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Composition The Earth's planetary atmosphere contains, besides other gases, water vapour and carbon dioxide, which produce carbonic acid in rain water, which therefore has an approximate natural pH of 5.0 to 5.5 (slightly acidic). (Water other than atmospheric water vapour fallen as fresh rain, such as fresh/sweet/po...
Troposphere
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Physical sciences
Atmosphere: General
Earth science
vital_articles
Pressure The maximum air pressure (weight of the atmosphere) is at sea level and decreases at high altitude because the atmosphere is in hydrostatic equilibrium, wherein the air pressure is equal to the weight of the air above a given point on the planetary surface. The relation between decreased air pressure and high ...
Troposphere
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Atmosphere: General
Earth science
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The difference in temperature derives from the planetary surface absorbing most of the energy from the sun, which then radiates outwards and heats the troposphere (the first layer of the atmosphere of Earth) while the radiation of surface heat to the upper atmosphere results in the cooling of that layer of the atmosphe...
Troposphere
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Physical sciences
Atmosphere: General
Earth science
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Humidity If the air contains water vapor, then cooling of the air can cause the water to condense, and the air no longer functions as an ideal gas. If the air is at the saturation vapor pressure, then the rate at which temperature decreases with altitude is called the saturated adiabatic lapse rate. The actual rate at ...
Troposphere
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Atmosphere: General
Earth science
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The tropopause is the atmospheric boundary layer between the troposphere and the stratosphere, and is located by measuring the changes in temperature relative to increased altitude in the troposphere and in the stratosphere. In the troposphere, the temperature of the air decreases at high altitude, however, in the stra...
Troposphere
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Physical sciences
Atmosphere: General
Earth science
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Zonal flow A zonal flow regime is the meteorological term meaning that the general flow pattern is west to east along the Earth's latitude lines, with weak shortwaves embedded in the flow. The use of the word "zone" refers to the flow being along the Earth's latitudinal "zones". This pattern can buckle and thus become ...
Troposphere
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Telephony ( ) is the field of technology involving the development, application, and deployment of telecommunications services for the purpose of electronic transmission of voice, fax, or data, between distant parties. The history of telephony is intimately linked to the invention and development of the telephone. Tel...
Telephony
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Telecommunications
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Until the 1970s, most telephones were permanently wired to the telephone line installed at customer premises. Later, conversion to installation of jacks that terminated the inside wiring permitted simple exchange of telephone sets with telephone plugs and allowed portability of the set to multiple locations in the prem...
Telephony
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Telecommunications
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Digital telephony Digital telephony is the use of digital electronics in the operation and provisioning of telephony systems and services. Since the late 20th century, a digital core network has replaced the traditional analog transmission and signaling systems, and much of the access network has also been digitized. ...
Telephony
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Telecommunications
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MOS technology eventually became practical for telephone applications with the MOS mixed-signal integrated circuit, which combines analog and digital signal processing on a single chip, developed by former Bell engineer David A. Hodges with Paul R. Gray at UC Berkeley in the early 1970s. In 1974, Hodges and Gray worked...
Telephony
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Uncompressed PCM digital audio with 8-bit depth and 8kHz sample rate requires a bit rate of 64kbit/s, which was impractical for early digital telecommunication networks with limited network bandwidth. A solution to this issue was linear predictive coding (LPC), a speech coding data compression algorithm that was first ...
Telephony
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A specialization of digital telephony, Internet Protocol (IP) telephony involves the application of digital networking technology that was the foundation to the Internet to create, transmit, and receive telecommunications sessions over computer networks. Internet telephony is commonly known as voice over Internet Proto...
Telephony
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Various communication cues are lost with the usage of the telephone. The communicating parties are not able to identify the body movements, and lack touch and smell. Although this diminished ability to identify social cues is well known, Wiesenfeld, Raghuram, and Garud point out that there is a value and efficiency to ...
Telephony
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A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency waveguides which direct electromagnetic waves other than light like radio waves. ...
Waveguide
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Specific examples: Optical fibers transmit light and signals for long distances with low attenuation and a wide usable range of wavelengths. In a microwave oven a waveguide transfers power from the magnetron, where waves are formed, to the cooking chamber. In a radar, a waveguide transfers radio frequency energy to ...
Waveguide
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The development of radio communication initially occurred at the lower frequencies because these could be more easily propagated over large distances. The long wavelengths made these frequencies unsuitable for use in hollow metal waveguides because of the impractically large diameter tubes required. Consequently, res...
Waveguide
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German academics were even allowed to continue publicly publishing their research in this field because it was not felt to be important. Immediately after World War II waveguide was the technology of choice in the microwave field. However, it has some problems; it is bulky, expensive to produce, and the cutoff freque...
Waveguide
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Propagation modes are computed by solving the Helmholtz equation alongside a set of boundary conditions depending on the geometrical shape and materials bounding the region. The usual assumption for infinitely long uniform waveguides allows us to assume a propagating form for the wave, i.e. stating that every field com...
Waveguide
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Impedance matching is important when components of an electric circuit are connected (waveguide to antenna for example): The impedance ratio determines how much of the wave is transmitted forward and how much is reflected. In connecting a waveguide to an antenna a complete transmission is usually required, so an effort...
Waveguide
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Other types of optical waveguide are also used, including photonic-crystal fiber, which guides waves by any of several distinct mechanisms. Guides in the form of a hollow tube with a highly reflective inner surface have also been used as light pipes for illumination applications. The inner surfaces may be polished meta...
Waveguide
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In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout m...
Group theory
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Algebra
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Galois, in the 1830s, was the first to employ groups to determine the solvability of polynomial equations. Arthur Cayley and Augustin Louis Cauchy pushed these investigations further by creating the theory of permutation groups. The second historical source for groups stems from geometrical situations. In an attempt to...
Group theory
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Algebra
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Matrix groups The next important class of groups is given by matrix groups, or linear groups. Here G is a set consisting of invertible matrices of given order n over a field K that is closed under the products and inverses. Such a group acts on the n-dimensional vector space Kn by linear transformations. This action ma...
Group theory
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The change of perspective from concrete to abstract groups makes it natural to consider properties of groups that are independent of a particular realization, or in modern language, invariant under isomorphism, as well as the classes of group with a given such property: finite groups, periodic groups, simple groups, so...
Group theory
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During the second half of the twentieth century, mathematicians such as Chevalley and Steinberg also increased our understanding of finite analogs of classical groups, and other related groups. One such family of groups is the family of general linear groups over finite fields. Finite groups often occur when consider...
Group theory
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Lie theory A Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in Fr...
Group theory
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There are several natural questions arising from giving a group by its presentation. The word problem asks whether two words are effectively the same group element. By relating the problem to Turing machines, one can show that there is in general no algorithm solving this task. Another, generally harder, algorithmicall...
Group theory
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Algebra
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The axioms of a group formalize the essential aspects of symmetry. Symmetries form a group: they are closed because if you take a symmetry of an object, and then apply another symmetry, the result will still be a symmetry. The identity keeping the object fixed is always a symmetry of an object. Existence of inverses is...
Group theory
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Algebra
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Algebraic topology is another domain which prominently associates groups to the objects the theory is interested in. There, groups are used to describe certain invariants of topological spaces. They are called "invariants" because they are defined in such a way that they do not change if the space is subjected to some ...
Group theory
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Physics In physics, groups are important because they describe the symmetries which the laws of physics seem to obey. According to Noether's theorem, every continuous symmetry of a physical system corresponds to a conservation law of the system. Physicists are very interested in group representations, especially of Lie...
Group theory
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In chemistry, there are five important symmetry operations. They are identity operation (E), rotation operation or proper rotation (Cn), reflection operation (σ), inversion (i) and rotation reflection operation or improper rotation (Sn). The identity operation (E) consists of leaving the molecule as it is. This is equi...
Group theory
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Inversion (i ) is a more complex operation. Each point moves through the center of the molecule to a position opposite the original position and as far from the central point as where it started. Many molecules that seem at first glance to have an inversion center do not; for example, methane and other tetrahedral mole...
Group theory
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Accuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements (observations or readings) are to their true value. Precision is how close the measurements are to each other. The International Organization for Standardization (ISO) defines a related measure: trueness, ...
Accuracy and precision
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Physical sciences
Measurement: General
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A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from...
Accuracy and precision
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Measurement: General
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Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the true value. The accuracy and precision of a measurement process is usually established by repeatedly measuring some traceable reference standard. Such standards are defined in the International Sys...
Accuracy and precision
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A reading of 8,000 m, with trailing zeros and no decimal point, is ambiguous; the trailing zeros may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: 8.0 × 103 m indicates that the first zero is significant (hence a margin of 50 m) while 8.0...
Accuracy and precision
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Accuracy is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both true positives and true negatives) among the total number of cases examined. As such, it compares estimates of pre- a...
Accuracy and precision
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In psychometrics and psychophysics In psychometrics and psychophysics, the term accuracy is interchangeably used with validity and constant error. Precision is a synonym for reliability and variable error. The validity of a measurement instrument or psychological test is established through experiment or correlation wi...
Accuracy and precision
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In cognitive systems In cognitive systems, accuracy and precision is used to characterize and measure results of a cognitive process performed by biological or artificial entities where a cognitive process is a transformation of data, information, knowledge, or wisdom to a higher-valued form. (DIKW Pyramid) Sometimes, ...
Accuracy and precision
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In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the com...
Electrical impedance
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Arthur Kennelly published an influential paper on impedance in 1893. Kennelly arrived at a complex number representation in a rather more direct way than using imaginary exponential functions. Kennelly followed the graphical representation of impedance (showing resistance, reactance, and impedance as the lengths of th...
Electrical impedance
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Physical sciences
Electrical circuits
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Where it is needed to add or subtract impedances, the cartesian form is more convenient; but when quantities are multiplied or divided, the calculation becomes simpler if the polar form is used. A circuit calculation, such as finding the total impedance of two impedances in parallel, may require conversion between form...
Electrical impedance
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Physical sciences
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A phasor is represented by a constant complex number, usually expressed in exponential form, representing the complex amplitude (magnitude and phase) of a sinusoidal function of time. Phasors are used by electrical engineers to simplify computations involving sinusoids (such as in AC circuits), where they can often red...
Electrical impedance
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Physical sciences
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This says that the ratio of AC voltage amplitude to alternating current (AC) amplitude across a resistor is , and that the AC voltage leads the current across a resistor by 0 degrees. This result is commonly expressed as Capacitor For a capacitor, there is the relation: Considering the voltage signal to be it follo...
Electrical impedance
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where is the complex Laplace parameter. As an example, according to the I-V-law of a capacitor, , from which it follows that . In the phasor regime (steady-state AC, meaning all signals are represented mathematically as simple complex exponentials and oscillating at a common frequency ), impedance can simply be cal...
Electrical impedance
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Physical sciences
Electrical circuits
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A DC voltage applied across a capacitor causes charge to accumulate on one side; the electric field due to the accumulated charge is the source of the opposition to the current. When the potential associated with the charge exactly balances the applied voltage, the current goes to zero. Driven by an AC supply, a capac...
Electrical impedance
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Physical sciences
Electrical circuits
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Measurement The measurement of the impedance of devices and transmission lines is a practical problem in radio technology and other fields. Measurements of impedance may be carried out at one frequency, or the variation of device impedance over a range of frequencies may be of interest. The impedance may be measured o...
Electrical impedance
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Physical sciences
Electrical circuits
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In general, neither impedance nor admittance can vary with time, since they are defined for complex exponentials in which . If the complex exponential voltage to current ratio changes over time or amplitude, the circuit element cannot be described using the frequency domain. However, many components and systems (e.g., ...
Electrical impedance
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Lidar (, also LIDAR, LiDAR or LADAR, an acronym of "light detection and ranging" or "laser imaging, detection, and ranging") is a method for determining ranges by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. Lidar may operate in a fixed directio...
Lidar
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Surveying tools
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The first practical terrestrial application of a colidar system was the "Colidar Mark II", a large rifle-like laser rangefinder produced in 1963, which had a range of 11 km and an accuracy of 4.5 m, to be used for military targeting. The first mention of lidar as a stand-alone word in 1963 suggests that it originated a...
Lidar
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The essential concept of lidar was originated by E. H. Synge in 1930, who envisaged the use of powerful searchlights to probe the atmosphere. Indeed, lidar has since been used extensively for atmospheric research and meteorology. Lidar instruments fitted to aircraft and satellites carry out surveying and mapping a rece...
Lidar
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Both types employ pulse models: either micropulse or high energy. Micropulse systems utilize intermittent bursts of energy. They developed as a result of ever-increasing computer power, combined with advances in laser technology. They use considerably less energy in the laser, typically on the order of one microjoule, ...
Lidar
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Phased arrays have been used in radar since the 1940s. On the order of a million optical antennas are used to see a radiation pattern of a certain size in a certain direction. To achieve this the phase of each individual antenna (emitter) are precisely controlled. It is very difficult, if possible at all, to use the sa...
Lidar
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Sensor Lidar uses active sensors that supply their own illumination source. The energy source hits objects and the reflected energy is detected and measured by sensors. Distance to the object is determined by recording the time between transmitted and backscattered pulses and by using the speed of light to calculate th...
Lidar
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In 2014, Lincoln Laboratory announced a new imaging chip with more than 16,384 pixels, each able to image a single photon, enabling them to capture a wide area in a single image. An earlier generation of the technology with one fourth as many pixels was dispatched by the U.S. military after the January 2010 Haiti earth...
Lidar
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Flash lidar In flash lidar, the entire field of view is illuminated with a wide diverging laser beam in a single pulse. This is in contrast to conventional scanning lidar, which uses a collimated laser beam that illuminates a single point at a time, and the beam is raster scanned to illuminate the field of view point-b...
Lidar
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Seeing at a distance requires a powerful burst of light. The power is limited to levels that do not damage human retinas. Wavelengths must not affect human eyes. However, low-cost silicon imagers do not read light in the eye-safe spectrum. Instead, gallium-arsenide imagers are required, which can boost costs to $200,00...
Lidar
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The main constituents of airborne lidar include digital elevation models (DEM) and digital surface models (DSM). The points and ground points are the vectors of discrete points while DEM and DSM are interpolated raster grids of discrete points. The process also involves capturing of digital aerial photographs. To inter...
Lidar
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Water depth measurable by lidar depends on the clarity of the water and the absorption of the wavelength used. Water is most transparent to green and blue light, so these will penetrate deepest in clean water. Blue-green light of 532 nm produced by frequency doubled solid-state IR laser output is the standard for airbo...
Lidar
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Full-waveform lidar Airborne lidar systems were traditionally able to acquire only a few peak returns, while more recent systems acquire and digitize the entire reflected signal. Scientists analysed the waveform signal for extracting peak returns using Gaussian decomposition. Zhuang et al, 2017 used this approach for e...
Lidar
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Terrestrial lidar mapping involves a process of occupancy grid map generation. The process involves an array of cells divided into grids which employ a process to store the height values when lidar data falls into the respective grid cell. A binary map is then created by applying a particular threshold to the cell valu...
Lidar
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Lidar is useful in GNSS-denied situations, such as nut and fruit orchards, where foliage causes interference for agriculture equipment that would otherwise utilize a precise GNSS fix. Lidar sensors can detect and track the relative position of rows, plants, and other markers so that farming equipment can continue opera...
Lidar
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Lidar can also help to create high-resolution digital elevation models (DEMs) of archaeological sites that can reveal micro-topography that is otherwise hidden by vegetation. The intensity of the returned lidar signal can be used to detect features buried under flat vegetated surfaces such as fields, especially when ma...
Lidar
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Autonomous vehicles may use lidar for obstacle detection and avoidance to navigate safely through environments. The introduction of lidar was a pivotal occurrence that was the key enabler behind Stanley, the first autonomous vehicle to successfully complete the DARPA Grand Challenge. Point cloud output from the lidar s...
Lidar
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Obstacle detection and road environment recognition using lidar This method proposed by Kun Zhou et al. not only focuses on object detection and tracking but also recognizes lane marking and road features. As mentioned earlier the lidar systems use rotating hexagonal mirrors that split the laser beam into six beams. T...
Lidar
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Lidar has also found many applications for mapping natural and managed landscapes such as forests, wetlands, and grasslands. Canopy heights, biomass measurements, and leaf area can all be studied using airborne lidar systems. Similarly, lidar is also used by many industries, including Energy and Railroad, and the Depar...
Lidar
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Lidar is also used in structural geology and geophysics as a combination between airborne lidar and GNSS for the detection and study of faults, for measuring uplift. The output of the two technologies can produce extremely accurate elevation models for terrain – models that can even measure ground elevation through tre...
Lidar
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Backscatter from the atmosphere directly gives a measure of clouds and aerosols. Other derived measurements from backscatter such as winds or cirrus ice crystals require careful selecting of the wavelength and/or polarization detected. Doppler lidar and Rayleigh Doppler lidar are used to measure temperature and wind sp...
Lidar
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Synthetic array lidar allows imaging lidar without the need for an array detector. It can be used for imaging Doppler velocimetry, ultra-fast frame rate imaging (millions of frames per second), as well as for speckle reduction in coherent lidar. An extensive lidar bibliography for atmospheric and hydrospheric applicati...
Lidar
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The Long-Range Biological Standoff Detection System (LR-BSDS) was developed for the U.S. Army to provide the earliest possible standoff warning of a biological attack. It is an airborne system carried by helicopter to detect synthetic aerosol clouds containing biological and chemical agents at long range. The LR-BSDS, ...
Lidar
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41958
https://en.wikipedia.org/wiki/Lidar
Technology
Surveying tools
null
vital_articles
Rock mechanics Lidar has been widely used in rock mechanics for rock mass characterization and slope change detection. Some important geomechanical properties from the rock mass can be extracted from the 3-D point clouds obtained by means of the lidar. Some of these properties are: Discontinuity orientation Disconti...
Lidar
Wikipedia
485
41958
https://en.wikipedia.org/wiki/Lidar
Technology
Surveying tools
null
vital_articles
Laser altimetry is used to make digital elevation maps of planets, including the Mars Orbital Laser Altimeter (MOLA) mapping of Mars, the Lunar Orbital Laser Altimeter (LOLA) and Lunar Altimeter (LALT) mapping of the Moon, and the Mercury Laser Altimeter (MLA) mapping of Mercury. It is also used to help navigate the he...
Lidar
Wikipedia
445
41958
https://en.wikipedia.org/wiki/Lidar
Technology
Surveying tools
null
vital_articles
Wind farm optimization Lidar can be used to increase the energy output from wind farms by accurately measuring wind speeds and wind turbulence. Experimental lidar systems can be mounted on the nacelle of a wind turbine or integrated into the rotating spinner to measure oncoming horizontal winds, winds in the wake of th...
Lidar
Wikipedia
463
41958
https://en.wikipedia.org/wiki/Lidar
Technology
Surveying tools
null
vital_articles
In 2020, Apple introduced the fourth generation of iPad Pro with a lidar sensor integrated into the rear camera module, especially developed for augmented reality (AR) experiences. The feature was later included in the iPhone 12 Pro lineup and subsequent Pro models. On Apple devices, lidar empowers portrait mode pictur...
Lidar
Wikipedia
139
41958
https://en.wikipedia.org/wiki/Lidar
Technology
Surveying tools
null
vital_articles
In electronics, gain is a measure of the ability of a two-port circuit (often an amplifier) to increase the power or amplitude of a signal from the input to the output port by adding energy converted from some power supply to the signal. It is usually defined as the mean ratio of the signal amplitude or power at the ou...
Gain (electronics)
Wikipedia
488
41968
https://en.wikipedia.org/wiki/Gain%20%28electronics%29
Physical sciences
Electrical circuits
null
vital_articles
Voltage gain The power gain can be calculated using voltage instead of power using Joule's first law ; the formula is: In many cases, the input impedance and output impedance are equal, so the above equation can be simplified to: This simplified formula, the 20 log rule, is used to calculate a voltage gain in decib...
Gain (electronics)
Wikipedia
512
41968
https://en.wikipedia.org/wiki/Gain%20%28electronics%29
Physical sciences
Electrical circuits
null
vital_articles
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortes...
Shortest path problem
Wikipedia
450
41985
https://en.wikipedia.org/wiki/Shortest%20path%20problem
Mathematics
Graph theory
null
vital_articles
Algorithms Several well-known algorithms exist for solving this problem and its variants. Dijkstra's algorithm solves the single-source shortest path problem with only non-negative edge weights. Bellman–Ford algorithm solves the single-source problem if edge weights may be negative. A* search algorithm solves for si...
Shortest path problem
Wikipedia
434
41985
https://en.wikipedia.org/wiki/Shortest%20path%20problem
Mathematics
Graph theory
null
vital_articles
Create a Residual Graph: For each edge (u, v) in the original graph, create two edges in the residual graph: (u, v) with capacity c(u, v) (v, u) with capacity 0 The residual graph represents the remaining capacity available in the network. Find the Shortest Path: Use a shortest path algorithm (e.g., Dijkstra's al...
Shortest path problem
Wikipedia
503
41985
https://en.wikipedia.org/wiki/Shortest%20path%20problem
Mathematics
Graph theory
null
vital_articles
Other applications, often studied in operations research, include plant and facility layout, robotics, transportation, and VLSI design. Road networks A road network can be considered as a graph with positive weights. The nodes represent road junctions and each edge of the graph is associated with a road segment betwee...
Shortest path problem
Wikipedia
410
41985
https://en.wikipedia.org/wiki/Shortest%20path%20problem
Mathematics
Graph theory
null
vital_articles
Paths with constraints Unlike the shortest path problem, which can be solved in polynomial time in graphs without negative cycles, shortest path problems which include additional constraints on the desired solution path are called Constrained Shortest Path First, and are harder to solve. One example is the constrained ...
Shortest path problem
Wikipedia
486
41985
https://en.wikipedia.org/wiki/Shortest%20path%20problem
Mathematics
Graph theory
null
vital_articles
The Bellman–Ford algorithm can be used to detect a negative cycle in time . Cherkassky and Goldberg survey several other algorithms for negative cycle detection. General algebraic framework on semirings: the algebraic path problem Many problems can be framed as a form of the shortest path for some suitably substitut...
Shortest path problem
Wikipedia
456
41985
https://en.wikipedia.org/wiki/Shortest%20path%20problem
Mathematics
Graph theory
null
vital_articles
To account for variability, researchers have suggested two alternative definitions for an optimal path under uncertainty. The most reliable path is one that maximizes the probability of arriving on time given a travel time budget. An α-reliable path is one that minimizes the travel time budget required to arrive on tim...
Shortest path problem
Wikipedia
63
41985
https://en.wikipedia.org/wiki/Shortest%20path%20problem
Mathematics
Graph theory
null
vital_articles
In physics and many other areas of science and engineering the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2), or kg⋅s−3 in base ...
Intensity (physics)
Wikipedia
493
41993
https://en.wikipedia.org/wiki/Intensity%20%28physics%29
Physical sciences
Optics
Physics
vital_articles
Anything that can transmit energy can have an intensity associated with it. For a monochromatic propagating electromagnetic wave, such as a plane wave or a Gaussian beam, if is the complex amplitude of the electric field, then the time-averaged energy density of the wave, travelling in a non-magnetic material, is give...
Intensity (physics)
Wikipedia
344
41993
https://en.wikipedia.org/wiki/Intensity%20%28physics%29
Physical sciences
Optics
Physics
vital_articles
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin...
Twin prime
Wikipedia
437
41997
https://en.wikipedia.org/wiki/Twin%20prime
Mathematics
Prime numbers
null
vital_articles
Twin prime conjecture The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years. This is the content of the twin prime conjecture, which states that there are infinitely many primes such that is also prime. In 1849, de Polignac made the mo...
Twin prime
Wikipedia
346
41997
https://en.wikipedia.org/wiki/Twin%20prime
Mathematics
Prime numbers
null
vital_articles
Other theorems weaker than the twin prime conjecture In 1940, Paul Erdős showed that there is a constant and infinitely many primes such that where denotes the next prime after . What this means is that we can find infinitely many intervals that contain two primes as long as we let these intervals grow slowly in s...
Twin prime
Wikipedia
475
41997
https://en.wikipedia.org/wiki/Twin%20prime
Mathematics
Prime numbers
null
vital_articles
The conjecture can be justified (but not proven) by assuming that describes the density function of the prime distribution. This assumption, which is suggested by the prime number theorem, implies the twin prime conjecture, as shown in the formula for above. The fully general first Hardy–Littlewood conjecture on pri...
Twin prime
Wikipedia
491
41997
https://en.wikipedia.org/wiki/Twin%20prime
Mathematics
Prime numbers
null
vital_articles
For a twin prime pair of the form (6n − 1, 6n + 1) for some natural number n > 1, n must end in the digit 0, 2, 3, 5, 7, or 8 (). If n were to end in 1 or 6, 6n would end in 6, and 6n −1 would be a multiple of 5. This is not prime unless n = 1. Likewise, if n were to end in 4 or 9, 6n would end in 4, and 6n +1 would...
Twin prime
Wikipedia
332
41997
https://en.wikipedia.org/wiki/Twin%20prime
Mathematics
Prime numbers
null
vital_articles
Plastic surgery is a surgical specialty involving the restoration, reconstruction, or alteration of the human body. It can be divided into two main categories: reconstructive surgery and cosmetic surgery. Reconstructive surgery covers a wide range of specialties, including craniofacial surgery, hand surgery, microsurge...
Plastic surgery
Wikipedia
457
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
Arabs practiced the plastic surgery, during the Abbasid Caliphate in 750 AD. The Arabic translations made their way into Europe via intermediaries. In Italy, the Branca family of Sicily and Gaspare Tagliacozzi (Bologna) became familiar with the techniques of Sushruta. All fields of surgery, the Arab physician, surgeon...
Plastic surgery
Wikipedia
501
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
Johann Friedrich Dieffenbach specialized in skin transplantation and early plastic surgery. His work in rhinoplastic and maxillofacial surgery established many modern techniques of reconstructive surgery. In 1845, Dieffenbach wrote a comprehensive text on rhinoplasty, titled Operative Chirurgie, and introduced the conc...
Plastic surgery
Wikipedia
298
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
The development of weapons such as machine guns and explosive shells during World War I created trench warfare, which led to a rapid increase in the number of mutilations to the faces and the heads of soldiers because the trenches mainly offered protection to the body. The surgeons, who were not prepared for these inju...
Plastic surgery
Wikipedia
243
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
It is the multidisciplinary approach to the treatment of facial lesions, bringing together plastic surgeons, dental surgeons, technicians, and specialized nurses, which has made it possible to develop techniques leading to the reconstruction of injured faces. Before the dentist Auguste Charles Valadier and then Gillies...
Plastic surgery
Wikipedia
382
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
During World War I, he worked as a medical minder with the Royal Army Medical Corps. After working with the French oral and maxillofacial surgeon Hippolyte Morestin on skin grafts, he persuaded the army's chief surgeon, Arbuthnot-Lane, to establish a facial injury ward at the Cambridge Military Hospital, Aldershot, lat...
Plastic surgery
Wikipedia
489
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
His other important work included the development of the walking-stalk skin graft, and the discovery that immersion in saline promoted healing as well as improving survival rates for patients with extensive burns—this was a serendipitous discovery drawn from observation of differential healing rates in pilots who had c...
Plastic surgery
Wikipedia
429
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
Hand surgery is concerned with acute injuries and chronic diseases of the hand and wrist, correction of congenital malformations of the upper extremities, and peripheral nerve problems (such as brachial plexus injuries or carpal tunnel syndrome). Hand surgery is an important part of training in plastic surgery, as well...
Plastic surgery
Wikipedia
370
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
Techniques and procedures In plastic surgery, the transfer of skin tissue (skin grafting) is a very common procedure. Skin grafts can be derived from the recipient or donors: Autografts are taken from the recipient. If absent or deficient of natural tissue, alternatives can be cultured sheets of epithelial cells in vi...
Plastic surgery
Wikipedia
224
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles
Cosmetic surgery is a voluntary or elective surgery that is performed on normal parts of the body with the only purpose of improving a person's appearance or removing signs of aging. Some cosmetic surgeries such as breast reduction are also functional and can help to relieve symptoms of discomfort such as back ache or ...
Plastic surgery
Wikipedia
362
42048
https://en.wikipedia.org/wiki/Plastic%20surgery
Biology and health sciences
Medical procedures
null
vital_articles