Lagrangian mechanicsIn physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, Mécanique analytique. Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space and a smooth function within that space called a Lagrangian. For many systems, where and are the kinetic and potential energy of the system, respectively.
HumidityHumidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present. Humidity depends on the temperature and pressure of the system of interest. The same amount of water vapor results in higher relative humidity in cool air than warm air. A related parameter is the dew point. The amount of water vapor needed to achieve saturation increases as the temperature increases.
Wavelet transformIn mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.
WaveletA wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.
Scale invarianceIn physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation). Dilatations can form part of a larger conformal symmetry. In mathematics, scale invariance usually refers to an invariance of individual functions or curves.
Wind shearWind shear (or windshear), sometimes referred to as wind gradient, is a difference in wind speed and/or direction over a relatively short distance in the atmosphere. Atmospheric wind shear is normally described as either vertical or horizontal wind shear. Vertical wind shear is a change in wind speed or direction with a change in altitude. Horizontal wind shear is a change in wind speed with a change in lateral position for a given altitude.
Discrete wavelet transformIn numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.
Wind powerWind power is the use of wind energy to generate useful work. Historically, wind power was used by sails, windmills and windpumps, but today it is mostly used to generate electricity. This article deals only with wind power for electricity generation. Today, wind power is generated almost completely with wind turbines, generally grouped into wind farms and connected to the electrical grid. In 2022, wind supplied over 2000 TWh of electricity, which was over 7% of world electricity and about 2% of world energy.
HygrometerA hygrometer is an instrument which measures the humidity of air or some other gas: that is, how much water vapor it contains. Humidity measurement instruments usually rely on measurements of some other quantities such as temperature, pressure, mass and mechanical or electrical changes in a substance as moisture is absorbed. By calibration and calculation, these measured quantities can lead to a measurement of humidity.
Gabor waveletGabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory applications. They are very similar to Morlet wavelets. They are also closely related to Gabor filters. The important property of the wavelet is that it minimizes the product of its standard deviations in the time and frequency domain. Put another way, the uncertainty in information carried by this wavelet is minimized.
