Saturation Model Research Articles

STABILITY RESULTS ASSUMING TAMENESS, MONSTER MODEL, AND CONTINUITY OF NONSPLITTING

Abstract Assuming the existence of a monster model, tameness, and continuity of nonsplitting in an abstract elementary class (AEC), we extend known superstability results: let $\mu>\operatorname {LS}(\mathbf {K})$ be a regular stability cardinal and let $\chi $ be the local character of $\mu $ -nonsplitting. The following holds: 1. When $\mu $ -nonforking is restricted to $(\mu ,\geq \chi )$ -limit models ordered by universal extensions, it enjoys invariance, monotonicity, uniqueness, existence, extension, and continuity. It also has local character $\chi $ . This generalizes Vasey’s result [37, Corollary 13.16] which assumed $\mu $ -superstability to obtain same properties but with local character $\aleph _0$ . 2. There is $\lambda \in [\mu ,h(\mu ))$ such that if $\mathbf {K}$ is stable in every cardinal between $\mu $ and $\lambda $ , then $\mathbf {K}$ has $\mu $ -symmetry while $\mu $ -nonforking in (1) has symmetry. In this case: (a) $\mathbf {K}$ has the uniqueness of $(\mu ,\geq \chi )$ -limit models: if $M_1,M_2$ are both $(\mu ,\geq \chi )$ -limit over some $M_0\in K_{\mu }$ , then $M_1\cong _{M_0}M_2$ ; (b) any increasing chain of $\mu ^+$ -saturated models of length $\geq \chi $ has a $\mu ^+$ -saturated union. These generalize [31] and remove the symmetry assumption in [10, 38] . Under $(<\mu )$ -tameness, the conclusions of (1), (2)(a)(b) are equivalent to $\mathbf {K}$ having the $\chi $ -local character of $\mu $ -nonsplitting. Grossberg and Vasey [18, 38] gave eventual superstability criteria for tame AECs with a monster model. We remove the high cardinal threshold and reduce the cardinal jump between equivalent superstability criteria. We also add two new superstability criteria to the list: a weaker version of solvability and the boundedness of the U-rank.

Event-Triggered Adaptive PID Fault-Tolerant Control of Underactuated ASVs Under Saturation Constraint

This article discusses a control problem of underactuated autonomous surface vehicles (ASVs) subject to internal/external uncertainties, input saturations, and actuator faults, and proposes a novel event-triggered adaptive PID fault-tolerant (ETAPID-FT) control solution. To resolve the design difficulty caused by the underactuated feature, a standard multivariate integral cascade form regarding the mathematical model of underactuated ASVs is established. And then, to facilitate the implementation of PID-based design framework, the nonsmooth actuator saturation nonlinearity caused by the saturation constraint is represented by a smooth saturation model. In the control design, considering full features of the actuator fault and smooth function, an indirect neural approximation with single-parameter-leaning technique is developed, which endows the function of self-tuning control gain for the control solution. To relieve the mechanical wear of actuator, an improved event-triggered protocol by implanting a decreasing function of ASV’s position error is proposed. Moreover, the theoretical results show that the proposed ETAPID-FT control solution can guarantee the boundedness of all the signals in the closed-loop control system of underactuated ASVs. Finally, the validity of the developed control solution is confirmed by the simulation and comparative results

Lateral response of a pile group embedded in the transversely isotropic saturated soil due to surcharge loads

This paper investigates the behavior of pile groups in the transversely isotropic saturated soil under an adjacent surcharge load using a coupling method. The analytical layer-element theory is utilized to the transversely isotropic saturated soil model, and the fundamental solutions of the soil are applied to derive the soil flexibility matrices. And the FEM is used for the piles modeled as Bernoulli–Euler beams considering pile–pile interaction. Then, the dynamic response equations of pile groups are derived by using the FEM–BEM coupled method and considering pile-soil boundary coordination condition. The results of the present model compared well with those in existing solutions. Numerical examples are presented to examine the influences of the soils’ transverse isotropy, the magnitude of the surcharge load, the pile's physical properties and the distance between the load and the pile on the behavior of pile groups. It is observed that as the surcharge load grows, the position of the pile maximum displacement response changes from the middle of the soft soil layer to the top of the pile. The impact of the surcharge load is not significant when the loading action distance is greater than twice the thickness of soft soil layer. Furthermore, relatively large bending moments appear in the middle of the soft soil layer and at the interface of the soil layers.

The Effect of Audiovisual Media on Students' Creative Thinking Ability in Class V Science Subject

The purpose of this study was to find out whether audio-visual media had an effect on students' creative thinking abilities at SDN Kampung Bambu 1 in science class V. This research was an experimental quantitative study. The sampling technique used was nonprobability sampling with a saturated sample model with a total of 70 students. The research instrument consisted of 16 essay questions and a questionnaire consisting of 20 statement items. The results of this study indicate that the use of audiovisual media affects students' creative thinking abilities in science subjects. The t-test shows that the use of audio-visual media has a significant effect of 0.001 <0.05 on the creative thinking of fifth grade students at SDN Kampung Bambu 1 in science subjects

Pulse oximetry values from 33,080 participants in the Apple Heart & Movement Study

Wearable devices that include pulse oximetry (SpO2) sensing afford the opportunity to capture oxygen saturation measurements from large cohorts under naturalistic conditions. We report here a cross-sectional analysis of 72 million SpO2 values collected from 33,080 individual participants in the Apple Heart and Movement Study, stratified by age, sex, body mass index (BMI), home altitude, and other demographic variables. Measurements aggregated by hour of day into 24-h SpO2 profiles exhibit similar circadian patterns for all demographic groups, being approximately sinusoidal with nadir near midnight local time, zenith near noon local time, and mean 0.8% lower saturation during overnight hours. Using SpO2 measurements averaged for each subject into mean nocturnal and daytime SpO2 values, we employ multivariate ordinary least squares regression to quantify population-level trends according to demographic factors. For the full cohort, regression coefficients obtained from models fit to daytime SpO2 are in close quantitative agreement with the corresponding values from published reference models for awake arterial oxygen saturation measured under controlled laboratory conditions. Regression models stratified by sex reveal significantly different age- and BMI-dependent SpO2 trends for females compared with males, although constant terms and regression coefficients for altitude do not differ between sexes. Incorporating categorical variables encoding self-reported race/ethnicity into the full-cohort regression models identifies small but statistically significant differences in daytime SpO2 (largest coefficient corresponding to 0.13% lower SpO2, for Hispanic study participants compared to White participants), but no significant differences between groups for nocturnal SpO2. Additional stratified analysis comparing regression models fit independently to subjects in each race/ethnicity group is suggestive of small differences in age- and sex-dependent trends, but indicates no significant difference in constant terms between any race/ethnicity groups for either daytime or nocturnal SpO2. The large diverse study population and study design employing automated background SpO2 measurements spanning the full 24-h circadian cycle enables the establishment of healthy population reference trends outside of clinical settings.

Influence of partial saturation on bulk modulus and attenuation: the experiment and the theoretical model

SUMMARY Modelling the dispersion and attenuation of seismic waves in partially saturated rocks is important for quantitative interpretation of seismic data. To observe the partial saturation effects on modulus and attenuation, three sandstone samples with different porosities were used in the laboratory experiment. The samples were measured by ultrasonic testing system under different water saturation using drainage process. The experimental results show that the bulk modulus more rapidly increased at higher saturations (>80 per cent), and attenuation peaks could be observed. Then we develop a new partial saturation model based on Chapman’s theory and poroelastic theory. The new model is consistent with the Gassmann equation when the water saturation is 0 or 100 per cent. By analysing the characteristic frequency, the new model can be concluded in the form of a standard linear solid model. A comparison of the new model with the White model and the measured data is conducted. The results show that the model performed well at predicting the effective bulk modulus and attenuation of the rock with different water saturation. Finally, we discussed the impact of frequency, fluids and pore structures on the new model. The results reveal that the new model will be helpful in discussing partial saturation in rocks.

Adaptive optimized consensus control for a class of nonlinear multi-agent systems with asymmetric input saturation constraints and hybrid faults

This article studies the adaptive optimized leader–follower consensus control problem for a class of discrete-time multi-agent systems with asymmetric input saturation constraints and hybrid faults based on the optimized backstepping technique. Different from the conventional saturation model, we consider an individual asymmetric saturation constraint for each actuator instead of a common upper and lower bound for all actuators. Besides, a set of hybrid faults is also considered, with the main focus on the partial fault and bias fault. To eliminate the effects of saturation and faults, a simplified smooth function is constructed to approximate the asymmetric saturation model, and designed compensation signals are used to cope with the two main types of faults to improve the fault-tolerance and system performance. Subsequently, long-term strategic utility functions and virtual control signals are approximated to the optimal levels by adopting the actor–critic neural network (NN) framework, and the actor–critic NN weights are adjusted in the light of a gradient descent method. According to the forward difference Lyapunov function approach, it is proved that the closed-loop system can be stabilized and all errors are semiglobally uniformly ultimately bounded. Finally, the validity of the proposed control scheme is demonstrated through two simulation examples.

Quantum image scaling with applications to image steganography and fusion

A quantum hue, saturation, and lightness model is proposed in which a triple qubit sequence (QHTS) is encoded and used as a data model for the implementation of quantum image scaling. The preparation and retrieval of QHTS images is presented, in which only q+2 qubits (where q is the bit depth) are required to encode color information while retaining relevant HSL image features and operability. A conventional nearest neighbor interpolation was adopted to implement quantum image up-scaling and down-scaling operations, from which two other scaling applications were developed. One such technique is a form of quantum steganography based on end-to-end encryption, which provides high capacity while ensuring the security of carrier images and secret messages. The other is a spatial remote sensing image fusion algorithm, based on QHTS images, which pioneers quantum pseudocolor composites of multi-spectral and panchromatic images. Simulation experiments demonstrated the proposed methodology provides an embedding capacity more than double that of existing quantum image steganography algorithms. In addition, a complexity analysis demonstrated the efficiency of the two proposed quantum image scaling applications, which take full advantage of quantum parallelism.

Simplified numerical algorithms for generalized strip saturated two equal collinear cracks in piezoelectric media using distributed dislocation technique

AbstractIn this paper, we present the distributed dislocation technique (DDT) based numerical algorithms to study the generalized strip saturated (GSS) models for two equal collinear cracks in 2‐D finite and infinite piezoelectric media. Numerical studies for particular cases such as linear, quadratic and cubic strip saturated models are simulated by considering their equivalent forms based on the principle of superposition. Two equal collinear cracks problem and its particular case of coalesced zones are considered in 2‐D semipermeable piezoelectric media under arbitrary poling direction and in‐plane electromechanical loadings. The results of saturated zone lengths (inner and outer) and local stress intensity factors (at inner and outer tips) are evaluated numerically for infinite and finite domain problems. The results of infinite domain obtained using DDT are compared with the reference analytical solutions. A good agreement of the results shows the efficacy of the proposed algorithms based on DDT for solving GSS two equal collinear cracks problems in 2‐D finite/infinite piezoelectric media.

Numerical convergence does not mean mathematical convergence: Examples of simple saturated steady-state groundwater models with pumping wells

Groundwater numerical studies do not include H-convergence tests, contrarily to computational fluid dynamics (CFD) studies. In regional groundwater studies with pumping wells, the grids may exceed 106 nodes. The authors examine whether H-convergence tests can help to calculate the numerical errors made by using large grids with element sizes in the 10–500 m range. First, the differences between numerical and mathematical convergences are explained. Then, a method is proposed that most users may easily implement for their groundwater studies to assess the numerical error linked to the element size, ES, and the aspect ratio, AR. A single problem, forming a simple part of a regional groundwater study, was examined and solved by using many uniform grids. The results show that most regional groundwater studies make errors in the 50–500% range, considering their usual values for ES and AR. The numerical convergence domain, NCD, is shown to be larger than the mathematical convergence domain, MCD. This means that the codes can provide a numerical solution for a large range of ES values, even for many values outside the MCD, which is a risky situation for designers who are unaware of the difference between NCD and MCD and ignore the H-convergence tests.

A smartphone-integrated imaging device for measuring nitrate and phosphate in soil and water samples

This research presents a smartphone-integrated imaging device to detect nitrate (NO3–) and phosphate (PO43-) in soil and water samples for agricultural input management and environmental pollution monitoring. This low-cost and field-deployable device uses a smartphone with a digital camera to take a color photograph of the extracted solution under test. The sensing principle is based on the standard colorimetric phenoldisulfonic acid and ascorbic acid methods for NO3– and PO43- in soil and water samples, respectively. A 3D printed device that houses the sensor's optical source and other optical components is coupled to the phone's built-in rear camera and turned into a compact handheld system. An android application, 'SMART NP,' is also developed to quantify the concentrations of NO3– and PO43- in soil and water samples using the Value (V) component of the Hue Saturation and Value (HSV) color space model. The results obtained with the proposed device were comparable to laboratory-grade spectrophotometer data. The limit of detection of the device for NO3– in soil, NO3– in water, PO43- in soil, and PO43- in water were calculated as 0.1 mg L-1, 0.07 mg L-1, 0.001 mg L-1, and 0.02 mg L-1, respectively, with good accuracy (≤1% bias) and precision (∼2% residual standard deviation). The device exhibited a sensitivity of 0.17 mg L-1, 0.12 mg L-1, 0.026 mg L-1, and 0.49 mg L-1 for NO3– in soil, NO3– in water, PO43- in soil, and PO43- in water, respectively. Overall, this sensing device has the potential to assist farmers or scientists in easily measuring NO3– and PO43- concentrations in soil and water media, without the need for laboratory equipment.

Adaptive Tracking Consensus Control of Nonlinear Multiagent Systems With Predefined Accuracy Under Disturbance Observer

This article aims to a predefined tracking precision consensus control issue for nonlinear uncertain multiagent systems (MASs) with disturbance and input saturation. Unlike the existing results of prespecified accuracy for MASs, the phenomenon of unknown control gains is solved in this article. A saturation model based on the Gaussian error function is applied due to the appearance of input saturation. The unknown disturbance is considered which can be solved by a disturbance observer. Also, to handle the problem of an unknown coefficient for the controller, the Nussbaum function is employed. Moreover, the radial basis function neural networks (RBF NNs) are utilized to estimate unknown nonlinear functions. On account of the Lyapunov stability method and backstepping technique, adaptive laws are created and the desired distributed controller is designed which guarantees that the consensus errors can converge to prescribed values. Finally, several simulation examples demonstrate the valid of the proposed method.

Models of Jacobians of curves

Abstract We show that the Jacobians of prestable curves over toroidal varieties always admit Néron models. These models are rarely quasi-compact or separated, but we also give a complete classification of quasi-compact separated group-models of such Jacobians. In particular, we show the existence of a maximal quasi-compact separated group model, which we call the saturated model, and has the extension property for all torsion sections. The Néron model and the saturated model coincide over a Dedekind base, so the saturated model gives an alternative generalization of the classical notion of Néron models to higher-dimensional bases; in the general case we give necessary and sufficient conditions for the Néron model and saturated model to coincide. The key result, from which most others descend, is that the logarithmic Jacobian of [S. Molcho and J. Wise, The logarithmic Picard group and its tropicalization, preprint 2018] is a log Néron model of the Jacobian.

Locally compact models for approximate rings

By an approximate subring of a ring we mean an additively symmetric subset X such that X·X∪(X+X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X\\cdot X \\cup (X +X)$$\\end{document} is covered by finitely many additive translates of X. We prove that each approximate subring X of a ring has a locally compact model, i.e. a ring homomorphism f:⟨X⟩→S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f :\\langle X \\rangle \\rightarrow S$$\\end{document} for some locally compact ring S such that f[X] is relatively compact in S and there is a neighborhood U of 0 in S with f-1[U]⊆4X+X·4X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f^{-1}[U] \\subseteq 4X + X \\cdot 4X$$\\end{document} (where 4X:=X+X+X+X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4X:=X+X+X+X$$\\end{document}). This S is obtained as the quotient of the ring ⟨X⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle X \\rangle $$\\end{document} interpreted in a sufficiently saturated model by its type-definable ring connected component. The main point is to prove that this component always exists. In order to do that, we extend the basic theory of model-theoretic connected components of definable rings [developed in Gismatullin et al. (J Symb Log First View: 1–35, 2022, https://doi.org/10.1017/jsl.2022.10) and Krupiński et al. (Ann Pure Appl Logic 173.7(July):103119, 2022) to the case of rings generated by definable approximate subrings and we answer a question from Krupiński et al. (2022) in the more general context of approximate subrings. Namely, let X be a definable (in a structure M) approximate subring of a ring and R:=⟨X⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R:=\\langle X \\rangle $$\\end{document}. Let X¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{X}}$$\\end{document} be the interpretation of X in a sufficiently saturated elementary extension and R¯:=⟨X¯⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{R}}:= \\langle {\\bar{X}} \\rangle $$\\end{document}. It follows from Massicot and Wagner (J Éc Polytech Math 2:55–63, 2015) that there exists the smallest M-type-definable subgroup of (R¯,+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\bar{R}},+)$$\\end{document} of bounded index, which is denoted by (R¯,+)M00\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\bar{R}},+)^{00}_M$$\\end{document}. We prove that (R¯,+)M00+R¯·(R¯,+)M00\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\bar{R}},+)^{00}_M + {\\bar{R}} \\cdot ({\\bar{R}},+)^{00}_M$$\\end{document} is the smallest M-type-definable two-sided ideal of R¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{R}}$$\\end{document} of bounded index, which we denote by R¯M00\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{R}}^{00}_M$$\\end{document}. Then S in the first sentence of the abstract is just R¯/R¯M00\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{R}}/{\\bar{R}}^{00}_M$$\\end{document} and f:R→R¯/R¯M00\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f: R \\rightarrow {\\bar{R}}/{\\bar{R}}^{00}_M$$\\end{document} is the quotient map. In fact, f is the universal “definable” (in a suitable sense) locally compact model. The existence of locally compact models can be seen as a general structural result about approximate subrings: every approximate subring X can be recovered up to additive commensurability as the preimage by a locally compact model f:⟨X⟩→S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f :\\langle X \\rangle \\rightarrow S$$\\end{document} of any relatively compact neighborhood of 0 in S. It should also have various applications to get more precise structural or even classification results. For example, in this paper, we deduce that every [definable] approximate subring X of a ring of positive characteristic is additively commensurable with a [definable] subring contained in 4X+X·4X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4X + X \\cdot 4X$$\\end{document}. This easily implies that for any given K,L∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K,L \\in \\mathbb {N}$$\\end{document} there exists a constant C(K, L) such that every K-approximate subring X (i.e. K additive translates of X cover X·X∪(X+X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X \\cdot X \\cup (X+X)$$\\end{document}) of a ring of positive characteristic ≤L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\le L$$\\end{document} is additively C(K, L)-commensurable with a subring contained in 4X+X·4X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4X + X \\cdot 4X$$\\end{document}. Another application of the existence of locally compact models is a classification of finite approximate subrings of rings without zero divisors: for every K∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K \\in \\mathbb {N}$$\\end{document} there exists N(K)∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N(K) \\in \\mathbb {N}$$\\end{document} such that for every finite K-approximate subring X of a ring without zero divisors either |X|<N(K)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|X| <N(K)$$\\end{document} or 4X+X·4X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4X + X \\cdot 4X$$\\end{document} is a subring which is additively K11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^{11}$$\\end{document}-commensurable with X.

Evaluation of Dynamic Interactions Between Sloped Ground and Pile Through Centrifuge Model Tests

ABSTRACT This study used centrifuge model tests to evaluate the dynamic behavior of piles and sloped ground. Two types of test models were created based on the ground’s saturation. The researchers calculated p-y loops to analyze the dynamic interaction between piles and sloped ground, which can lead to liquefaction. In the dry sand model, the passive earth pressure of the slope greatly influenced pile behavior, while in the saturated sand model with liquefaction, the kinematic force of the slope had a significant effect. The study also derived a p-multiplier that can be applied to medium-dense soil based on the experimental results.

Fitting and Testing Log-Linear Subpopulation Models with Known Support.

In this paper, the support of the joint probability distribution of categorical variables in the total population is treated as unknown. From a general total population model with unknown support, a general subpopulation model with its support equal to the set of all observed score patterns is derived. In maximum likelihood estimation of the parameters of any such subpopulation model, the evaluation of the log-likelihood function only requires the summation over a number of terms equal to at most the sample size. It is made clear that the parameters of a hypothesized total population model are consistently and asymptotically efficiently estimated by the values that maximize the log-likelihood function of the corresponding subpopulation model. Next, new likelihood ratio goodness-of-fit tests are proposed as alternatives to the Pearson chi-square goodness-of-fit test and the likelihood ratio test against the saturated model. In a simulation study, the asymptotic bias and efficiency of maximum likelihood estimators and the asymptotic performance of the goodness-of-fit tests are investigated.

ON GROUPS WITH DEFINABLE F-GENERICS DEFINABLE IN P-ADICALLY CLOSED FIELDS

AbstractThe aim of this paper is to develop the theory of groups definable in the p-adic field ${{\mathbb {Q}}_p}$ , with “definable f-generics” in the sense of an ambient saturated elementary extension of ${{\mathbb {Q}}_p}$ . We call such groups definable f-generic groups.So, by a “definable f-generic” or $dfg$ group we mean a definable group in a saturated model with a global f-generic type which is definable over a small model. In the present context the group is definable over ${{\mathbb {Q}}_p}$ , and the small model will be ${{\mathbb {Q}}_p}$ itself. The notion of a $\mathrm {dfg}$ group is dual, or rather opposite to that of an $\operatorname {\mathrm {fsg}}$ group (group with “finitely satisfiable generics”) and is a useful tool to describe the analogue of torsion-free o-minimal groups in the p-adic context.In the current paper our group will be definable over ${{\mathbb {Q}}_p}$ in an ambient saturated elementary extension $\mathbb {K}$ of ${{\mathbb {Q}}_p}$ , so as to make sense of the notions of f-generic type, etc. In this paper we will show that every definable f-generic group definable in ${{\mathbb {Q}}_p}$ is virtually isomorphic to a finite index subgroup of a trigonalizable algebraic group over ${{\mathbb {Q}}_p}$ . This is analogous to the o-minimal context, where every connected torsion-free group definable in $\mathbb {R}$ is isomorphic to a trigonalizable algebraic group [5, Lemma 3.4]. We will also show that every open definable f-generic subgroup of a definable f-generic group has finite index, and every f-generic type of a definable f-generic group is almost periodic, which gives a positive answer to the problem raised in [28] of whether f-generic types coincide with almost periodic types in the p-adic case.

Determination of adsorption parameters in shale gas resource/reserve calculation: Case study of Wufeng Formation–Longmaxi Formation in the Sichuan Basin

In the calculation of shale gas resources/reserves, isothermal adsorption parameters are mainly determined by dry sample data at the laboratory temperature, and the regression effect of total organic carbon content (TOC) isothermal adsorption parameters is poor. Based on the physical significance of key parameters in Langmuir and Henry adsorption models, the problems in determining the isothermal adsorption parameters in the calculation of shale gas reserves/reserves are analyzed by taking the marine shale in the Upper Ordovician Wufeng Forming–Lower Silurian Longmaxi Formation in the Sichuan Basin as an example. Based on a large number of measured isothermal adsorption data, the effects of TOC, temperature and water saturation on the shale gas adsorption parameters are analyzed. The influence model of TOC, temperature and water saturation on isothermal adsorption parameters of shale gas is established, and a novel method for calculating the adsorption parameters of shale gas from under experimental conditions to original reservoir conditions is proposed. The results are obtained as follows. First, there are problems in the calculation of shale gas resources/reserves, such as poor and contradictory fitting relation between isothermal adsorption parameters and TOC, difficulty in the conversion of Van't Hoff equation, and difficulty in direct application of water saturation (Sw) in resource/reserves calculation. Second, the problem of poor direct fitting relation between Langmuir pressure (pL) and TOC is solved by integrating the Langmuir adsorption model with the Henry adsorption model and by establishing a new parameter – Henry constant a for methane adsorption capacity of shale. Third, when Sw<40%, the Langmuir volume (VL) is linearly negatively correlated with Sw; when Sw<20%, a is constant relatively; by establishing the relationship between the normalized absolute adsorption capacity and Sw (<50%) under the pressure exceeding 30 MPa, the effect of Sw on the isothermal adsorption capacity can be calculated. Fourth, the in-situ stress in the Wufeng Formation–Longmaxi Formation shale reservoir affects the adsorption capacity of shale. For shale reservoirs with the same TOC, the higher the in-situ stress, the smaller the VL and a values. Under high pressure (>30 MPa), the effect of Sw on the methane adsorption capacity of shale shows a similar trend, and the effect of water molecules on the adsorption capacity on shale pore surface is constant. It is concluded that the proposed novel method for determining the isothermal adsorption parameters of shale with different TOC, temperature and water saturation conditions provides a technical support for the accurate calculation of shale gas resources/reserves and contributes to the scientific development of shale gas industry.

Predictive modeling of oil and water saturation during secondary recovery with supervised learning

In the petroleum reservoir, the secondary oil recovery (SOR) process is employed by injecting water into wells to enhance the moment of oil toward the production wells. The SOR process gives rise to the instability (fingering) phenomena due to the injecting force and the difference in the wettability and viscosity of the oil and water at the common interface. Since the late 1800s, mathematical models of petroleum reservoirs have been extensively used in the oil and gas industry. In this paper, we investigated the saturation of two immiscible fluid (oil and water) flows through homogeneous porous media during the SOR process by solving the modeled partial differential equation using the supervised machine learning algorithm based on feedforward back-propagated neural networks (FFBNNs) and Levenberg–Marquardt (LM) optimization algorithm. The designed scientific computing technique (FFBNN-LMA) is further employed to study the detailed sensitivity analysis of the approximate solutions. Performance measures like average absolute deviations, Theils' inequality measure, regression, and Nash–Sutcliffe model efficiency coefficient.

(005) When Paying Attention is Inconvenient: The Effect of Negative Thoughts During Sex on Female Sexual Response

Abstract Introduction To evaluate the presence of negative thoughts and how these interfere with sexual functioning (as hypothesized by Barlow, 1986), Nobre and Pinto-Gouveia (2003) developed the Automatic Negative Thoughts scale (ANT). Research using this scale has shown that negative thoughts during sex interferes with subjective sexual arousal (SSA), lubrication, and orgasm (Cuntim and Nobre, 2011; Nobre &amp; Pinto-Gouveia, 2003). While this early work has made a crucial contribution toward understanding how negative thoughts are associated with female sexual response, the ANT has important limitations. One limitation is that some items are not relevant to the constructs they are supposed to measure (e.g., “I have more important matters to deal with” is part of the “Sexual Abuse Thoughts” factor; and “This way of having sex is immoral” is part of the “Partner’s Lack of Affection” factor), and thus in some cases it is not clear what the scales themselves are measuring. Moreover, effect sizes on sexual functioning are modest, and the full measure is long. Objective The aim of this study was to test a new measure of negative thoughts during sex (NTs) and to investigate the associations between specific types of NTs and specific domains of sexual functioning. Using fewer and more focused questions we also aimed at having a shorter and more precise measure. Methods A sample of 138 female university students completed questionnaires investigating frequency of specific NTs and female sexual functioning (measured through the FSFI). Structural equation modelling was used to test the effect of NTs, as a latent construct, on three dimensions of sexual functioning, namely SSA, lubrication, and orgasm. Next, the effect of the four individual domains of NTs (i.e., orgasm, body image, fear of being hurt, and external thoughts) on SSA, lubrication and orgasm, was tested. Results The first SEM model fits the data well (CFI = .97; NFI = .93; RMSEA = .08). This model is presented in Figure 1 and shows that NTs have strong direct negative effects on SSA (78% variance explained), lubrication (76% variance explained), and orgasm (63% variance explained). Moreover, NTs also have an indirect effect on lubrication, mediated by SSA. The effects of single domains of NTs are presented in Figure 2 (saturated model). Overall, NTs about orgasm and fear of being hurt showed negative associations with orgasm and SSA, external thoughts showed an effect on SSA and lubrication, and NTs about body image showed no significant association. Conclusions The new measure of NTs has advantages of brevity, specificity, and stronger effect sizes as compared to the ANT. These data provide increasingly strong evidence that NTs significantly interfere with women’s sexual response, and that some domains of NTs have a stronger impact than others on different domains of sexual functioning. More work is needed to understand the sources and types of NTs, and their role in different aspects of sexual response. Furthermore, neuroimaging technology should be exploited to shed light on the neural pathways involved in cognitive interference and sexual inhibition, which are expected to be linked with the presence of NTs. Disclosure No