KnotA knot is an intentional complication in cordage which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bends, loop knots, and splices: a hitch fastens a rope to another object; a bend fastens two ends of a rope to each another; a loop knot is any knot creating a loop; and splice denotes any multi-strand knot, including bends and loops. A knot may also refer, in the strictest sense, to a stopper or knob at the end of a rope to keep that end from slipping through a grommet or eye.
Knot theoryIn topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself.
Knot (mathematics)In mathematics, a knot is an embedding of the circle S^1 into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of R3 which takes one knot to the other. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot.
Chiral knotIn the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed). An oriented knot that is equivalent to its mirror image is an amphicheiral knot, also called an achiral knot. The chirality of a knot is a knot invariant. A knot's chirality can be further classified depending on whether or not it is invertible. There are only five knot symmetry types, indicated by chirality and invertibility: fully chiral, invertible, positively amphicheiral noninvertible, negatively amphicheiral noninvertible, and fully amphicheiral invertible.
Prime knotIn knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be composite knots or composite links. It can be a nontrivial problem to determine whether a given knot is prime or not. A family of examples of prime knots are the torus knots. These are formed by wrapping a circle around a torus p times in one direction and q times in the other, where p and q are coprime integers.
Compressive strengthIn mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.
Ultimate tensile strengthUltimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials the ultimate tensile strength is close to the yield point, whereas in ductile materials the ultimate tensile strength can be higher. The ultimate tensile strength is usually found by performing a tensile test and recording the engineering stress versus strain.
Robot-assisted surgeryRobot-assisted surgery or robotic surgery are any types of surgical procedures that are performed using robotic systems. Robotically assisted surgery was developed to try to overcome the limitations of pre-existing minimally-invasive surgical procedures and to enhance the capabilities of surgeons performing open surgery. In the case of robotically assisted minimally-invasive surgery, instead of the surgeon directly moving the instruments, the surgeon uses one of two methods to perform dissection, hemostasis and resection, using a direct telemanipulator, or through computer control.
Empirical evidenceEmpirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms evidence and empirical are to be defined. Often different fields work with quite different conceptions.
Strength of materialsThe field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.
Human natureHuman nature is a concept that denotes the fundamental dispositions and characteristics—including ways of thinking, feeling, and acting—that humans are said to have naturally. The term is often used to denote the essence of humankind, or what it 'means' to be human. This usage has proven to be controversial in that there is dispute as to whether or not such an essence actually exists. Arguments about human nature have been a central focus of philosophy for centuries and the concept continues to provoke lively philosophical debate.
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).
Specific strengthThe specific strength is a material's (or muscle's) strength (force per unit area at failure) divided by its density. It is also known as the strength-to-weight ratio or strength/weight ratio or strength-to-mass ratio. In fiber or textile applications, tenacity is the usual measure of specific strength. The SI unit for specific strength is Pa⋅m3/kg, or N⋅m/kg, which is dimensionally equivalent to m2/s2, though the latter form is rarely used.
Critical phenomenaIn physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking.
Coupled Model Intercomparison ProjectIn climatology, the Coupled Model Intercomparison Project (CMIP) is a collaborative framework designed to improve knowledge of climate change. It was organized in 1995 by the Working Group on Coupled Modelling (WGCM) of the World Climate Research Programme (WCRP). It is developed in phases to foster the climate model improvements but also to support national and international assessments of climate change. A related project is the Atmospheric Model Intercomparison Project (AMIP) for global coupled ocean-atmosphere general circulation models (GCMs).
Fail-safeIn engineering, a fail-safe is a design feature or practice that, in the event of a specific type of failure, inherently responds in a way that will cause minimal or no harm to other equipment, to the environment or to people. Unlike inherent safety to a particular hazard, a system being "fail-safe" does not mean that failure is impossible or improbable, but rather that the system's design prevents or mitigates unsafe consequences of the system's failure.
Pre-Socratic philosophyPre-Socratic philosophy, also known as Early Greek Philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of these early philosophers spanned the workings of the natural world as well as human society, ethics, and religion. They sought explanations based on natural law rather than the actions of gods. Their work and writing has been almost entirely lost.
Da Vinci Surgical SystemThe da Vinci Surgical System is a robotic surgical system that uses a minimally invasive surgical approach. The system is manufactured by the company Intuitive Surgical. The system is used for prostatectomies, and increasingly for cardiac valve repair, and for renal and gynecologic surgical procedures. It was used in an estimated 200,000 surgeries in 2012, most commonly for hysterectomies and prostate removals. The system is called "da Vinci" in part because Leonardo da Vinci's study of human anatomy eventually led to the design of the first known robot in history.
Nature (philosophy)Nature has two inter-related meanings in philosophy and natural philosophy. On the one hand, it means the set of all things which are natural, or subject to the normal working of the laws of nature. On the other hand, it means the essential properties and causes of individual things. How to understand the meaning and significance of nature has been a consistent theme of discussion within the history of Western Civilization, in the philosophical fields of metaphysics and epistemology, as well as in theology and science.
Passive nuclear safetyPassive nuclear safety is a design approach for safety features, implemented in a nuclear reactor, that does not require any active intervention on the part of the operator or electrical/electronic feedback in order to bring the reactor to a safe shutdown state, in the event of a particular type of emergency (usually overheating resulting from a loss of coolant or loss of coolant flow).
