Smoothness Conditions Research Articles

Harnessing the regenerative effects of human amniotic stem cells (hAFSCs) on restoring erectile function in a bilateral cavernous nerve crush (BCNC) injury rat model.

Intracavernous (IC) injections of stem cells has been shown to ameliorate cavernous nerve (CN)-induced erectile dysfunction (ED). However, the regenerative effects underlying the recovery of erectile function (EF) in human amniotic fluid-derived stem cells (hAFSCs) remain unclear. In the bilateral cavernous nerve crushing (BCNC) injury rat paradigm, we sought to ascertain the effects of hAFSC treatment on EF recovery during the incipient phase. Three groups of 45 male rats were used in this study: sham (Group 1), saline IC injection after BCNC (Group 2), and hAFSC intracavernous injection (ICI) after BCNC (Group 3). hAFSCs from the fourth passage showed potential to differentiate into trilineage cells. All animals were subjected to EF analysis on the 28th day post-injection and tissues were retrieved for histopathological and immunohistochemical analyses. IC injections of hAFSC significantly improved EF parameters in BCNC-ED rats at 28 days post-injury. AFSC treatment enhanced the smooth muscle condition and increased the smooth muscle/collagen ratio, as evidenced by histological analysis. Immunohistology revealed increased expression of 𝛼-SMA andvWf in the corpus cavernosum and enhanced expression of nNOS in the dorsal penile nerve in BCNC-ED rats (p < 0.05). Western blotting showed that hAFSC treatment significantly increased α-SMA expression in the hAFSC group compared with that in the BCNC group. Electron microscopy revealed significantly elevated myelination in the CN (p < 0.05), maintenance of smooth muscle structures, and restoration of EF in BCNC-ED rats treated with hAFSC. hAFSC treatment increased EF in BCNC-ED rats at a single dose. As BCNC-ED resembles ED caused by radical prostatectomy (RP), this therapy has high potential for ED patients after RP surgery.

On the analytical construction of radially symmetric solutions for the relativistic Euler equations

AbstractThis paper is concerned with the analytical construction of piecewise smooth solutions containing a single shock wave for the radially symmetric relativistic Euler equations with polytropic gases. We derive meticulously the a priori ‐estimates on the Riemann invariants of the governing system under some assumptions on the piecewise initial data. Based on these estimates, we show that the long time of existence of smooth solutions in the angular region bounded by a characteristic curve and a shock curve. The piecewise smooth initial conditions ensured the existence of smooth solutions in the angular region are discussed. Moreover, it is verified that the existence time is proportional to the initial discontinuous position.

On partially observed jump diffusions III: regularity of the filtering density

AbstractThe filtering equations associated to a partially observed jump diffusion model $$(Z_t)_{t\in [0,T]}=(X_t,Y_t)_{t\in [0,T]}$$ ( Z t ) t ∈ [ 0 , T ] = ( X t , Y t ) t ∈ [ 0 , T ] , driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding articles on the filtering equations, the regularity of the conditional density of the signal $$X_t$$ X t , given observations $$(Y_s)_{s\in [0,t]}$$ ( Y s ) s ∈ [ 0 , t ] , is investigated, when the conditional density of $$X_0$$ X 0 given $$Y_0$$ Y 0 exists and belongs to a Sobolev space, and the coefficients satisfy appropriate smoothness and growth conditions.

Regularity and uniqueness of solutions for compressible non-newtonian MHD equations with variable electrical conductivity and energy effects

This paper examines the existence, uniqueness, and regularity of solutions for a system of compressible non-Newtonian magnetohydrodynamics (MHD) equations with variable electrical conductivity and considering the energy equation. We establish the necessary conditions on fluid properties, external forces, and initial and boundary conditions to ensure the well-posedness of the system. Our results demonstrate the existence of regular solutions in appropriate functional spaces, the uniqueness of these solutions, and their higher regularity under smooth initial and boundary conditions. These findings provide a mathematical baseline for the study of complex interactions in compressible non-Newtonian MHD flows, and particularly the findings can be considered to support more accurate numerical simulations concerning a physical situation as well as deeper analytical solutions.

Bond performance of fly ash-based geopolymer mortar in simulated concrete sewer substrate

Geopolymers have been extensively explored as a promising repair material for deteriorated Ordinary Portland Cement (OPC) concrete elements. However, knowledge of the adhesion performance of geopolymer to concrete substrates is limited. This study investigates the bond performance of low calcium fly ash geopolymer (FAGP) mortar and concrete for holistic acidic environmental conditions, such as in sewer rehabilitation. The bond evaluation was conducted by slant-shear test, performed at different substrate conditions, namely Rough-Dry, Rough-Saturated, Smooth-Dry and Smooth-Saturated, to simulate the in-service condition of a typical sewer pipe wall. The standard OPC repair mortar and a commercially available proprietary geopolymer repair product (P-GP) were evaluated and compared as controls to ascertain the viability of geopolymer for repair application. The shear bond strength of FAGP mortar was found to be in the order of 14 MPa, outperforming OPC and P-GP in all substrate conditions. Even though FAGP bond strength was insensitive to roughened substrate moisture levels, the synergistic effect of smoothness and moisture condition appeared detrimental. The testing of the prototype geopolymer-coated concrete pipe under line loading showed no sign of delamination at the bond plane. OPC and P-GP exhibited a distinct bond separation, which commenced at only 20 % of the ultimate load. The acid resistance and low permeability of FAGP mortar appeared to aid in preserving the repair bond.

On the tractive rolling nanocontact of an exponentially graded coating-substrate structure

This paper studies the tractive rolling nanocontact occurring between an exponentially graded coating-substrate structure and a circular rigid indenter. Employing the framework of Steigmann–Ogden surface elasticity, it models the surface effects inherent in the nanocontact of graded coatings. The contact area is assumed to comprise a central stick zone bounded by two distinct slip zones. Central to the investigation is the utilization of the nonclassical Flamant solution, which serves as the foundational framework for deriving integral equations governing the continuity of both vertical and tangential displacement gradients. Utilizing Gauss–Chebyshev quadratures, the paper discretizes and collocates these integral equations, along with the force equilibrium conditions and shear traction smooth condition at the leading side stick/slip transition point. An iterative algorithm is then developed to tackle the resultant algebraic system, particularly concerning the discretized contact pressure and friction traction. The paper rigorously validates its proposed solution method and numerical algorithm against existing literature results, showcasing their accuracy and reliability. Moreover, it conducts extensive parametric studies to unravel the effects of various parameters, such as surface material properties, coefficient of friction, inhomogeneity index, and thickness of the exponentially graded coating. These analyses uncover the significant role of surface effects in shaping contact pressure, frictional traction, stresses, subsidence distributions, and stick–slip zones. Notably, the inclusion of surface effects is found to reduce maximum stress and subsidence while inducing a shift of the stick region towards the rolling direction. The parametric exploration of graded coating properties also offers insights into tailoring nanocontact responses for gradient nanostructures.

Prenatal exposure to dibutyl phthalate contributes to erectile dysfunction in offspring male rats by activating the RhoA/ROCK signalling pathway

Prenatal exposure to dibutyl phthalate (DBP) has been reported to cause erectile dysfunction (ED) in adult offspring rats. However, its underlying mechanisms are not fully understood. Previously, we found that DBP activates the RhoA/ROCK pathway in the male reproductive system. This study investigated how prenatal exposure to DBP activates the RhoA/ROCK signalling pathway, leading to ED in male rat offspring. Pregnant rats were stratified into DBP-exposed and NC groups, with the exposed group receiving 750 milligrams per kilogram per day (mg/kg/day) of DBP through gavage from days 14–18 of gestation. DBP exposure activated the RhoA/ROCK pathway in the penile corpus cavernosum (CC) of descendants, causing smooth muscle cell contraction, fibrosis, and apoptosis, all of which contribute to ED. In vitro experiments confirmed that DBP induces apoptosis and RhoA/ROCK pathway activation in CC smooth muscle cells. Treatment of DBP-exposed offspring with the ROCK inhibitor Y-27632 for 8 weeks significantly improved smooth muscle cell condition, erectile function, and reduced fibrosis. Thus, prenatal DBP exposure induces ED in offspring through RhoA/ROCK pathway activation, and the ROCK inhibitor Y-27632 shows potential as an effective treatment for DBP-induced ED.

Impact of random nanoscale roughness on gas-scattering dynamics.

The impact of nanoscale wall roughness on rarefied gas transport is widely acknowledged, yet the associated scattering dynamics largely remain elusive. In this paper, we develop a scattering kernel for surfaces having nanoscale roughness that distinctly characterizes the two major types of interactions between gas molecules and rough surfaces. Namely these are (a) the weak perturbations arising from the thermal motion of wall atoms, essentially gas-phonon collisions, which are captured by the well-established Cercignani-Lampis model, and (b) the hard collisions owing to the irregularities of the rough, static potential energy surface, which are generally described by the fully diffuse model. Drawing an analogy between wave-surface and gas-surface scattering, a pseudo Debye-Waller factor is incorporated into the modeling as a weighting coefficient to allow the transition between smooth and rough surface conditions. The proposed scattering kernel is validated through high-fidelity molecular dynamics simulations that are performed for systems with varying roughness, temperature, and gas-surface combinations. The results indicate that the model well captures the scattering dynamics of gas molecular beams impinging on surfaces at different velocities, specifically for the accommodation coefficients and reflection patterns. Additionally, in flow and heat transport cases, it accurately predicts macroscopic quantities such as velocity slip and temperature jumps across the range of tested conditions.

Investigating the ability of PINNs to solve Burgers’ PDE near finite-time blowup

Physics Informed Neural Networks (PINNs) have been achieving ever newer feats of solving complicated Partial Differential Equations (PDEs) numerically while offering an attractive trade-off between accuracy and speed of inference. A particularly challenging aspect of PDEs is that there exist simple PDEs which can evolve into singular solutions in finite time starting from smooth initial conditions. In recent times some striking experiments have suggested that PINNs might be good at even detecting such finite-time blow-ups. In this work, we embark on a program to investigate this stability of PINNs from a rigorous theoretical viewpoint. Firstly, we derive error bounds for PINNs for Burgers’ PDE, in arbitrary dimensions, under conditions that allow for a finite-time blow-up. Our bounds give a theoretical justification for the functional regularization terms that have been reported to be useful for training PINNs near finite-time blow-up. Then we demonstrate via experiments that our bounds are significantly correlated to the ℓ2 -distance of the neurally found surrogate from the true blow-up solution, when computed on sequences of PDEs that are getting increasingly close to a blow-up.

Gradient‐based approach to sufficient dimension reduction with functional or longitudinal covariates

AbstractIn this paper, we focus on the sufficient dimension reduction problem in regression analysis with real‐valued response and functional or longitudinal covariates. We propose a new method based on gradients of the conditional distribution function to estimate the sufficient dimension reduction subspace. While existing inverse‐regression‐type methods relies on a linearity condition, our method is based on the gradient of conditional distribution function and its validity only requires smoothness conditions on the population parameters. Practically, the proposed estimator can be obtained by standard algorithm of functional principal component analysis. The proposed method is demonstrated through extensive simulations and two empirical examples.

Generalizing orthomodularity to unsharp contexts: properties, blocks, residuation

Abstract This paper essentially originates from the notion of a block in an orthomodular lattice. What happens to orthomodularity when orthocomplementation is weakened? We will show that, under definitely smooth conditions, a great deal of the theory of orthomodular lattices carries over naturally.

The influence of smoothness and speed of stand-to-sit movement on joint kinematics, kinetics, and muscle activation patterns.

Stand-to-sit (StandTS) is an important daily activity widely used in rehabilitation settings to improve strength, postural stability, and mobility. Modifications in movement smoothness and speed significantly influence the kinematics, kinetics, and muscle activation patterns of the movement. Understanding the impact of StandTS speed and smoothness on movement control can provide valuable insights for designing effective and personalized rehabilitation training programs. How do the smoothness and speed of StandTS movement affect joint kinematics, kinetics, muscle activation patterns, and postural stability during StandTS? Twelve healthy younger adults participated in this study. There were two StandTS conditions. In the reference condition, participants stood in an upright position with their feet positioned shoulder-width apart on the force plate. Upon receiving a visual cue, participants performed StandTS at their preferred speed. In the smooth condition, participants were instructed to perform StandTS as smoothly as possible, aiming to minimize contact pressure on the seat. Lower leg kinetics, kinematics, and coordination patterns of muscle activation during StandTS were measured: (1) angular displacement of the trunk, knee, and hip flexion; (2) knee and hip extensor eccentric work; (3) muscle synergy pattern derived from electromyography (EMG) activity of the leg muscles; and (4) postural sway in the anterior-posterior (A-P), medio-lateral (M-L), and vertical directions. Compared to the reference condition, the smooth condition demonstrated greater eccentric knee extensor flexion and increased joint work in both the knee and hip joints. Analysis of specific muscle synergy from EMG activity revealed a significant increase in the relative contribution of hip joint muscles during the smooth condition. Additionally, a negative correlation was observed between knee extensor and vertical postural sway, as well as hip extensor work and M-L postural sway. Smooth StandTS facilitates enhanced knee eccentric control and increased joint work at both the hip and knee joints, along with increased involvement of hip joint muscles to effectively manage falling momentum during StandTS. Furthermore, the increased contributions of knee and hip joint work reduced postural sway in the vertical and M-L directions, respectively. These findings provide valuable insights for the development of targeted StandTS rehabilitation training.

Estimating a Function and Its Derivatives Under a Smoothness Condition

We consider the problem of estimating an unknown function [Formula: see text] and its partial derivatives from a noisy data set of n observations, where we make no assumptions about [Formula: see text] except that it is smooth in the sense that it has square integrable partial derivatives of order m. A natural candidate for the estimator of [Formula: see text] in such a case is the best fit to the data set that satisfies a certain smoothness condition. This estimator can be seen as a least squares estimator subject to an upper bound on some measure of smoothness. Another useful estimator is the one that minimizes the degree of smoothness subject to an upper bound on the average of squared errors. We prove that these two estimators are computable as solutions to quadratic programs, establish the consistency of these estimators and their partial derivatives, and study the convergence rate as [Formula: see text]. The effectiveness of the estimators is illustrated numerically in a setting where the value of a stock option and its second derivative are estimated as functions of the underlying stock price.

Online composite optimization with time-varying regularizers

This paper investigates online composite optimization in dynamic environments, where each objective or loss function contains a time-varying nondifferentiable regularizer. To resolve it, an online proximal gradient algorithm is studied for two distinct scenarios, including convex and strongly convex objectives without the smooth condition. In both scenarios, unlike most of works, an extended version of the conventional path variation is employed to bound the considered performance metric, i.e., dynamic regret. In the convex scenario, a bound O(T1−βDβ(T)+T) is obtained which is comparable to the best-known result, where Dβ(T) is the extended path variation with β∈[0,1) and T being the total number of rounds. In strongly convex case, a bound O(logT(1+T−βDβ(T))) on the dynamic regret is established. In the end, numerical examples are presented to support the theoretical findings.

On smoothness conditions and selection of the edge of a scattering surface in one class of 3D time-optimal problems

A class of time-optimal problems in three-dimensional space with a spherical velocity vectogram is considered. The target set is a parametrically defined smooth curve. Numerical and analytical approaches to constructing the bisector of the target set — the scattering surface — in the time-optimal problem are proposed. The algorithms are based on formulas for the edge points of the scattering surface, written in terms of curve invariants. It is shown that these points form the edge of the bisector and lie at the centers of the touching spheres to the curve. A theorem on sufficient conditions for the smoothness of a scattering surface is proven. The equations of the tangent plane to the bisector are found for those points from which exactly two optimal trajectories emerge. An example of solving a time-optimal problem in the form of a set of level surfaces of the optimal result function is given, highlighting the surface of their non-smoothness.

Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment

Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries.

Stability of Krein-von Neumann self-adjoint operator extension under unbounded perturbations

We have considered a fourth order difference operator defined on the Hilbert space of square summable sequences on N. We investigated the stability of existence of Krein-von Neumann self-adjoint extension of difference operators under bounded and unbounded coefficients. Using asymptotic summation based on discretised Levinson's theorem and appropriate smoothness and decay conditions, we have shown that unlike the case of deficiency indices and discrete spectrum, the existence of positive self-adjoint operator extensions is stable under unbounded perturbations. These results now exhaustively characterise the spectral and structural properties of difference operators with unbounded coefficients.

Study on Vehicle-Bridge Coupled Vibration of Curved Girder Bridges under Different Road Surface Grades

This study explores the impact of different levels of road surface smoothness on the dynamic response of bridges. By conducting a detailed analysis under five different conditions of road surface smoothness, the mechanisms by which road surface irregularities affect the dynamic characteristics and safety performance of bridge structures are revealed. The research employs the finite element simulation method to compare and analyze the changes in key dynamic indicators such as vertical displacement, torsional angle, torque, and bending moment of bridges under different grades of road surface smoothness. The results indicate that a decrease in road surface smoothness significantly increases the dynamic response of bridges. The findings provide important reference information for bridge engineers in the design and maintenance of bridges.

Sectoral uncertainty spillovers in emerging markets: A quantile time–frequency connectedness approach

This study investigates the sectoral expected uncertainty connectedness in emerging markets across different frequencies and quantiles using the novel quantile time–frequency connectedness approach of Chatziantoniou et al. (2022a). The employed dataset spans from January 1st, 2003 to October 4th, 2022, encompassing 10 key sectors. The findings reveal a robust and notable interconnection among these sectors, with a substantial total connectedness index of 91.01%. We also note that the largest proportion of the sectoral total connectedness is associated with long-term spillovers. Consumer Cyclicals emerges as the primary source of net risk transmission. Conversely, the Communications & Networking and Healthcare appear to be the greatest net receivers of shocks at the median level. Furthermore, we find that the degree of interconnectedness substantially varies over time, frequency, and quantile, and by economic events. In addition, we find suggestive evidence of asymmetric sectoral uncertainty connectedness effects as the uncertainty spillovers are higher during turbulent market conditions than normal market conditions. A positive relationship between uncertainty measures and sectoral connectedness is also observed during periods of smooth and normal market conditions. Besides, we also conduct different portfolio analyses illustrating the importance of risk diversification to reduce investment uncertainty. This has important implications for international investors and policymakers in forming optimal investment portfolios reducing adverse risk spillovers.

An improved wall boiling model for numerical simulation of subcooled flow boiling on a new hybrid micro/nanostructured surface

Previous studies have demonstrated that micro/nanostructured surfaces have great potential for heat transfer enhancement. However, simulating subcooled flow boiling on such surfaces is difficult owing to the lack of proper bubble characteristic parameter models, because most models used in flow boiling simulations were developed based on smooth surface conditions, which may limit their applications in engineering design. In this study, we improved upon one validated bubble characteristic parameter model suitable for subcooled flow boiling on smooth surfaces to adapt to the new hybrid micro/nanostructured surfaces proposed by Huang et al. [“Experimental investigation of a new hybrid structured surface for subcooled flow boiling heat transfer enhancement,” Appl. Therm. Eng. 192, 116929 (2021)]. The new bubble characteristic parameter model incorporates both basic correction terms to account for boiling bubble behaviors and ad hoc parameters to account for other unknown effects. Through sensitivity analysis and detailed calibration, the model was simplified to a set of correlations and only one constant parameter. With this improved model, subcooled flow boiling heat transfer simulations were conducted for three target surface specifications under conditions of 4–10 MW/m2 incident heat flux and 1–5 m/s flow velocity and the related heat-transfer mechanisms were further compared and discussed. The maximum error between the simulation and experimental results remains less than 3.5%, indicating that the established model has considerable accuracy in predicting the heat transfer performance for this type of micro/nanostructured surface in high-heat-flux engineering design applications. The heat transfer enhancement for subcooled flow boiling on this type of hybrid micro/nanostructured surface is greatly beneficial owing to its proper organization of convection, evaporation, and quenching heat transfer.