Modulus Function Research Articles

Simulation and Experimental Study on Indentation Rolling Resistance of a Belt Conveyor

In this paper, in order to reduce the indentation rolling resistance of a belt conveyor and improve its operation efficiency, the indentation rolling resistance of a belt conveyor is studied. Firstly, the theoretical calculation of the indentation rolling resistance caused by the contact between a conveyor belt and an idler is studied. Additionally, the expression of the indentation rolling resistance including the multi-element Maxwell relaxation modulus is simplified and deduced using the assumption of small deformation, and the steps of iterative calculation of the indentation rolling resistance through setting the initial values are designed. Then, the multi-component Maxwell relaxation modulus function of the conveyor belt tested in the previous work of the authors is substituted into COMSOL 5.6 finite element software, and the stress distribution caused by the contact between the conveyor belt and the idler under different working conditions is analyzed. Also, a series of measures to reduce the indentation rolling resistance are found through the laws presented by the simulation results. Finally, the experimental study of the indentation rolling resistance is carried out using the indentation rolling resistance testing device from our research group. By comparing the experimental results for the indentation rolling resistance under different working conditions with the theoretical calculation results for the indentation rolling resistance, it was found that the relative error was less than 13%, which proved the feasibility of the indentation rolling resistance and relaxation modulus testing method, as well as the theoretical calculation method for indentation rolling resistance.

Some Results on Neutrosophic I-Statistically Convergence

This paper introduces the neutrosophic -statistical convergent difference sequence spaces defined through a modulus function. Additionally, we establish new topological spaces and examine various topological properties within these neutrosophic -statistical convergent difference sequence spaces.

Fault identification of rolling bearing based on improved salp swarm algorithm

Due to the rapid development of industrial manufacturing technology, modern mechanical equipment involves complex operating conditions and structural characteristics of hardware systems. Therefore, the state of components directly affects the stable operation of mechanical parts. To ensure engineering reliability improvement and economic benefits, bearing diagnosis has always been a concern in the field of mechanical engineering. Therefore, this article studies an effective machine learning method to extract useful fault feature information from actual bearing vibration signals and identify bearing faults. Firstly, variational mode decomposition decomposes the source signal into several intrinsic mode functions according to the actual situation. The vibration signal of the bearing is decomposed and reconstructed. By iteratively solving the variational model, the optimal modulus function can be obtained, which can better describe the characteristics of the original signal. Then, the feature subset is efficiently searched using the wrapper method of feature selection and the improved binary salp swarm algorithm (IBSSA) to effectively reduce redundant feature vectors, thereby accurately extracting fault feature frequency signals. Finally, support vector machines are used to classify and identify fault types, and the advantages of support vector machines are verified through extensive experiments, improving the ability of global search potential solutions. The experimental findings demonstrate the superior fault recognition performance of the IBSSA algorithm, with a highest recognition accuracy of 97.5%. By comparing different recognition methods, it is concluded that this method can accurately identify bearing failure.

A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces

Abstract The applications of a Fibonacci sequence in mathematics extend far beyond their initial discovery and theoretical significance. The Fibonacci sequence proves to be a versatile tool with real-world implications and the practical utility of manifests in various fields, including optimization algorithms, computer science and finance. In this research paper, we introduce new versions of convergence and summability of sequences in normed spaces with the help of the Fibonacci sequence called weak Fibonacci φ-lacunary statistical convergence and weak Fibonacci φ-lacunary summability, where φ is a modulus function under certain conditions. Furthermore, we obtain some relations related to these concepts in normed spaces.

Lacunary Statistically Convergence via Modulus Function Sequences

Modifying the definition of density functions is one method used to generalise statistical convergence. In the present study, we use sequences of modulus functions and order $\alpha \in \left( 0,1\right] $ to introduce a new density. Based on this density framework, we define strong $(f_k)$-lacunary summability of order $\alpha $ and $(f_k)$-lacunary statistical convergence of order $\alpha $ for a sequence of modulus functions $(f_k)$. This concept holds an intermediate position between the usual convergence and the statistical convergence for lacunary sequences. We also establish inclusion theorems and relations between these two concepts in the study.

Prediction of asphalt concrete energy release rate from Texas Overlay Test using machine learning

This study aimed to apply machine learning (ML) models to predict the energy release rate (ERR) in the Texas Overlay Test (TXOT) for the reflective cracking of asphalt concrete (AC) overlay. The Generalised Finite Element Method model was developed with TXOT experimental results. Subsequently, a TXOT Finite Element database was constructed. Four different cases were formulated, each utilising distinct input variables and the same output variable (i.e. ERR). Five ML models were trained and evaluated for ERR prediction. The model performances were compared across four cases to determine the optimal set of input variables. Shapley Additive exPlanations methods were employed to interpret ML models. The results demonstrated that ML models performed differently across different cases. Artificial Neural Network achieved the highest accuracy in the case which included crack length, crack opening, AC modulus, and sigmoidal function parameters. Therefore, ML models prove to be accurate and reliable for predicting ERR.

Applications of fractional difference operators for new version of Brudno-Mazur Orlicz bounded consistency theorem

In this paper, we intend to prove that the modulus $\mathcal{A}-$lacunary statistical convergence of fractional difference double sequences and modulus lacunary fractional matrix of four-dimensions taken over the space of modulus $\mathcal{A}-$lacunary fractional difference uniformly integrable real sequences are equivalent. We represent another version of the Brudno-Mazur Orlicz bounded consistency theorem by using modulus function, lacunary sequence, and fractional difference operator. We show that the four-dimensional $RH-$ regular matrices $\mathcal{A}$ and $\mathcal{B}$ are modulus lacunary fractional difference consistent over the multipliers space of modulus fractional difference $\mathcal{A}-$summable sequences and an algebra $Z.$

λ-Statistically convergent and λ-statistically bounded sequences defined by modulus functions

In this research paper, we introduce some concepts of λf-density in connection with modulus functions under certain conditions. Furthermore, we establish some relations between the sets of λf-statistically convergent and λf-statistically bounded sequences.

Mucus-coated, magnetically-propelled fecal surrogate to mimic fecal shear forces on colonic epithelium

The relationship between the mechanical forces associated with bowel movement and colonic mucosal physiology is understudied. This is partly due to the limited availability of physiologically relevant fecal models that can exert these mechanical stimuli in in vitro colon models in a simple-to-implement manner. In this report, we created a mucus-coated fecal surrogate that was magnetically propelled to produce a controllable sweeping mechanical stimulation on primary intestinal epithelial cell monolayers. The mucus layer was derived from purified porcine stomach mucins, which were first modified with reactive vinyl sulfone (VS) groups followed by reaction with a thiol crosslinker (PEG-4SH) via a Michael addition click reaction. Formation of mucus hydrogel network was achieved at the optimal mixing ratio at 2.5 % w/v mucin-VS and 0.5 % w/v PEG-4SH. The artificial mucus layer possessed similar properties as the native mucus in terms of its storage modulus (66 Pa) and barrier function (resistance to penetration by 1-μm microbeads). This soft, but mechanically resilient mucus layer was covalently linked to a stiff fecal hydrogel surrogate (based on agarose and magnetic particles, with a storage modulus of 4600 Pa). The covalent bonding between the mucus and agarose ensured its stability in the subsequent fecal sliding movement when tested at travel distances as long as 203 m. The mucus layer served as a lubricant and protected epithelial cells from the moving fecal surrogate over a 1 h time without cell damage. To demonstrate its utility, this mucus-coated fecal surrogate was used to mechanically stimulate a fully differentiated, in vitro primary colon epithelium, and the physiological stimulated response of mucin-2 (MUC2), interleukin-8 (IL-8) and serotonin (5HT) secretion was quantified. Compared with a static control, mechanical stimulation caused a significant increase in MUC2 secretion into luminal compartment (6.4 × ), a small but significant increase in IL-8 secretion (2.5 × and 3.5 × , at both luminal and basal compartments, respectively), and no detectable alteration in 5HT secretion. This mucus-coated fecal surrogate is expected to be useful in in vitro colon organ-on-chips and microphysiological systems to facilitate the investigation of feces-induced mechanical stimulation on intestinal physiology and pathology.

On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences

In this study, we first introduced the definition ∆_ρ^m-statistical convergence for sequences of fuzzy numbers using the generalized difference operator ∆^m. Furthermore, we defined the strong N_F^ρ (∆^m,q)-summable sequence set and the strong N_F^ρ (∆^m,f,q)-summable sequence set for fuzzy difference sequences aided by a modulus function f. Subsequently, we provided certain inclusion theorems between these sets and the S_F^ρ (∆^m ) set.

Modulated Lacunary 𝒫-Statistical Convergence of Order γ of Sequences of Fuzzy Functions

The central objective of this paper is to investigate the lacunary statistical convergence of order [Formula: see text] and strong lacunary summability of order [Formula: see text] for sequences of fuzzy functions by using the modulus function and a regular matrix. We examine the relevant inclusion relations between these spaces under specific conditions. Additionally, we study properties related to these spaces and establish several interesting results.

Unraveling the dielectric and electrical properties of binary BaTiO3/Ba0.98Ca0.01Mg0.01Fe12O19 composites

In this study, composite materials of barium titanate (BaTiO3 or BTO) phase embedded with different contents of Ba0.96Ca0.02Mg0.02Fe12O19 (BCMFO) hexaferrite phase as (BTO)1-x/(BCMFO)x (x = 0.00, 0.02, 0.05, 0.10, and 1.00) composites were prepared. The successful formation of the desired samples was established via X-ray diffraction. Additional peaks showing a chemical reaction between the two phases as a result of the heat treatment were not found. The co-existence of the two-component phases was further confirmed via field emission scanning electron microscopy and energy dispersive X-ray spectroscopy, wherein rounded spherical grains (with nanometric size <200 nm) correspond to the BTO phase while plates-like shaped grains with larger size (with micrometric size) correspond to the BCMFO hexaferrite phase. This study also investigates the impact of the composition ratio of BCMFO to BTO composites on electrical and dielectric properties through comprehensive parameter-based analyses using impedance spectroscopy. Parameters explored include conductivity, dielectric constant, dielectric loss, dissipation factor, and complex modulus, alongside Nyquist analysis of Cole-Cole modulus functions. The activation energies range from approximately 40 to 431 meV. The study suggests the involvement of electron-hole hopping, polaronic, and ionic mechanisms in conduction within intra-grains and grain boundaries. Results reveal strong dependencies of all dielectric parameters on both frequency and composition ratio. Nyquist plots demonstrate distinct semicircles reflecting contributions from intra-grain, grain boundary, and BCMFO components. The extent of dielectric loss is found to be influenced by factors such as porosity, density, homogeneity, and grain size, influenced by sintering and composition conditions. The presence of these semicircles in Nyquist plots indicates different relaxation phenomena associated with charge carrier mobility within the grain boundary and the grain itself. Additionally, the diameter of these semicircles correlates with the resistance values of both grain boundary and grain. These findings suggest the potential for tuning dielectric parameters by adjusting composition ratios, particularly relevant for applications in micro-device technologies such as multilayer chip capacitors and multilayer chip inductors, facing new challenges.

Penyisipan Data Secara Reversible Pada Gambar Medis Menggunakan Metode Difference Expansion of Quad dan Fungsi Modulus

The rapid advancement of the Internet of Things (IoT) brings convenience across various domains, but raises its own challenges, particularly concerning data security and privacy. Cryptography and steganography are two techniques used to secure data. Cryptography protects information by encrypting messages, while steganography hides the existence of data in other media. The embedding of data into other media like medical images necessitates specialized approaches to prevent potential distortion that may compromise their integrity. Distortion in medical images could lead to erroneous diagnoses. In this study, we introduce a reversible data embedding technique capable of returning storage media to its original state without distortion, utilizing the Difference Expansion of Quad and Modulus Function. This approach employs 2×2 pixel blocks to embed 3-bits of data. Our experiments on six medical images demonstrate that the proposed method offers substantial embedding capacity while maintaining high visual quality. The embedding capacity can reach 0.4834 bits per pixel (bpp) with a PSNR of 49.4330 dB. Experimental findings indicate that the proposed method outperforms previous techniques.

Three-dimensional elastic properties of open-cell porous structures: Analytic and finite element modelling

The current paper introduces a three-dimensional micromechanical model of open-cell cellular solid materials and presents the homogenization of the model to an orthotropic continuum. An orthotropic microstructural beam model was created and tested under pure stretch and pure angular distortion to identify the dominant deformation modes by mapping the contributions of normal-, bending- and torsional stiffness to the total strain energy. In the case of unidirectional tension, the deformation mode was dependent primarily on the proportion of normal- and bending stiffnesses, except for the cases with similarly small bending- and torsional stiffness values, where the contribution of torsion was significant. In the case of the pure angular distortion, the key deformation mode was defined by the ratio of bending- and torsional stiffness values, except for the case of large normal- and torsional stiffness values, which resulted in normal-deformation-driven behaviour.The homogenization of the micromodel was conducted by creating an equivalent spring model, by means of which the equivalent elastic modulus values for the main directions of orthotropy have been derived as functions of the geometric and elastic properties of the beams. With the aid of the equivalent spring models, the relative density dependence of Young’s modulus and shear modulus have been examined. The typical second-degree relationship was found to become inaccurate in the range of lower porosity. In the case of increasing relative density values, the exponent of the elastic modulus function decreased while the exponent of the shear modulus increased.

The sets of $$\left( \alpha ,\beta \right) $$-statistically convergent and $$\left( \alpha ,\beta \right) $$-statistically bounded sequences of order $$\gamma $$ defined by modulus functions

The sets of $$\left( \alpha ,\beta \right) $$-statistically convergent and $$\left( \alpha ,\beta \right) $$-statistically bounded sequences of order $$\gamma $$ defined by modulus functions

Laboratory Evaluation of Tensile Creep Behavior of Concrete at Early Ages

Short-term uniaxial tensile creep tests were conducted for early-age concrete at different ages in an effort to characterize early-age concrete as an aging viscoelastic material. Based on the test results, the viscoelastic material properties of the test concrete were characterized in terms of the Dirichlet series creep compliance and relaxation modulus functions. Applications of the model to the numerical analysis of the test samples showed a good agreement between the tests and computational results for the samples tested at different ages. This paper presents the test procedures and data analysis with a brief introduction of theoretical background.

Applications of $$T^r$$-strongly convergent sequences to Fourier series by means of modulus functions

Applications of $$T^r$$-strongly convergent sequences to Fourier series by means of modulus functions

A new mathematical model for the estimation of shear modulus for unsaturated compacted soils

Small-strain shear modulus ( G) is an essential parameter for many geotechnical analyses. Most of shallow foundations are constructed in an unsaturated soil and the shear modulus of the unsaturated soil fluctuates because of the precipitation, evaporation, and rising of ground water table. In this paper, a new mathematical model is proposed for the estimation of the shear modulus function, Gunsat, which defines the relationship between small-strain modulus of unsaturated soil and matric suction. In the proposed model, the soil-water characteristic curve in the form of the degree of saturation is used as the input information. There are additional two parameters named n and C, which can be calibrated with the experimental data, are adopted in the proposed model. The estimated results show good agreement with the experimental data from literature. The proposed method can be used to track the tendency of Gunsat and minimize the data points from the laboratory tests.

Persistent transcendental Bézout theorems

Abstract An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical prediction that the count of zeros of holomorphic self-mappings of the complex linear space should be controlled by the maximum modulus function. We prove that such a bound holds for a modified coarse count inspired by the theory of persistence modules originating in topological data analysis.

Alternating direction method of multipliers for displacement estimation in ultrasound strain elastography.

Ultrasound strain imaging, which delineates mechanical properties to detect tissue abnormalities, involves estimating the time delay between two radio-frequency (RF) frames collected before and after tissue deformation. The existing regularized optimization-based time-delay estimation (TDE) techniques suffer from at least one of the following drawbacks: (1) The regularizer is not aligned with the tissue deformation physics due to taking only the first-order displacement derivative into account; (2) The -norm of the displacement derivatives, which oversmooths the estimated time-delay, is utilized as the regularizer; (3) The modulus function defined mathematically should be approximated by a smooth function to facilitate the optimization of -norm. Our purpose is to develop a novel TDE technique that resolves the aforementioned shortcomings of the existing algorithms. Herein, we propose employing the alternating direction method of multipliers (ADMM) for optimizing a novel cost function consisting of -norm data fidelity term and -norm first- and second-order spatial continuity terms. ADMM empowers the proposed algorithm to use different techniques for optimizing different parts of the cost function and obtain high-contrast strain images with smooth backgrounds and sharp boundaries. We name our technique ADMM for totaL variaTion RegUlarIzation in ultrasound STrain imaging (ALTRUIST). ALTRUIST's efficacy is quantified using absolute error (AE), Structural SIMilarity (SSIM), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and strain ratio (SR) with respect to GLUE, OVERWIND, and -SOUL, three recently published energy-based techniques, and UMEN-Net, a state-of-the-art deep learning-based algorithm. Analysis of variance (ANOVA)-led multiple comparison tests and paired -tests at overall significance level were conducted to assess the statistical significance of our findings. The Bonferroni correction was taken into account in all statistical tests. Two simulated layer phantoms, three simulated resolution phantoms, one hard-inclusion simulated phantom, one multi-inclusion simulated phantom, one experimental breast phantom, and three in vivo liver cancer datasets have been used for validation experiments. We have published the ALTRUIST code at http://code.sonography.ai. ALTRUIST substantially outperforms the four state-of-the-art benchmarks in all validation experiments, both qualitatively and quantitatively. ALTRUIST yields up to , , and SNR improvements and , , and CNR improvements over -SOUL, its closest competitor, for simulated, phantom, and in vivo liver cancer datasets, respectively, where the asterisk (*) indicates statistical significance. In addition, ANOVA-led multiple comparison tests and paired -tests indicate that ALTRUIST generally achieves statistically significant improvements over GLUE, UMEN-Net, OVERWIND, and -SOUL in terms of AE, SSIM map, SNR, andCNR. A novel ultrasonic displacement tracking algorithm named ALTRUIST has been developed. The principal novelty of ALTRUIST is incorporating ADMM for optimizing an -norm regularization-based cost function. ALTRUIST exhibits promising performance in simulation, phantom, and in vivoexperiments.