Decay Conditions Research Articles

Prevalence of Decay and Tooth Condition Changes Adjacent to Restored Dental Implants: A Retrospective Radiographic Study.

This study examined the association between a dental implant and changes in adjacent teeth over time. Electronic health records of 1818 patients who received a dental implant were retrospectively evaluated over 14 years (2005-2019) in a university setting. The status of the adjacent tooth and vertical and horizontal distance from the implant platform to adjacent teeth were determined using digital intraoral radiographs taken at baseline and the last follow-up visit (1-14 years, median 4 years). In total, 1085 dental implants were evaluated. There were 234 instances of a change in the adjacent tooth. Decay was observed in 83 (7.6%) of adjacent teeth; the mean time to development was 4 years (range 1-14 years). Approximately 9% of adjacent teeth received direct restorations, 4.8% received indirect restorations, 1% received endodontic root canal treatment, and 5.6% were extracted. The mean horizontal distance between the implant platform and the adjacent teeth was 3.56 mm; the mean vertical distance from the contact point to the alveolar crest on the tooth side was 6.2 mm at the first time of the reported decay on X ray. These distances did not significantly influence the occurrence of caries. The prevalence of interproximal contact loss was higher on the mesial of the implant crown at 63% compared with 20% on the distal side. This large retrospective analysis identified that teeth adjacent to a dental implant were at risk of decay and changes in their condition. In addition, the implant-to-tooth distance and inadequate emergence profile may contribute as caries risk factors in addition to hygiene and a high sugar level diet. These findings appear essential for clinicians when making treatment decisions and discussing outcomes with patients.

Current Accessibility Challenges to Dental Care

Introduction. Access to dental care is a key aspect of ensuring public health and well-being. Modern health-care systems face many challenges related to the provision of high-quality dental services to all patients seeking for medical help. There is a wide range of challenges, from financial and organizational issues to social and cultural aspects. Lack of dental care affects not only oral health but health in general. Limited access to dental care can lead to tooth decay or other conditions that require expensive treatment in hospital settings, thus disrupting more urgent medical needs.The purpose of this work was to consider the current problems related to the accessibility of dental care. To this purpose, an analysis of Russian and foreign scientific literature was carried out.Materials and methods. This study used general scientific research methods (generalization, analysis, and synthesis). Papers by Russian and foreign authors as well as analytical reports on public and private pro-grams that contribute to increasing the availability of dental medical care were studied.Results. In the context of universal health care, access to dental care is considered a vital public health issue. Financial, geographical, cultural, and social barriers to dental care are considered the most significant. In the Russian Federation, according to the Federal State Statistics Service (Rosstat), about 30% of the popu-lation does not have regular access to dental services due to financial and geographical barriers.

Microbial community structure of decayed trunks of Populus euphratica desert riparian forests in the lower Tarim River, Xinjiang, China

Rich microbial communities are associated with tree decay, and they markedly impact the degradation of tree species and material cycling within ecosystems. The native Populus euphratica forests along the lower Tarim River of China are mostly mature or over-mature, with many tree trunks exhibiting features of extensive cavity decay and slow regeneration. In this study, a growth cone was used to drill a wood core at varying degrees of decay, and 16S and internal transcribed spacer techniques were used to identify the microbial structure (fungi and bacteria) within the wood core. Changes in the trunk microbial community under varying decay conditions were also examined. For healthy, lightly decayed, and heavily decayed trunk, the dominant bacterial and fungal phyla were Firmicutes and Actinobacteria, Ascomycota, and Basidiomycota, respectively. As decay progressed, the alpha diversity index of the microbial community tended to decline. The maximum number of differential species was found in healthy trunks, where leaner discriminant analysis effect size (LEfSe) of fungi and bacteria revealed 1 and 15 different species, respectively. Species network analysis showed that interspecific linkages were more complex within bacterial communities than within fungal communities, with the complexity of fungal interspecific relationship increasing as decay progressed. The microbial communities of P. euphratica trunks differed significantly with the varying degrees of decay. Microbes such as Ralstonia may also play key roles in the decay process. In addition to providing a foundation for the sustainable management of desert riparian forests, investigating the mechanisms through which microbial communities influence the deterioration of P. euphratica trunks provides information about the general health of P. euphratica forests.

Asymptotic behavior of a semilinear non-autonomous wave equation with distributed delay and analytic nonlinearity

This paper is concerned with a semilinear non-autonomous wave equation with distributed delay and analytic nonlinearity. The distributed delay is represented by an integral operator integrating on the delay interval, which considers a segment of the past dynamic information. Firstly we show the global boundedness of solutions and then prove that every globally bounded solution has a relative compact range in the phase space. By the Łojasiewicz–Simon inequality, we prove the convergence to an equilibrium of globally bounded solutions and then show the convergence rate dependence on the Łojasiewicz exponent and the decay conditions on non-autonomous term. The existence and uniqueness of a global strong solution is finally proved. Note that the result of existence and uniqueness of the solution does not need any restrictions on the coefficients between the damping and the delay. The presence of an integral kernel makes distributed delays more difficult to be analyzed compared to its pointwise counterpart.

On the optimality and decay of p-Hardy weights on graphs

We construct optimal Hardy weights to subcritical energy functionals h associated with quasilinear Schrödinger operators on infinite graphs. Here, optimality means that the weight w is the largest possible with respect to a partial ordering, and that the corresponding shifted energy functional h-w\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h-w$$\\end{document} is null-critical. Moreover, we show a decay condition of Hardy weights in terms of their integrability with respect to certain integral weights. As an application of the decay condition, we show that null-criticality implies optimality near infinity. We also briefly discuss an uncertainty-type principle, a Rellich-type inequality and examples.

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

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

Infinitely many solutions for linearly coupled Schrödinger systems in ℝ3

In this paper, we consider the following linearly coupled nonlinear Schrödinger system: where , and are radial, positive, and continuous and satisfying that When and satisfy some weak power decay condition at infinity; we show that problem has infinitely many nonradial positive solutions by using the Lyapunov–Schmidt reduction method.

Size-dependent effect on the interaction of surface waves in micropolar thermoelastic medium with dual pore connectivity

This research tackles a critical knowledge gap in Rayleigh surface wave propagation. It offers a comprehensive analysis that surpasses previous limitations. A size-dependent micropolar medium with unique void distributions and thermal effects is considered in this work. The constitutive relations and equations of motion for a nonlocal micropolar thermoelastic medium with double voids (MTMWDV) have been established by using Eringen’s nonlocal elasticity theory. Employing the three-phase-lag thermoelasticity theory (TPLTE), the study utilizes a wave-mode method to derive analytical solutions for Rayleigh waves in a nonlocal MTMWDV. To gain a comprehensive understanding of wave behavior, we solve the characteristic equation and analyze its roots, applying a filter based on the surface wave decay condition. A medium with stress-free and isothermal boundaries is explored through computational simulations to determine the attenuation coefficient and phase velocity. Furthermore, particle motion analysis is conducted to complement the analytical and computational approaches. Moreover, the influence of the nonlocal parameter and various thermoelastic models on these wave phenomena is investigated. The validity of the current mathematical model is confirmed through the derivation of particular scenarios.

Poincaré inequalities and Ap weights on bow-ties

A metric space X is called a bow-tie if it can be written as ▪, where ▪ and ▪ are closed subsets of X. We show that a doubling measure μ on X supports a (q,p)-Poincaré inequality on X if and only if X satisfies a quasiconvexity-type condition, μ supports a (q,p)-Poincaré inequality on both ▪ and ▪, and a variational ▪-capacity condition holds. This capacity condition is in turn characterized by a sharp measure decay condition at the point x0. In particular, we study the bow-tie XRn consisting of the positive and negative hyperquadrants in Rn equipped with a radial doubling weight and characterize the validity of the ▪-Poincaré inequality on XRn in several ways. For such weights, we also give a general formula for the capacity of annuli around the origin.

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.

Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields

We resolve both a conjecture and a problem of Z. Shen from the 90's regarding non-asymptotic bounds on the eigenvalue counting function of the magnetic Schrödinger operator La,V=−(∇−ia)2+V with a singular or irregular magnetic field B on Rn, n≥3. We do this by constructing a new landscape function for La,V, and proving its corresponding uncertainty principle, under certain directionality assumptions on B, but with no assumption on ∇B. These results arise as applications of our study of the Filoche-Mayboroda landscape function u, a solution to the equation LVu=−divA∇u+Vu=1, on unbounded Lipschitz domains in Rn, n≥1, and 0≤V∈Lloc1, under a mild decay condition on the Green's function. For LV, we prove a priori exponential decay of Green's function, eigenfunctions, and Lax-Milgram solutions in an Agmon distance with weight 1/u, which may degenerate. Similar a priori results hold for La,V. Furthermore, when n≥3 and V satisfies a scale-invariant Kato condition and a weak doubling property, we show that 1/u is pointwise equivalent to the Fefferman-Phong-Shen maximal function m(⋅,V) (also known as Shen's critical radius function); in particular this gives a setting where the Agmon distance with weight 1/u is not too degenerate. Finally, we extend results from the literature for La,V regarding exponential decay of the fundamental solution and eigenfunctions, to the situation of irregular magnetic fields with directionality assumptions.

Relevant sampling in a reproducing kernel subspace of Orlicz space

In this paper, we aim to provide a general paradigm for dealing with the sampling and random sampling problem in a reproducing kernel subspace of Orlicz space [Formula: see text]. We consider the function space [Formula: see text] as the image of an idempotent integral operator on [Formula: see text], where the integral kernel satisfies certain off-diagonal decay and regularity conditions. The model example of such reproducing kernel subspace of [Formula: see text] includes the finitely generated shift-invariant space and signal space with a finite rate of innovation. We show that a signal in [Formula: see text] can be stably reconstructed from its samples at distinct points separated by a sufficiently small gap. Next, we deduce that the random sampling inequality holds with a high probability for the class of functions in [Formula: see text] concentrated on a cube [Formula: see text], when the samples collected at i.i.d. random points are drawn on [Formula: see text] of order [Formula: see text].

Impact of memory-dependent heat transfer on Rayleigh waves propagation in nonlocal piezo-thermo-elastic medium with voids

PurposeThis paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.Design/methodology/approachThe analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.FindingsComputational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.Research limitations/implicationsThe results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.Practical implicationsThis investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.Originality/valueThis study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

Tree marking guidelines for northern hardwoods: a review of criteria for assessing vigour and quality

Recent studies have highlighted the need to update hardwood tree marking guides by changing the criteria used to assess vigour and quality, and thus the priority for deciding which trees to remove and retain during selection harvests. However, these studies have recommended different criteria, so it remains uncertain which should be included in the classification systems used to assess vigour and quality. We review these studies with the aim of reducing this uncertainty and identifying potential improvements to the provincial tree marking guides for northern hardwood forests in Canada, particularly the Ontario Tree Marking Guide. We review the differences in methodologies and summarize which defects have been shown to affect vigour and/or quality. The defects that should be used to assess vigour are canopy dieback, cankers, and fungi. Decaying wounds, wounds without decay, canopy density, and bark condition could also be used as secondary criteria for borderline cases in which the primary criteria are not decisive. The defects that should be used to assess quality are cankers, fungi, cracks, cavities, and decay (including black bark and wounds with moisture or soft wood). We present a new classification system based on these results and identify potential challenges to its implementation.

Accelerating the convergence of a two-dimensional periodic nonuniform sampling series through the incorporation of a bivariate Gaussian multiplier

<p>Recently, in the field of periodic nonuniform sampling, researchers (Wang et al., 2019; Asharabi, 2023) have investigated the incorporation of a Gaussian multiplier in the one-dimensional series to improve its convergence rate. Building on these developments, this paper aimed to accelerate the convergence of the two-dimensional periodic nonuniform sampling series by incorporating a bivariate Gaussian multiplier. This approach utilized a complex-analytic technique and is applicable to a wide range of functions. Specifically, it applies to the class of bivariate entire functions of exponential type that satisfy a decay condition, as well as to the class of bivariate analytic functions defined on a bivariate horizontal strip. The original convergence rate of the two-dimensional periodic nonuniform sampling is given by $ O(N^{-p}) $, where $ p \geq 1 $. However, through the implementation of this acceleration technique, the convergence rate improved drastically and followed an exponential order, specifically $ \mathrm{e}^{-\alpha N} $, where $ \alpha > 0 $. To validate the theoretical analysis presented, the paper conducted rigorous numerical experiments.</p>

Absence of embedded eigenvalues of Pauli and Dirac operators

We consider eigenvalues of the Pauli operator in R3 embedded in the continuous spectrum. In our main result we prove the absence of such eigenvalues above a threshold which depends on the asymptotic behavior of the magnetic and electric field at infinity. We show moreover that the decay conditions on the magnetic and electric field are sharp. Analogous results are obtained for purely magnetic Dirac operators.

Estimates for generalized wave‐type Fourier multipliers on modulation spaces and applications

AbstractWe consider the boundedness of the Fourier multipliers on modulation spaces, where defined on is a positive homogeneous function with degree and is a smooth function satisfying some decay conditions. We prove the boundedness of this kind of Fourier multipliers and obtain its asymptotic estimates as goes to infinity. We remote the restriction in Deng, Ding, and Sun's result in [Nonlinear Anal. 85 (2013), 78–92], and we consider the more general form of this multiplier. As applications, we obtain the grow‐up rate of the solutions for the Cauchy problems for the generalized wave and Klein–Gordon equations, and we obtain the local well‐posedness of nonlinear wave and Klein–Gordon equations in modulation spaces.

Removing rotated discretely self-similar singularity for the Euler equations

In this paper we exclude the scenario of rotated discretely self-similar singularities of the 3D incompressible Euler equations in the case when the singularity point is isolated and the vorticity satisfies appropriate decay condition at spatial infinity. For the proof we use the maximum principle for the transformed self-similar equations.

The environmental factors affecting the archaeological buildings in Egypt, “IV deterioration by synergistic marine effects”

This paper investigates the marine effects that affect Qait Bey Fortress in Alexandria—Egypt. It presents the results of scientific studies and examinations to evaluate the deterioration conditions that affected archaeological buildings in the marine environment. In Alexandria, many monumental sites and stone buildings have suffered from many aggressive factors of deterioration (mechanical, chemical, and biological), which have caused great harmful appearances and threatened to eradicate them. These effects include the chemical actions resulting from seawater and marine aerosol and the mechanical actions of water waves. (Qait Bey Fortress), as a case study, was periodically investigated by many scientific techniques over five years to check its decay conditions and to define the most suitable conservation approaches and non-destructive methods for preservation. Different techniques and examinations were carried out to evaluate the current deterioration state of the fortress. For example, XRD analysis and PM investigation were used to study the mineralogical compositions, lithotype, and petrographic characteristics of the stone samples. SEM was used to investigate the morphological features of the same samples. AAS was also used for studying the chemical constituents of seawater samples. In addition, microbiological investigations were conducted to evaluate the colored hard crusts that affected the stone surfaces in the fortress. Our results proved that severe deterioration factors influenced the fortress by collaborating with chemical, mechanical, and biological mechanisms. These mechanisms caused several manifestations, such as abrasion and attrition, crystallizing of salt species, mortar desegregation, pitting and minerals’ honeycomb (Alveolar), color changes, in addition to the accumulation of black and colored biogenic hard crusts composed of numerous tightly adjoining pits of several centimeters. Crusts, such as yellow to bluish green, resulted from P. aeruginosa and granular appearance having brownish ting in the center resulted from P. clacis. In addition, other pigmented features resulted from Bacillus firmus and Bacillus atrophaeus. The presence of some black and dark color crusts was attributed to the growth of some fungal species, such as A. niger, A. phoenicis, Cladosporium cladosporioides, and Alternaria alternata.

Multibump positive solutions for Choquard equation with double potentials in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$

In this paper, we construct a new family of multibump solutions to the following Choquard equation where and are radial positive functions and both of them satisfy some decay conditions at infinity. The centers of these bumps are located in points on two circles. More precisely, the new type of solutions has polygonal symmetry in the ‐plane and even symmetry about the ‐axis.