set of experimental results. We then compare the bubble pressure in a compressible flow field in both the first and second oscillation periods with that in an incompressible flow field. The results of this comparison confirm that it is necessary to consider the compressibility of the fluid and the multiperiod pulsations of a bubble in pressure calculations. We present a comprehensive discussion of the pressure characteristics in the central axial and circumferential directions induced by a nonspherical bubble in a free field. Finally, we obtain a critical bubble–wall distance rw > 1.8 for which the bubble is prevented from splitting after the first jet impact, and we investigate the pressure characteristics of a bubble near a rigid wall for both cases of rw < 1.8 and rw > 1.8.