Tooth whiteningTooth whitening or tooth bleaching is the process of lightening the color of human teeth. Whitening is often desirable when teeth become yellowed over time for a number of reasons, and can be achieved by changing the intrinsic or extrinsic color of the tooth enamel. The chemical degradation of the chromogens within or on the tooth is termed as bleaching. Hydrogen peroxide (H2O2) is the active ingredient most commonly used in whitening products and is delivered as either hydrogen peroxide or carbamide peroxide.
Galerkin methodIn mathematics, in the area of numerical analysis, Galerkin methods are named after the Soviet mathematician Boris Galerkin. They convert a continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying linear constraints determined by finite sets of basis functions.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Human tooth developmentTooth development or odontogenesis is the complex process by which teeth form from embryonic cells, grow, and erupt into the mouth. For human teeth to have a healthy oral environment, all parts of the tooth must develop during appropriate stages of fetal development. Primary (baby) teeth start to form between the sixth and eighth week of prenatal development, and permanent teeth begin to form in the twentieth week. If teeth do not start to develop at or near these times, they will not develop at all, resulting in hypodontia or anodontia.
Human toothHuman teeth function to mechanically break down items of food by cutting and crushing them in preparation for swallowing and digesting. As such, they are considered part of the human digestive system. Humans have four types of teeth: incisors, canines, premolars, and molars, which each have a specific function. The incisors cut the food, the canines tear the food and the molars and premolars crush the food. The roots of teeth are embedded in the maxilla (upper jaw) or the mandible (lower jaw) and are covered by gums.
Tooth decayTooth decay, also known as cavities or caries, is the breakdown of teeth due to acids produced by bacteria. The cavities may be a number of different colors from yellow to black. Symptoms may include pain and difficulty with eating. Complications may include inflammation of the tissue around the tooth, tooth loss and infection or abscess formation. The cause of cavities is acid from bacteria dissolving the hard tissues of the teeth (enamel, dentin and cementum).
Enamel hypoplasiaEnamel hypoplasia is a defect of the teeth in which the enamel is deficient in quantity, caused by defective enamel matrix formation during enamel development, as a result of inherited and acquired systemic condition(s). It can be identified as missing tooth structure and may manifest as pits or grooves in the crown of the affected teeth, and in extreme cases, some portions of the crown of the tooth may have no enamel, exposing the dentin. It may be generalized across the dentition or localized to a few teeth.
Tooth enamelTooth enamel is one of the four major tissues that make up the tooth in humans and many animals, including some species of fish. It makes up the normally visible part of the tooth, covering the crown. The other major tissues are dentin, cementum, and dental pulp. It is a very hard, white to off-white, highly mineralised substance that acts as a barrier to protect the tooth but can become susceptible to degradation, especially by acids from food and drink. Calcium hardens the tooth enamel.
Tooth pathologyTooth pathology is any condition of the teeth that can be congenital or acquired. Sometimes a congenital tooth diseases are called tooth abnormalities. These are among the most common diseases in humans The prevention, diagnosis, treatment and rehabilitation of these diseases are the base to the dentistry profession, in which are dentists and dental hygienists, and its sub-specialties, such as oral medicine, oral and maxillofacial surgery, and endodontics.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Tooth lossTooth loss is a process in which one or more teeth come loose and fall out. Tooth loss is normal for deciduous teeth (baby teeth), when they are replaced by a person's adult teeth. Otherwise, losing teeth is undesirable and is the result of injury or disease, such as dental avulsion, tooth decay, and gum disease. The condition of being toothless or missing one or more teeth is called edentulism. Tooth loss has been shown to causally reduce overall health and wellbeing as it increases the probability of depression.
Tooth impactionAn impacted tooth is one that fails to erupt into the dental arch within the expected developmental window. Because impacted teeth do not erupt, they are retained throughout the individual's lifetime unless extracted or exposed surgically. Teeth may become impacted because of adjacent teeth, dense overlying bone, excessive soft tissue or a genetic abnormality. Most often, the cause of impaction is inadequate arch length and space in which to erupt.
Dental implantA dental implant (also known as an endosseous implant or fixture) is a prosthesis that interfaces with the bone of the jaw or skull to support a dental prosthesis such as a crown, bridge, denture, or facial prosthesis or to act as an orthodontic anchor. The basis for modern dental implants is a biological process called osseointegration, in which materials such as titanium or zirconia form an intimate bond to the bone. The implant fixture is first placed so that it is likely to osseointegrate, then a dental prosthetic is added.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Conformal mapIn mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let and be open subsets of . A function is called conformal (or angle-preserving) at a point if it preserves angles between directed curves through , as well as preserving orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation.
Electric machineIn electrical engineering, electric machine is a general term for machines using electromagnetic forces, such as electric motors, electric generators, and others. They are electromechanical energy converters: an electric motor converts electricity to mechanical power while an electric generator converts mechanical power to electricity. The moving parts in a machine can be rotating (rotating machines) or linear (linear machines).
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
Explicit and implicit methodsExplicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes. Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one.
