Inverse Function Research Articles

A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains

AbstractConditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so‐called weak ‐functions. It featured prominently in the monograph Orlicz Spaces and Generalized Orlicz Spaces [P. Harjulehto and P. Hästö, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019]. While generally successful, the inverse function formulation of the decay condition (A2) in the monograph contains a flaw, which we explain and correct in this note. We also present some new results related to the conditions, including a more general result for the density of smooth functions.

Damage detection for high-speed railway standard box girders based on time–frequency characteristics of train-induced strain

This paper presents a novel approach for detecting damage in high-speed railway standard box girders by leveraging the time–frequency characteristics of train-induced strain. Based on the mechanical and deformation characteristics of high-speed railway box girders, the method involves segmenting the box girder into distinct components based on plate element analysis to identify their damage separately. It utilizes coefficients derived from wavelet transforms as indicators sensitive to damage, and employs the particle swarm optimization algorithm (PSO) to determine the ideal frequency intervals in terms of number and position. Within these optimal frequency intervals, the sum of wavelet coefficients is only sensitive to damage features while remaining unaffected by environmental and operational variations. A convolutional denoising autoencoder is employed to remove noise from the strain time–frequency image, improving the robustness of the proposed method. By utilizing the Gaussian inverse cumulative distribution function to estimate confidence boundary (CB) for damage features (DF), outliers are detected, allowing for precise damage localization and quantification. A case study for the high-speed railway box girder show that the proposed method can effectively identify, locate and quantify damage across all components in the critical key section by using data acquired from just 4 strain sensors. This method holds promise for facilitating the development of effective maintenance strategies for high-speed railway box girders.

Study of quantum calculus for a new subclass of bi-univalent functions associated with the cardioid domain

In this article, we make use of the concepts of subordination and the q-calculus theory to analyze a new class of analytic bi-univalent functions associated to the cardioid domain. Our main focus is to derive a sharp inequality for a newly defined class of analytic and bi-univalent functions in the open unit disc U. We explore the bounds of initial coefficients, Fekete-Szegö type problems, and coefficient inequalities for newly established families. In addition, we explore some recent findings for the bi-univalent function and inverse function. Additionally, a few well-known results are mentioned to help make links between earlier and current results.

Photometric Analysis for Asteroid (81) Terpsichore using Convex Inversion and Phase Function Fitting Methods

The shapes and rotation states (periods and pole orientations) of main-belt asteroids are important for understanding their formation and evolution. In order to obtain sufficient photometric data covering different apparitions for asteroid (81) Terpsichore, ground-based photometric observations in 2020 and 2021 were carried out. By combining published and newly obtained photometric data, we calculated the shape and spin parameters for (81) Terpsichore using the convex inversion method. With this method, we have derived a best fitted pole orientation— ( 22.2±3.13.3◦,17.5±5.510.8◦ ) with a spin period of 10.94 ±0.010.01 h. Based on the derived convex shape of (81) Terpsichore, we have fitted the H, G 1, G 2 phase function using the calibrated TESS data and Gaia data after accounting for the lightcurve amplitude correction. As a result, we have derived its absolute magnitude H = 8.68 ±0.190.22 mag with corresponding phase function parameters G 1 = 0.82 ±0.100.09 and G 2 = 0.02 ±0.020.03 .

Improved Snake Optimizer Using Sobol Sequential Nonlinear Factors and Different Learning Strategies and Its Applications

The Snake Optimizer (SO) is an advanced metaheuristic algorithm for solving complicated real-world optimization problems. However, despite its advantages, the SO faces certain challenges, such as susceptibility to local optima and suboptimal convergence performance in cases involving discretized, high-dimensional, and multi-constraint problems. To address these problems, this paper presents an improved version of the SO, known as the Snake Optimizer using Sobol sequential nonlinear factors and different learning strategies (SNDSO). Firstly, using Sobol sequences to generate better distributed initial populations helps to locate the global optimum solution faster. Secondly, the use of nonlinear factors based on the inverse tangent function to control the exploration and exploitation phases effectively improves the exploitation capability of the algorithm. Finally, introducing learning strategies improves the population diversity and reduces the probability of the algorithm falling into the local optimum trap. The effectiveness of the proposed SNDSO in solving discretized, high-dimensional, and multi-constraint problems is validated through a series of experiments. The performance of the SNDSO in tackling high-dimensional numerical optimization problems is first confirmed by using the Congress on Evolutionary Computation (CEC) 2015 and CEC2017 test sets. Then, twelve feature selection problems are used to evaluate the effectiveness of the SNDSO in discretized scenarios. Finally, five real-world technical multi-constraint optimization problems are employed to evaluate the performance of the SNDSO in high-dimensional and multi-constraint domains. The experiments show that the SNDSO effectively overcomes the challenges of discretization, high dimensionality, and multi-constraint problems and outperforms superior algorithms.

A Rapid Detection Method for Coal Ash Content in Tailings Suspension Based on Absorption Spectra and Deep Feature Extraction

Traditional visual detection methods that employ image data are often unstable due to environmental influences like lighting conditions. However, microfiber spectrometers are capable of capturing the specific wavelength characteristics of tail coal suspensions, effectively circumventing the instability caused by lighting variations. Utilizing spectral analysis techniques for detecting ash content in tail coal appears promising as a more stable method of indirect ash detection. In this context, this paper proposes a rapid detection method for the coal ash content in tailings suspensions based on absorption spectra and deep feature extraction. Initially, a preprocessing method, the inverse time weight function (ITWF), is presented, focusing on the intrinsic connection between the sedimentation phenomena of samples. This enables the model to learn and retain spectral time memory features, thereby enhancing its analytical capabilities. To better capture the spectral characteristics of tail coal suspensions, we designed the DSFN (DeepSpectraFusionNet) model. This model has an MSCR (multi-scale convolutional residual) module, addressing the conventional models’ oversight of the strong correlation between adjacent wavelengths in the spectrum. This facilitates the extraction of relative positional information. Additionally, to uncover potential temporal relationships in sedimentation, we propose a CLSM-CS (convolutional long-short memory with candidate states) module, designed to strengthen the capturing of local information and sequential memory. Ultimately, the method employs a fused convolutional deep classifier to integrate and reconstruct both temporal memory and positional features. This results in a model that effectively correlates the ash content of suspensions with their absorption spectral characteristics. Experimental results confirmed that the proposed model achieved an accuracy of 80.65%, an F1-score of 80.45%, a precision of 83.43%, and a recall of 80.65%. These results outperformed recent coal recognition models and classical temporal models, meeting the high standards required for industrial on-site ash detection tasks.

Unveiling the Doping- and Temperature-Dependent Properties of Organic Semiconductor Orthorhombic Rubrene from First Principles

Due to its large hole mobility, organic rubrene (C42H28) has attracted research questions regarding its applications in electronic devices. In this work, extensive first-principles calculations are performed to predict some temperature- and doping-dependent properties of organic semiconductor rubrene. We use density functional theory (DFT) to investigate the electronic structure, elastic and transport properties of the orthorhombic phase of the rubrene compound. The calculated band structure shows that the orthorhombic phase has a direct bandgap of 1.26 eV. From the Vickers hardness (1.080 GPa), our calculations show that orthorhombic rubrene is not a super hard material and can find useful application as a flexible semiconductor. The calculated transport inverse effective mass and electronic fitness function show that the orthorhombic rubrene crystal structure is a p-type thermoelectric material at high temperatures.

Evaluation of crankshaft phenomenon after posterior fusion for early onset scoliosis using an inverse trigonometric function: a multicenter retrospective cohort study.

The crankshaft phenomenon (CSP) is a corrective loss after posterior surgery for early onset scoliosis (EOS). However, an accurate method for CSP evaluation has yet to be developed. In this study, we evaluated pedicle screw (PS) length and rotation angle using an inverse trigonometric function and investigated the prevalence of the CSP. Fifty patients from nine institutions (mean age 10.6years, male/female ratio 4:46) who underwent early definitive fusion surgery at ≤ 11years of age were included. The rotation angle was calculated as arctan (lateral/frontal PS length) using radiography. Measurements were taken at the apex and lower instrumented vertebra (LIV) immediate, 2-, and 5-year postoperatively. CSP was defined as a rotation angle progression ≥ 5°. We divided patients into CSP and non-CSP groups and measured the demographic parameters, Risser grade, state of the triradiate cartilage, major coronal Cobb angle, T1-T12 length, T1-S1 length, and presence of distal adding-on (DAO). We compared these variables between groups and investigated the correlation between the measured variables and vertebral rotation. Logistic regression analysis investigated factors associated with CSP. The rotation angle progressed by 2.4 and 1.3° over 5years for the apex and LIV, respectively. CSP occurred in 15 cases (30%), DAO in 11 cases (22%), and CSP and DAO overlapped in 4 cases (8%). In the CSP group, the T1-T12 length was low immediate postoperatively. The rotation angle was negatively correlated with preoperative height (r = -0.33), T1-T12 length (r = -0.35), and T1-S1 length (r = -0.30). A lower preoperative T1-T12 length was associated with CSP (odds ratio: 0.996, p = 0.048). CSP occurred in 30% of patients with EOS who underwent definitive fusion. The presence of CSP was associated with a lower preoperative T1-T12 length. Diagnosis, level IV.

High-Resolution Depth-Discrete Analysis of PFAS Distribution and Leaching for a Vadose-Zone Source at an AFFF-Impacted Site.

The long-term leaching of polyfluoroalkyl substances (PFAS) within the vadose zone of an AFFF application site for which the depth to groundwater is approximately 100 m was investigated by characterizing the vertical distribution of PFAS in a high spatial resolution. The great majority (99%) of PFAS mass resides in the upper 3 m of the vadose zone. The depths to which each PFAS migrated, quantified by moment analysis, is an inverse function of molar volume, demonstrating chromatographic separation. The PFAS were operationally categorized into three chain-length groups based on the three general patterns of retention observed. The longest-chain (>∼335 cm3/mol molar volume) PFAS remained within the uppermost section of the core, exhibiting minimal leaching. Conversely, the shortest-chain (<∼220 cm3/mol) PFAS accumulated at the bottom of the interval, which coincides with the onset of a calcic horizon. PFAS with intermediate-chain lengths were distributed along the length of the core, exhibiting differential magnitudes of leaching. The minimal or differential leaching observed for the longest- and intermediate-chain-length PFAS, respectively, demonstrates that retention processes significantly impacted migration. The accumulation of shorter-chain PFAS at the bottom of the core is hypothesized to result from limited deep infiltration and potential-enhanced retention associated with the calcic horizon.

A depth-variant wavelet extraction method based on the orthogonal matching pursuit for direct inversion

The results of pre-stack depth migration reflect subsurface structures directly. However, it is an urgent geophysical problem that how to deal with this non-stationarity exhibited by depth-domain seismic data and achieve high precision reservoir prediction. To address this issue, we develop a depth-variant wavelet extraction method based on the orthogonal matching pursuit and attain direct inversion of the depth-domain acoustic impedance using the depth-variant wavelets. First, the parameters of source wavelets estimated by complex seismic trace analysis are utilized to construct the overcomplete dictionary. Secondly, the overcomplete dictionary is used to decompose the depth-domain seismic traces by orthogonal matching pursuit. Thirdly, we extract the depth-variant Ricker wavelets from the decomposed optimal atoms. Test of examples demonstrates that the proposed depth-variant wavelet method has high accuracy. The synthetic seismogram obtained by the proposed method has high Pearson correlation coefficients of 99%, which verifies that our method is feasible and accurate. Next, a depth-domain impedance trend constraint is introduced into the objective function of the conventional basis pursuit inversion to enhance the lateral continuity. Finally, the objective function with impedance trend constraint is solved by basis pursuit for depth-domain acoustic impedance. We test the direct depth-domain acoustic impedance inversion method on the synthetic and field data, which indicates that our method has high accuracy and robustness. The mean relative error of its inversion result is only 0.9% for the noise-free example and about 5% for the strong noisy example. Therefore, our method can be effectively applied to the seismic-well calibration and seismic impedance inversion in the depth domain. And it has powerful potential in reservoir characterization, fluid prediction and attribute extraction in the depth domain. Additionally, the energy distribution features of the Ricker wavelet are derived and analyzed, which can guide the application of the Ricker wavelet in seismic signal analysis.

The second Hankel determinant for logarithmic coefficients of inverse functions of bounded turning of a given order

The sharp bound of the second Hankel determinant of logarithmic coefficients of inverse functions of bounded turning of order α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is computed.

Conjunctive Queries with Negation and Aggregation: A Linear Time Characterization

In this paper, we study the complexity of evaluating Conjunctive Queries with negation (\cqneg). First, we present an algorithm with linear preprocessing time and constant delay enumeration for a class of CQs with negation called free-connex signed-acyclic queries. We show that no other queries admit such an algorithm subject to lower-bound conjectures. Second, we extend our algorithm to Conjunctive Queries with negation and aggregation over a general semiring, which we call Functional Aggregate Queries with negation (\faqneg). Such an algorithm achieves constant delay enumeration for the same class of queries but with a slightly increased preprocessing time, which includes an inverse Ackermann function. We show that this surprising appearance of the Ackermmann function is probably unavoidable for general semirings but can be removed when the semiring has a specific structure. Finally, we show an application of our results to computing the difference of CQs.

Dispersion Analysis of Perpendicular Modes Using a Hybrid Two-Trace Two-Dimensional (2T2D) Smart Error Sum.

Using linear dichroism theory, one would assume that a z-cut of a uniaxial crystal is equivalent to an x-cut to determine the perpendicular component of the dielectric tensor and the corresponding oscillator parameters. However, Fresnel's equations show that the effect of interfaces in the form of the continuity relations of the different components of the electric field must be considered. A consequence of the continuity relations is that perpendicular modes increase less significantly in strength with increasing angle of incidence than expected. This is a consequence of the fact that it is the inverse of the perpendicular component of the dielectric function that increasingly becomes important with a growing angle of incidence. An inverse dielectric function, however, has typically much smaller values than the dielectric function. An additional consequence is that perpendicular modes are blueshifted and coupled in such a way that oscillator strength is transferred to the higher wavenumber mode. Thus, the spectral signatures of perpendicular modes are often weak and masked by the parallel modes when two modes overlap. Accordingly, to enable dispersion analysis, it is suggested to use a hybrid of the conventional residual sum of squares and the two-trace two-dimensional (2T2D) smart error sum, which can correct systematic multiplicable errors in the experimental spectrum. As demonstrated for fresnoite (Ba2TiSi2O8), this is an important step toward determining the perpendicular component of the dielectric tensor and the corresponding oscillator parameters using dispersion analysis, since asynchronous 2T2D correlation spectra are, in particular, sensitive to perpendicular modes.

Abstract PO3-23-07: Evaluation of the role of axillary ultrasound to estimate axillary nodal burden to guide de-escalation of upfront axillary surgery in node positive early breast cancer patients

Abstract Background: Axillary surgery is now routinely de-escalated in clinically node negative breast cancer patients with limited axillary nodal burden (up to 2 involved sentinel nodes) based on the results of ACOSOG-Z0011 and AMAROS trials. However, patients with proven axillary metastasis following on ultrasound (AUS) guided core needle biopsy (CNB), undergoing primary surgery are still subjected to an axillary lymph node dissection (ALND) irrespective of the magnitude of the axillary nodal burden. If we could predict axillary nodal burden with a low false negative rate (FNR) for the presence of extensive axillary nodal involvement, we can then hypothesize that axillary surgery could be safely de-escalated in this cohort of patients. We investigated whether pre-operative AUS suggesting limited axillary burden is sensitive enough to rule out gross axillary disease burden. Methods: A single institution retrospective study. We undertook an electronic chart review of all T1 to T3 patients undergoing upfront ALND with either mastectomy or breast conserving surgery between January 2019 and June 2023. Patients with palpable axillary nodes, locally advanced breast cancer or a completion ALND after positive sentinel lymph node biopsy (SLNB) were excluded from the study. Clinical and pathological characteristics associated with nodal burden of disease were evaluated. Limited axillary burden was defined as &amp;lt; 2 involved nodes with ≥3 taken as gross nodal burden for primary analyses. Sensitivity analyses were carried out with limited axillary burden defined as &amp;lt; 3 involved nodes (N1) and ≥4 (N2) taken as gross nodal burden. Subgroup analyses in T1 or T2 tumors were carried out as well. The probabilities of discordant events, defined as limited burden on AUS-CNB but gross burden on final histopathology evaluation (HPE), assuming 10% FNR, were estimated using inverse cumulative binomial distribution function. Results: Data on the exact number of suspicious nodes on AUS were missing for 2 patients, therefore, the final study cohort included 39 patients. The correlation between AUS nodal burden and that on HPE was moderate (Spearman’s rho = 0.48; p = 0.0018). The sensitivity and specificity of AUS in identifying gross nodal burden were 61% and 81% respectively. Observation of 9 discordant events in 22 patients with low burden on AUS ruled out an FNR of &amp;lt; 10% with 99.99% certainty. The sensitivity and specificity in T1/T2 subgroup were 60% and 75% respectively. The sensitivity analyses classifying N1 as limited and N2 as gross axillary burden showed the sensitivity and specificity of 35% and 82% respectively and an FNR of &amp;lt; 10% was ruled out with 99.996% certainty. Conclusion: Pre-operative AUS alone lacks the sensitivity and specificity to accurately predict the true axillary nodal burden to safely guide de-escalation of axillary surgery. AUS followed by targeted axillary dissection (TAD) in conjunction with a dual technique SLNB may provide the desired sensitivity and specificity to guide de-escalation of axillary surgery. A prospective evaluation of this approach is merited. Given the limited number of patients that could be enrolled in such prospective study from individual institutions, an international collaborative effort is needed to address this important research question. Citation Format: Nidhi Garg, Mangesh Thorat, Hisham Hamed, Ashutosh Kothari. Evaluation of the role of axillary ultrasound to estimate axillary nodal burden to guide de-escalation of upfront axillary surgery in node positive early breast cancer patients [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO3-23-07.

Interactive AI Virtual Teaching Resource Intelligent Recommendation Algorithm Based on Similarity Measurement on the Internet of Things Platform

Abstract To tackle the issues of low recommender system correctness and the long time of recommendation in the traditional intelligent recommendation algorithm of interactive artificial intelligence (AI) virtual teaching resources, a similarity measurement-based intelligent recommendation algorithm of interactive AI virtual teaching resources is proposed. According to the contact frequency of adjacent learners, the behavior patterns of learners are mined, and the user characteristics are selected on the basis of the mutual information feature selection method. In the context of the category attribute matrix and learner category attribute scoring matrix of interactive AI virtual teaching resources, the user interest matrix is constructed by the Relevance Feedback based on Inverse Learning Function (RF-ILF) method. The user similarity is calculated and the neighbor set is found in the similar user clusters after clustering. According to the results of the simulation, the suggested algorithm is more efficient and provides more accurate recommendations when recommending interactive AI virtual teaching resources.

Spatio-temporal relation of urban density and surface urban heat island index

Spatio-temporal relation of urban density and surface urban heat island index

Mechanistic insight into phosphorus migration pathways from oolitic hematite using in-situ observations during roasting and reduction process

Oolitic hematite is a promising alternative resource, in facing the iron ore downgrading. As oolitic hematite is often rich in phosphorus, an efficient separation of iron and phosphorus is necessary, in terms of utilizing both elements. Therefore, a close insight into the transformation of phosphorus-bearing minerals in the unique oolitic structure during the reduction process is important. To capture the real-time transformation of the apatite ring in the oolitic structure, in-situ observations under roasting, and CO/carbon reducing conditions were adopted by high-temperature confocal laser scanning microscopy. The results indicated that the apatite ring was transformed by four stages during the roasting process from 25 °C to 1400 °C: stabilization, defluorination, partial melting, and complete melting, which was: Ca5(PO4)3F → Ca3(PO4)2 → Ca3(PO4)2 + P2O5 liquid → P2O5 liquid. Under the CO reduction, the partial reduction of the phosphate at 1400 °C generated a Fe-Plow alloy. While the carbon reduction promoted iron phase absorption of phosphorus, forming Fe-Phigh alloy at 1400 °C. In addition, interfacial phenomena between apatite and slag melt were observed, and the dissolution of apatite (Ca/P molar ratio) into the slag melt was affected by the Fe/(Al + Si) molar ratio of the slag. Finally, using inverse error function methods, the diffusion coefficients of P and Ca increased significantly from the roasting to CO reduction and then to carbon reduction. These findings can benefit to understand phosphorus migration mechanisms, improving effective dephosphorization strategies for high-phosphorus oolitic hematite.

A New Generalized Definition of Fractal–Fractional Derivative with Some Applications

In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law. The main elements of classical differential calculus are introduced in terms of this new derivative. Thus, we establish and demonstrate the basic operations with derivatives, chain rule, mean value theorems with their immediate applications and inverse function’s derivative. We complete the theory of generalized FF calculus by proposing a notion of integration and presenting two important results of integral calculus: the fundamental theorem and Barrow’s rule. Finally, we analytically solve interesting FF ordinary differential equations by applying our proposed definition.

Research on the Construction of Emergency Relief Center Site Selection Model Based on Firefly Algorithm

Aiming at the problem of site selection of rescue center under multi-objective after natural disaster, this paper constructs a site selection model to minimize the freight cost and maximize the time satisfaction of disaster victims. Firstly, the site selection model framework will be constructed according to the objectives, secondly, the model framework will be set up with specific constraints, and finally, the improved firefly optimization algorithm (SGSO) will be applied to conduct virtual simulation experiments. The SGSO algorithm is only used with the theory of the set of good points for the algorithm to initialize the population, and at the same time, it combines the inverse chord function with the step convergence factor, and it designs a formula for updating the position of the individuals in the population. On the basis of passing 8 standard test functions, virtual simulation experiments are carried out, and it is concluded that the SGSO algorithm can effectively solve the multi-objective siting problem, and provide more ideas and guarantees for the future research.

Crystallographic texture evolution during friction stir processing of AA7075 alloy

This study investigates the effects of heat input on the crystallographic texture evolution during friction stir processing of AA7075 alloys. Three different heat input levels were applied to develop friction stir-modified regions. Electron backscattered diffraction (EBSD) was utilized to measure the micro-texture in the as-received base metal and friction stir processed (FSPed) stir zones. In particular, inverse pole figure (IPF) maps, pole figures, and orientation distribution functions were employed to compare the micro-textures of different processed regions. The results indicate that as the heat input decreases, the average microhardness of the nugget zone declines, accompanied by an increase in the size of recrystallized grains. The base metal AA7075 exhibits a predominantly rotated cube texture ({001} <110>). After friction stir processing, the stir zone transitions to a rotated cube texture with decreased intensities and the presence of copper texture ({112} <111>). Notably, as the heat input increases, the rotated cube texture transforms into a copper texture.