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In mathematics, a sequence of positive integers an is called an irrationality sequence if it has the property that for every sequence xn of positive integers, the sum of the series
∑
n
=
1
∞
1
a
n
x
n
{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{a_{n}x_{n}}}}
exists (that is, it converges) and is an irrational number. The problem of characterizing irrationality sequences was posed by Paul Erdős and Ernst G. Straus, who originally called the property of being an irrationality sequence "Property P" | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and theoretical computer science, a k-regular sequence is a sequence satisfying linear recurrence equations that reflect the base-k representations of the integers. The class of k-regular sequences generalizes the class of k-automatic sequences to alphabets of infinite size.
Definition
There exist several characterizations of k-regular sequences, all of which are equivalent | https://huggingface.co/datasets/fmars/wiki_stem |
The Katydid sequence is a sequence of numbers first defined in Clifford A. Pickover's book Wonders of Numbers (2001).
Description
A Katydid sequence is the smallest sequence of integers that can be reached from 1 by a sequence of the two operations n ↦ 2n + 2 and 7n + 7 (in any order) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the (signed and unsigned) Lah numbers are coefficients expressing rising factorials in terms of falling factorials and vice-versa. They were discovered by Ivo Lah in 1954. Explicitly, the unsigned Lah numbers
L
(
n
,
k
)
{\displaystyle L(n,k)}
are given by the formula involving the binomial coefficient
for
n
≥
k
≥
1
{\displaystyle n\geq k\geq 1}
| https://huggingface.co/datasets/fmars/wiki_stem |
The Lambek–Moser theorem is a mathematical description of partitions of the natural numbers into two complementary sets. For instance, it applies to the partition of numbers into even and odd, or into prime and non-prime (one and the composite numbers). There are two parts to the Lambek–Moser theorem | https://huggingface.co/datasets/fmars/wiki_stem |
The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point inside the circle, but up to seven if they do not. This problem can be formalized mathematically as one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, see arrangement of hyperplanes | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a Leyland number is a number of the form
x
y
+
y
x
{\displaystyle x^{y}+y^{x}}
where x and y are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are
8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124 (sequence A076980 in the OEIS) | https://huggingface.co/datasets/fmars/wiki_stem |
In combinatorial mathematics, the Lobb number Lm,n counts the number of ways that n + m open parentheses and n − m close parentheses can be arranged to form the start of a valid sequence of balanced parentheses. Lobb numbers form a natural generalization of the Catalan numbers, which count the number of complete strings of balanced parentheses of a given length. Thus, the nth Catalan number equals the Lobb number L0,n | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, the numbers of the form x2 + xy + y2 for integer x, y are called the Löschian numbers (or Loeschian numbers). These numbers are named after August Lösch. They are the norms of the Eisenstein integers | https://huggingface.co/datasets/fmars/wiki_stem |
The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers). The term was introduced in 1956 in a paper by Gardiner, Lazarus, Metropolis and Ulam | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a meander or closed meander is a self-avoiding closed curve which crosses a given line a number of times, meaning that it intersects the line while passing from one side to the other. Intuitively, a meander can be viewed as a meandering river with a straight road crossing the river over a number of bridges. The points where the line and the curve cross are therefore referred to as "bridges" | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the Mian–Chowla sequence is an integer sequence defined
recursively in the following way. The sequence starts with
a
1
=
1.
{\displaystyle a_{1}=1 | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, the multiplicative digital root of a natural number
n
{\displaystyle n}
in a given number base
b
{\displaystyle b}
is found by multiplying the digits of
n
{\displaystyle n}
together, then repeating this operation until only a single-digit remains, which is called the multiplicative digital root of
n
{\displaystyle n}
.
The multiplicative digital root for the first few positive integers are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, 3, 6, 9, 2, 5, 8, 2, 8, 4, 0. (sequence A031347 in the OEIS)Multiplicative digital roots are the multiplicative equivalent of digital roots | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a multiplicative partition or unordered factorization of an integer
n
{\displaystyle n}
is a way of writing
n
{\displaystyle n}
as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the factors. The number
n
{\displaystyle n}
is itself considered one of these products. Multiplicative partitions closely parallel the study of multipartite partitions, which are additive partitions of finite sequences of positive integers, with the addition made pointwise | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a noncototient is a positive integer n that cannot be expressed as the difference between a positive integer m and the number of coprime integers below it. That is, m − φ(m) = n, where φ stands for Euler's totient function, has no solution for m. The cototient of n is defined as n − φ(n), so a noncototient is a number that is never a cototient | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a nontotient is a positive integer n which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(x) = n has no solution x. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1, since it has the solutions x = 1 and x = 2 | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, an odious number is a positive integer that has an odd number of 1s in its binary expansion. Non-negative integers that are not odious are called evil numbers.
In computer science, an odious number is said to have odd parity | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the number of weak orderings on a set of
n
{\displaystyle n}
elements. Weak orderings arrange their elements into a sequence allowing ties, such as might arise as the outcome of a horse race). Starting from
n
=
0
{\displaystyle n=0}
, these numbers are
The ordered Bell numbers may be computed via a summation formula involving binomial coefficients, or by using a recurrence relation | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, the Padovan sequence is the sequence of integers P(n) defined by the initial values
P
(
0
)
=
P
(
1
)
=
P
(
2
)
=
1
,
{\displaystyle P(0)=P(1)=P(2)=1,}
and the recurrence relation
P
(
n
)
=
P
(
n
−
2
)
+
P
(
n
−
3
)
.
{\displaystyle P(n)=P(n-2)+P(n-3). }
The first few values of P(n) are
1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4.
No closed-form expression for the partition function is known, but it has both asymptotic expansions that accurately approximate it and recurrence relations by which it can be calculated exactly | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number.
The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, one applies the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and adds together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.
Examples
For example, there are six positive integers less than 9 and relatively prime to it, so the totient of 9 is 6; there are two numbers less than 6 and relatively prime to it, so the totient of 6 is 2; and there is one number less than 2 and relatively prime to it, so the totient of 2 is 1; and 9 = 6 + 2 + 1, so 9 is a perfect totient number | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the Perrin numbers are defined by the recurrence relation
P(n) = P(n − 2) + P(n − 3) for n > 2,with initial values
P(0) = 3, P(1) = 0, P(2) = 2. The sequence of Perrin numbers starts with
3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, . | https://huggingface.co/datasets/fmars/wiki_stem |
In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a 'magic' number of protons or neutrons are much more stable than other nuclei. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126 (sequence A018226 in the OEIS) | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite. The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two | https://huggingface.co/datasets/fmars/wiki_stem |
A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are:
1, 10, 100, 1,000, 10,000, 100,000, 1,000,000, 10,000,000 | https://huggingface.co/datasets/fmars/wiki_stem |
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, the prime omega functions
ω
(
n
)
{\displaystyle \omega (n)}
and
Ω
(
n
)
{\displaystyle \Omega (n)}
count the number of prime factors of a natural number
n
.
{\displaystyle n. }
Thereby
ω
(
n
)
{\displaystyle \omega (n)}
(little omega) counts each distinct prime factor, whereas the related function
Ω
(
n
)
{\displaystyle \Omega (n)}
(big omega) counts the total number of prime factors of
n
,
{\displaystyle n,}
honoring their multiplicity (see arithmetic function) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number.
For example: 7 = 71, 9 = 32 and 64 = 26 are prime powers, while
6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 32 are not.
The sequence of prime powers begins:
2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, … (sequence A246655 in the OEIS) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics a primitive abundant number is an abundant number whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because:
The sum of its proper divisors is 1 + 2 + 4 + 5 + 10 = 22, so 20 is an abundant number.
The sums of the proper divisors of 1, 2, 4, 5 and 10 are 0, 1, 3, 1 and 8 respectively, so each of these numbers is a deficient number | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into |X| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive.
While primitive permutation groups are transitive, not all transitive permutation groups are primitive | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number.
The first few semiperfect numbers are: 6, 12, 18, 20, 24, 28, 30, 36, 40, | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, and more particularly in number theory, primorial, denoted by "#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers.
The name "primorial", coined by Harvey Dubner, draws an analogy to primes similar to the way the name "factorial" relates to factors.
Definition for prime numbers
For the nth prime number pn, the primorial pn# is defined as the product of the first n primes:
p
n
#
=
∏
k
=
1
n
p
k
{\displaystyle p_{n}\#=\prod _{k=1}^{n}p_{k}}
,where pk is the kth prime number | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn (i. e. the product of the first n primes) | https://huggingface.co/datasets/fmars/wiki_stem |
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form
n
(
n
+
1
)
.
{\displaystyle n(n+1). }
The study of these numbers dates back to Aristotle | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1. Equivalently, n is the sum of its non-trivial divisors (that is, its divisors excluding 1 and n). No quasiperfect numbers have been found so far | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and computer science, Recamán's sequence is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.
It takes its name after its inventor Bernardo Recamán Santos, a Colombian mathematician | https://huggingface.co/datasets/fmars/wiki_stem |
A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that
τ
(
n
)
∣
n
{\displaystyle \tau (n)\mid n}
. The first few refactorable numbers are listed in (sequence A033950 in the OEIS) as
1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96, 104, 108, 128, 132, 136, 152, 156, 180, 184, 204, 225, 228, 232, 240, 248, 252, 276, 288, 296, . | https://huggingface.co/datasets/fmars/wiki_stem |
Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 = 48 × 75, so as divisors of a power of 60 both 48 and 75 are regular | https://huggingface.co/datasets/fmars/wiki_stem |
A k-rough number, as defined by Finch in 2001 and 2003, is a positive integer whose prime factors are all greater than or equal to k. k-roughness has alternately been defined as requiring all prime factors to strictly exceed k.
Examples (after Finch)
Every odd positive integer is 3-rough | https://huggingface.co/datasets/fmars/wiki_stem |
Daylight harvesting systems use daylight to offset the amount of electric lighting needed to properly light a space, in order to reduce energy consumption. This is accomplished using lighting control systems that are able to dim or switch electric lighting in response to changing daylight availability. The term Daylight Harvesting has become the standard in the fields of lighting, sustainable architecture, and active daylighting industries | https://huggingface.co/datasets/fmars/wiki_stem |
Daylighting is the practice of placing windows, skylights, other openings, and reflective surfaces so that direct or indirect sunlight can provide effective internal lighting. Particular attention is given to daylighting while designing a building when the aim is to maximize visual comfort or to reduce energy use. Energy savings can be achieved from the reduced use of artificial (electric) lighting or from passive solar heating | https://huggingface.co/datasets/fmars/wiki_stem |
Digital Addressable Lighting Interface (DALI) is a trademark for network-based products that control lighting. The underlying technology was established by a consortium of lighting equipment manufacturers as a successor for 1-10 V/0–10 V lighting control systems, and as an open standard alternative to several proprietary protocols. The DALI, DALI-2 and D4i trademarks are owned by the lighting industry alliance, DiiA (Digital Illumination Interface Alliance) | https://huggingface.co/datasets/fmars/wiki_stem |
A dimmer is a device connected to a light fixture and used to lower the brightness of the light. By changing the voltage waveform applied to the lamp, it is possible to lower the intensity of the light output. Although variable-voltage devices are used for various purposes, the term dimmer is generally reserved for those intended to control light output from resistive incandescent, halogen, and (more recently) compact fluorescent lamps (CFLs) and light-emitting diodes (LEDs) | https://huggingface.co/datasets/fmars/wiki_stem |
A disco ball (also known as a mirror ball or glitter ball) is a roughly spherical object that reflects light directed at it in many directions, producing a complex display. Its surface consists of hundreds or thousands of facets, nearly all of approximately the same shape and size, and each having a mirrored surface. Usually it is mounted well above the heads of the people present, suspended from a device that causes it to rotate steadily on a vertical axis and illuminated by spotlights, so that stationary viewers experience beams of light flashing over them, and see myriad spots of light spinning around the walls of the room | https://huggingface.co/datasets/fmars/wiki_stem |
An electric light, lamp, or light bulb is an electrical component that produces light. It is the most common form of artificial lighting. Lamps usually have a base made of ceramic, metal, glass, or plastic, which secures the lamp in the socket of a light fixture, which is often called a "lamp" as well | https://huggingface.co/datasets/fmars/wiki_stem |
Electroluminescence (EL) is an optical and electrical phenomenon, in which a material emits light in response to the passage of an electric current or to a strong electric field. This is distinct from black body light emission resulting from heat (incandescence), chemical reactions (chemiluminescence), reactions in a liquid (electrochemiluminescence), sound (sonoluminescence), or other mechanical action (mechanoluminescence).
Mechanism
Electroluminescence is the result of radiative recombination of electrons & holes in a material, usually a semiconductor | https://huggingface.co/datasets/fmars/wiki_stem |
Electroluminescent Displays (ELDs) are a type of flat panel display created by sandwiching a layer of electroluminescent material such as Gallium arsenide between two layers of conductors. When current flows, the layer of material emits radiation in the form of visible light. Electroluminescence (EL) is an optical and electrical phenomenon where a material emits light in response to an electric current passed through it, or to a strong electric field | https://huggingface.co/datasets/fmars/wiki_stem |
Electroluminescent wire (often abbreviated as EL wire) is a thin copper wire coated in a phosphor that produces light through electroluminescence when an alternating current is applied to it. It can be used in a wide variety of applications—vehicle and structure decoration, safety and emergency lighting, toys, clothing etc. —much as rope light or Christmas lights are often used | https://huggingface.co/datasets/fmars/wiki_stem |
EULUMDAT is a data file format used for specification of photometric data especially intensity distributions from light sources such as lamps and luminaries. The file extension is . ldt | https://huggingface.co/datasets/fmars/wiki_stem |
A flare, also sometimes called a fusée, fusee, or bengala, bengalo in several European countries, is a type of pyrotechnic that produces a bright light or intense heat without an explosion. Flares are used for distress signaling, illumination, or defensive countermeasures in civilian and military applications. Flares may be ground pyrotechnics, projectile pyrotechnics, or parachute-suspended to provide maximum illumination time over a large area | https://huggingface.co/datasets/fmars/wiki_stem |
Flashes per minute (FPM) is simply the number of times a flashing light blinks per minute. Police and emergency vehicles use warning lights with flashing rates that typically fall in a range from 60 to 240 FPM. In North America, grade crossing signals have a flashing rate ranging between 45 and 65 FPM with the ideal rate being 60 FPM | https://huggingface.co/datasets/fmars/wiki_stem |
In visual perception, flicker is a human-visible change in luminous flux of an illuminated surface or light source which can be due to fluctuations of the light source itself, or due to external causes such as due to rapid fluctuations in the voltage of the power supply (power-line flicker) or incompatibility with an external dimmer.
Twinkling, also called scintillation, is a generic term for variations in apparent brightness, colour, or position of a distant luminous object viewed through a medium.
Flicker exists for other organisms having different perceptual thresholds | https://huggingface.co/datasets/fmars/wiki_stem |
Full-spectrum light is light that covers the electromagnetic spectrum from infrared to near-ultraviolet, or all wavelengths that are useful to plant or animal life; in particular, sunlight is considered full spectrum, even though the solar spectral distribution reaching Earth changes with time of day, latitude, and atmospheric conditions.
"Full-spectrum" is not a technical term when applied to an electrical light bulb. Rather, it implies that the product emulates some important quality of natural light | https://huggingface.co/datasets/fmars/wiki_stem |
Gas lighting is the production of artificial light from combustion of a fuel gas such as hydrogen, methane, carbon monoxide, propane, butane, acetylene, ethylene, coal gas (town gas) or natural gas. The light is produced either directly by the flame, generally by using special mixes (typically propane or butane) of illuminating gas to increase brightness, or indirectly with other components such as the gas mantle or the limelight, with the gas primarily functioning as a heat source for the incandescence of the gas mantle or lime. Before electricity became sufficiently widespread and economical to allow for general public use, gas was the most prevalent method of outdoor and indoor lighting in cities and suburbs, areas where the infrastructure for distribution of the gaseous fuel was practical | https://huggingface.co/datasets/fmars/wiki_stem |
A Globar is used as a thermal light source for infrared spectroscopy. The preferred material for making Globar is silicon carbide that is shaped as rods or arches of various sizes. When inserted into a circuit that provides it with electric current, it emits radiation from ~ 2 to 50 micrometres wavelength via the Joule heating phenomenon | https://huggingface.co/datasets/fmars/wiki_stem |
A glow discharge is a plasma formed by the passage of electric current through a gas. It is often created by applying a voltage between two electrodes in a glass tube containing a low-pressure gas. When the voltage exceeds a value called the striking voltage, the gas ionization becomes self-sustaining, and the tube glows with a colored light | https://huggingface.co/datasets/fmars/wiki_stem |
A glow stick, also known as a light stick, chem light, light wand, light rod, and rave light, is a self-contained, short-term light-source. It consists of a translucent plastic tube containing isolated substances that, when combined, make light through chemiluminescence. The light cannot be turned off and can be used only once | https://huggingface.co/datasets/fmars/wiki_stem |
A grow light is an electric light to help plants grow. Grow lights either attempt to provide a light spectrum similar to that of the sun, or to provide a spectrum that is more tailored to the needs of the plants being cultivated (typically a varying combination of red and blue light, which generally appears pink to purple to the human eye). Outdoor conditions are mimicked with varying colour temperatures and spectral outputs from the grow light, as well as varying the intensity of the lamps | https://huggingface.co/datasets/fmars/wiki_stem |
Haitz's law is an observation and forecast about the steady improvement, over many years, of light-emitting diodes (LEDs).
It claims that every decade, the cost per lumen (unit of useful light emitted) falls by a factor of 10, and the amount of light generated per LED package increases by a factor of 20, for a given wavelength (color) of light. It is considered the LED counterpart to Moore's law, which states that the number of transistors in a given integrated circuit doubles every 18 to 24 months | https://huggingface.co/datasets/fmars/wiki_stem |
A headlamp, headlight, or head torch (UK) is a light source affixed to the head typically for outdoor activities at night or in dark conditions such as caving, orienteering, hiking, skiing, backpacking, camping, mountaineering or mountain biking. Headlamps may also be used in adventure races. Headlamps are often used by workers in underground mining, search and rescue, surgeons, and by other workers who need hands-free directed lighting | https://huggingface.co/datasets/fmars/wiki_stem |
High-CRI LED lighting is a light-emitting diode (LED) lighting source that offers a high color rendering index (CRI).
CRI is a quantitative measure of a light's ability to reproduce the colors of objects faithfully in comparison with an ideal or natural light source. In general terms, CRI is a measure of a light source's ability to show object colors "realistically" or "naturally" compared to a familiar reference source, either incandescent light or sunlight | https://huggingface.co/datasets/fmars/wiki_stem |
High-mast lighting is a tall pole with lighting attached to the top pointing towards the ground, usually but not always used to light a highway or recreational field. It is used at sites that require lighting over a large area. The pole that the lighting is mounted on is generally at least 30 m (98 ft) tall (under this height it is referred to as conventional lighting system), while the lighting consists of a luminaire ring surrounding the pole with one or several independent lighting fixtures mounted around it | https://huggingface.co/datasets/fmars/wiki_stem |
Holiday lighting technology has been subject to considerable development and variation since the replacement of candles by electric lights. While originally used during the Christmas holidays as Christmas lights, modern electric light arrays have become popular around the world in many cultures and are used both during religious festivals and for other purposes unconnected to any festivities.
Incandescent lights
Incandescent light bulbs have been commonly used in holiday lights until recently | https://huggingface.co/datasets/fmars/wiki_stem |
Hybrid solar lighting (HSL) or hybrid lighting systems combine the use of solar with artificial light for interior illumination by channelling sunlight through fiber optic cable bundles to provide solar light into rooms without windows or skylights, and by supplementing this natural light with artificial light—typically LED—as required. The bundles are led from exterior/rooftop optical light collectors through small openings or cable ducts and carry the light to where it is needed. The optical fibers end in hybrid luminaires where the sunlight is joined with electric light, either on demand or to automatically maintain a constant light level even as the available sunlight decreases | https://huggingface.co/datasets/fmars/wiki_stem |
Indiglo is a product feature on watches marketed by Timex, incorporating an electroluminescent panel as a backlight for even illumination of the watch dial.
The brand is owned by Indiglo Corporation, which is in turn solely owned by Timex, and the name derives from the word indigo, as the original watches featuring the technology emitted a green-blue light. The Indiglo name was originally developed by Austin Innovations Inc | https://huggingface.co/datasets/fmars/wiki_stem |
The Indoor Environmental Quality Global Alliance (IEQ-GA) was initiated in 2014 aiming to improve the actual, delivered indoor environmental quality in buildings through coordination, education, outreach and advocacy. The alliance works to supply information, guidelines and knowledge on the indoor environmental quality (IEQ) in buildings and workplaces, and to provide occupants in buildings and workplaces with an acceptable indoor environmental quality (indoor air quality (IAQ), thermal conditions, visual quality, and acoustical quality) and help promote implementation in practice of knowledge from research on the field.
The group has already begun work to collect and critique IEQ standards and is organising and presenting programmes at the conferences of member organisations and others | https://huggingface.co/datasets/fmars/wiki_stem |
Candlepower (abbreviated as cp or CP) is a unit of measurement for luminous intensity. It expresses levels of light intensity relative to the light emitted by a candle of specific size and constituents. The historical candlepower is equal to 0 | https://huggingface.co/datasets/fmars/wiki_stem |
Köhler illumination is a method of specimen illumination used for transmitted and reflected light (trans- and epi-illuminated) optical microscopy. Köhler illumination acts to generate an even illumination of the sample and ensures that an image of the illumination source (for example a halogen lamp filament) is not visible in the resulting image. Köhler illumination is the predominant technique for sample illumination in modern scientific light microscopy | https://huggingface.co/datasets/fmars/wiki_stem |
The Lampette was a brand of small electric high-intensity telescoping desk lamps that was designed and distributed by Koch Creations but manufactured by various subcontractors from the early 1960s to the late 1980s.
History
According to an article published in the June 1965 issue of the Kiplinger's Personal Finance magazine, smaller high-intensity lamps for personal use only came to the market in 1963, after a "professional work light", invented in 1959 by Jay Monroe and then manufactured by Monroe's Tensor Corporation in 1960. The work light was marketed as the "Tensor lamp", and was initially sold to jewelers, watchmakers, and other similar craftsmen | https://huggingface.co/datasets/fmars/wiki_stem |
Landscape lighting or garden lighting refers to the use of outdoor illumination of private gardens and public landscapes; for the enhancement and purposes of safety, nighttime aesthetics, accessibility, security, recreation and sports, and social and event uses.
Light pollution exacerbated by excessive, misdirected or obtrusive use of light, but even carefully used light fundamentally alters natural conditions. As a major side-effect of urbanization, it is blamed for compromising health, disrupting ecosystems and spoiling aesthetic environments | https://huggingface.co/datasets/fmars/wiki_stem |
As an element of architecture, a laylight is a glazed panel usually set flush with the ceiling for the purpose of admitting natural or artificial light. Laylights typically utilize stained glass or lenses in their glazing. A laylight differs from a glazed (or closed) skylight in that a skylight functions as a roof window or aperture, while a laylight is flush with the ceiling of an interior space | https://huggingface.co/datasets/fmars/wiki_stem |
Light & Sound International (LSi) is a UK monthly entertainment technology magazine published in Eastbourne by PLASA Media Ltd, a commercial arm of the Professional Lighting and Sound Association (PLASA) and is distributed around the world in English. Light & Sound International covers the broad range of the entertainment, presentation and events industries worldwide, including theatre, live touring, clubs, themed venues, corporate events and presentations, as well as in-depth profiles of the people and companies who put it all together – and the issues affecting them.
Operational
While Light & Sound International does work to promote the interests of PLASA's membership, and the activities and initiatives of the Association itself, it is not positioned as a PLASA members newsletter or as a service to PLASA members | https://huggingface.co/datasets/fmars/wiki_stem |
Light extraction in LEDs involves the set of particular problems that is connected with getting light from the light emitting p-n junction in an LED to the surroundings, such that the light might be useful, for instance for lighting.
The refractive index of most LED semiconductor materials is quite high, so in almost all cases the light from the LED is coupled into a much lower-index medium. The large index difference makes the reflection quite substantial (per the Fresnel coefficients) | https://huggingface.co/datasets/fmars/wiki_stem |
Light in school buildings traditionally is from a combination of daylight and electric light to illuminate learning spaces (e. g. classrooms, labs, studios, etc | https://huggingface.co/datasets/fmars/wiki_stem |
Light mast is a tall lighting specified mast, which has several big searchlights on top of it. Light masts illuminates large areas and are possible to move, which is why they are used (for example) as farming, construction and emergency works implement. The device works with its own electric generator or with external power source | https://huggingface.co/datasets/fmars/wiki_stem |
A light meter is a device used to measure the amount of light. In photography, a light meter (more correctly an exposure meter) is used to determine the proper exposure for a photograph. The meter will include either a digital or analog calculator which displays the correct shutter speed and f-number for optimum exposure, given a certain lighting situation and film speed | https://huggingface.co/datasets/fmars/wiki_stem |
Light pollution is the presence of unwanted, inappropriate, or excessive artificial lighting. In a descriptive sense, the term light pollution refers to the effects of any poorly implemented lighting, during the day or night. Light pollution can be understood not only as a phenomenon resulting from a specific source or kind of pollution, but also as a contributor to the wider, collective impact of various sources of pollution | https://huggingface.co/datasets/fmars/wiki_stem |
A light tower is a piece of mobile equipment which has one or more high-intensity electric lamps and a mast. Almost always, the lights are attached to the mast, which is attached to a trailer, with a generator set to power the lamps. Normally the lamps are metal halide bulbs and the generator is powered by a diesel engine | https://huggingface.co/datasets/fmars/wiki_stem |
Light tubes (also known as light pipes, tubular skylights or sun tunnels) are structures that transmit or distribute natural or artificial light for the purpose of illumination and are examples of optical waveguides.
In their application to daylighting, they are also often called tubular daylighting devices, sun pipes, sun scopes, or daylight pipes. They can be divided into two broad categories: hollow structures that contain the light with reflective surfaces; and transparent solids that contain the light by total internal reflection | https://huggingface.co/datasets/fmars/wiki_stem |
A lightcast is a functional analysis and mapping of the illumination produced by a light source. It is used to map the physical characteristics of light emission for use in functional systems. A lightcast includes the entire zone of illumination while a ray cast measures lighting of a single point in space near the light source | https://huggingface.co/datasets/fmars/wiki_stem |
Lighting as a service (LaaS), also known as light as a service, is a service-based business model in which light service is charged on a subscription basis rather than via a one-time payment. It is managed by third parties, more precisely, by specialized service providers and may include light design, financing, installation, maintenance and other services. The model enables customers to outsource lighting aspects of their business over a set time | https://huggingface.co/datasets/fmars/wiki_stem |
The Lighting Industry Association is Europe's largest trade association for lighting equipment professionals. This includes lighting manufacturers, suppliers, retailers, wholesalers, designers and all professionals active in the UK lighting market.
History
The NEW Lighting Industry Association was formed on 1 January 2012 from the merging of the Lighting Industry Federation and the Lighting Association | https://huggingface.co/datasets/fmars/wiki_stem |
A lighting control system incorporates communication between various system inputs and outputs related to lighting control with the use of one or more central computing devices. Lighting control systems are widely used on both indoor and outdoor lighting of commercial, industrial, and residential spaces. Lighting control systems are sometimes referred to under the term smart lighting | https://huggingface.co/datasets/fmars/wiki_stem |
Designing lighting for the elderly requires special consideration and care from architects and lighting designers. As people age, they experience neurodegeneration in the retina and in the suprachiasmatic nucleus (SCN). Less light reaches the back of the eyes because the pupils decrease in size as you age, the lens inside your eye becomes thicker, and the lens scatters more light, causing objects and colors to appear less vivid | https://huggingface.co/datasets/fmars/wiki_stem |
The issue of lighting in libraries is one that is still discussed and debated today. Well-designed and carefully positioned lighting makes patrons feel good and comfortable in their surroundings; bad lighting creates problems for patrons when they are reading, studying or searching for books and may keep their visit to the library short. Lighting can even have a negative impact on library staff too | https://huggingface.co/datasets/fmars/wiki_stem |
Lighting Research & Technology is a peer-reviewed scientific journal covering all aspects of light and lighting. Its editor-in-chief is Steve Fotios (University of Sheffield). It was established in 1969 and is published by SAGE Publications on behalf of the Society of Light and Lighting (part of the Chartered Institution of Building Services Engineers) | https://huggingface.co/datasets/fmars/wiki_stem |
In architecture, a lightwell, sky-well, or air shaft is an unroofed or roofed external space provided within the volume of a large building to allow light and air to reach what would otherwise be a dark or unventilated area. Lightwells may be lined with glazed bricks to increase the reflection of sunlight within the space. Lightwells may have sunlight reflecting mirrors on the top of light well | https://huggingface.co/datasets/fmars/wiki_stem |
A link-boy (or link boy or linkboy) was a boy who carried a flaming torch to light the way for pedestrians at night. Linkboys were common in London in the days before the introduction of gas lighting in the early to mid 19th century. The linkboy's fee was commonly one farthing, and the torch was often made from burning pitch and tow | https://huggingface.co/datasets/fmars/wiki_stem |
A lithophane is a thin plaque of translucent material, normally porcelain, which has been moulded to varying thickness, such that when lit from behind the different thicknesses show as different shades, forming an image. Only when lit from behind does the image display properly. They were invented in the 19th century and became very popular, typically for lampshades, nightlights, or to be hung on windows | https://huggingface.co/datasets/fmars/wiki_stem |
Lumen maintenance is the most useful gauge to determine the lifetime or useful light output rating of an LED light source. Unlike traditional light sources such as incandescent lamps, LEDs rarely fail outright and instead continue to emit light, albeit at slowly diminishing rate over time. Lumen maintenance is the luminous flux remaining (expressed as a percentage of the initial output) at any selected elapsed operating time | https://huggingface.co/datasets/fmars/wiki_stem |
In lighting design, the lumen method, (also called zonal cavity method), is a simplified method to calculate the light level in a room. The method is a series of calculations that uses horizontal illuminance criteria to establish a uniform luminaire layout in a space. In its simplest form, the lumen method is merely the total number of lumens available in a room divided by the area of the room | https://huggingface.co/datasets/fmars/wiki_stem |
Luminous efficacy is a measure of how well a light source produces visible light. It is the ratio of luminous flux to power, measured in lumens per watt in the International System of Units (SI). Depending on context, the power can be either the radiant flux of the source's output, or it can be the total power (electric power, chemical energy, or others) consumed by the source | https://huggingface.co/datasets/fmars/wiki_stem |
Mood lighting is igniting or illumination, designed to create a temporary state of mind or feeling.
Effects of lighting on humans
Field studies have shown in office settings that blue-enriched lighting over the course of several weeks can lead to improved alertness, performance, and sleep quality in comparison to lighting with a lower color temperature.
Effects of indoor lighting
Indoor lighting can have a variety of effects on human subjects living within an artificial indoor environment | https://huggingface.co/datasets/fmars/wiki_stem |
The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the luminosity function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and ISO | https://huggingface.co/datasets/fmars/wiki_stem |
A phosphor is a substance that exhibits the phenomenon of luminescence; it emits light when exposed to some type of radiant energy. The term is used both for fluorescent or phosphorescent substances which glow on exposure to ultraviolet or visible light, and cathodoluminescent substances which glow when struck by an electron beam (cathode rays) in a cathode-ray tube.
When a phosphor is exposed to radiation, the orbital electrons in its molecules are excited to a higher energy level; when they return to their former level they emit the energy as light of a certain color | https://huggingface.co/datasets/fmars/wiki_stem |
Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy (including light) in terms of absolute power. In modern photometry, the radiant power at each wavelength is weighted by a luminosity function that models human brightness sensitivity | https://huggingface.co/datasets/fmars/wiki_stem |
In fiber optics, the radiation angle is half the vertex angle of the cone of light emitted at the exit face of an optical fiber.
The cone boundary is usually defined (a) by the angle at which the far-field irradiance has decreased to a specified fraction of its maximum value or (b) as the cone within which there is a specified fraction of the total radiated power at any point in the far field.
See also
Guided ray
Numerical aperture
References
This article incorporates public domain material from Federal Standard 1037C | https://huggingface.co/datasets/fmars/wiki_stem |
Remote Skylights are optical systems capable of providing natural light to unlit locations. An arrangement of parabolic reflectors and optical fiber cables, transport natural sunlight to areas that would otherwise be dark or be lit artificially.
Remote skylights are composed chiefly of a solar collection dish, a "heliotube" and a distribution dish | https://huggingface.co/datasets/fmars/wiki_stem |
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