Insect flightInsects are the only group of invertebrates that have evolved wings and flight. Insects first flew in the Carboniferous, some 300 to 350 million years ago, making them the first animals to evolve flight. Wings may have evolved from appendages on the sides of existing limbs, which already had nerves, joints, and muscles used for other purposes. These may initially have been used for sailing on water, or to slow the rate of descent when gliding. Two insect groups, the dragonflies and the mayflies, have flight muscles attached directly to the wings.
Analytic continuationIn complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation which initially defined the function becomes divergent. The step-wise continuation technique may, however, come up against difficulties. These may have an essentially topological nature, leading to inconsistencies (defining more than one value).
Free surfaceIn physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture). Unlike liquids, gases cannot form a free surface on their own. Fluidized/liquified solids, including slurries, granular materials, and powders may form a free surface. A liquid in a gravitational field will form a free surface if unconfined from above.
Numerical weather predictionNumerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.
Flow diagramFlow diagram is a collective term for a diagram representing a flow or set of dynamic relationships in a system. The term flow diagram is also used as a synonym for flowchart, and sometimes as a counterpart of the flowchart. Flow diagrams are used to structure and order a complex system, or to reveal the underlying structure of the elements and their interaction. The term flow diagram is used in theory and practice in different meanings. Most commonly the flow chart and flow diagram are used in an interchangeable way in the meaning of a representation of a process.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Multivalued functionIn mathematics, a multivalued function, also called multifunction and many-valued function, is a set-valued function with continuity properties that allow considering it locally as an ordinary function. Multivalued functions arise commonly in applications of the implicit function theorem, since this theorem can be viewed as asserting the existence of a multivalued function. In particular, the inverse function of a differentiable function is a multivalued function, and is single-valued only when the original function is monotonic.
Data-flow diagramA data-flow diagram is a way of representing a flow of data through a process or a system (usually an information system). The DFD also provides information about the outputs and inputs of each entity and the process itself. A data-flow diagram has no control flowthere are no decision rules and no loops. Specific operations based on the data can be represented by a flowchart. There are several notations for displaying data-flow diagrams. The notation presented above was described in 1979 by Tom DeMarco as part of structured analysis.
SimulationA simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
