Auxiliary Method Research Articles

The high-order exponential semi-implicit scalar auxiliary variable approach for the general nonlocal Cahn-Hilliard equation

The nonlocal Cahn-Hilliard equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard equation. In this paper, based on the exponential semi-implicit scalar auxiliary variable method, the highly efficient and accurate schemes (in time) with unconditional energy stability for solving the nonlocal Cahn-Hilliard equation are proposed. On the one hand, we have demonstrated the unconditional energy stability and mass conservation for the nonlocal Cahn-Hilliard equation with its high-order numerical schemes in the continuous and discrete level carefully and rigorously. On the other hand, in order to reduce the calculation and storage cost in numerical simulation, we use the fast solver based on fast Fourier transform and conjugate gradient approach for spatial discretization. Some numerical simulations involving the Gaussian kernel are presented and show the stability, accuracy, efficiency and unconditional energy stability of the proposed schemes.

Optimization of Selection Suppliers for Rice Raw Material Using AHP (Analytical Hierarchy Processes) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) Methods in CV Gembira

CV Gembira is engaged in the production of Rice Mill with the trademark Osing Rice, and has 3 variants, namely Osing Super, Osing Premium and Osing Gold. Problems CV Gembira one of them is the delay in the delivery of rice raw materials carried out by supplier and also the quality of goods that do not meet the criteria. The AHP method is the preferred method. There are several reasons, namely, AHP provides a hierarchical representation of a problem that is useful in assisting decision making. The selection of the TOPSIS method as an auxiliary method is based on simple logic and has the farthest distance to the negative ideal solution. After performing calculations using the AHP and TOPSIS methods, alternative sequence results are obtained supplier the best that can be used by CV Gembira with a preference value of 0.6249 is owned by UD Bintang Timur.

The use of point-impact techniques in stone processing (pecking) in the sites of forest Trans-Urals

For processing of stone and manufacture of tools, ancient man mastered a variety of methods and tech-niques — beating, splitting into flakes and plates, impact and spin retouching, grinding, sawing, drilling and some others. Of these, the least studied and insufficiently covered in the literature is the point-impact technique (pe-cking). Pecking could have been used both as an auxiliary technique and as the main one. When processing large tools (axes, adzes, pestles), which subsequently were polished, it was an auxiliary method. But when mak-ing a circular groove for tying and hollowing out a blind or through hole, it would have become the main one. In the forest Trans-Urals, the pecking technique was already known in the Mesolithic. A treasure hoard containing six stone axes has been found at the Mesolithic settlement of Ogurdino (Perm Krai). The axes were treated by beating and pecking techniques, followed by partial surface polishing. Also, two axe blanks with lugs (trunnions) from the site of Beregovaya IX in the Gorbunovsky peat bog (Sverdlovsk Region) belong to the Mesolithic. The edges of the tools and the protruding lugs were processed by pecking. A perforated disk-pommel in the shape of a kind of disguise was found in the Late Mesolithic layer of the 2nd Beregovaya site in the Gorbunovsky peat bog. A rounded hole 2.8–3.1 cm in diameter was made in the center of the disc by deep pecking on both sides. The majority of the items processed by pecking were found on mixed sites and date to a wide chronological range from the Neolithic to Bronze Age. Some of them represent accidental single finds. Stone sculptures, tops of maces, axes, adzes, plows, chisels, pestles, fishing sinkers, “ironings” were processed using point-impact re-touching. Tying lines on hammers made of massive pebbles were designed exclusively by pecking. During the Early Iron Age, the pecking technique only further expanded its application. Moreover, it was used not only for shaping products, but for making complex figured ornaments on sculptures and bas-reliefs.

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.

Smartphone-assisted portable paper-based biosensors for rapid and sensitive detection of biomarkers in urine

In the increasing demand for real-time testing, the imperative for a straightforward, rapid, portable, and effective biosensor is evident. In this study, an intelligent paper-based biosensor was developed, employing cost-effective and readily available filter paper as a matrix to prepare boronate affinity paper-based materials. The immobilization of horseradish peroxidase (HRP) from crude horseradish extract onto the material surface was realized. Ultimately, a cold assembly technique was employed to construct this intelligent paper-based biosensor, which combined with a smartphone APP, facilitated the easy, accurate, and simultaneous detection of the content of glucose (GLU), uric acid (UA), and sarcosine (SAR) in urine, significantly enhancing the convenience and practicality of real-time monitoring. Additionally, UV spectroscopy served as an auxiliary method to affirm the reliability of the detection outcomes. For the detection of GLU, UA, and SAR, the biosensor exhibited linear ranges of 2–200, 2–500, and 2–500 µmol L–1, respectively, with detection limits (LODs) of 1 µmol L–1 for all analytes. In practical urine sample analysis, the recovery rates of GLU, UA, and SAR detected by the intelligent paper-based biosensors were within a reasonable range, with relative standard deviations below 3.5 %. This fully demonstrates the high accuracy and reliability of the intelligent paper-based biosensor. The development of this low-cost, portable biosensor provides a new method for the detection of biomarkers related to H2O2.

Risk Evaluate and Control of Volunteer Firefighters Using Group Decision Making

Risk management encompasses all measures taken before the occurrence of risk events to mitigate potential future losses. Although volunteer firefighters serve in a voluntary capacity, their disaster response duties expose them to various risks similar to those faced by professional firefighters. Furthermore, due to differences in training, auxiliary methods, and physical conditions, they may encounter distinct risk factors and potentially higher disaster risks. This paper explores risk identification, control, and reduction for volunteer firefighters through organizational responsibilities and risk management perspectives, employing a group decision making model. Utilizing the Operational Risk Management Integration Tools (ORMIT) and the modified Delphi method, the analysis identifies 54 major risk factors for Taitung County's volunteer firefighters during disaster response duties. These risk factors are categorized according to the 5M model (Man, Machine, Media, Management, Mission), prioritized and addressed using the Main Operational Risk Management List (MOL) and the Risk Control Option Matrix (COM). After proposing corresponding risk control measures, the Average Risk Index (ARI) for the "Potential Risks in Volunteer Firefighters' Disaster Response Duties" decreased from 14.31 to 5.06. The Average Risk Rating (ARR) improved from a high-risk level (H-7) to a low-risk level (L-16). The results demonstrate that through risk identification, assessment, and control procedures, the potential risks faced by volunteer firefighters in disaster response can be significantly reduced.

Use of Endoscopic Ultrasound Elastography to Differentiate between Gastrointestinal Stromal Tumor and Leiomyoma Localized in the Upper Gastrointestinal Tract.

Gastrointestinal stromal tumors (GISTs) have malignant potential. Distinction of GISTs from leiomyoma is important to the decision of follow-up or treatment for upper gastrointestinal tract subepithelial lesions (SELs). There are few studies on the evaluation of gastrointestinal SELs with endoscopic ultrasound (EUS) elastography. To evaluate the efficiency of strain ratio (SR) measurement and Giovannini's classification (Gc) by EUS elastography in differentiating GISTs from leiomyomas. Twenty-three lesions with histopathological diagnoses of 13 GISTs and 10 leiomyomas were evaluated. The lesions' SR values were obtained from EUS reports retrospectively. Giovannini's classification was performed according to the elastography images recorded in the system. The effectiveness of SR and Gc in the distinction between GIST and leiomyomas was evaluated. Twelve of the GISTs and 3 of the leiomyomas were with scores 4 and 5 according to Gc (p = 0.006). Gastrointestinal stromal tumors had a higher SR than leiomyomas (p = 0.001). For the diagnosis of GISTs, sensitivity/specificity/diagnostic accuracy were 92.3%/80%/87% for SR alone, 92.3%/70%/82.6% for Gc alone, and 84.6%/80%/82.6% for the use of both SR and Gc. This is the first study in which semi-quantitative (SR) and qualitative (Gc) methods were evaluated together for the distinction of GISTs and leiomyomas. The sensitivity of SR alone for diagnosing GIST is higher than that of Gc alone or the combination of both methods. Although SR alone does not diagnose GIST, it can be used as an auxiliary method in biopsy and follow-up decisions. Erdem RE, Bektaş M, Ellik ZM, et al. Use of Endoscopic Ultrasound Elastography to Differentiate between Gastrointestinal Stromal Tumor and Leiomyoma Localized in the Upper Gastrointestinal Tract. Euroasian J Hepato-Gastroenterol 2024;14(1):20-23.

A multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy

Multimodal multi-objective optimization problems (MMOPs), which aim to identify as many optimal solutions as possible and exhibit multiple equivalent Pareto optimal solution sets (PSs) that correspond to the same Pareto optimal front (PF), commonly arise in a wide range of optimization problems in the real world. However, some dominated solutions that exhibit greater diversity in the decision space may be substituted by non-dominated solutions with a higher level of decision space crowding. To tackle this issue, this paper proposes a multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy (MMODE_SPDN), which can balance convergence, objective space diversity and decision space diversity. Specifically, two archives are initially updated serially followed by the overall update of the parallel structure, in which the serial-first approach can enhance population diversity and the parallel structure can greatly reduce the amount of calculation. In addition, a dynamic neighbor strategy which utilizes adaptive selection among neighbors to generate difference vectors in the decision space and objective space and then adopts the main and auxiliary parent method during the mutation process is proposed. Furthermore, the utilization of an auxiliary archive and the clustering-based special crowding distance (CSCD) method are employed to facilitate the updating of the archive, thereby enhancing diversity. MMODE_SPDN is compared with other multimodal multi-objective optimization evolutionary algorithms (MMOEAs) on numerous test problems and the experimental results demonstrate that MMODE_SPDN exhibits superior performance.

Dynamics of pulse propagation with solitary waves in monomode optical fibers with nonlinear Fokas system

In this study, a unified auxiliary equation method, which is one of the powerful methods for exploring nonlinear model solutions, is used in the Fokas system, with complex functions representing nonlinear pulse propagation in monomode optical fibers. As a result, we get some solutions, including dark–bright, singular, periodic, bright–dark, Jacobi elliptic functions, trigonometric, hyperbolic and exponential ones. In addition, we use a computer program to generate 3D, 2D and counterplot graphics from the obtained solutions by assigning specific values to the involved parameters. While discussing, the graphs for various values of an arbitrary constant are examined. These findings constitute an important step in understanding how solitary waves are generated in nonlinear media. Since the studied model is used in many domains, including Bose–Einstein condensates and plasma physics, these results improve our theoretical knowledge and open up new avenues for potential real-world applications and the development of cutting-edge technologies.

P‐128: An auxiliary diagnostic method of brain atrophy based on MRI images

Brain atrophy is a structural change in cerebral cortex, which is detected by means of imaging, and clinically diagnosed by a doctor who reads the films. To solve the problem of automatic diagnosis of brain atrophy, a method of automatic segmentation of brain atrophy regions was designed. Under the condition of no human intervention, the widened sulcus region produced by brain atrophy in MRI images is automatically analyzed, and by calculating the ratio of the atrophied region of the posterior sulcus to the brain tissue, it is judged whether the patient has brain atrophy or not. Compared with the traditional diagnosis by reading the film, it is more efficient, clearer and the degree of brain atrophy is quantified parametrically, which has practical application value.

Prior-Guided Adversarial Learning With Hypergraph for Predicting Abnormal Connections in Alzheimer's Disease.

Alzheimer's disease (AD) is characterized by alterations of the brain's structural and functional connectivity during its progressive degenerative processes. Existing auxiliary diagnostic methods have accomplished the classification task, but few of them can accurately evaluate the changing characteristics of brain connectivity. In this work, a prior-guided adversarial learning with hypergraph (PALH) model is proposed to predict abnormal brain connections using triple-modality medical images. Concretely, a prior distribution from anatomical knowledge is estimated to guide multimodal representation learning using an adversarial strategy. Also, the pairwise collaborative discriminator structure is further utilized to narrow the difference in representation distribution. Moreover, the hypergraph perceptual network is developed to effectively fuse the learned representations while establishing high-order relations within and between multimodal images. Experimental results demonstrate that the proposed model outperforms other related methods in analyzing and predicting AD progression. More importantly, the identified abnormal connections are partly consistent with previous neuroscience discoveries. The proposed model can evaluate the characteristics of abnormal brain connections at different stages of AD, which is helpful for cognitive disease study and early treatment.

Effects of Pilates-Combined Training on the Improvement of Flexibility and Pain Relief in Elite Fencers

PURPOSE: This study aimed to examine the effects of incorporating Pilates into the training regimen of elite fencers, focusing on enhancing flexibility and alleviating pain commonly experienced in the sport.METHODS: Twenty-five collegiate male elite fencers were stratified into two groups: a fencing training group (FT, n = 12, age = 18.92 ± 1.08, weight = 71.78 ± 7.43 kg, body mass index [BMI] = 22.32 ± 2.09 kg/m2) and a fencing-Pilates combined training group (FPT, n = 13, age = 19.92 ± 0.64, weight = 70.97 ± 9.14 kg, BMI = 22.61 ± 1.71 kg/m2). Evaluations, including body composition; physical fitness factors; shoulder strength; and joint range of motion in the upper extremities, lower extremities, neck, and spine, were conducted before and after 12 weeks of the intervention. Additionally, examinations of pain catastrophizing and anxiety levels during competitive engagements were performed.RESULTS: There were no statistical differences in body composition, physical fitness factors, or upper-limb strength between the FT and FPT groups. However, the FPT group exhibited a notable enhancement in shoulder abduction of the upper limb when holding a sword, in contrast to the unchanged metrics observed in the FT group. The positive impact of Pilates-combined treatment on flexibility extended to the neck; waist; and lower extremities, such as hip flexion, hip extension, hip abduction, medial rotation, and ankle dorsiflexion, coupled with significant improvements in psychological aspects, such as pain relief and related competition anxiety.CONCLUSIONS: This study confirmed that Pilates-combined treatment can have a beneficial effect on improving flexibility and pain in fencers, and verified the effectiveness of Pilates as an auxiliary training method for elite fencers.

Optical solutions for perturbed conformable Fokas–Lenells equation via Kudryashov auxiliary equation method

This paper is dedicated to the study of optical soliton solutions for the perturbed Fokas–Lenells equation with conformable derivative using the Kudryashov auxiliary equation method. The studied optical solutions include a class of categories, comprising dark, mixed dark-bright, multi bell-shaped, bell-shaped, and wave optical solutions. Furthermore, we analyzed the magnitude of the perturbed conformable Fokas–Lenells equation by investigating the impact of the conformable parameter and the effect of the time parameter on the novel optical solutions. It can be claimed that the current optical soliton solutions are novel and have not existed in the literature. The results obtained illustrate that the proposed method is robust, efficient, and readily applicable for constructing new solutions to a wide range of nonlinear fractional partial differential equations. The results of this study are expected to shed light on the field of soliton theory in nonlinear optics and mathematical physics.

Option pricing under market maker's inventory risk: A case study of China

Recently the pivotal role of financial intermediaries, especially market makers, in the domain of option pricing has received significant attention. This study advances the modeling framework introduced by Fournier (2020) by incorporating market maker's inventory risk into option pricing for the Chinese market. Building on empirical findings, the dynamic of the ratio of market makers’ inventory risks to wealth is modified as continuous GARCH model. Moreover, we propose a general and innovative analytical formulation for option pricing and implied volatility, utilizing the auxiliary model method. The concluding empirical tests affirm the enhanced accuracy of our model over conventional approaches.

On optical soliton solutions of the higher-order Lakshmanan-Porsezian-Daniel model having the cubic-quintic-septic law in the presence of spatio-temporal and chromatic dispersion

The higher-order Lakshmanan-Porsezian-Daniel equation (LPDE) with the cubic-quintic-septic (CQS) law having spatiotemporal and chromatic dispersion terms (STD-CD) is examined to derive new optical soliton solutions. To accomplish this aim, we operated on a simple version of the new extended auxiliary equation method (SAEM26). The optical soliton solutions of the LPDE with CQS as well as STD-CD are constructed in detail. Moreover, 3D-surface, contour, and 2D plots are presented for the bright and periodic singular soliton solutions. Additionally, the effects of diverse model parameters on the bright soliton structure are surveyed, and these effects are displayed with 2D graphics. The findings established in this work can positively contribute to research in nonlinear optics, while the SAEM26 can be effectively applied to similar nonlinear models.

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.

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

This article investigates the non-linear generalized geophysical KdV equation, which describes shallow water waves in an ocean. The proposed generalized projective Riccati equation method and modified auxiliary equation method extract a more efficient and broad range of soliton solutions. These include U-shaped, W-shaped, singular, periodic, bright, dark, kink-type, breather soliton, multi-singular soliton, singular soliton with high amplitude, multiple periodic, multiple lump wave soliton, and flat kink-type soliton solutions. The travelling wave patterns of the model are graphically presented with suitable parameter values using the modern software Maple and Wolfram Mathematica. The visual representation of the solutions in 3D, 2D, and contour surfaces enhances understanding of parameter impact. Sensitivity and modulation instability analyses were performed to offer insights into the dynamics of the examined model. The observed dynamics of the proposed model were presented, revealing quasi-periodic chaotic, periodic systems, and quasi-periodic behaviour. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations.

Stability analysis and retrieval of new solitary waves of (2+1)- and (3+1)-dimensional potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations using auxiliary equation technique

The Kadomtsev–Petviashvili (KP) equations are nonlinear partial differential equations which are widely used for the modeling of wave propagation in hydrodynamic and plasma systems. This study aims to make a valuable contribution to the literature by providing new solitary waves to the (2+1)- and (3+1)-dimensional potential Kadomtsev–Petviashvili (pKP)-B-type Kadomtsev–Petviashvili (BKP) equations. For this, the auxiliary equation method associated with Bernoulli equation is used and new solutions for the considered equations are obtained. The stability of obtained solutions is demonstrated using nonlinear analysis. It is shown that this method for the considered pKP–BKP equations is an important step forward in an overall mathematical framework for similar equations.

Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization.

By using the power-exponential function method and the extended hyperbolic auxiliary equation method, we present the explicit solutions of the subsidiary elliptic-like equation. With the aid of the subsidiary elliptic-like equation and a simple transformation, we obtain the exact solutions of Hirota equation which include bright solitary wave, dark solitary wave, bell profile solitary wave solutions and Jacobian elliptic function solutions. Some of these solutions are found for the first time, which may be useful for depicting nonlinear physical phenomena. This approach can also be applied to solve the other nonlinear partial differential equations.