Linear Growth Function Research Articles

Analysis of basalt fiber reinforcement on static shear properties of Beibu Gulf sea sand

Basalt fibers are a reinforcing material with excellent mechanical properties and durability. In contrast, although Beibu Gulf sea sand is widely in engineering, it exhibits low strength and poor stability, which can be improved by adding basalt fibers. In this study, the effects of fiber content, fiber length, and effective confining pressure on the static shear strength of fiber-reinforced sea sand were investigated using a triaxial shear test. The maximum improvement on the static shear characteristics and deformation resistance of sea sand were achieved for a fiber content and length of 0.8% and 12 mm, respectively. The cohesion and internal friction angle of sea sand were improved and the secant modulus and strain before and after basalt fiber reinforcement showed a nonlinear attenuation tendency. The reinforcement effect coefficient R and the basalt fiber content under different dosages were in accordance with the law of the Gaussian function. The value of R conformed to a linear growth and exponential function law under different fiber lengths and effective confining pressures, respectively. This study provides a solid theoretical basis for the sustainable utilization of sea sand resources and fiber reinforcement for road and coastal protection engineering in the Beibu Gulf region.

Nonzero-Sum Stochastic Impulse Games with an Application in Competitive Retail Energy Markets

We study a nonzero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The objective of each player is to maximize her total expected discounted profits. The resolution methodology relies on the connection between Nash equilibrium and the corresponding system of quasi-variational inequalities (QVIs in short). We prove, by means of the weak dynamic programming principle for the stochastic differential game, that the equilibrium expected payoff of each player is a constrained viscosity solution to the associated QVIs system in the class of linear growth functions. We also introduce a family of equilibrium expected payoffs converging to our equilibrium expected payoff of each player, and which is characterized as the unique constrained viscosity solutions of an approximation of our QVIs system. This convergence result is useful for numerical purpose. We apply a probabilistic numerical scheme which approximates the solution of the QVIs system to the case of the competition between two electricity retailers. We show how our model reproduces the qualitative behavior of electricity retail competition.

Do Distance-Dependent Competition Indices Contribute to Improve Diameter and Total Height Tree Growth Prediction in Juvenile Cork Oak Plantations?

Competition indices may improve tree growth modelling in high-density stands, found often in new cork oak plantations. Distance-dependent competition indices have hardly been considered for juvenile cork oak plantations since existing models were developed for low-density mature stands. This study aims at inspecting the potential of including distance-dependent competition indices into diameter at breast height (d) and total height (h) growth models for Quercus suber L., comparing several distance-dependent and distance-independent competition indices. Annual d and h growth were modelled with linear and non-linear growth functions, formulated as difference equations. Base models were initially fitted considering parameter estimates depending only on site index (S) and/or stand density (N). They were refitted, testing the significance of adding each competition index to the model parameters. Selected models included the best-performing distance-dependent or -independent competition indices as additional predictors. Best base d and h growth models showed a modelling efficiency (ef) of ef = 0.9833 and ef = 0.9900, respectively. Adding a distance-dependent competition index slightly improved growth models, to an ef = 0.9851 for d and ef = 0.9902 for h. Best distance-dependent competition indices slightly overperformed distance-independent ones in diameter growth models. Neither S nor N were included on best fitted models. If inter-tree competition is present in juvenile undebarked cork oak plantations, it does not yet strongly impact individual tree growth, which may diminish the importance of using, at this stage, more complex spatially explicit competition indices on predicting individual tree growth.

Constrained simulations of the local Universe with modified gravity

We present a methodology for constructing modified gravity (MG) constrained simulations of the local Universe using positions and peculiar velocities from the CosmicFlows data set. Our analysis focuses on the following MG models: the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model and Hu-Sawicki $f(R)$ model. We develop a model independent methodology for constructing constrained simulations with any given power spectra and numerically calculated linear growth functions. Initial conditions (ICs) for a set of constrained simulations are constructed for the standard cosmological model $\Lambda$CDM and the MG models. Differences between the model's reconstructed Wiener filtered density and the resultant simulation density are presented showing the importance for the generation of MG constrained ICs to study the subtle effects of MG in the local Universe. These are the first MG constrained simulations ever produced. The current work paves the way to improved approximate methods for models with scale-dependent growth functions, such as $f(R)$, and for high-resolution hydrodynamical MG zoom-in simulations of the local Universe.

Extending linear growth functionals to functions of bounded fractional variation

In this paper we consider the minimization of a novel class of fractional linear growth functionals involving the Riesz fractional gradient. These functionals lack the coercivity properties in the fractional Sobolev spaces needed to apply the direct method. We therefore utilize the recently introduced spaces of bounded fractional variation and study the extension of the linear growth functional to these spaces through relaxation with respect to the weak* convergence. Our main result establishes an explicit representation for this relaxation, which includes an integral term accounting for the singular part of the fractional variation and features the quasiconvex envelope of the integrand. The role of quasiconvexity in this fractional framework is explained by a technique to switch between the fractional and classical settings. We complement the relaxation result with an existence theory for minimizers of the extended functional.

Asymptotic profiles for positive solutions of diffusive logistic equations

In this paper, we study the asymptotic profiles of positive solutions for diffusive logistic equations. The aim is to study the sharp effect of linear growth and nonlinear function. Both the classical reaction-diffusion equation and nonlocal dispersal equation are investigated. Our main results reveal that the linear and nonlinear parts of reaction term play quite different roles in the study of positive solutions.

Sobolev regularity for linear growth functionals acting on ℂ-elliptic operators

Abstract In this paper, we prove the higher Sobolev regularity of minimizers for convex integral functionals evaluated on linear differential operators of order one. This work intends to generalize the already existing theory for the cases of full and symmetric gradients to the entire class of ${\mathbb C}$-elliptic operators therein including the trace-free symmetric gradient for dimension $n \geq 3$.

A maximum principle for mean-field stochastic control system with noisy observation

This paper is concerned with an optimal control problem driven by mean-field stochastic differential equation, where the state is partially observed via a noisy process. A new feature of the control problem is that the drift coefficient of observation equation is allowed to be a linear growth function, which immediately causes a difficulty in studying the control problem. A backward separation method with a dominated growth rate idea is used to overcome the difficulty. A maximum principle for optimality of the control problem is derived by an approximate technique. An asset–liability management problem for an insurance firm is studied. An optimal premium strategy in a feedback form is explicitly obtained.

Anxiety and Cognition in Cre- Collagen Type II Sirt1 K/O Male Mice.

IntroductionUsing transgenic collagen type II-specific Sirt1 knockout (CKO) mice we studied the role of Sirt1 in nutritional induced catch up growth (CUG) and we found that these mice have a less organized growth plate and reduced efficiency of CUG. In addition, we noted that they weigh more than control (CTL) mice. Studying the reason for the increased weigh, we found differences in activity and brain function.MethodsSeveral tests for behavior and activity were used: open field; elevated plus maze, Morris water maze, and home cage running wheels. The level of Glu- osteocalcin, known to connect bone and brain function, was measured by Elisa; brain Sirt1 was analyzed by western blot.ResultsWe found that CKO mice had increased anxiety, with less spatial memory, learning capabilities and reduced activity in their home cages. No significant differences were found between CKO and CTL mice in Glu- osteocalcin levels; nor in the level of brain SIRT1.Discussion/ConclusionUsing transgenic collagen type II-specific Sirt1 knockout (CKO) mice we found a close connection between linear growth and brain function. Using a collagen type II derived system we affected a central regulatory mechanism leading to hypo activity, increased anxiety, and slower learning, without affecting circadian period. As children with idiopathic short stature are more likely to have lower IQ, with substantial deficits in working memory than healthy controls, the results of the current study suggest that SIRT1 may be the underlying factor connecting growth and brain function.

Testing generalized logotropic models with cosmic growth

We check the dynamical and observational features of four typologies of logotropic dark energy models, leading to a thermodynamic cosmic speed up fueled by a single fluid that unifies dark energy and dark matter. We first present two principal Anton-Schmidt fluids where the Gr\"uneisen parameter ${\ensuremath{\gamma}}_{\mathrm{G}}$ is free to vary and then fixed to the special value ${\ensuremath{\gamma}}_{\mathrm{G}}=\frac{5}{6}$. We also investigate the pure logotropic model, corresponding to ${\ensuremath{\gamma}}_{\mathrm{G}}=\ensuremath{-}\frac{1}{6}$. Finally, we propose a new logotropic paradigm that works as a generalized logotropic fluid, in which we split the role of dark matter and baryons. We demonstrate that the logotropic paradigms may present drawbacks in perturbations, showing a negative adiabatic sound speed which make perturbations unstable. We thus underline which model is favored over the rest. The Anton-Schmidt model with ${\ensuremath{\gamma}}_{\mathrm{G}}=\frac{5}{6}$ is ruled out while the generalized logotropic fluid seems to be the most suitable one, albeit weakly disfavored than the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. To fix numerical constraints, we combine low- and higher-redshift domains through experimental fits based on Monte Carlo Markov Chain procedures, taking into account the most recent Pantheon supernovae Ia catalog, Hubble measurements, and ${\ensuremath{\sigma}}_{8}$ data points based on the linear growth function for the large scale structures. We also consider two model selection criteria to infer the statistical significance of the four models under examination. We conclude there is a statistical advantage to handle the Anton-Schmidt fluid with the Gr\"uneisen parameter free to vary and/or fixed to ${\ensuremath{\gamma}}_{\mathrm{G}}=\ensuremath{-}\frac{1}{6}$. The generalized logotropic fluid indicates suitable results, more statistically favored than the other models until the sound speed is positive, becoming unstable in perturbations elsewhere. We emphasize that the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ paradigm works statistically better than any kind of logotropic and generalized logotropic models, while the Chevallier-Polarski-Linder parametrization is statistically comparable with logotropic scenarios. Finally, we propose that generalizing the Gr\"uneisen parameter by including the effects of temperature would guarantee the sound speed to be positive definite at all redshifts.

The linear and nonlinear growth functions in Cubic Galileon

<p indent=0mm>We introduce the Lagrangian perturbation theory under ΛCDM model, and extend it to the Cubic Galileon (G3) model. We present the second order growth function in G3 model based on the Lagrangian perturbation theory. We find that the effective Newtonian constant in G3 model is almost scale independent. Its value is bigger than that of the ΛCDM model. In the late time dark energy dominated epoch, its value is enhanced by a factor about 2. Based on this, the linear and nonlinear growth functions in the structure formation for G3 model are larger than that of the ΛCDM model. It means G3 model has stronger galaxy clustering effect than ΛCDM model. Besides of this, we find the second order growth function can be separated into spatial and temporal dependent parts. Hence, one only needs to convolve different momentum configurations at the initial stage. This will significantly accelerate the numerical calculation.

A Lagrangian perturbation theory in the presence of massive neutrinos

We develop a Lagrangian Perturbation Theory (LPT) framework to study the clustering of cold dark matter (CDM) in cosmologies with massive neutrinos. We follow the trajectories of CDM particles with Lagrangian displacements fields up to third order in perturbation theory. Once the neutrinos become non-relativistic, their density fluctuations are modeled as being proportional to the CDM density fluctuations, with a scale-dependent proportionality factor. This yields a gravitational back-reaction that introduces additional scales to the linear growth function, which is accounted for in the higher order LPT kernels. Through non-linear mappings from Eulerian to Lagrangian frames, we ensure that our theory has a well behaved large scale behavior free of unwanted UV divergences, which are common when neutrino and CDM densities are not treated on an equal footing, and in resummation schemes that manifestly break Galilean invariance. We use our theory to construct correlation functions for both the underlying matter field, as well as for biased tracers using Convolution-LPT. Redshift-space distortions effects are modeled using the Gaussian Streaming Model. When comparing our analytical results to simulated data from the \ extsc{Quijote} simulation suite, we find good accuracy down to r=20 Mpc h−1 at redshift z=0.5, for the real space and redshift space monopole particle correlation functions with no free parameters. The same accuracy is reached for the redshift space quadrupole if we additionally consider an effective field theory parameter that shifts the pairwise velocity dispersion. For modeling the correlation functions of tracers we adopt a simple Lagrangian biasing scheme with only density and curvature operators, which we find sufficient to reach down to r=20 Mpc h−1 when comparing to simulated halos.

The Regularity of Minima for the Dirichlet Problem on BD

We establish that the Dirichlet problem for linear growth functionals on {text {BD}}, the functions of bounded deformation, gives rise to the same unconditional Sobolev and partial {text {C}}^{1,alpha }-regularity theory as presently available for the full gradient Dirichlet problem on {text {BV}}. Functions of bounded deformation play an important role in, for example plasticity, however, by Ornstein’s non-inequality, contain {text {BV}} as a proper subspace. Thus, techniques to establish regularity by full gradient methods for variational problems on BV do not apply here. In particular, applying to all generalised minima (that is, minima of a suitably relaxed problem) despite their non-uniqueness and reaching the ellipticity ranges known from the {text {BV}}-case, this paper extends previous Sobolev regularity results by Gmeineder and Kristensen (in J Calc Var 58:56, 2019) in an optimal way.

Catch-up growth in height and cognitive function: Why definitions matter

There is substantial evidence that early growth retardation, indicated by stunting, is associated with poorer cognitive function among children. There are, however, contradictory findings on the extent to which subsequent ‘catch-up’ growth among stunted children is associated with similar ‘catch-up’ cognitive functioning. In this paper we show that the apparent contradictions in the literature may be a result of differences in the definition of catch up used in the different studies. We explore two variations in definition: the age from which catch-up growth is measured, and the extent of growth required to be classified as ‘caught up’. Using cohort data from South Africa with repeated measures of length in early childhood, we first show that varying the starting age from which catch up is measured from 1y to 2y greatly affects the conclusions drawn with respect to cognitive outcomes, as the prevalence of stunting tends to peak around 2y. Second, we show how the results differ when we vary what counts as catch up, and here we explore five definitions ranging from most lenient to strictest. The strictest definition requires children to have caught up sufficiently that their height-for-age falls within the ‘normal’ range at follow-up; very few children catch up to this extent. For all definitions of catch-up, except the strictest, we find that children who are stunted at 2 years of age who subsequently experience catch-up growth, on average, do worse on cognitive tests than children who were never stunted, and almost as poorly as children who remain stunted (with the coefficient ranging from -1.584; p < 0.01 to -1.753; p < 0.01). This suggests the timing of investments in early childhood is key, with intervention in the first two years to prevent deprivation that affects both linear growth and cognitive function.

Novel modified distribution functions of fiber length in fiber reinforced thermoplastics

Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λα and λβ) can be considered as the linear growth function of ln. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT.

Lower semicontinuity and [formula omitted]-convergence of a class of linear growth functionals

We prove some new results for linear growth functionals ∫Ωφ(x,Du), u∈BVΩ, where φ(x,p)=g(x,|p|)if|p|≤βψ(x)|p|+k(x)if|p|>β,ψ∈CΩ∩L∞Ω,ψ≥0 on Ω, and φ is convex in p. In particular, we give conditions on φ for which ∫Ωφ(x,Du) is lower semicontinuous in L1Ω. Notably, we make no lower semicontinuity assumption for φ in (x,p) and no differentiability assumption for φ in p, as is done in earlier work. We also consider more general linear growth functionals ∫Ωg(x,|Du|) with g(x,|p|) convex in |p| and prove Γ-convergence of functionals of the form ∫Ωφ(x,Du) to ∫Ωg(x,|Du|). Finally, functionals with specified trace values for u are also considered.

Economic order quantity model for growing items with imperfect quality

While the basic economic order quantity model has found some practical applications, it makes a number of assumptions which do not reflect most real life inventory systems. This paper proposes an inventory system where the items ordered are capable of growing during the course of the inventory replenishment cycle, for example livestock. Furthermore, it is assumed that a certain fraction of the items is of poorer quality than desired. It is also assumed that live newborn items are ordered and fed until they grow to a customer-preferred weight, after which they are slaughtered. Before all the slaughtered items are put on sale, they are screened so as to separate the good quality items from those of poorer quality. In order to determine the optimal inventory policy, a model, which aims to maximize the expected total profit, is developed and numerical examples are provided to illustrate the model and the solution procedure. The logistic growth function is compared to the linear and split linear growth functions. The margin of error between the results of the split linear function and the logistic growth function were found to be smaller than between the logistic and linear function. In addition, it was found that the optimal order quantity was most sensitive to the target slaughter weight.

The Role of the Quality of College‐Based Relationship on Social Media in College‐to‐Work Transition of Korean College Students: The Longitudinal Examination of Intimacy on Social Media, Social Capital, and Loneliness

AbstractThis study investigated the mediation effects of social capital on the associations between the quality of relationship, intimacy in particular, with college friends on social media and loneliness during college‐to‐work transition of Korean college students. Longitudinal data were collected from three surveys with a 6‐month interval. The first wave of the survey was completed by 521 participants; 110 graduates participated in the second wave, and 175 in the third wave. Latent growth modeling analysis revealed that the linear growth function produced a better fit than the no‐growth models for intimacy on social media, social capital, and loneliness. While intimacy on social media and bonding capital increased during the three‐time interval, bridging capital and loneliness decreased. In addition, the slope of intimacy on social media was positively related to the slopes of bridging and bonding capital, both of which, in turn, had a negative association with the slope of loneliness. These findings indicate the beneficial role of the quality of relationship on social media in college‐to‐work transition.

Burosumab Therapy in Children with X-Linked Hypophosphatemia

BackgroundX-linked hypophosphatemia is characterized by increased secretion of fibroblast growth factor 23 (FGF-23), which leads to hypophosphatemia and consequently rickets, osteomalacia, and skeletal deformities. We investigated burosumab, a monoclonal antibody that targets FGF-23, in patients with X-linked hypophosphatemia.MethodsIn an open-label, phase 2 trial, we randomly assigned 52 children with X-linked hypophosphatemia, in a 1:1 ratio, to receive subcutaneous burosumab either every 2 weeks or every 4 weeks; the dose was adjusted to achieve a serum phosphorus level at the low end of the normal range. The primary end point was the change from baseline to weeks 40 and 64 in the Thacher rickets severity total score (ranging from 0 to 10, with higher scores indicating greater disease severity). In addition, the Radiographic Global Impression of Change was used to evaluate rachitic changes from baseline to week 40 and to week 64. Additional end points were changes in pharmacodynamic markers, linear growth, physical ability, and patient-reported outcomes and the incidence of adverse events.ResultsThe mean Thacher rickets severity total score decreased from 1.9 at baseline to 0.8 at week 40 with every-2-week dosing and from 1.7 at baseline to 1.1 at week 40 with every-4-week dosing (P<0.001 for both comparisons); these improvements persisted at week 64. The mean serum phosphorus level increased after the first dose in both groups, and more than half the patients in both groups had levels within the normal range (3.2 to 6.1 mg per deciliter [1.0 to 2.0 mmol per liter]) by week 6. Stable serum phosphorus levels were maintained through week 64 with every-2-week dosing. Renal tubular phosphate reabsorption increased from baseline in both groups, with an overall mean increase of 0.98 mg per deciliter (0.32 mmol per liter). The mean dose of burosumab at week 40 was 0.98 mg per kilogram of body weight with every-2-week dosing and 1.50 mg per kilogram with every-4-week dosing. Across both groups, the mean serum alkaline phosphatase level decreased from 459 U per liter at baseline to 369 U per liter at week 64. The mean standing-height z score increased in both groups, with greater improvement seen at all time points with every-2-week dosing (an increase from baseline of 0.19 at week 64) than with every-4-week dosing (an increase from baseline of 0.12 at week 64). Physical ability improved and pain decreased. Nearly all the adverse events were mild or moderate in severity.ConclusionsIn children with X-linked hypophosphatemia, treatment with burosumab improved renal tubular phosphate reabsorption, serum phosphorus levels, linear growth, and physical function and reduced pain and the severity of rickets. (Funded by Ultragenyx Pharmaceutical and Kyowa Hakko Kirin; ClinicalTrials.gov number, NCT02163577; EudraCT number, 2014-000406-35).

Constraints on modified Chaplygin gas from large scale structure

We study cosmological models with modified Chaplygin gas (MCG) to determine observational constraints on its EoS parameters using the background and the growth tests data. The background test data consists of \(H(z)-z\) data, Baryonic Acoustic Oscillations peak parameter, CMB shift parameter, SN Ia data and the growth test data consists of the linear growth function for the large scale structures of the universe are considered to study MCG in favor of dark energy. For a given range of redshift, the Wiggle-Z measurements and rms mass fluctuations from Ly-\(\alpha \) data, employed for analyzing cosmological models numerically to constrain the MCG parameters. The Wang-Steinhardt ansatz for the growth index (\(\gamma \)) and growth function (\(f\)) are also considered for numerical analysis. The best-fit values of EoS parameters determined here are used to study the variation of \(f\), growth index (\(\gamma \)), EoS parameter, squared sound speed and deceleration parameter with redshift. The constraints on the MCG parameters found here are compared with that of GCG (generalized Chaplygin gas) model for viable cosmology. Cosmologies with MCG satisfactorily describe late acceleration followed by a matter dominated phase. The range of values of EoS parameters, the associated parameters (\(f\), \(\gamma \), \(\omega \), \(\varOmega \), \(c^{2}_{s}\), \(q\)) are also determined from observational data in order to understand the suitability of the MCG model.