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This is the list of the 802 isomers of tridecane , with their IUPAC names.
"Constitutional Isomers of Alkanes" . Scribd . 23 May 2011 . Retrieved 27 November 2015 . | https://en.wikipedia.org/wiki/List_of_isomers_of_tridecane |
This is the list of 159 isomers of undecane . | https://en.wikipedia.org/wiki/List_of_isomers_of_undecane |
This is a list of notable job scheduler software . Job scheduling applications are designed to carry out repetitive tasks as defined in a schedule based upon calendar and event conditions. This category of software is also called workload automation . Only products with their own article are listed: | https://en.wikipedia.org/wiki/List_of_job_scheduler_software |
Knot theory is the study of mathematical knots . While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space , R 3 . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R 3 upon itself (known as an ambient isotopy ); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.
Notation used in knot theory:
General types of links: | https://en.wikipedia.org/wiki/List_of_knot_theory_topics |
— Columns detailing the features covered by the binding are missing. — | https://en.wikipedia.org/wiki/List_of_language_bindings_for_Qt_5 |
Below is a list of the largest aluminum -producing companies by output (in 1,000,000 metric tons), accurate as of 2022 according to Statista . [ 1 ] | https://en.wikipedia.org/wiki/List_of_largest_aluminum_producers_by_output |
Chemical & Engineering News publishes an annual list of the world's largest chemical producers by sales, excluding formulated products such as pharmaceutical drugs and coatings . [ 1 ] In 2018, sales of the top fifty companies amounted to US$ 951,000,000,000, an increase of 11.8% compared to the top fifty producers of 2017. [ 2 ] The American Chemistry Council estimated that global chemical sales in 2014 rose by 3.7% to US$ 5,389,000,000,000. [ 3 ]
In 2018, Forty-eight of the companies on the list disclosed chemical profits, which totaled US$ 110,100,000,000, an increase of 1.3% from 2017. The average profit margin for chemical operations for these companies was 9.6%. [ 1 ]
Since Chemical & Engineering News began keeping records in 1989, BASF has been the world's largest chemical producer by annual sales more frequently than any other company. The other companies that have headed the list are Dow Chemical, DowDuPont (which broke up into Dow, a new DuPont, and Corteva Agriscience in 2019), Hoechst (which merged with Rhône-Poulenc in 1999 and is now a subsidiary of Sanofi ), ICI (acquired by AkzoNobel in 2008) and Bayer. | https://en.wikipedia.org/wiki/List_of_largest_chemical_producers |
Following are the largest impact craters on various worlds of the Solar System . For a full list of named craters, see List of craters in the Solar System . The ratio column compares the crater diameter with the diameter of the impacted celestial body. The maximum crater diameter is 157% of the body diameter (the circumference along a great circle ). | https://en.wikipedia.org/wiki/List_of_largest_craters_in_the_Solar_System |
This is a list of the world's largest machines, both static and movable in history. | https://en.wikipedia.org/wiki/List_of_largest_machines |
This is a list of the largest plants by clade . Measurements are based on height, volume , length, diameter, and weight , depending on the most appropriate way(s) of measurement for the clade.
The conifer division of plants includes the tallest organism, and the largest single-stemmed plants by wood volume , wood mass , and main stem circumference . The largest by wood volume and mass is the giant sequoia ( Sequoiadendron giganteum ), native to Sierra Nevada and California; it grows to an average height of 70–85 m (230–279 ft) and 5–7 m (16–23 ft) in diameter. [ 1 ] Specimens have been recorded up to 94.9 m (311 ft) in height and (not the same individual) 8.98 m (29.5 ft) in diameter; the largest individual still standing is the General Sherman Tree , with a volume of 1,489 m 3 (52,600 cu ft). [ 2 ]
Although typically not so large in volume, the closely related coast redwood ( Sequoia sempervirens ) of the Pacific coast in North America is taller, reaching a maximum height of 115.55 m (379.1 ft) – the Hyperion Tree , which ranks it as the world's tallest known living tree and organism (not including its roots underground). [ 3 ] The largest historical specimen (and largest known single-stem organism) was the Lindsay Creek Tree , a coast redwood with a minimum trunk volume of over 2,500 m 3 (88,000 cu ft) and a mass of over 3,000,000 kg (6,600,000 lb; 3,300 short tons). It fell during a storm in 1905. [ 4 ]
The conifers also include the largest tree by circumference in the world, the Montezuma cypress ( Taxodium mucronatum ). The thickest recorded tree, found in Mexico, is called Árbol del Tule , with a circumference of 57.9 m (190 ft) at its base and a diameter of 14.5 m (48 ft) at 1.5 m (4.9 ft) above ground level; its height is over 39.4 m (129 ft). [ 5 ] These trees dwarf any other non-communal organism, as even the largest blue whales are likely to weigh one-sixteenth as much as a large giant sequoia or coast redwood. See list of superlative trees for other tree records.
The largest single-stemmed species of cycad is Hope's cycad ( Lepidozamia hopei ), endemic to the Australian state of Queensland . The largest examples of this species have been over 15 m (49 ft) tall and have had a circumference of 1.5 m (4.9 ft). [ 6 ] However the multi-stemmed [ 7 ] Encephalartos laurentianus ( Zamiaceae ) of Bandundu Province in Congo (Kinshasa) and in adjoining parts of Angola is much more massive. The stems, which can be upright when young, but sprawling when mature, are up to 65 feet (20 meters) in length, [ 8 ] and up to 4 ft 1 in (124 cm) in diameter. [ 9 ] [ 10 ] Assuming a density of 1.0, an old much-branched specimen could weigh up to 45 tonnes (50 short tons).
This is the most diverse and numerous division of plants, with upwards of 400,000 species.
For two-dimensional area, the largest known clonal flowering plant, and indeed largest plant and organism, is a grove of male Aspen in Utah , nicknamed Pando ( Populus tremuloides ). The grove is connected by a single root system, and each stem above the ground is genetically identical. It is estimated to weigh approximately 6,000,000 kg (13,000,000 lb; 6,600 short tons), [ 11 ] and covers 43.6 ha (108 acres). [ 12 ]
A form of flowering plant that far exceeds Pando as the largest organism on earth in breadth, is the giant marine plant, Posidonia australis , living in Shark Bay , Australia. Its length is about 180 km (112 mi) and it covers an area of 200 km 2 (77 sq mi). [ 13 ] It is estimated to be over 4,500 years old. Believed to have sprouted from a single seed, it grows at about the same rate as a lawn, up to 35 centimetres (14 inches) a year. [ 14 ]
Another form of flowering plant Posidonia oceanica discovered in the Mediterranean may be the oldest living organism in the world, with an estimated age of 100,000 years. [ 15 ]
By a stricter definition of individuality, and using contending measures of size, Ficus benghalensis , the giant banyan trees of India are the largest trees in the world. [ 16 ] In these trees, a network of interconnected stems and branches has grown entirely by vegetative, "branching" propagation. One individual, Thimmamma Marrimanu , in Andhra Pradesh , covers 19,107 square metres, making it the largest single tree by two-dimensional canopy coverage area. This tree is also the world's largest known tree by a related measure, perimeter length, with a distance of 846 metres required to walk around the edge of the canopy. Thimmama Marrimanu is likely also the world's largest tree by three-dimensional canopy volume.
The tallest flowering plant species known is Eucalyptus regnans , of which a living specimen has been measured at 100.5 m (330 ft) in Southern Tasmania . [ 17 ] [ 18 ] The longest vine to be accurately measured is "Rattan Manau" ( Calamus manan ) of the palm family (historically Palmae, but now often Arecaceae ) and native to the Malay Peninsula , Sumatra and Java . One unbranched stem at Buitenzorg (now Bogor ) Botanic Garden, Java was carefully measured to a length of 787 feet (240 meters). [ 19 ]
Of herbaceous plants, plants without persistent woody growth above ground, Musa ingens [ 20 ] is the largest. It can reach about 15 meters tall with a pseudostem diameter of around a meter. It also holds the record for the longest petioles or leaf stalks of any plant.
Bamboos are a subfamily ( Bambusoideae ) of flowering perennial plants in the grass family Poaceae , comprising three tribes : Arundinarieae , Bambuseae , and Olyreae . Dendrocalamus is a tropical genus of giant clumping bamboo found throughout Southeast Asia . It includes Dendrocalamus giganteus , which can reach heights up to 30 m. [ 21 ]
Other records among flowering plants include, the title of largest flower , which belongs to the species Rafflesia arnoldii . One of these flowers can reach a diameter of 1 m (3.3 ft) and weigh up to 11 kg (24 lb). [ 22 ] The largest unbranched inflorescence , resembling (but not qualifying as) a giant flower, belongs to the titan arum ( Amorphophallus titanum ), reaching almost 3 m (9.8 ft) in height. [ 23 ] The absolute largest inflorescence, at up to 8 m (26 ft) long, is borne by the talipot palm ( Corypha umbraculifera ) of India. [ 24 ] The largest leaves belong to either Gunnera manicata , Raphia regalis , Manicaria saccifera , Marojejya darianii , Johannesteijsmannia altifrons , or Victoria boliviana , depending on criteria. [ 25 ]
The largest of horsetail is the species Equisetum myriochaetum , native to Nicaragua, Costa Rica, Colombia, Venezuela, Ecuador, Peru and Mexico. The biggest specimen known was 8 m (26 ft) tall and had a diameter of 2.5 cm (0.98 in). [ 26 ]
The largest species of fern is probably Cyathea brownii of Norfolk Island , which may be 20 m (66 ft) or more in height. [ 27 ]
The largest species of liverwort is a New Zealand species, Schistochila appendiculata . The top size of this species is 1.1 m (3.6 ft) long, a diameter of 2.5 cm (0.98 in) and a stem length of 10 cm (3.9 in). [ 28 ] [ 29 ] [ 30 ] [ 31 ] Another New Zealand liĬverwort, Plagiochila gigantea (Jungermaniaceae) is a cushion plant up to three feet (91 centimeters) in width and up to 2.5 feet (75 centimeters) in height. It is endemic to the Southern Alps of South Island. [ 32 ]
The world's most massive moss is Dawsonia superba , of Australia and New Zealand. This species has numerous 50 cm (20 in) tall, upright shoots, joined by a network of rhizomes. [ 33 ] The tallest moss is Spiridens reinwardtii of the family Hypnodendraceae and native to Indonesia , Malaysia , Papua New Guinea , the Philippines , Melanesia and Taiwan . S. reinwardtii is a vine which is typically 30 to 40 centimeters (12 to 16 inches) high but can climb to a height of 3 meters (9.8 feet). [ 34 ] Spiridens reinwardtii is the only true vine among mosses and climbs by twining. The longest individuals seem to be in New Guinea. | https://en.wikipedia.org/wiki/List_of_largest_plants |
The following is a list of the fourteen reservoirs , in the United States state of Wyoming , that contain at least 40,000 acre-feet (49 million cubic meters ) when at full capacity. In addition to in-stream reservoirs, the list includes enhanced natural lakes , notably Jackson Lake . With five of the fourteen largest reservoirs in the state, the North Platte River is the most dammed river in the state, and provides much of the state's water storage. [ citation needed ]
These reservoirs provide 10,221,672 acre-feet (13 billion cubic metres) of storage. ( Some [ which? ] of this storage capacity, or of the water held in it, is allocated otherwise than for normal use within the state.) [ citation needed ] [ how? ]
Download coordinates as: | https://en.wikipedia.org/wiki/List_of_largest_reservoirs_in_Wyoming |
Following are the longest, widest, and deepest rifts and valleys in various worlds of the Solar System . | https://en.wikipedia.org/wiki/List_of_largest_rifts,_canyons_and_valleys_in_the_Solar_System |
The top 5 best selling pharmaceuticals 2015–2019. Sales in billion USD. [ 1 ]
The top 16 best selling pharmaceuticals of 2017/18. [ 2 ]
MabThera
Prevenar 13
Drugs with sales above $5 billion in 2015 included: [ 3 ] [ 4 ]
Pfizer
Rheumatoid Arthritis
Rituxan
Leukemia
Autoimmune disorders
Genentech
Genentech
Genentech
Myelodysplastic syndromes
Advair
Chronic obstructive pulmonary disease
For the fourth quarter of 2013, the largest selling drugs were: [ 5 ] | https://en.wikipedia.org/wiki/List_of_largest_selling_pharmaceutical_products |
The following is a list of learning management systems ( LMS ). | https://en.wikipedia.org/wiki/List_of_learning_management_systems |
This following is a list of lemmas (or, " lemmata ", i.e. minor theorems , or sometimes intermediate technical results factored out of proofs). See also list of axioms , list of theorems and list of conjectures . | https://en.wikipedia.org/wiki/List_of_lemmas |
This list of lichenicolous fungi of Iceland is based on a compiled checklist from 2009 [ 1 ] with the taxonomy of the fungi revised in 2022 using the Global Biodiversity Information Facility online database. | https://en.wikipedia.org/wiki/List_of_lichenicolous_fungi_of_Iceland |
This list of life sciences comprises the branches of science that involve the scientific study of life – such as microorganisms , plants , and animals including human beings . This science is one of the two major branches of natural science , the other being physical science , which is concerned with non-living matter. Biology is the overall natural science that studies life, with the other life sciences as its sub-disciplines.
Some life sciences focus on a specific type of organism. For example, zoology is the study of animals, while botany is the study of plants. Other life sciences focus on aspects common to all or many life forms, such as anatomy and genetics . Some focus on the micro-scale (e.g. molecular biology , biochemistry ) other on larger scales (e.g. cytology , immunology , ethology , pharmacy, ecology). Another major branch of life sciences involves understanding the mind – neuroscience . Life sciences discoveries are helpful in improving the quality and standard of life and have applications in health, agriculture, medicine, and the pharmaceutical and food science industries. For example, it has provided information on certain diseases which has overall aided in the understanding of human health. [ 1 ] | https://en.wikipedia.org/wiki/List_of_life_sciences |
This is a list of named linear ordinary differential equations . | https://en.wikipedia.org/wiki/List_of_linear_ordinary_differential_equations |
A live CD or live DVD is a CD-ROM or DVD-ROM containing a bootable computer operating system . Live CDs are unique in that they have the ability to run a complete, modern operating system on a computer lacking mutable secondary storage, such as a hard disk drive.
These are directly based on Debian:
A large number of live CDs are based on Knoppix. The list of those is in the derivatives section of the Knoppix article .
These are based at least partially on Ubuntu , which is based on Debian:
Microsoft representatives have described third-party efforts at producing Windows-based live CDs as "improperly licensed" uses of Windows, unless used solely to rescue a properly licensed installation. However, Nu2 Productions believes the use of BartPE is legal provided that one Windows license is purchased for each BartPE CD, and the Windows license is used for nothing else. [ 5 ]
Systems based on the former open source "OS/net Nevada" or ONNV open source project by Sun Microsystems.
Illumos is a fork of the former OpenSolaris ONNV aiming to further develop the ONNV and replacing the closed source parts while remaining binary compatible. The following products are based upon Illumos:
This list is for operating systems distributions that are specifically designed to boot off a (writable) USB flash drive, often called a USB stick .
(This does not include operating system distributions with a simplified "installer" designed to boot from a USB drive, but the full OS is intended to be installed on a hard drive).
In addition, many other operating systems can be made to run from a USB flash drive,
possibly using one of the List of tools to create Live USB systems . | https://en.wikipedia.org/wiki/List_of_live_CDs |
This is an incomplete list of log-structured file system implementations.
Some kinds of storage media, such as flash memory and CD-RW , slowly degrade as they are written to and have a limited number of erase/write cycles at any one location. Log-structured file systems are sometimes used on these media because they make fewer in-place writes and thus prolong the life of the device by wear leveling . The more common such file systems include: | https://en.wikipedia.org/wiki/List_of_log-structured_file_systems |
In mathematics , many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes.
Trivial mathematical identities are relatively simple (for an experienced mathematician), though not necessarily unimportant. The trivial logarithmic identities are as follows:
By definition, we know that:
where b ≠ 0 {\displaystyle b\neq 0} and b ≠ 1 {\displaystyle b\neq 1} .
Setting x = 0 {\displaystyle x=0} ,
we can see that: b x = y ⟺ b ( 0 ) = y ⟺ 1 = y ⟺ y = 1 {\displaystyle b^{x}=y\iff b^{(0)}=y\iff 1=y\iff y=1} . So, substituting these values into the formula, we see that: log b ( y ) = x ⟺ log b ( 1 ) = 0 {\displaystyle \log _{b}(y)=x\iff \log _{b}(1)=0} , which gets us the first property.
Setting x = 1 {\displaystyle x=1} ,
we can see that: b x = y ⟺ b ( 1 ) = y ⟺ b = y ⟺ y = b {\displaystyle b^{x}=y\iff b^{(1)}=y\iff b=y\iff y=b} . So, substituting these values into the formula, we see that: log b ( y ) = x ⟺ log b ( b ) = 1 {\displaystyle \log _{b}(y)=x\iff \log _{b}(b)=1} , which gets us the second property.
Logarithms and exponentials with the same base cancel each other. This is true because logarithms and exponentials are inverse operations—much like the same way multiplication and division are inverse operations, and addition and subtraction are inverse operations.
Both of the above are derived from the following two equations that define a logarithm:
(note that in this explanation, the variables of x {\displaystyle x} and x {\displaystyle x} may not be referring to the same number)
Looking at the equation b x = y {\displaystyle b^{x}=y} , and substituting the value for x {\displaystyle x} of log b ( y ) = x {\displaystyle \log _{b}(y)=x} , we get the following equation: b x = y ⟺ b log b ( y ) = y ⟺ b log b ( y ) = y {\displaystyle b^{x}=y\iff b^{\log _{b}(y)}=y\iff b^{\log _{b}(y)}=y} , which gets us the first equation.
Another more rough way to think about it is that b something = y {\displaystyle b^{\text{something}}=y} ,
and that that " something {\displaystyle {\text{something}}} " is log b ( y ) {\displaystyle \log _{b}(y)} .
Looking at the equation log b ( y ) = x {\displaystyle \log _{b}(y)=x} , and substituting the value for y {\displaystyle y} of b x = y {\displaystyle b^{x}=y} , we get the following equation: log b ( y ) = x ⟺ log b ( b x ) = x ⟺ log b ( b x ) = x {\displaystyle \log _{b}(y)=x\iff \log _{b}(b^{x})=x\iff \log _{b}(b^{x})=x} , which gets us the second equation.
Another more rough way to think about it is that log b ( something ) = x {\displaystyle \log _{b}({\text{something}})=x} ,
and that that something " something {\displaystyle {\text{something}}} " is b x {\displaystyle b^{x}} .
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [ 2 ] The first three operations below assume that x = b c and/or y = b d , so that log b ( x ) = c and log b ( y ) = d . Derivations also use the log definitions x = b log b ( x ) and x = log b ( b x ) .
Where b {\displaystyle b} , x {\displaystyle x} , and y {\displaystyle y} are positive real numbers and b ≠ 1 {\displaystyle b\neq 1} , and c {\displaystyle c} and d {\displaystyle d} are real numbers.
The laws result from canceling exponentials and the appropriate law of indices. Starting with the first law:
The law for powers exploits another of the laws of indices:
The law relating to quotients then follows:
Similarly, the root law is derived by rewriting the root as a reciprocal power:
These are the three main logarithm laws/rules/principles, [ 3 ] from which the other properties listed above can be proven. Each of these logarithm properties correspond to their respective exponent law, and their derivations/proofs will hinge on those facts. There are multiple ways to derive/prove each logarithm law – this is just one possible method.
To state the logarithm of a product law formally:
Derivation:
Let b ∈ R + {\displaystyle b\in \mathbb {R} _{+}} , where b ≠ 1 {\displaystyle b\neq 1} ,
and let x , y ∈ R + {\displaystyle x,y\in \mathbb {R} _{+}} . We want to relate the expressions log b ( x ) {\displaystyle \log _{b}(x)} and log b ( y ) {\displaystyle \log _{b}(y)} . This can be done more easily by rewriting in terms of exponentials, whose properties we already know. Additionally, since we are going to refer to log b ( x ) {\displaystyle \log _{b}(x)} and log b ( y ) {\displaystyle \log _{b}(y)} quite often, we will give them some variable names to make working with them easier: Let m = log b ( x ) {\displaystyle m=\log _{b}(x)} , and let n = log b ( y ) {\displaystyle n=\log _{b}(y)} .
Rewriting these as exponentials, we see that
From here, we can relate b m {\displaystyle b^{m}} (i.e. x {\displaystyle x} ) and b n {\displaystyle b^{n}} (i.e. y {\displaystyle y} ) using exponent laws as
To recover the logarithms, we apply log b {\displaystyle \log _{b}} to both sides of the equality.
The right side may be simplified using one of the logarithm properties from before: we know that log b ( b m + n ) = m + n {\displaystyle \log _{b}(b^{m+n})=m+n} , giving
We now resubstitute the values for m {\displaystyle m} and n {\displaystyle n} into our equation, so our final expression is only in terms of x {\displaystyle x} , y {\displaystyle y} , and b {\displaystyle b} .
This completes the derivation.
To state the logarithm of a quotient law formally:
Derivation:
Let b ∈ R + {\displaystyle b\in \mathbb {R} _{+}} , where b ≠ 1 {\displaystyle b\neq 1} ,
and let x , y ∈ R + {\displaystyle x,y\in \mathbb {R} _{+}} .
We want to relate the expressions log b ( x ) {\displaystyle \log _{b}(x)} and log b ( y ) {\displaystyle \log _{b}(y)} . This can be done more easily by rewriting in terms of exponentials, whose properties we already know. Additionally, since we are going to refer to log b ( x ) {\displaystyle \log _{b}(x)} and log b ( y ) {\displaystyle \log _{b}(y)} quite often, we will give them some variable names to make working with them easier: Let m = log b ( x ) {\displaystyle m=\log _{b}(x)} , and let n = log b ( y ) {\displaystyle n=\log _{b}(y)} .
Rewriting these as exponentials, we see that:
From here, we can relate b m {\displaystyle b^{m}} (i.e. x {\displaystyle x} ) and b n {\displaystyle b^{n}} (i.e. y {\displaystyle y} ) using exponent laws as
To recover the logarithms, we apply log b {\displaystyle \log _{b}} to both sides of the equality.
The right side may be simplified using one of the logarithm properties from before: we know that log b ( b m − n ) = m − n {\displaystyle \log _{b}(b^{m-n})=m-n} , giving
We now resubstitute the values for m {\displaystyle m} and n {\displaystyle n} into our equation, so our final expression is only in terms of x {\displaystyle x} , y {\displaystyle y} , and b {\displaystyle b} .
This completes the derivation.
To state the logarithm of a power law formally:
Derivation:
Let b ∈ R + {\displaystyle b\in \mathbb {R} _{+}} , where b ≠ 1 {\displaystyle b\neq 1} , let x ∈ R + {\displaystyle x\in \mathbb {R} _{+}} , and let r ∈ R {\displaystyle r\in \mathbb {R} } . For this derivation, we want to simplify the expression log b ( x r ) {\displaystyle \log _{b}(x^{r})} . To do this, we begin with the simpler expression log b ( x ) {\displaystyle \log _{b}(x)} . Since we will be using log b ( x ) {\displaystyle \log _{b}(x)} often, we will define it as a new variable: Let m = log b ( x ) {\displaystyle m=\log _{b}(x)} .
To more easily manipulate the expression, we rewrite it as an exponential. By definition, m = log b ( x ) ⟺ b m = x {\displaystyle m=\log _{b}(x)\iff b^{m}=x} , so we have
Similar to the derivations above, we take advantage of another exponent law. In order to have x r {\displaystyle x^{r}} in our final expression, we raise both sides of the equality to the power of r {\displaystyle r} :
where we used the exponent law ( b m ) r = b m r {\displaystyle (b^{m})^{r}=b^{mr}} .
To recover the logarithms, we apply log b {\displaystyle \log _{b}} to both sides of the equality.
The left side of the equality can be simplified using a logarithm law, which states that log b ( b m r ) = m r {\displaystyle \log _{b}(b^{mr})=mr} .
Substituting in the original value for m {\displaystyle m} , rearranging, and simplifying gives
This completes the derivation.
To state the change of base logarithm formula formally: ∀ a , b ∈ R + , a , b ≠ 1 , ∀ x ∈ R + , log b ( x ) = log a ( x ) log a ( b ) {\displaystyle \forall a,b\in \mathbb {R} _{+},a,b\neq 1,\forall x\in \mathbb {R} _{+},\log _{b}(x)={\frac {\log _{a}(x)}{\log _{a}(b)}}}
This identity is useful to evaluate logarithms on calculators. For instance, most calculators have buttons for ln and for log 10 , but not all calculators have buttons for the logarithm of an arbitrary base.
Let a , b ∈ R + {\displaystyle a,b\in \mathbb {R} _{+}} , where a , b ≠ 1 {\displaystyle a,b\neq 1} Let x ∈ R + {\displaystyle x\in \mathbb {R} _{+}} . Here, a {\displaystyle a} and b {\displaystyle b} are the two bases we will be using for the logarithms. They cannot be 1, because the logarithm function is not well defined for the base of 1. [ citation needed ] The number x {\displaystyle x} will be what the logarithm is evaluating, so it must be a positive number. Since we will be dealing with the term log b ( x ) {\displaystyle \log _{b}(x)} quite frequently, we define it as a new variable: Let m = log b ( x ) {\displaystyle m=\log _{b}(x)} .
To more easily manipulate the expression, it can be rewritten as an exponential. b m = x {\displaystyle b^{m}=x}
Applying log a {\displaystyle \log _{a}} to both sides of the equality, log a ( b m ) = log a ( x ) {\displaystyle \log _{a}(b^{m})=\log _{a}(x)}
Now, using the logarithm of a power property, which states that log a ( b m ) = m log a ( b ) {\displaystyle \log _{a}(b^{m})=m\log _{a}(b)} , m log a ( b ) = log a ( x ) {\displaystyle m\log _{a}(b)=\log _{a}(x)}
Isolating m {\displaystyle m} , we get the following: m = log a ( x ) log a ( b ) {\displaystyle m={\frac {\log _{a}(x)}{\log _{a}(b)}}}
Resubstituting m = log b ( x ) {\displaystyle m=\log _{b}(x)} back into the equation, log b ( x ) = log a ( x ) log a ( b ) {\displaystyle \log _{b}(x)={\frac {\log _{a}(x)}{\log _{a}(b)}}}
This completes the proof that log b ( x ) = log a ( x ) log a ( b ) {\displaystyle \log _{b}(x)={\frac {\log _{a}(x)}{\log _{a}(b)}}} .
This formula has several consequences:
log b a = 1 log a b {\displaystyle \log _{b}a={\frac {1}{\log _{a}b}}}
log b n a = log b a n {\displaystyle \log _{b^{n}}a={\log _{b}a \over n}}
log b a = log b e ⋅ log e a = log b e ⋅ ln a {\displaystyle \log _{b}a=\log _{b}e\cdot \log _{e}a=\log _{b}e\cdot \ln a}
b log a d = d log a b {\displaystyle b^{\log _{a}d}=d^{\log _{a}b}}
− log b a = log b ( 1 a ) = log 1 / b a {\displaystyle -\log _{b}a=\log _{b}\left({1 \over a}\right)=\log _{1/b}a}
log b 1 a 1 ⋯ log b n a n = log b π ( 1 ) a 1 ⋯ log b π ( n ) a n , {\displaystyle \log _{b_{1}}a_{1}\,\cdots \,\log _{b_{n}}a_{n}=\log _{b_{\pi (1)}}a_{1}\,\cdots \,\log _{b_{\pi (n)}}a_{n},}
where π {\textstyle \pi } is any permutation of the subscripts 1, ..., n . For example log b w ⋅ log a x ⋅ log d c ⋅ log d z = log d w ⋅ log b x ⋅ log a c ⋅ log d z . {\displaystyle \log _{b}w\cdot \log _{a}x\cdot \log _{d}c\cdot \log _{d}z=\log _{d}w\cdot \log _{b}x\cdot \log _{a}c\cdot \log _{d}z.}
The following summation/subtraction rule is especially useful in probability theory when one is dealing with a sum of log-probabilities:
Note that the subtraction identity is not defined if a = c {\displaystyle a=c} , since the logarithm of zero is not defined. Also note that, when programming, a {\displaystyle a} and c {\displaystyle c} may have to be switched on the right hand side of the equations if c ≫ a {\displaystyle c\gg a} to avoid losing the "1 +" due to rounding errors. Many programming languages have a specific log1p(x) function that calculates log e ( 1 + x ) {\displaystyle \log _{e}(1+x)} without underflow (when x {\displaystyle x} is small).
More generally: log b ∑ i = 0 N a i = log b a 0 + log b ( 1 + ∑ i = 1 N a i a 0 ) = log b a 0 + log b ( 1 + ∑ i = 1 N b ( log b a i − log b a 0 ) ) {\displaystyle \log _{b}\sum _{i=0}^{N}a_{i}=\log _{b}a_{0}+\log _{b}\left(1+\sum _{i=1}^{N}{\frac {a_{i}}{a_{0}}}\right)=\log _{b}a_{0}+\log _{b}\left(1+\sum _{i=1}^{N}b^{\left(\log _{b}a_{i}-\log _{b}a_{0}\right)}\right)}
A useful identity involving exponents: x log ( log ( x ) ) log ( x ) = log ( x ) {\displaystyle x^{\frac {\log(\log(x))}{\log(x)}}=\log(x)} or more universally: x log ( a ) log ( x ) = a {\displaystyle x^{\frac {\log(a)}{\log(x)}}=a}
1 1 log x ( a ) + 1 log y ( a ) = log x y ( a ) {\displaystyle {\frac {1}{{\frac {1}{\log _{x}(a)}}+{\frac {1}{\log _{y}(a)}}}}=\log _{xy}(a)} 1 1 log x ( a ) − 1 log y ( a ) = log x y ( a ) {\displaystyle {\frac {1}{{\frac {1}{\log _{x}(a)}}-{\frac {1}{\log _{y}(a)}}}}=\log _{\frac {x}{y}}(a)}
Based on, [ 4 ]
All are accurate around x = 0 {\displaystyle x=0} , but not for large numbers.
The following identity relates log semiring to the min-plus semiring . lim T → 0 − T log ( e − s T + e − t T ) = m i n { s , t } {\displaystyle \lim _{T\rightarrow 0}-T\log(e^{-{\frac {s}{T}}}+e^{-{\frac {t}{T}}})=\mathrm {min} \{s,t\}}
The last limit is often summarized as "logarithms grow more slowly than any power or root of x ".
To modify the limits of integration to run from x {\displaystyle x} to 1 {\displaystyle 1} , we change the order of integration, which changes the sign of the integral:
Therefore:
for Δ x = n k {\displaystyle \textstyle \Delta x={\frac {n}{k}}} and x i {\displaystyle x_{i}} is a sample point in each interval.
The natural logarithm ln ( 1 + x ) {\displaystyle \ln(1+x)} has a well-known Taylor series [ 5 ] expansion that converges for x {\displaystyle x} in the open-closed interval (−1, 1] :
ln ( 1 + x ) = ∑ n = 1 ∞ ( − 1 ) n + 1 x n n = x − x 2 2 + x 3 3 − x 4 4 + x 5 5 − x 6 6 + ⋯ . {\displaystyle \ln(1+x)=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}x^{n}}{n}}=x-{\frac {x^{2}}{2}}+{\frac {x^{3}}{3}}-{\frac {x^{4}}{4}}+{\frac {x^{5}}{5}}-{\frac {x^{6}}{6}}+\cdots .}
Within this interval, for x = 1 {\displaystyle x=1} , the series is conditionally convergent , and for all other values, it is absolutely convergent . For x > 1 {\displaystyle x>1} or x ≤ − 1 {\displaystyle x\leq -1} , the series does not converge to ln ( 1 + x ) {\displaystyle \ln(1+x)} . In these cases, different representations [ 6 ] or methods must be used to evaluate the logarithm.
It is not uncommon in advanced mathematics, particularly in analytic number theory and asymptotic analysis , to encounter expressions involving differences or ratios of harmonic numbers at scaled indices. [ 7 ] The identity involving the limiting difference between harmonic numbers at scaled indices and its relationship to the logarithmic function provides an intriguing example of how discrete sequences can asymptotically relate to continuous functions . This identity is expressed as [ 8 ]
which characterizes the behavior of harmonic numbers as they grow large. This approximation (which precisely equals ln ( n + 1 ) {\displaystyle \ln(n+1)} in the limit) reflects how summation over increasing segments of the harmonic series exhibits integral properties , giving insight into the interplay between discrete and continuous analysis. It also illustrates how understanding the behavior of sums and series at large scales can lead to insightful conclusions about their properties. Here H k {\displaystyle H_{k}} denotes the k {\displaystyle k} -th harmonic number, defined as
The harmonic numbers are a fundamental sequence in number theory and analysis, known for their logarithmic growth. This result leverages the fact that the sum of the inverses of integers (i.e., harmonic numbers) can be closely approximated by the natural logarithm function, plus a constant , especially when extended over large intervals. [ 9 ] [ 7 ] [ 10 ] As k {\displaystyle k} tends towards infinity, the difference between the harmonic numbers H k ( n + 1 ) {\displaystyle H_{k(n+1)}} and H k {\displaystyle H_{k}} converges to a non-zero value. This persistent non-zero difference, ln ( n + 1 ) {\displaystyle \ln(n+1)} , precludes the possibility of the harmonic series approaching a finite limit, thus providing a clear mathematical articulation of its divergence. [ 11 ] [ 12 ] The technique of approximating sums by integrals (specifically using the integral test or by direct integral approximation) is fundamental in deriving such results. This specific identity can be a consequence of these approximations, considering:
The limit explores the growth of the harmonic numbers when indices are multiplied by a scaling factor and then differenced. It specifically captures the sum from k + 1 {\displaystyle k+1} to k ( n + 1 ) {\displaystyle k(n+1)} :
This can be estimated using the integral test for convergence, or more directly by comparing it to the integral of 1 / x {\displaystyle 1/x} from k {\displaystyle k} to k ( n + 1 ) {\displaystyle k(n+1)} :
As the window's lower bound begins at k + 1 {\displaystyle k+1} and the upper bound extends to k ( n + 1 ) {\displaystyle k(n+1)} , both of which tend toward infinity as k → ∞ {\displaystyle k\to \infty } , the summation window encompasses an increasingly vast portion of the smallest possible terms of the harmonic series (those with astronomically large denominators), creating a discrete sum that stretches towards infinity, which mirrors how continuous integrals accumulate value across an infinitesimally fine partitioning of the domain. In the limit, the interval is effectively from 1 {\displaystyle 1} to n + 1 {\displaystyle n+1} where the onset k {\displaystyle k} implies this minimally discrete region.
The harmonic number difference formula for ln ( m ) {\displaystyle \ln(m)} is an extension [ 8 ] of the classic, alternating identity of ln ( 2 ) {\displaystyle \ln(2)} :
which can be generalized as the double series over the residues of m {\displaystyle m} :
where ⟨ m ⟩ {\displaystyle \langle m\rangle } is the principle ideal generated by m {\displaystyle m} . Subtracting 1 x {\displaystyle \textstyle {\frac {1}{x}}} from each term 1 x − r {\displaystyle \textstyle {\frac {1}{x-r}}} (i.e., balancing each term with the modulus) reduces the magnitude of each term's contribution, ensuring convergence by controlling the series' tendency toward divergence as m {\displaystyle m} increases. For example:
This method leverages the fine differences between closely related terms to stabilize the series. The sum over all residues r ∈ N {\displaystyle r\in \mathbb {N} } ensures that adjustments are uniformly applied across all possible offsets within each block of m {\displaystyle m} terms. This uniform distribution of the "correction" across different intervals defined by x − r {\displaystyle x-r} functions similarly to telescoping over a very large sequence. It helps to flatten out the discrepancies that might otherwise lead to divergent behavior in a straightforward harmonic series. Note that the structure of the summands of this formula matches those of the interpolated harmonic number H x {\displaystyle H_{x}} when both the domain and range are negated (i.e., − H − x {\displaystyle -H_{-x}} ). However, the interpretation and roles of the variables differ.
A fundamental feature of the proof is the accumulation of the subtrahends 1 x {\textstyle {\frac {1}{x}}} into a unit fraction, that is, m x = 1 n {\textstyle {\frac {m}{x}}={\frac {1}{n}}} for m ∣ x {\displaystyle m\mid x} , thus m = ω + 1 {\displaystyle m=\omega +1} rather than m = | Z m ∩ N | {\displaystyle m=|\mathbb {Z} _{m}\cap \mathbb {N} |} , where the extrema of Z m ∩ N {\displaystyle \mathbb {Z} _{m}\cap \mathbb {N} } are [ 0 , ω ] {\displaystyle [0,\omega ]} if N = N 0 {\displaystyle \mathbb {N} =\mathbb {N} _{0}} and [ 1 , ω ] {\displaystyle [1,\omega ]} otherwise , with the minimum of 0 {\displaystyle 0} being implicit in the latter case due to the structural requirements of the proof. Since the cardinality of Z m ∩ N {\displaystyle \mathbb {Z} _{m}\cap \mathbb {N} } depends on the selection of one of two possible minima, the integral ∫ 1 t d t {\displaystyle \textstyle \int {\frac {1}{t}}dt} , as a set-theoretic procedure, is a function of the maximum ω {\displaystyle \omega } (which remains consistent across both interpretations) plus 1 {\displaystyle 1} , not the cardinality (which is ambiguous [ 13 ] [ 14 ] due to varying definitions of the minimum). Whereas the harmonic number difference computes the integral in a global sliding window, the double series, in parallel, computes the sum in a local sliding window—a shifting m {\displaystyle m} -tuple—over the harmonic series, advancing the window by m {\displaystyle m} positions to select the next m {\displaystyle m} -tuple, and offsetting each element of each tuple by 1 m {\textstyle {\frac {1}{m}}} relative to the window's absolute position. The sum ∑ n = 1 k ∑ 1 x − r {\textstyle \sum _{n=1}^{k}\sum {\frac {1}{x-r}}} corresponds to H k m {\displaystyle H_{km}} which scales H m {\displaystyle H_{m}} without bound. The sum ∑ n = 1 k − 1 n {\textstyle \sum _{n=1}^{k}-{\frac {1}{n}}} corresponds to the prefix H k {\displaystyle H_{k}} trimmed from the series to establish the window's moving lower bound k + 1 {\displaystyle k+1} , and ln ( m ) {\displaystyle \ln(m)} is the limit of the sliding window (the scaled, truncated [ 15 ] series):
∑ n = 1 k ∑ r = 1 ω ( 1 m n − r − 1 m n ) = ∑ n = 1 k ∑ r = 0 ω ( 1 m n − r − 1 m n ) = ∑ n = 1 k ( − 1 n + ∑ r = 0 ω 1 m n − r ) = − H k + ∑ n = 1 k ∑ r = 0 ω 1 m n − r = − H k + ∑ n = 1 k ∑ r = 0 ω 1 ( n − 1 ) m + m − r = − H k + ∑ n = 1 k ∑ j = 1 m 1 ( n − 1 ) m + j = − H k + ∑ n = 1 k ( H n m − H m ( n − 1 ) ) = − H k + H m k {\displaystyle {\begin{aligned}\sum _{n=1}^{k}\sum _{r=1}^{\omega }\left({\frac {1}{mn-r}}-{\frac {1}{mn}}\right)&=\sum _{n=1}^{k}\sum _{r=0}^{\omega }\left({\frac {1}{mn-r}}-{\frac {1}{mn}}\right)\\&=\sum _{n=1}^{k}\left(-{\frac {1}{n}}+\sum _{r=0}^{\omega }{\frac {1}{mn-r}}\right)\\&=-H_{k}+\sum _{n=1}^{k}\sum _{r=0}^{\omega }{\frac {1}{mn-r}}\\&=-H_{k}+\sum _{n=1}^{k}\sum _{r=0}^{\omega }{\frac {1}{(n-1)m+m-r}}\\&=-H_{k}+\sum _{n=1}^{k}\sum _{j=1}^{m}{\frac {1}{(n-1)m+j}}\\&=-H_{k}+\sum _{n=1}^{k}\left(H_{nm}-H_{m(n-1)}\right)\\&=-H_{k}+H_{mk}\end{aligned}}} lim k → ∞ H k m − H k = ∑ x ∈ ⟨ m ⟩ ∩ N ∑ r ∈ Z m ∩ N ( 1 x − r − 1 x ) = ln ( ω + 1 ) = ln ( m ) {\displaystyle \lim _{k\to \infty }H_{km}-H_{k}=\sum _{x\in \langle m\rangle \cap \mathbb {N} }\sum _{r\in \mathbb {Z} _{m}\cap \mathbb {N} }\left({\frac {1}{x-r}}-{\frac {1}{x}}\right)=\ln(\omega +1)=\ln(m)}
To remember higher integrals, it is convenient to define
where H n {\displaystyle H_{n}} is the n th harmonic number :
Then
The identities of logarithms can be used to approximate large numbers. Note that log b ( a ) + log b ( c ) = log b ( ac ) , where a , b , and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime , 2 32,582,657 −1 . To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2) , getting 9,808,357.09543 = 9,808,357 + 0.09543 . We can then get 10 9,808,357 × 10 0.09543 ≈ 1.25 × 10 9,808,357 .
Similarly, factorials can be approximated by summing the logarithms of the terms.
The complex logarithm is the complex number analogue of the logarithm function. No single valued function on the complex plane can satisfy the normal rules for logarithms. However, a multivalued function can be defined which satisfies most of the identities. It is usual to consider this as a function defined on a Riemann surface . A single valued version, called the principal value of the logarithm, can be defined which is discontinuous on the negative x axis, and is equal to the multivalued version on a single branch cut .
In what follows, a capital first letter is used for the principal value of functions, and the lower case version is used for the multivalued function. The single valued version of definitions and identities is always given first, followed by a separate section for the multiple valued versions.
The multiple valued version of log( z ) is a set, but it is easier to write it without braces and using it in formulas follows obvious rules.
When k is any integer:
Principal value forms:
Multiple value forms, for any k an integer:
Principal value forms:
Multiple value forms:
A complex power of a complex number can have many possible values.
Principal value form:
Multiple value forms:
Where k 1 , k 2 are any integers:
As a consequence of the harmonic number difference , the natural logarithm is asymptotically approximated by a finite series difference, [ 8 ] representing a truncation of the integral at k = n {\displaystyle k=n} :
where T [ n ] {\displaystyle T[n]} is the n th triangular number , and 2 T [ n ] {\displaystyle 2T[n]} is the sum of the first n even integers . Since the n th pronic number is asymptotically equivalent to the n th perfect square , it follows that:
The prime number theorem provides the following asymptotic equivalence:
where π ( n ) {\displaystyle \pi (n)} is the prime counting function . This relationship is equal to: [ 8 ] : 2
where H ( x 1 , x 2 , … , x n ) {\displaystyle H(x_{1},x_{2},\ldots ,x_{n})} is the harmonic mean of x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} . This is derived from the fact that the difference between the n {\displaystyle n} th harmonic number and ln n {\displaystyle \ln n} asymptotically approaches a small constant , resulting in H n 2 − H n ∼ H n {\displaystyle H_{n^{2}}-H_{n}\sim H_{n}} . This behavior can also be derived from the properties of logarithms : ln n {\displaystyle \ln n} is half of ln n 2 {\displaystyle \ln n^{2}} , and this "first half" is the natural log of the root of n 2 {\displaystyle n^{2}} , which corresponds roughly to the first 1 n {\displaystyle \textstyle {\frac {1}{n}}} th of the sum H n 2 {\displaystyle H_{n^{2}}} , or H n {\displaystyle H_{n}} . The asymptotic equivalence of the first 1 n {\displaystyle \textstyle {\frac {1}{n}}} th of H n 2 {\displaystyle H_{n^{2}}} to the latter n − 1 n {\displaystyle \textstyle {\frac {n-1}{n}}} th of the series is expressed as follows:
which generalizes to:
and:
for fixed k {\displaystyle k} . The correspondence sets H n {\displaystyle H_{n}} as a unit magnitude that partitions H n k {\displaystyle H_{n^{k}}} across powers, where each interval 1 n {\displaystyle \textstyle {\frac {1}{n}}} to 1 n 2 {\displaystyle \textstyle {\frac {1}{n^{2}}}} , 1 n 2 {\displaystyle \textstyle {\frac {1}{n^{2}}}} to 1 n 3 {\displaystyle \textstyle {\frac {1}{n^{3}}}} , etc., corresponds to one H n {\displaystyle H_{n}} unit, illustrating that H n k {\displaystyle H_{n^{k}}} forms a divergent series as k → ∞ {\displaystyle k\to \infty } .
These approximations extend to the real-valued domain through the interpolated harmonic number . For example, where x ∈ R {\displaystyle x\in \mathbb {R} } :
The natural logarithm is asymptotically related to the harmonic numbers by the Stirling numbers [ 17 ] and the Gregory coefficients . [ 18 ] By representing H n {\displaystyle H_{n}} in terms of Stirling numbers of the first kind , the harmonic number difference is alternatively expressed as follows, for fixed k {\displaystyle k} : | https://en.wikipedia.org/wiki/List_of_logarithmic_identities |
This is a list of unusually long mathematical proofs . Such proofs often use computational proof methods and may be considered non-surveyable .
As of 2011 [update] , the longest mathematical proof, measured by number of published journal pages, is the classification of finite simple groups with well over 10000 pages. There are several proofs that would be far longer than this if the details of the computer calculations they depend on were published in full.
The length of unusually long proofs has increased with time. As a rough rule of thumb, 100 pages in 1900, or 200 pages in 1950, or 500 pages in 2000 is unusually long for a proof.
There are many mathematical theorems that have been checked by long computer calculations. If these were written out as proofs, many would be far longer than most of the proofs above. There is not really a clear distinction between computer calculations and proofs, as several of the proofs above, such as the 4-color theorem and the Kepler conjecture, use long computer calculations as well as many pages of mathematical argument. For the computer calculations in this section, the mathematical arguments are only a few pages long, and the length is due to long but routine calculations. Some typical examples of such theorems include:
Kurt Gödel showed how to find explicit examples of statements in formal systems that are provable in that system but whose shortest proof is absurdly long. For example, the statement:
is provable in Peano arithmetic but the shortest proof has at least a googolplex symbols. It has a short proof in a more powerful system: in fact, it is easily provable in Peano arithmetic together with the statement that Peano arithmetic is consistent (which cannot be proved in Peano arithmetic by Gödel's incompleteness theorem ).
In this argument, Peano arithmetic can be replaced by any more powerful consistent system, and a googolplex can be replaced by any number that can be described concisely in the system.
Harvey Friedman found some explicit natural examples of this phenomenon, giving some explicit statements in Peano arithmetic and other formal systems whose shortest proofs are ridiculously long ( Smoryński 1982 ). For example, the statement
is provable in Peano arithmetic, but the shortest proof has length at least 1000 2, where 0 2 = 1 and n +1 2 = 2 ( n 2) ( tetrational growth). The statement is a special case of Kruskal's theorem and has a short proof in second order arithmetic . | https://en.wikipedia.org/wiki/List_of_long_mathematical_proofs |
This is a list of the longest-living biological organisms : the individual(s) (or in some instances, clones ) of a species with the longest natural maximum life spans . For a given species, such a designation may include:
The definition of "longest-living" used in this article considers only the observed or estimated length of an individual organism's natural lifespan – that is, the duration of time between its birth or conception, or the earliest emergence of its identity as an individual organism, and its death – and does not consider other conceivable interpretations of "longest-living", such as the length of time between the earliest appearance of a species in the fossil record and the present (the historical "age" of the species as a whole), the time between a species' first speciation and its extinction (the phylogenetic "lifespan" of the species), or the range of possible lifespans of a species' individuals. This list includes long-lived organisms that are currently still alive as well as those that are dead.
Determining the length of an organism's natural lifespan is complicated by many problems of definition and interpretation, as well as by practical difficulties in reliably measuring age, particularly for extremely old organisms and for those that reproduce by asexual cloning. In many cases the ages listed below are estimates based on observed present-day growth rates, which may differ significantly from the growth rates experienced thousands of years ago. Identifying the longest-living organisms also depends on defining what constitutes an "individual" organism, which can be problematic, since many asexual organisms and clonal colonies defy one or both of the traditional colloquial definitions of individuality (having a distinct genotype and having an independent, physically separate body). Additionally, some organisms maintain the capability to reproduce through very long periods of metabolic dormancy, during which they may not be considered "alive" by certain definitions but nonetheless can resume normal metabolism afterward; it is unclear whether the dormant periods should be counted as part of the organism's lifespan.
If the mortality rate of a species does not increase after maturity, the species does not age and is said to be biologically immortal . There are numerous plants and animals for which the mortality rate has been observed to actually decrease with age, for all or part of the life cycle. [ 2 ] Hydra were observed for four years without any increase in mortality rate. [ 3 ] If the mortality rate remains constant, the rate determines the mean lifespan. The lifespan may be long or short, though the species technically does not "age".
Individuals of other species have been observed to regress to a larval state and regrow into adults multiple times. The hydrozoan species Turritopsis dohrnii (formerly Turritopsis nutricula ) is capable of cycling from a mature adult stage to an immature polyp stage and back again. This means no natural limit to its lifespan is known. [ 4 ] No single specimen has been observed for any extended period, however, and estimating the age of a specimen is not possible by any known means. At least one other hydrozoan ( Laodicea undulata [ 5 ] ), one scyphozoan ( Aurelia sp. 1 [ 6 ] ) and one tentaculata ( Mnemiopsis leiydi [ 7 ] [ 8 ] ) can also revert from a medusa stage into a polyp stage.
Similarly, the larvae of skin beetles undergo a degree of "reversed development" when starved, and later grow back to the previously attained level of maturity. This cycle can be repeated many times. However, repeated cycles result in physiological deterioration, suggesting that these beetle larvae still age. [ 9 ]
If the definition of lifespan does not exclude time spent in metabolically inactive states, many organisms may be said to have lifespans that are millions of years in length. Various claims have been made about reviving bacterial spores to active metabolism after millions of years of dormancy. Spores preserved in amber have been revived after 40 million years, [ 10 ] and spores from salt deposits in New Mexico have been revived after 250 million years, making these bacteria by far the longest-living organisms ever recorded. [ 11 ] Similarly, in May 2022 prokaryotic and eukaryotic microorganisms were found in crystals of halite ; these could be over 800 million years old but it remains uncertain if they are alive or if they could be revived. [ 12 ] [ 13 ] In a related find, a scientist was able to coax a 34,000-year-old salt-captured bacteria to reproduce. These results were subsequently duplicated independently. [ 14 ]
In July 2018, scientists from four Russian institutions collaborating with Princeton University reported that they had analyzed about 300 prehistoric nematode worms recovered from permafrost above the Arctic Circle in Sakha Republic , and that after being thawed, two of the nematodes revived and began moving and eating. One found in a Pleistocene squirrel burrow in the Duvanny Yar outcrop on the Kolyma River was believed to be about 32,000 years old, while the other, recovered in 2015 near the Alazeya River , was dated at approximately 30,000-40,000 years old. These nematodes were believed to be the oldest living multicellular organisms on Earth. [ 15 ] [ 16 ] In 2021, biologists reported the restoration of bdelloid rotifers frozen for 24,000 years in the Siberian permafrost . [ 17 ] [ 18 ] In 2023, it was reported that nematodes of the previously undescribed Panagrolaimus kolymaensis were revived after 46,000 years in cryptobiosis . [ 19 ]
Like bacterial spores, plant seeds are often capable of germinating after very long periods of metabolic inactivity. A seed from the previously extinct Judean date palm was revived and managed to sprout after nearly 2,000 years. Named " Methuselah ", it is currently growing at Kibbutz Ketura , Israel. [ 20 ] Similarly, the flowering plant Silene stenophylla was grown from frozen fruit found in an ancient squirrel's cache. The germinated plants bore viable seeds. The fruit was dated at 31,800 ± 300 years old. [ 21 ] In 1994, a seed from a sacred lotus ( Nelumbo nucifera ), dated at roughly 1,300 ± 270 years old, was successfully germinated. [ 22 ] [ 23 ] In 2024, a never-before-seen species of Commiphora was grown from a successfully germinated seed that is estimated to be 1,000 years old. [ 24 ]
During the 1990s, Raul Cano, a microbiologist at California Polytechnic State University, San Luis Obispo , US, reported reviving yeast trapped in amber for 25 million years, although doubts were raised as to its antiquity. [ 25 ] [ 26 ] [ citation needed ] Cano founded a brewery [ 27 ] and crafted an "amber ale" with a 45-million-year-old variant of Saccharomyces cerevisiae . [ 28 ]
Some endoliths have extremely long lives. In August 2013, researchers reported evidence of endoliths in the ocean floor, perhaps millions of years old, with a generation time of 10,000 years. [ 29 ] These are slowly metabolizing and not in a dormant state. Some Actinomycetota found in Siberia are estimated to be half a million years old. [ 30 ] [ 31 ] [ 32 ]
In July 2020, marine biologists reported that aerobic microorganisms (mainly), in " quasi-suspended animation ", were found in organically poor sediments , which had been dated by previous research using cobalt-based techniques to 4.3 to 101.5 million years old, 68.9 metres (226 feet) below the seafloor in the South Pacific Gyre (SPG) ("the deadest spot in the ocean"), and could be the longest-living life forms ever found, [ 33 ] [ 34 ] yet in October 2024, scientists reported aerobic microorganisms in a 2 billion years old rock drilled from 15 meters underground from a formation known as the Bushveld Igneous Complex in northeastern South Africa, but the age of the microorganisms is unknown. [ 35 ] [ 36 ]
As with all long-lived plant and fungal species, no individual part of a clonal colony is alive (in the sense of active metabolism ) for more than a very small fraction of the life of the entire colony. Some clonal colonies may be fully connected via their root systems , while most are not interconnected but are nonetheless genetically identical clones that populated an area through vegetative reproduction . Ages for clonal colonies are estimates, often based on current growth rates. [ 37 ]
Humans are among the longest living land mammals. [ 112 ]
These are single examples; for a broader view, see life expectancy (includes humans). | https://en.wikipedia.org/wiki/List_of_longest-living_organisms |
Below is a list of notable low-code development platforms . | https://en.wikipedia.org/wiki/List_of_low-code_development_platforms |
This is a list of notable electronic mailing list software, which facilitate the widespread distribution of email to many Internet users.
3.4.2 [ 2 ]
2025-03-26; 48 days ago [±]
Systems listed on a light purple background are no longer in active development. | https://en.wikipedia.org/wiki/List_of_mailing_list_software |
Mass migrations take place, or used to take place, by the following mammals : [ 1 ]
Africa:
North America:
North America and Eurasia:
Eurasia:
Of these migrations, those of the springbok, black wildebeest, blesbok, scimitar-horned oryx, and kulan have ceased. [ 2 ] | https://en.wikipedia.org/wiki/List_of_mammals_that_perform_mass_migrations |
Mass spectrometry software is used for data acquisition, analysis, or representation in mass spectrometry .
In protein mass spectrometry, tandem mass spectrometry (also known as MS/MS or MS 2 ) experiments are used for protein / peptide identification. Peptide identification algorithms fall into two broad classes: database search and de novo search. The former search takes place against a database containing all amino acid sequences assumed to be present in the analyzed sample. In contrast, the latter infers peptide sequences without knowledge of genomic data.
De novo peptide sequencing algorithms are, in general, based on the approach proposed in Bartels et al. (1990). [ 27 ]
It can be used for the calculation of: | https://en.wikipedia.org/wiki/List_of_mass_spectrometry_software |
Materials testing is used to assess product quality , functionality, safety , reliability and toxicity of both materials and electronic devices . Some applications of materials testing include defect detection, failure analysis , material development, basic materials science research, and the verification of material properties for application trials. This is a list of organizations and companies that publish materials testing standards or offer materials testing laboratory services.
These organizations create materials testing standards or conduct active research in the fields of materials analysis and reliability testing.
These organizations provide materials testing laboratory services. | https://en.wikipedia.org/wiki/List_of_materials-testing_resources |
This is a list of analysis methods used in materials science . Analysis methods are listed by their acronym, if one exists. | https://en.wikipedia.org/wiki/List_of_materials_analysis_methods |
A material property is an intensive property of a material , i.e., a physical property or chemical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another can be compared, thereby aiding in materials selection .
A property having a fixed value for a given material or substance is called material constant or constant of matter . [ 1 ] (Material constants should not be confused with physical constants , that have a universal character.)
A material property may also be a function of one or more independent variables , such as temperature. Materials properties often vary to some degree according to the direction in the material in which they are measured, a condition referred to as anisotropy . Materials properties that relate to different physical phenomena often behave linearly (or approximately so) in a given operating range [ further explanation needed ] . Modeling them as linear functions can significantly simplify the differential constitutive equations that are used to describe the property.
Equations describing relevant materials properties are often used to predict the attributes of a system.
The properties are measured by standardized test methods . Many such methods have been documented by their respective user communities and published through the Internet; see ASTM International . | https://en.wikipedia.org/wiki/List_of_materials_properties |
This is a list of scientific journals in materials science . | https://en.wikipedia.org/wiki/List_of_materials_science_journals |
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a general theorem, could perhaps be considered an "example"). The discussion page for list of mathematical topics has some comments on this. Eventually this page may have its own discussion page. This page links to itself in order that edits to this page will be included among related changes when the user clicks on that button.
The concrete example within the article titled Rao-Blackwell theorem is perhaps one of the best ways for a probabilist ignorant of statistical inference to get a quick impression of the flavor of that subject. | https://en.wikipedia.org/wiki/List_of_mathematical_examples |
This is a list of mathematical logic topics .
For traditional syllogistic logic, see the list of topics in logic . See also the list of computability and complexity topics for more theory of algorithms . | https://en.wikipedia.org/wiki/List_of_mathematical_logic_topics |
A list of articles with mathematical proofs : | https://en.wikipedia.org/wiki/List_of_mathematical_proofs |
This is a list of mathematical theories . | https://en.wikipedia.org/wiki/List_of_mathematical_theories |
This is a list of mathematical topics in quantum theory , by Wikipedia page. See also list of functional analysis topics , list of Lie group topics , list of quantum-mechanical systems with analytical solutions .
See list of string theory topics | https://en.wikipedia.org/wiki/List_of_mathematical_topics_in_quantum_theory |
This is a list of mathematical topics in relativity , by Wikipedia page. | https://en.wikipedia.org/wiki/List_of_mathematical_topics_in_relativity |
See also: List of reference tables | https://en.wikipedia.org/wiki/List_of_mathematics_reference_tables |
A measuring instrument is a device to measure a physical quantity . In the physical sciences , quality assurance , and engineering , measurement is the activity of obtaining and comparing physical quantities of real-world objects and events . Established standard objects and events are used as units , and the process of measurement gives a number relating the item under study and the referenced unit of measurement. Measuring instruments, and formal test methods which define the instrument's use, are the means by which these relations of numbers are obtained. All measuring instruments are subject to varying degrees of instrument error and measurement uncertainty .
These instruments may range from simple objects such as rulers and stopwatches to electron microscopes and particle accelerators . Virtual instrumentation is widely used in the development of modern measuring instruments.
In the past, a common time measuring instrument was the sundial . Today, the usual measuring instruments for time are clocks and watches . For highly accurate measurement of time an atomic clock is used. Stopwatches are also used to measure time in some sports.
Energy is measured by an energy meter. Examples of energy meters include:
An electricity meter measures energy directly in kilowatt-hours .
A gas meter measures energy indirectly by recording the volume of gas used. This figure can then be converted to a measure of energy by multiplying it by the calorific value of the gas.
A physical system that exchanges energy may be described by the amount of energy exchanged per time- interval , also called power or flux of energy.
For the ranges of power-values see: Orders of magnitude (power) .
Action describes energy summed up over the time a process lasts (time integral over energy). Its dimension is the same as that of an angular momentum .
For the ranges of length-values see: Orders of magnitude (length)
For the ranges of area-values see: Orders of magnitude (area)
If the mass density of a solid is known, weighing allows to calculate the volume.
For the ranges of volume-values see: Orders of magnitude (volume)
See also the section about navigation below.
This includes basic quantities found in classical - and continuum mechanics ; but strives to exclude temperature-related questions or quantities.
For the ranges of speed-values see: Orders of magnitude (speed)
For the ranges of mass-values see: Orders of magnitude (mass)
For the ranges of pressure-values see: Orders of magnitude (pressure)
For the value-ranges of angular velocity see: Orders of magnitude (angular velocity)
For the ranges of frequency see: Orders of magnitude (frequency)
Considerations related to electric charge dominate electricity and electronics .
Electrical charges interact via a field . That field is called electric field.If the charge doesn't move. If the charge moves, thus realizing an electric current, especially in an electrically neutral conductor, that field is called magnetic .
Electricity can be given a quality — a potential . And electricity has a substance-like property, the electric charge.
Energy (or power) in elementary electrodynamics is calculated by multiplying the potential by the amount of charge (or current) found at that potential: potential times charge (or current). (See Classical electromagnetism and Covariant formulation of classical electromagnetism )
For the ranges of charge values see: Orders of magnitude (charge)
See also the relevant section in the article about the magnetic field .
For the ranges of magnetic field see: Orders of magnitude (magnetic field)
Temperature -related considerations dominate thermodynamics. There are two distinct thermal properties: A thermal potential — the temperature. For example: A glowing coal has a different thermal quality than a non-glowing one.
And a substance-like property, — the entropy ; for example: One glowing coal won't heat a pot of water, but a hundred will.
Energy in thermodynamics is calculated by multiplying the thermal potential by the amount of entropy found at that potential: temperature times entropy.
Entropy can be created by friction but not annihilated.
See also Temperature measurement and Category:Thermometers . More technically related may be seen thermal analysis methods in materials science .
For the ranges of temperature-values see: Orders of magnitude (temperature)
This includes thermal mass or temperature coefficient of energy, reaction energy , heat flow , ...
Calorimeters are called passive if gauged to measure emerging energy carried by entropy, for example from chemical reactions. Calorimeters are called active or heated if they heat the sample, or reformulated: if they are gauged to fill the sample with a defined amount of entropy.
Entropy is accessible indirectly by measurement of energy and temperature.
Phase change calorimeter's energy value divided by absolute temperature give the entropy exchanged. Phase changes produce no entropy and therefore offer themselves as an entropy measurement concept. Thus entropy values occur indirectly by processing energy measurements at defined temperatures, without producing entropy.
The given sample is cooled down to (almost) absolute zero (for example by submerging the sample in liquid helium). At absolute zero temperature any sample is assumed to contain no entropy (see Third law of thermodynamics for further information). Then the following two active calorimeter types can be used to fill the sample with entropy until the desired temperature has been reached: (see also Thermodynamic databases for pure substances )
Processes transferring energy from a non-thermal carrier to heat as a carrier do produce entropy (Example: mechanical/electrical friction, established by Count Rumford ).
Either the produced entropy or heat are measured (calorimetry) or the transferred energy of the non-thermal carrier may be measured.
Entropy lowering its temperature—without losing energy—produces entropy (Example: Heat conduction in an isolated rod; "thermal friction").
Concerning a given sample, a proportionality factor relating temperature change and energy carried by heat. If the sample is a gas, then this coefficient depends significantly on being measured at constant volume or at constant pressure. (The terminology preference in the heading indicates that the classical use of heat bars it from having substance-like properties.)
The temperature coefficient of energy divided by a substance-like quantity ( amount of substance , mass , volume ) describing the sample. Usually calculated from measurements by a division or could be measured directly using a unit amount of that sample.
For the ranges of specific heat capacities see: Orders of magnitude (specific heat capacity)
See also Thermal analysis , Heat .
This includes mostly instruments which measure macroscopic properties of matter: In the fields of solid-state physics ; in condensed matter physics which considers solids, liquids, and in-betweens exhibiting for example viscoelastic behavior; and furthermore, in fluid mechanics , where liquids, gases , plasmas , and in-betweens like supercritical fluids are studied.
This refers to particle density of fluids and compact(ed) solids like crystals, in contrast to bulk density of grainy or porous solids.
For the ranges of density-values see: Orders of magnitude (density)
This section and the following sections include instruments from the wide field of Category:Materials science , materials science .
Such measurements also allow to access values of molecular dipoles .
For other methods see the section in the article about magnetic susceptibility .
See also Category:Electric and magnetic fields in matter
Phase conversions like changes of aggregate state , chemical reactions or nuclear reactions transmuting substances, from reactants into products , or diffusion through membranes have an overall energy balance. Especially at constant pressure and constant temperature, molar energy balances define the notion of a substance potential or chemical potential or molar Gibbs energy , which gives the energetic information about whether the process is possible or not - in a closed system .
Energy balances that include entropy consist of two parts: A balance that accounts for the changed entropy content of the substances, and another one that accounts for the energy freed or taken by that reaction itself, the Gibbs energy change. The sum of reaction energy and energy associated to the change of entropy content is also called enthalpy . Often the whole enthalpy is carried by entropy and thus measurable calorimetrically.
For standard conditions in chemical reactions either molar entropy content and molar Gibbs energy with respect to some chosen zero point are tabulated. Or molar entropy content and molar enthalpy with respect to some chosen zero are tabulated. (See Standard enthalpy change of formation and Standard molar entropy )
The substance potential of a redox reaction is usually determined electrochemically current-free using reversible cells .
Other values may be determined indirectly by calorimetry. Also by analyzing phase-diagrams.
(See also Spectroscopy and List of materials analysis methods .)
Microphones in general, sometimes their sensitivity is increased by the reflection- and concentration principle realized in acoustic mirrors .
(for lux meter , see the section about human senses and human body)
See also Category:Optical devices
The measure of the total power of light emitted.
Ionizing radiation includes rays of "particles" as well as rays of "waves". Especially X-rays and gamma rays transfer enough energy in non-thermal, (single-) collision processes to separate electron(s) from an atom.
This could include chemical substances , rays of any kind, elementary particles , and quasiparticles . Many measurement devices outside this section may be used or at least become part of an identification process.
For identification and content concerning chemical substances, see also Analytical chemistry , List of chemical analysis methods , and List of materials analysis methods .
Photometry is the measurement of light in terms of its perceived brightness to the human eye . Photometric quantities derive from analogous radiometric quantities by weighting the contribution of each wavelength by a luminosity function that models the eye's spectral sensitivity . For the ranges of possible values, see the orders of magnitude in: illuminance , luminance , and luminous flux .
Synthetic Aperture Radar (SAR) instruments measure radar brightness, Radar Cross Section (RCS) , which is a function of the reflectivity and moisture of imaged objects at wavelengths which are too long to be perceived by the human eye. Black pixels mean no reflectivity (e.g. water surfaces), white pixels mean high reflectivity (e.g. urban areas). Colored pixels can be obtained by combining three gray-scaled images which usually interpret the polarization of electromagnetic waves. The combination R-G-B = HH-HV-VV combines radar images of waves sent and received horizontally (HH), sent horizontally and received vertically (HV) and sent and received vertically (VV). The calibration of such instruments is done by imaging objects (calibration targets) whose radar brightness is known.
Blood-related parameters are listed in a blood test .
See also: Category:Physiological instruments and Category:Medical testing equipment .
See also Category:Meteorological instrumentation and equipment .
See also Category:Navigational equipment and Category:Navigation .
See also Surveying instruments .
See also Astronomical instruments and Category:Astronomical observatories .
Some instruments, such as telescopes and sea navigation instruments, have had military applications for many centuries. However, the role of instruments in military affairs rose exponentially with the development of technology via applied science, which began in the mid-19th century and has continued through the present day. Military instruments as a class draw on most of the categories of instrument described throughout this article, such as navigation , astronomy , optics, and imaging, and the kinetics of moving objects. Common abstract themes that unite military instruments are seeing into the distance, seeing in the dark, knowing an object's geographic location, and knowing and controlling a moving object's path and destination. Special features of these instruments may include ease of use , speed , reliability , and accuracy .
The alternate spelling " -metre " is never used when referring to a measuring device. | https://en.wikipedia.org/wiki/List_of_measuring_instruments |
This is a list of mechanical engineers , noted for their contribution to the field of mechanical engineering.
See also List of engineers for links to other engineering professions. | https://en.wikipedia.org/wiki/List_of_mechanical_engineers |
This is a list of notable journals related to medical and health informatics . | https://en.wikipedia.org/wiki/List_of_medical_and_health_informatics_journals |
A list of drugs or therapeutic agents administered via inhalation . | https://en.wikipedia.org/wiki/List_of_medical_inhalants |
In medicinal chemistry , the term "contamination" is used to describe harmful intrusions, such as the presence of toxins or pathogens in pharmaceutical drugs . [ 1 ]
The following list encompasses notable medicine contamination and adulteration incidents. | https://en.wikipedia.org/wiki/List_of_medicine_contamination_incidents |
This list identifies various pieces of body armour worn from the medieval to early modern period in the Western world , mostly plate but some mail armour , arranged by the part of body that is protected and roughly by date. It does not identify fastening components or various appendages such as lance rests or plumeholders, or clothing such as tabards or surcoats , which were often worn over a harness.
There are a variety of alternative names and spellings (such as cowter or couter ; bassinet , bascinet or basinet ; and besagew or besague ) which often reflect a word introduced from French. Generally, the English spelling has been preferred (including mail instead of the lately used maille or the inauthentic term chainmail ). The part of armour on the hand is called the gauntlet , which is based on a French word.
The following components of Japanese armour roughly match the position and function of certain components of occidental armour: | https://en.wikipedia.org/wiki/List_of_medieval_armour_components |
This is a list of megaprojects , which may be defined as projects that cost more than US$1 billion and attract a large amount of public attention because of their effects on communities , the natural and built environment , and budgets ; or more simply "initiatives that are physical, very expensive, and public". [ 1 ]
Megaprojects can be found in many fields of human endeavor, including bridges, tunnels, highways, railways, hospitals, airports, seaports, power plants, dams, wastewater projects, Special Economic Zones (SEZ), oil and natural gas extraction projects, public buildings, information technology systems, aerospace projects, and military weapons. The following lists are far from comprehensive.
While most megaprojects are planned and undertaken with careful forethought, some are undertaken out of necessity after a natural disaster occurs. There have also been a few human-made disasters . Major restoration was necessary after the destruction caused by World War I and II , some of which was paid for by German reparations for World War I and for World War II .
Every Olympic Games and FIFA World Cup in the latter part of the twentieth century and entering into the 21st century has cost more than $1 billion in arenas, hotels etc., usually several billions. The Olympic Games are considered to be the world's foremost international sporting event with over 200 nations participating. Sports-related costs for the Summer Games since 1960 is on average $5.2 billion (USD) and for the Winter Games $393.1 million dollars. The highest recorded total cost was the 2014 Sochi Winter Olympics , costing approximately US$55 billion. The International Olympic Committee requires a minimum of 40,000 hotel rooms available for visiting spectators and an Olympic Village that is able to house 15,000 athletes, referees, and officials.
Ground transportation systems like roads, tunnels, bridges, terminals, railways, and mass transit systems are often megaprojects. Numerous large airports and terminals used for airborne passenger and cargo transportation are built as megaprojects.
[ 118 ] [ 119 ] [ 120 ]
CBI Rate equivalent $5.2 billion USD
[ 224 ] [ 225 ]
Ports, waterways, canals, and locks for ships carrying passengers and cargo are built as megaprojects. | https://en.wikipedia.org/wiki/List_of_megaprojects |
This is a list of megaprojects of Bangladesh , i.e. projects characterized by large investment commitment, vast complexity (especially in organizational terms), and long-lasting impact on the economy , the environment , and society. This is a dynamic list and may require constant updates. The Finance Minister of Bangladesh has recently unveiled an extensive roster of ambitious mega projects encompassing various sectors. These projects primarily focus on the construction of hospitals, schools, colleges, and other essential infrastructures. Consequently, this development surge is expected to generate a substantial demand for cement within the country. [ 1 ] | https://en.wikipedia.org/wiki/List_of_megaprojects_in_Bangladesh |
This is a list of megaprojects in India . " Megaprojects are temporary endeavours (i.e., projects) characterized by large investment commitment, vast complexity (especially in organisational terms), and long-lasting impact on the economy, the environment, and society". [ 2 ]
Source: [ 74 ]
Alphabetical list by the state and union territories of India.
Ropeways in Arunachal Pradesh are:
Ropeways in Assam are:
Ropeways in Gujarat are:
Ropeways in Haryana are:
Ropeways in Himachal Pradesh are:
Ropeways in Jammu and Kashmir are:
Ropeways in Jharkhand are:
Ropeways in Madhya Pradesh are:
Ropeways in Odisha are:
Ropeways in Rajasthan are:
Ropeways in Sikkim are:
Ropeways in Uttarakhand are:
Ropeways in Uttar Pradesh are:
Ropeways in West Bengal are:
Source: [ 128 ]
There are also private ports under construction/reopening.
Astrosat is a multi-wavelength astronomy mission on an IRS-class satellite into a near-Earth, equatorial orbit. The five instruments on board cover the visible (320–530 nm), near UV (180–300 nm), far UV (130–180 nm), soft X-ray (0.3–8 keV and 2–10 keV) and hard X-ray (3–80 keV and 10–150 keV) regions of the electromagnetic spectrum. | https://en.wikipedia.org/wiki/List_of_megaprojects_in_India |
In chemistry, a precursor is a compound that contributes in a chemical reaction and produces another compound, or a chemical substance that gives rise to another more significant chemical product. Since several years metal-organic compounds are widely used as molecular precursors for the chemical vapor deposition process (MOCVD). The success of this method is mainly due to its adaptability and to the increasing interest for the low temperature deposition processes. Correlatively, the increasing demand of various thin film materials for new industrial applications is also a significant reason for the rapid development of MOCVD. Certainly, a wide variety of materials which could not be deposited by the conventional halide CVD process, because halide reactive do not exist or are not volatile, can now be grown by MOCVD. This includes metals and different multi-component materials such as semiconductor and intermetallic compounds as well as carbides, nitrides, oxides, borides, silicides and chalcogenides. Further significant advantages of MOCVD over physical processes are a capability for large scale production, an easier automation, a good conformal coverage, the selectivity and the ability to produce metastable materials. [ 1 ]
Thus, much effort has been aimed at the synthesis of new molecular precursors. A productive overview is provided by several exceptional reviews covering fields of MOCVD such as, for instance, epitaxial growth of semiconductor compounds, [ 2 ] [ 3 ] [ 4 ] and low temperature deposition of metals. [ 5 ] [ 6 ] An overview of metal-organic compounds used for the MOCVD growth of different kind of materials is reported in the following reviews. [ 7 ] [ 8 ] [ 9 ] This is a list of prominent precursor complexes synthesized thus far with suited properties to be utilized for MOCVD processes.
[ 2 ] https://www.sigmaaldrich.com/catalog/product/aldrich/156671?lang=de®ion=DE [ 3 ] Labbow, R., Michalik, D., Reiß, F., Schulz, A. and Villinger, A., 2016. Isolation of Labile Pseudohalogen NSO Species. Angewandte Chemie International Edition, 55(27), pp. 7680–7684.
2774(2) A˚ 3, Z = 4, Dc = 1.478 g cm−3
conditions results in a solid residue of ≈7% what shows that evaporation and decomposition of this compound goes simultaneously (full decomposition of Nb(thd)4 to Nb2O5 should leave 16.1% residue). [ 1 ]
2007, 515, 4975. [ 3 ] Sigma-Aldritch | https://en.wikipedia.org/wiki/List_of_metal-organic_chemical_vapour_deposition_precursors |
A meteorite mineral is a mineral found chiefly or exclusively within meteorites or meteorite-derived material. [ citation needed ] This is a list of those minerals, excluding minerals also commonly found in terrestrial rocks. As of 1997 there were approximately 295 mineral species which have been identified in meteorites. [ 1 ]
[] indicates repeating units | https://en.wikipedia.org/wiki/List_of_meteorite_minerals |
This is the list of healthy vaginal microbiota (VMB), which is defined as the group of species and genera that generally are found to have lack of symptoms, absence of various infections, and result in good pregnancy outcomes. [ 1 ] VMB is dominated mainly by Lactobacillus species. This is the list of organisms that are found in the lower reproductive tract of sexually mature women who are not immunocompromised . A partial description of pathogens that can be found in the lower and upper reproductive tract of women can be found in the article sexually transmitted infection . The organisms listed below are capable of causing illness if for some reason there is a change in vaginal pH or a change in the ratio of one organism to another. For example, Candida is a normal inhabitant of a healthy reproductive tract but an overgrowth of this organism can cause candidiasis . [ 2 ] [ 3 ] [ 4 ]
This is the list of the normal flora that are found in the lower reproductive tract of sexually mature women who exhibit no symptoms of illness and who are not immunocompromised . Lactobacilli predominate. [ 4 ] [ 5 ] [ 6 ] These organisms protect against infection. Vaginal microbiota composition may have a genetic component . [ 3 ]
These bacteria may be detected as transients or are marginally discernable with PCR techniques. They are also opportunistic pathogens, and their overgrowth is considered an infection though symptoms and signs may be absent.
While the vaginal microbiota is populated predominantly by Lactobacillus spp. in 71% of women, 29% of asymptomatic, healthy women possess a microbiota essentially lacking in Lactobacillus and instead the following groups have been isolated from this population. This microbiota is affiliated with ethnicity:
Candida albicans and other spp. [ 2 ]
Pre-pubescent girls, women in menarche , and postmenopausal women have lower populations of Lactobacillus spp. in proportion to the other species. Hormone replacement therapy in postmenopausal women restores the microbiota to that of a reproductive-aged woman. The microbiota populations change in response to the menstrual cycle. Pregnancy alters the microbiota, with a reduction in species/genus diversity. [ 3 ] Overgrowth of Candida albicans or other Candida ( yeast infections ) sometimes occurs after antibiotic therapy. [ 2 ] Bacterial vaginosis results in altered populations and ratios of the normal microbiota. [ 10 ] [ 3 ] [ 11 ] There has been no link demonstrated between taking oral probiotics and maintaining normal microbiota populations of lactobacilli. [ 4 ] | https://en.wikipedia.org/wiki/List_of_microbiota_species_of_the_lower_reproductive_tract_of_women |
Sourdough is a mixture of flour and water inhabited by a symbiosis of Lactic acid bacteria and yeasts . It is used in baking to leaven and acidify bread. | https://en.wikipedia.org/wiki/List_of_microorganisms_found_in_sourdough |
The survival of some microorganisms exposed to outer space has been studied using both simulated facilities and low Earth orbit exposures. Bacteria were some of the first organisms investigated, when in 1960 a Russian satellite carried Escherichia coli , Staphylococcus , and Enterobacter aerogenes into orbit. [ 1 ] Many kinds of microorganisms have been selected for exposure experiments since, as listed in the table below.
Experiments of the adaption of microbes in space have yielded unpredictable results. While sometimes the microorganism may weaken, they can also increase in their disease-causing potency. [ 1 ]
It is possible to classify these microorganisms into two groups, the human-borne and the extremophiles . Studying the human-borne microorganisms is significant for human welfare and future crewed missions in space , whilst the extremophiles are vital for studying the physiological requirements of survival in space. [ 2 ] NASA has pointed out that normal adults have ten times as many microbial cells as human cells in their bodies. [ 3 ] They are also nearly everywhere in the environment and, although normally invisible, can form slimy biofilms . [ 3 ]
Extremophiles have adapted to live in some of the most extreme environments on Earth. This includes hypersaline lakes , arid regions , deep sea , acidic sites, cold and dry polar regions and permafrost . [ 4 ] The existence of extremophiles has led to the speculation that microorganisms could survive the harsh conditions of extraterrestrial environments and be used as model organisms to understand the fate of biological systems in these environments. The focus of many experiments has been to investigate the possible survival of organisms inside rocks ( lithopanspermia ), [ 2 ] or their survival on Mars for understanding the likelihood of past or present life on that planet. [ 2 ] Because of their ubiquity and resistance to spacecraft decontamination, bacterial spores are considered likely potential forward contaminants on robotic missions to Mars . Measuring the resistance of such organisms to space conditions can be applied to develop adequate decontamination procedures. [ 5 ]
Research and testing of microorganisms in outer space could eventually be applied for directed panspermia or terraforming . | https://en.wikipedia.org/wiki/List_of_microorganisms_tested_in_outer_space |
This is a list of software systems that are used for visualizing microscopy data.
For each software system, the table below indicates which type of data can be displayed: EM = Electron microscopy ; MG = Molecular graphics ; Optical = Optical microscopy . | https://en.wikipedia.org/wiki/List_of_microscopy_visualization_systems |
Mineral tests are simple physical and chemical methods of testing samples, which can help to identify the mineral type. [ 1 ] This approach is used widely in mineralogy , ore geology and general geological mapping. [ 2 ]
The following tests are some examples of those that are used on hand specimens, or on field samples, or on thin sections with the aid of a polarizing microscope. | https://en.wikipedia.org/wiki/List_of_mineral_tests |
This is a list of minor-planet discoverers credited by the Minor Planet Center with the discovery of one or several minor planets (such as near-Earth and main-belt asteroids , Jupiter trojans and distant objects ). [ 1 ] As of January 2022 [update] , the discovery of 612,011 numbered minor planets are credited to 1,141 astronomers and 253 observatories , telescopes or surveys (see § Discovering dedicated institutions ) .
On how a discovery is made, see observations of small Solar System bodies . For a description of the tables below, see § Notes .
The discovery table consist of the following fields: | https://en.wikipedia.org/wiki/List_of_minor_planet_discoverers |
The following is a list of numbered minor planets (essentially the same as asteroids ) in ascending numerical order. Minor planets are defined as small bodies in the Solar System , including asteroids , distant objects , and dwarf planets , but not including comets. The catalog consists of hundreds of pages, each containing 1,000 minor planets. Every year, the Minor Planet Center , which operates on behalf of the International Astronomical Union , publishes thousands of newly numbered minor planets in its Minor Planet Circulars (see index ) . [ 1 ] [ 2 ] As of March 2025 [update] , there are 793,066 numbered minor planets (secured discoveries) out of a total of 1,424,223 observed small Solar System bodies, with the remainder being unnumbered minor planets and comets. [ 3 ]
The catalog's first object is 1 Ceres , discovered by Giuseppe Piazzi in 1801, while its best-known entry is Pluto , listed as 134340 Pluto . The vast majority (97.3%) of minor planets are asteroids from the asteroid belt (the catalog uses a color code to indicate a body's dynamical classification ). There are more than a thousand different minor-planet discoverers observing from a growing list of registered observatories . In terms of numbers, the most prolific discoverers are Spacewatch , LINEAR , MLS , NEAT and CSS . There are also 25,208 named minor planets mostly after people, places and figures from mythology and fiction , [ 4 ] which account for only 3.3% of all numbered catalog entries. (4596) 1981 QB and 773906 Larisaromanova are currently the lowest-numbered unnamed and highest-numbered named minor planets, respectively. [ 1 ] [ 4 ]
It is expected that the upcoming survey by the Vera C. Rubin Observatory will discover another 5 million minor planets during the next ten years—almost a tenfold increase from current numbers. [ 5 ] While all main-belt asteroids with a diameter above 10 km (6.2 mi) have already been discovered, there might be as many as 10 trillion 1 m (3.3 ft)-sized asteroids or larger out to the orbit of Jupiter; and more than a trillion minor planets in the Kuiper belt . [ 5 ] [ 6 ] For minor planets grouped by a particular aspect or property, see § Specific lists .
The list of minor planets consists of more than 700 partial lists, each containing 1000 minor planets grouped into 10 tables. The data is sourced from the Minor Planet Center (MPC) and expanded with data from the JPL SBDB (mean-diameter), Johnston's archive (sub-classification) and others (see detailed field descriptions below) . For an overview of all existing partial lists, see § Main index .
The information given for a minor planet includes a permanent and provisional designation ( § Designation ) , a citation that links to the meanings of minor planet names (only if named), the discovery date, location, and credited discoverers ( § Discovery and § Discoverers ) , a category with a more refined classification than the principal grouping represented by the background color ( § Category ) , a mean-diameter, sourced from JPL's SBDB or otherwise calculated estimates in italics ( § Diameter ) , and a reference (Ref) to the corresponding pages at MPC and JPL SBDB.
The MPC may credit one or several astronomers, a survey or similar program, or even the observatory site with the discovery. In the first column of the table, an existing stand-alone article is linked in boldface, while (self-)redirects are never linked. Discoverers, discovery site and category are only linked if they differ from the preceding catalog entry.
The example above shows five catalog entries from one of the partial lists . All five asteroids were discovered at Palomar Observatory by the Palomar–Leiden survey (PLS). The MPC directly credits the survey's principal investigators, that is, the astronomers Cornelis van Houten , Ingrid van Houten-Groeneveld and Tom Gehrels . (This is the only instance where the list of minor planets diverges from the Discovery Circumstances in the official MPC list. [ 7 ] ) 189004 Capys , discovered on 16 October 1977, is the only named minor planet among these five. Its background color indicates that it is a Jupiter trojan (from the Trojan camp at Jupiter's L 5 ), estimated to be approximately 12 kilometers in diameter. All other objects are smaller asteroids from the inner (white), central (light-grey) and outer regions (dark grey) of the asteroid belt . The provisional designation for all objects is an uncommon survey designation .
After discovery, minor planets generally receive a provisional designation , e.g. 1989 AC , then a leading sequential number in parentheses, e.g. (4179) 1989 AC , turning it into a permanent designation (numbered minor planet). Optionally, a name can be given, replacing the provisional part of the designation, e.g. 4179 Toutatis . (On Wikipedia, named minor planets also drop their parentheses.)
In modern times, a minor planet receives a sequential number only after it has been observed several times over at least 4 oppositions. [ 8 ] Minor planets whose orbits are not (yet) precisely known are known by their provisional designation. This rule was not necessarily followed in earlier times, and some bodies received a number but subsequently became lost minor planets . The 2000 recovery of 719 Albert , which had been lost for nearly 89 years, eliminated the last numbered lost asteroid. [ 9 ] Only after a number is assigned is the minor planet eligible to receive a name. Usually the discoverer has up to 10 years to pick a name; many minor planets now remain unnamed. Especially towards the end of the twentieth century, large-scale automated asteroid discovery programs such as LINEAR have increased the pace of discoveries so much that the vast majority of minor planets will most likely never receive names.
For these reasons, the sequence of numbers only approximately matches the timeline of discovery. In extreme cases, such as lost minor planets, there may be a considerable mismatch: for instance the high-numbered 69230 Hermes was originally discovered in 1937, but it was lost until 2003. Only after it was rediscovered could its orbit be established and a number assigned.
The MPC credits more than 1,000 professional and amateur astronomers as discoverers of minor planets . Many of them have discovered only a few minor planets or even just co-discovered a single one. Moreover, a discoverer does not need to be a human being. There are about 300 programs, surveys and observatories credited as discoverers . Among these, a small group of U.S. programs and surveys actually account for most of all discoveries made so far (see pie chart) . As the total of numbered minor planets is growing by the tens of thousands every year, all statistical figures are constantly changing. In contrast to the Top 10 discoverers displayed in this articles, the MPC summarizes the total of discoveries somewhat differently, that is by a distinct group of discoverers. For example, bodies discovered in the Palomar–Leiden Survey are directly credited to the program's principal investigators.
Observatories, telescopes and surveys that report astrometric observations of small Solar System bodies to the Minor Planet Center receive a numeric or alphanumeric MPC code such as 675 for the Palomar Observatory , or G96 for the Mount Lemmon Survey . On numbering, the MPC may directly credit such an observatory or program as the discoverer of an object, rather than one or several astronomers.
In this catalog, minor planets are classified into one of 8 principal orbital groups and highlighted with a distinct color. These are:
The vast majority of minor planets are evenly distributed between the inner-, central and outer parts of the asteroid belt , which are separated by the two Kirkwood gaps at 2.5 and 2.82 AU . Nearly 97.5% of all minor planets are main-belt asteroids (MBA), while Jupiter trojans , Mars-crossing and near-Earth asteroids each account for less than 1% of the overall population. Only a small number of distant minor planets , that is the centaurs and trans-Neptunian objects , have been numbered so far. In the partial lists, table column "category" further refines this principal grouping:
If available, a minor planet's mean diameter in meters (m) or kilometers (km) is taken from the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer , which the Small-Body Database has also adopted. [ 21 ] Mean diameters are rounded to two significant figures if smaller than 100 kilometers. Estimates are in italics and calculated from a magnitude-to-diameter conversion, using an assumed albedo derived from the body's orbital parameters or, if available, from a family -specific mean albedo (also see asteroid family table ) . [ e ]
This is an overview of all existing partial lists of numbered minor planets ( LoMP ). Each table stands for 100,000 minor planets, each cell for a specific partial list of 1,000 sequentially numbered bodies. The data is sourced from the Minor Planet Center . [ 1 ] For an introduction, see § top .
The following are lists of minor planets by physical properties, orbital properties, or discovery circumstances:
Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Local Hole → Observable universe → Universe Each arrow ( → ) may be read as "within" or "part of". | https://en.wikipedia.org/wiki/List_of_minor_planets |
Chemical elements that have been mistakenly "discovered". Further investigation showed that their discovery was either mistaken, that they have been mistaken from an already-known element, or mixture of two elements, or that they indicated a failing in theory where a new element had been assumed rather than some previously unknown behaviour. [ i ] | https://en.wikipedia.org/wiki/List_of_misidentified_chemical_elements |
As of 2024, the United States , the Soviet Union , Japan , and the European Space Agency have conducted missions to comets .
Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Local Hole → Observable universe → Universe Each arrow ( → ) may be read as "within" or "part of". | https://en.wikipedia.org/wiki/List_of_missions_to_comets |
This list of mobile app distribution platforms includes digital distribution platforms , or marketplace ' app stores ', intended to provide mobile applications, aka 'apps' to mobile devices . For information on each mobile platform and its market share, see the mobile operating system and smartphone articles. A comparison of the development capabilities of each mobile platform can be found in the article on mobile app development . For cross-platform development, see the mobile development framework. The mobile app article contains other general information.
These application marketplaces, or 'm' are native to the major mobile operating systems. Anyway, the relative store APK can often be installed in other compatible systems without rooting a device, as it happens for Huawei AppGallery and stock Android.
There are 17 native mobile app distribution platforms currently on this list.
(1M iPad apps) (Mar 2016) [ 5 ]
[ 19 ]
HarmonyOS SDK , DevEco Studio
Third-party platforms are software distribution platforms which are used as alternatives to operating system native distribution platforms. Independent operating systems are software collections that use their own software distribution, customised user interface (UI), software development kit (SDK) and application programming interface (API) (except billing API which is related only to the application store).
There are 17 third-party mobile app distribution platforms currently on this list. | https://en.wikipedia.org/wiki/List_of_mobile_app_distribution_platforms |
This is a list of mobile device management software.
These are the discontinued Mobile Device Management solutions: | https://en.wikipedia.org/wiki/List_of_mobile_device_management_software |
A mobile network operator , also known as a wireless service provider, wireless carrier, cellular company, or mobile network carrier is a provider of wireless communication services.
The main mobile network operators in Europe are listed below.
Albania as per has 3.66 million subscribers, of whom 2.49 million are active users (101% penetration rate) (Q1 2021).
Active users are considered those who have communicated in the last three months. [ 1 ]
The regulatory authority for telecommunication in Albania is the AKEP .
In 2022 4iG group, owning ONE Telecommunications, acquired a majority stake of ALBtelecom Mobile , 80.27%, [ 2 ] to a network merger in 2023.
LTE , LTE-A VoLTE
3400/3500 MHz 5G NR
3700 MHz/3800 MHz 5G NR
Andorra has 88,109 mobile subscribers [ 6 ] or about 113.63% mobile penetration.
Armenia has 3.5 million subscribers in total, and a 120% penetration rate. [ 9 ]
Austria has 13.0 million assigned numbers (i.e. 2.0 2G, 10.8 3G and 0.1 4G SIM cards), or a 151.0% penetration rate (Q4 2014). [ 11 ]
The regulatory authority for telecommunication in Austria is the Austrian Regulatory Authority for Broadcasting and Telecommunications (RTR).
( roams on 3 's UMTS network where no UMTS )
800/900/1800/2100/2600 MHz LTE , LTE-A VoLTE , VoWiFi 700/3500 MHz 5G NR
In December 2005, Azerbaijan had 2 million subscribers in total, a 25% penetration rate. [ citation needed ] In 2014, Azerbaijan had over 10 million subscribers in total, or a 130% penetration rate. [ citation needed ]
Belarus has 12.0 million subscribers in total, or a 126% penetration rate in Q4 of 2020.
The regulatory authority for telecommunication in Belarus is the Ministry of Communications and Informatization.
Belgium has 13.89 million subscribers in total, or a 124% penetration rate [ 19 ] (Q4 2014).
The regulatory authority for telecommunication in Belgium is the Belgian Institute for Postal Services and Telecommunications (BIPT).
In December 2022, Bosnia and Herzegovina had 3.811 million subscribers in total, [ 25 ] or a 115% penetration rate.
The regulatory authority for telecommunication in Bosnia and Herzegovina is the Communications Regulatory Agency (Regulatorna agencija za komunikacije, RAK). [ 26 ]
(formerly GSM-BIH )
VoLTE , ViLTE , eSIM (postpaid only)
5G NR (in development)
(formerly MOBI'S)
VoLTE , ViLTE , eSIM (postpaid only)
(formerly HTmobile)
VoLTE , ViLTE , eSIM
5G NR (in development)
Hrvatski Telekom (39.10%), Hrvatska pošta (5.23%), free float (5.27%)
(MVNO of ERONET )
VoLTE , ViLTE , eSIM
Hrvatski Telekom (39.10%, Hrvatska pošta (5.23%), free float (5.27%)
(MVNO of m:tel )
eSIM
(MVNO of m:tel )
Bulgaria has 8 014 473 subscribers in total, or a 124.3% penetration rate according to the CRC annual report for 2023. [ 27 ]
The regulatory authority for Telecommunication in Bulgaria is the Communications Regulation Commission (CRC).
(in millions)
Croatia has 4,404,652 subscribers in total, or a 102.8% penetration rate. (Q4 2019) [ 29 ]
The regulatory authority for telecommunication in Croatia is the Hrvatska agencija za poštu i elektronicke komunikacije (website available in Croatian and English language).
700/3400-3800 MHz - 5G NR eSIM (postpaid only)
Cyprus has 1,392,480 subscribers in total, or a 151.7% penetration rate (excludes Northern Cyprus) (Q4 2022). [ 32 ]
The regulatory authority for telecommunication in Cyprus (excluding Northern Cyprus) is OCECPR (Office of the Commissioner of Electronic Communications and Postal Regulation).
The Czech Republic has 16.121 million subscribers in total, or a 151% penetration rate (December 2019). [ 39 ]
Denmark has 8.208 million subscribers in total, or a 146% penetration rate [ 42 ] (Q1 2014)
In 2011, Denmark liquidated IT- og Telestyrelsen , it's telecommunications regulator. [ 43 ] [ 44 ]
Former regulator's tasks are divided among four institutions: [ 45 ]
(shares network with Telenor)
(shares network with Norlys)
Estonia has 2.524 million subscribers in total, or a 188% penetration rate [ 52 ] (December 2008).
(formerly EMT )
3G (UMTS, HSPA) has been shut down in 2023
(formerly Q-GSM )
700/3500 MHz - 5G NR
The Faroe Islands have 61,388 subscribers, or a 126% penetration rate (population 48,652) [ 56 ] (2020).
Finland has 7.700 million subscribers in total, or a 144.59% penetration rate [ 27 ] (December 2009).
France has 75.5 million subscribers in total, or a 115.2% penetration rate (September 2015). [ 57 ]
The regulatory authority for telecommunication in France is ARCEP .
As of November 2024, Georgia has 5,623,128 subscribers in total.
The regulatory authority for telecommunication in Georgia is the Georgian National Communications Commission . [ 63 ] [ 64 ]
5G is on FDD 700 MHz (N28) with a bandwidth of 20 MHz (2x10MHz), FDD 2600 MHz (N7) with a bandwidth of 60 MHz (2x30MHz) and TDD 3500 MHz (N78) with a bandwidth of 100 MHz. Magticom currently has the biggest 5G coverage in the country. [ 65 ]
5G –2100 MHz (Only in central Tbilisi from Freedom Square to Bagebi). Silknet has not participated in any of the 5G license auctions announced by the GNCC and has chosen to instead use its existing neutral license for 2100 MHz. Silknet currently remains the only MNO in Georgia without 5G-specific licenses and has the smallest 5G coverage.
5G – Currently in skiing resorts Bakuriani and Gudauri, seaside resorts Batumi, Gonio, Kvariati, Shekvetili, Kobuleti, as well as some of Tbilisi's neighbourhoods, such as Didube and Didi Dighomi. There is also coverage in Zugdidi. 5G is on 10 MHz (2X5 MHz) frequency resource, within the Uplink 703 - 708 MHz and Downlink 758 - 763 MHz resources; 50 MHz frequency resource within the 3550-3600 MHz resource. Cellfie also owns licenses for 2100 MHz and 2600 MHz.
Germany has 114.1 million subscribers in total, or a 140% penetration rate [ 27 ] (December 2011).
The regulatory authority for telecommunication in Germany is the Bundesnetzagentur (BNetzA) .
Gibraltar , the British overseas territory, has 0.028 million subscribers in total, or a 92.12% penetration rate [ 27 ] (December 2009).
In 2022, Greece had 11.326 million subscribers in total, or a 109% penetration rate. [ 2 ] The regulatory authority for telecommunications in Greece is the Hellenic Telecommunications and Post Commission (EETT) .
The British Crown dependency Guernsey has 0.055 million subscribers in total, or a 95% penetration rate [ citation needed ] (December 2005).
LTE
LTE
Hungary has 11.8 million subscribers in total [ 71 ] (December 2017).
The regulatory authority for telecommunication in Hungary is NMHH – Nemzeti Média-, és Hírközlési Hatóság.
(LTE 800 MHz is in cooperating with Yettel) 700/2100 MHz 5G NR (DSS)
(LTE 800 MHz is in cooperating with Magyar Telekom) 3500 MHz 5G NR/5G SA
• Includes the previous UPC Hungary and DIGI Mobile and Line 21 networks. || GSM -900/1800 MHz ( GPRS , EDGE ) 700/800/900/1800/2100/2600 MHz LTE , LTE-A VoLTE , VoWiFi 700 MHz 5G NR (DSS)
*900 MHz Hungarian 3G services have been suspended since July 2022.
Iceland has 0.470 million subscribers in total, or a 129.19% penetration rate [ 27 ] (July 2019).
VoLTE
As the end of March 2022 Ireland had 8.117 million mobile subscribers in total, representing a 158.4% penetration rate.
If mobile broadband and M2M subscriptions are excluded, the total number of mobile subscribers was 5.414 million, representing a 105.6% penetration rate. [ 75 ]
The regulatory authority for telecommunication in Ireland is the Commission for Communications Regulation (ComReg).
* 3G Network has been fully shutdown in 2024
The British Crown dependency Isle of Man has an unknown number of subscribers in total and an unknown percentage penetration rate.
800/1800 MHz LTE , LTE-A
As of March 2022, Italy has 106.5 million active lines in total, or a 174% penetration rate. [ 77 ] The country's telecom regulator is AGCOM .
In 2016 3 Italy and Wind agreed to complete a merger that was approved by European and national authorities, and since March 2020 all consumer and business offers are sold under the new brand Wind Tre . [ 78 ]
A new operator, Iliad entered the Italian market in May 2018 as a consequence of this merger. [ 79 ]
In 2024 Swisscom acquired Vodafone Italy from Vodafone Group with the aim of merging it with its subsidiary Fastweb . [ 80 ]
(formerly SIP )
(formerly 3 Italy and Wind )
(formerly Omnitel)
LTE
LTE
Kosovo has 1.88 million subscribers in total, or a 103.47% penetration rate [ 83 ] (June 2018). As of February 2023, Vala and Ipko have been awarded with 5G licenses and are currently under deployment. [ 84 ]
800/3600 MHz 5G NR
800/3600 MHz 5G NR
Latvia has 2.243 million subscribers in total, or a 99.72% penetration rate [ 27 ] (December 2009).
VoLTE
Liechtenstein has 0.039 million subscribers in total, or a 105% penetration rate [ 27 ] (April 2015).
The Liechtenstein mobile phone system is attached to Switzerland, and customers of these three providers can roam on Swiss networks without additional fees.
Lithuania has 4.49 million subscribers in total, or a 161% penetration rate (Q4 2023). [ 90 ]
Each of the three largest network operators have flanker brands – Pildyk (Tele2), Ežys (Telia) and Labas (Bite).
The regulator is Ryšių Reguliavimo Tarnyba (RRT).
700 MHz, 3500 MHz - 5G NR
700 MHz, 3500 MHz - 5G NR
2300 MHz TDD, 2600 MHz TDD - 5G NR
Luxembourg has 719,000 subscribers in total, or a 148% penetration rate [ 27 ] (December 2009).
Malta has 0.702 million subscribers in total, or a 130.19% penetration rate [ 91 ] (June 2023).
Moldova has 4.263 million subscribers in total, or a 120% penetration rate [ 93 ] (2012).
The country's telecommunications regulator is ANRCETI.
Monaco has 0.023 million subscribers on the Monaco Telecom network, or a 70.1% penetration rate [ 27 ] (December 2009).
The French networks are also widely available in Monaco, but they do not disclose subscriber figures for Monaco.
Montenegro has 1,097,574 subscribers in total, or a 177.02% penetration rate (October 2013). [ 98 ]
The regulatory authority for telecommunication in Montenegro is (Agencija za elektronske komunikacije i poštansku djelatnost).
The Netherlands has 22.12 million subscribers in total, or a 125.7% penetration rate [ 100 ] (Q1 2023).
The regulatory authorities for telecommunication in the Netherlands are the Netherlands Authority for Consumers and Markets (ACM: Autoriteit Consument & Markt) and the Dutch Authority for Digital Infrastructure (RDI: Rijksdienst Digitale Infrastructuur).
North Macedonia has 2.299 million subscribers in total, or a 105% penetration rate (Q3 2012). [ 108 ]
The regulatory authority for telecommunication in North Macedonia is AEC.
Norway has 5.730 million subscribers in total, or a 108.97% penetration rate [ 27 ] (December 2016).
The regulatory authority for telecommunication in Norway is the Norwegian Post and Telecommunications Authority .
Government of Norway (54%)
Poland has 58.6 million subscribers in total (Q4 2020). [ 117 ]
The country's telecom regulator is UKE (Urząd Komunikacji Elektronicznej).
(shares network with T-Mobile)
(shares network with Orange)
Portugal has 17.6 million subscribers in total, or a 170.5% penetration rate (13.1 million active subscribers or 127.4% penetration rate) [ 118 ] (Q3 2017).
The country's telecom regulator is ANACOM .
Romania has 23.4 million active subscribers in total, or a 107% penetration rate (2023). [ 122 ] The country's telcom regulator is ANCOM.
LTE-A , VoLTE , VoWiFi 2600FDD/ 2600TDD/3500 MHz 5G
LTE-A , VoLTE , ViLTE , VoWiFi 2100/3500 MHz 5G
The country's telecom regulator is Roskomnadzor (RKN) .
San Marino has 0.037 million subscribers in total, or a 116.95% penetration rate [ 27 ] (December 2013).
Serbia has 9.1987 million subscribers based on the three-month customer activity, or a 128.09% penetration rate [ 136 ] (December 2013).
Slovakia has 7.68 million subscribers in total, or a 132.79% penetration rate. All facts are based on the three-month customer activity base [ 138 ] (October 2019).
The regulatory authority for electronic communications "telecommunication" in Slovakia is Úrad pre reguláciu elektronických komunikácií a poštových služieb (RÚ).
VoLTE , VoWiFi , RCS
Slovenia has 2,772,546 subscribers in total, or a 130% penetration rate [ 141 ] (Q4 2024).
Spain has 61.424 million subscribers in total, or a 123.80% penetration rate (Jan 2025). [ 142 ]
The regulatory authority for telecommunication in Spain is CNMC (Comisión Nacional de los Mercados y la Competencia).
Note: The number of subscribers of each operator includes the subscribers of the main brand and the rest of its brands and subsidiaries.
Sweden has 14.3 million subscribers in total, approximately 140% penetration rate (2020). [ 143 ] The country's telcom regulator is Swedish Post and Telecom Authority .
There are four main network operators, and they share various 2G , 3G , 4G and 5G network infrastructure through co-ownership in separate network companies. Tele2 and Telenor share network infrastructure through their company Net4Mobility . [ 144 ] Telia and Tele2 share network infrastructure through UMTS Nät AB . [ 145 ] Tre and Telenor share network infrastructure through 3GIS. [ 146 ] [ 147 ]
Sweden also has a number of flanker brands and virtual operators , most notable are Halebop , Comviq , Fello , Hallon, Vimla, Mybeat, Tellusmobil and Chilimobil.
Some of world's largest producers of mobile network equipment have strong ties to Sweden. Ericsson [ 148 ] is based in Sweden while Nokia , Siemens , Huawei and ZTE have major research centers in the country, often clustered around Kista and Lund . [ 149 ] [ 150 ]
LTE , LTE-A 700/3500 MHz 5G NR
3500 MHz 5G NR
2100/2600/3500 MHz 5G NR VoLTE , VoWiFi
Switzerland has 11.365 million mobile subscribers and a 138% penetration rate [ 152 ] (December 2014).
The country's telecom regulator is BAKOM.
LTE , LTE-A VoLTE , VoWiFi 700/2100/3500 MHz 5G NR
Turkey has 94.5 million subscribers in total, or a 110.7% penetration rate [ 156 ] (Q3 2024).
The telecom regulator in Turkey is Information and Communication Technologies Authority (BTK : Bilgi Teknolojileri ve İletişim Kurumu).
Ukraine has 55.860 million subscribers in total, or a 129.8% penetration rate [ 158 ] (October 2018).
The country's telecom regulator is NKRZI.
(Including previous Beeline Ukraine network)
VoLTE , VoWi-Fi
(Network in Odesa region only until 01.01.2025)
(Own 3G network in Kyiv city centre only.) (as Utel )
Free 2G/3G roaming on Vodafone network available.
0.054 (Q4 2021) as Lycamobile
*Due to the Russian invasion of Ukraine the national roaming among other operators is free and it includes voice calls, SMS and mobile 2G / 3G Internet at speed up to 512 kbit/s. [ 159 ]
The United Kingdom has 92 million subscribers in total, or an approximate 139% penetration rate (Q3 2018). [ 160 ]
The country's telecom regulator is Ofcom .
(Includes Giffgaff )
(50% Telefónica , 50% Liberty Global )
(Includes BT Mobile )
(Includes VOXI )
(Includes SMARTY ) | https://en.wikipedia.org/wiki/List_of_mobile_network_operators_in_Europe |
This is a list of model organisms used in scientific research.
Phages (infecting prokaryotes):
Animal viruses:
Plant viruses: | https://en.wikipedia.org/wiki/List_of_model_organisms |
This is a list of notable software systems that are used for visualizing macromolecules. [ 1 ]
The tables below indicate which types of data can be visualized in each system: | https://en.wikipedia.org/wiki/List_of_molecular_graphics_systems |
The moment of inertia , denoted by I , measures the extent to which an object resists rotational acceleration about a particular axis ; it is the rotational analogue to mass (which determines an object's resistance to linear acceleration ). The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2 ). It should not be confused with the second moment of area , which has units of dimension L 4 ([length] 4 ) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia or sometimes as the angular mass .
For simple objects with geometric symmetry, one can often determine the moment of inertia in an exact closed-form expression . Typically this occurs when the mass density is constant, but in some cases, the density can vary throughout the object as well. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. In calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and the perpendicular axis theorems.
This article considers mainly symmetric mass distributions, with constant density throughout the object, and the axis of rotation is taken to be through the center of mass unless otherwise specified.
Following are scalar moments of inertia. In general, the moment of inertia is a tensor : see below.
I x = I y = 1 4 m ( r 1 2 + r 2 2 ) {\displaystyle I_{x}=I_{y}={\frac {1}{4}}m(r_{1}^{2}+r_{2}^{2})}
I x = I y = 1 4 π ρ A ( r 2 4 − r 1 4 ) {\displaystyle I_{x}=I_{y}={\frac {1}{4}}\pi \rho _{A}(r_{2}^{4}-r_{1}^{4})}
I z = 1 2 m ( r 2 2 + r 1 2 ) = m r 2 2 ( 1 − t + t 2 2 ) {\displaystyle I_{z}={\frac {1}{2}}m\left(r_{2}^{2}+r_{1}^{2}\right)=mr_{2}^{2}\left(1-t+{\frac {t^{2}}{2}}\right)} [ 1 ] [ 2 ] where t = r 2 − r 1 r 2 {\displaystyle t={\frac {r_{2}-r_{1}}{r_{2}}}} is a normalized thickness ratio; I x = I y = 1 12 m ( 3 ( r 2 2 + r 1 2 ) + h 2 ) {\displaystyle I_{x}=I_{y}={\frac {1}{12}}m\left(3\left(r_{2}^{2}+r_{1}^{2}\right)+h^{2}\right)} [ citation needed ]
which coincides with the geometric center of the cylinder.
If the xy plane is at the base of the cylinder, i.e. offset by d = h 2 , {\displaystyle d={\frac {h}{2}},} then by the parallel axis theorem the following formula applies: I x = I y = 1 12 m ( 3 ( r 2 2 + r 1 2 ) + 4 h 2 ) {\displaystyle I_{x}=I_{y}={\frac {1}{12}}m\left(3\left(r_{2}^{2}+r_{1}^{2}\right)+4h^{2}\right)}
I x = I y = π ρ h 12 ( 3 ( r 2 4 − r 1 4 ) + h 2 ( r 2 2 − r 1 2 ) ) {\displaystyle I_{x}=I_{y}={\frac {\pi \rho h}{12}}\left(3(r_{2}^{4}-r_{1}^{4})+h^{2}(r_{2}^{2}-r_{1}^{2})\right)}
I h o l l o w = 1 12 m s 2 {\displaystyle I_{\mathrm {hollow} }={\frac {1}{12}}ms^{2}\,\!} [ 3 ]
I x , s o l i d = I y , s o l i d = I z , s o l i d = 39 ϕ + 28 150 m s 2 {\displaystyle I_{x,\mathrm {solid} }=I_{y,\mathrm {solid} }=I_{z,\mathrm {solid} }={\frac {39\phi +28}{150}}ms^{2}\,\!} (where ϕ = 1 + 5 2 {\displaystyle \phi ={\frac {1+{\sqrt {5}}}{2}}} ) [ 3 ]
I x , s o l i d = I y , s o l i d = I z , s o l i d = ϕ 2 10 m s 2 {\displaystyle I_{x,\mathrm {solid} }=I_{y,\mathrm {solid} }=I_{z,\mathrm {solid} }={\frac {\phi ^{2}}{10}}ms^{2}\,\!} [ 3 ]
When r 1 becomes close to r 2 the ratio r 2 5 − r 1 5 r 2 3 − r 1 3 {\displaystyle {\frac {r_{2}^{5}-r_{1}^{5}}{r_{2}^{3}-r_{1}^{3}}}} approaches the value of 5 3 r 2 2 {\displaystyle {\frac {5}{3}}r_{2}^{2}} ,
and in the limit the body becomes a thin hollow sphere with I = 2 5 m ⋅ 5 3 r 2 2 = 2 3 m r 2 2 . {\displaystyle I={\frac {2}{5}}m\cdot {\frac {5}{3}}r_{2}^{2}={\frac {2}{3}}mr_{2}^{2}.}
About an axis passing through the tip: I x = I y = m ( 3 20 r 2 + 3 5 h 2 ) {\displaystyle I_{x}=I_{y}=m\left({\frac {3}{20}}r^{2}+{\frac {3}{5}}h^{2}\right)\,\!} [ 4 ] About an axis passing through the base: I x = I y = m ( 3 20 r 2 + 1 10 h 2 ) {\displaystyle I_{x}=I_{y}=m\left({\frac {3}{20}}r^{2}+{\frac {1}{10}}h^{2}\right)\,\!} About an axis passing through the center of mass: I x = I y = m ( 3 20 r 2 + 3 80 h 2 ) {\displaystyle I_{x}=I_{y}=m\left({\frac {3}{20}}r^{2}+{\frac {3}{80}}h^{2}\right)\,\!} About a slanted axis passing through the apex (origin) and along the side generating line: I slant = 3 20 m r 2 ( 1 + 5 h 2 h 2 + r 2 ) {\displaystyle I_{\text{slant}}={\frac {3}{20}}mr^{2}\left(1+5{\frac {h^{2}}{h^{2}+r^{2}}}\right)\,\!}
where Q n = ‖ P n ‖ 2 + P n ⋅ P n + 1 + ‖ P n + 1 ‖ 2 {\displaystyle Q_{n}=\left\|\mathbf {P} _{n}\right\|^{2}+\mathbf {P} _{n}\cdot \mathbf {P} _{n+1}+\left\|\mathbf {P} _{n+1}\right\|^{2}}
ρ ( x ) = m exp ( − 1 2 x T Σ − 1 x ) ( 2 π ) 2 | Σ | {\displaystyle \rho ({\mathbf {x} })=m{\frac {\exp \left(-{\frac {1}{2}}{\mathbf {x} }^{\mathrm {T} }{\boldsymbol {\Sigma }}^{-1}{\mathbf {x} }\right)}{\sqrt {(2\pi )^{2}|{\boldsymbol {\Sigma }}|}}}}
This list of moment of inertia tensors is given for principal axes of each object.
To obtain the scalar moments of inertia I above, the tensor moment of inertia I is projected along some axis defined by a unit vector n according to the formula:
n ⋅ I ⋅ n ≡ n i I i j n j , {\displaystyle \mathbf {n} \cdot \mathbf {I} \cdot \mathbf {n} \equiv n_{i}I_{ij}n_{j}\,,}
where the dots indicate tensor contraction and the Einstein summation convention is used. In the above table, n would be the unit Cartesian basis e x , e y , e z to obtain I x , I y , I z respectively.
I = [ 2 3 m r 2 0 0 0 2 3 m r 2 0 0 0 2 3 m r 2 ] {\displaystyle I={\begin{bmatrix}{\frac {2}{3}}mr^{2}&0&0\\0&{\frac {2}{3}}mr^{2}&0\\0&0&{\frac {2}{3}}mr^{2}\end{bmatrix}}}
I = [ 1 3 m l 2 0 0 0 0 0 0 0 1 3 m l 2 ] {\displaystyle I={\begin{bmatrix}{\frac {1}{3}}ml^{2}&0&0\\0&0&0\\0&0&{\frac {1}{3}}ml^{2}\end{bmatrix}}}
I = [ 1 12 m l 2 0 0 0 0 0 0 0 1 12 m l 2 ] {\displaystyle I={\begin{bmatrix}{\frac {1}{12}}ml^{2}&0&0\\0&0&0\\0&0&{\frac {1}{12}}ml^{2}\end{bmatrix}}}
I = [ 1 12 m ( 3 r 2 + h 2 ) 0 0 0 1 12 m ( 3 r 2 + h 2 ) 0 0 0 1 2 m r 2 ] {\displaystyle I={\begin{bmatrix}{\frac {1}{12}}m(3r^{2}+h^{2})&0&0\\0&{\frac {1}{12}}m(3r^{2}+h^{2})&0\\0&0&{\frac {1}{2}}mr^{2}\end{bmatrix}}}
I = [ 1 12 m ( 3 ( r 2 2 + r 1 2 ) + h 2 ) 0 0 0 1 12 m ( 3 ( r 2 2 + r 1 2 ) + h 2 ) 0 0 0 1 2 m ( r 2 2 + r 1 2 ) ] {\displaystyle I={\begin{bmatrix}{\frac {1}{12}}m(3(r_{2}^{2}+r_{1}^{2})+h^{2})&0&0\\0&{\frac {1}{12}}m(3(r_{2}^{2}+r_{1}^{2})+h^{2})&0\\0&0&{\frac {1}{2}}m(r_{2}^{2}+r_{1}^{2})\end{bmatrix}}} | https://en.wikipedia.org/wiki/List_of_moments_of_inertia |
This list contains rivers and other streams that have been regarded, currently or historically, as among the most polluted in the world due to their quantity of pollution, the severity of different components of the stream's pollution, its impact on the local population, or a combination of all factors.
Second among a group of ten rivers responsible for about 90% of all the plastic that reaches the oceans. [ 48 ] [ 49 ]
Receives 800 million litres of largely untreated sewage and additional 44 million litres of industrial effluents each day. [ 87 ] [ 88 ] | https://en.wikipedia.org/wiki/List_of_most-polluted_rivers |
Below are lists of the most massive known star clusters in solar masses ( M ☉ ) and sorted in descending order.
Globular cluster masses can be determined by observing the proper motion of nearby stars influenced by the cluster [ 1 ] [ 2 ] or by estimating the cluster's relaxation time. [ 3 ]
The masses of open star clusters can be estimated by measuring the falloff of radial and tangential velocities of surrounding stars at a particular distance. [ 4 ] | https://en.wikipedia.org/wiki/List_of_most_massive_star_clusters |
This is a list of multivariable calculus topics . See also multivariable calculus , vector calculus , list of real analysis topics , list of calculus topics . | https://en.wikipedia.org/wiki/List_of_multivariable_calculus_topics |
This is a list of software for creating, performing, learning, analyzing, researching, broadcasting and editing music. This article only includes software, not services.
For streaming services such as iHeartRadio , Pandora , Prime Music, and Spotify, see Comparison of on-demand streaming music services .
For storage, uploading, downloading and streaming of music via the cloud , see Comparison of online music lockers .
This list does not include discontinued historic or legacy software, with the exception of trackers that are still supported. [ 1 ] [ 2 ]
If a program fits several categories, such as a comprehensive digital audio workstation or a foundation programming language (e.g. Pure Data ), listing is limited to its top three categories.
This section only includes software, not services. For services programs like Spotify, Pandora, Prime Music, etc. see Comparison of on-demand streaming music services . Likewise, list includes music RSS apps, widgets and software, but for a list of actual feeds, see Comparison of feed aggregators . For music broadcast software lists in the cloud, see Content delivery network and Comparison of online music lockers .
[ 5 ]
Historical tracker software: | https://en.wikipedia.org/wiki/List_of_music_software |
A music tracker (sometimes referred to as a tracker for short) is a type of music sequencer software for creating music. The music is represented as discrete musical notes positioned in several channels at chronological positions on a vertical timeline. [ 1 ] A music tracker's user interface is traditionally number based. Notes, parameter changes, effects and other commands are entered with the keyboard into a grid of fixed time slots as codes consisting of letters, numbers and hexadecimal digits. [ 2 ] Separate patterns have independent timelines; a complete song consists of a master list of repeated patterns.
Later trackers departed from solely using module files , adding other options both to the sound synthesis (hosting generic synthesizers and effects or MIDI output) and to the sequencing (MIDI input and recording), effectively becoming general purpose sequencers with a different user interface .
In the 2010s, tracker music is still featured in demoscene products for old hardware platforms and demoparties have often separate tracker music competitions. Tracker music may also be used in games which borrow aesthetics from past decades .
The term tracker derives from Ultimate Soundtracker (the first tracker software [ 3 ] ) written by Karsten Obarski and released in 1987 by EAS Computer Technik for the Amiga . [ 4 ] Ultimate Soundtracker was a commercial product, but soon shareware clones such as NoiseTracker (1989 [ 5 ] ) appeared as well. The general concept of step-sequencing samples numerically, as used in trackers, is also found in the Fairlight CMI sampling workstation of the early 1980s. Some early tracker-like programs appeared for the MSX ( Yamaha CX5M ) and Commodore 64 , before 1987, such as Chris Huelsbeck 's SoundMonitor, but these did not feature sample playback, instead playing notes on the computer's internal synthesizer. Later, programs like Rock Monitor also supported additional sample playback, usually with short drum samples loaded in RAM memory.
The first trackers supported four pitch and volume modulated channels of 8-bit PCM samples , a limitation derived from the Amiga's Paula audio chipset and the commonplace 8SVX format used to store sampled sound. However, since the notes were samples, the limitation was less important than those of synthesizing music chips. [ 6 ]
During the 1990s, tracker musicians gravitated to the PC as software production in general switched from the Amiga platform to the PC. Although the IBM and compatibles initially lacked the hardware sound processing capabilities of the Amiga, with the advent of the Sound Blaster line from Creative , PC audio slowly began to approach CD Quality ( 44.1 kHz/16 bit/Stereo ) with the release of the SoundBlaster 16 .
Another sound card popular on the PC tracker scene was the Gravis Ultrasound , which continued the hardware mixing tradition, with 32 internal channels and onboard memory for sample storage. For a time, it offered unparalleled sound quality and became the choice of discerning tracker musicians. Understanding that the support of tracker music would benefit sales, Gravis gave away some 6000 GUS cards to participants. Coupled with excellent developer documentation, this gesture quickly prompted the GUS to become an integral component of many tracking programs and software. Inevitably, the balance was largely redressed with the introduction of the Sound Blaster AWE32 and its successors, which also featured on-board RAM and wavetable (or sample table) mixing.
The responsibility for audio mixing passed from hardware to software (the main CPU ) which gradually enabled the use of more channels. From the typical 4 MOD channels of the Amiga, the limit had moved to 7 with TFMX players and 8, first with Oktalyzer and later with the vastly more popular OctaMED (Amiga, 1989), then 32 with ScreamTracker 3 (PC, 1994) and 16 with FastTracker 2 (PC, 1994) and on to 64 with Impulse Tracker (PC, 1995) and MED SoundStudio (updated version of OctaMED). An Amiga tracker called Symphonie Pro even supported 256 channels.
As such, hardware mixing did not last. As processors got faster and acquired special multimedia processing abilities (e.g. MMX ) and companies began to push Hardware Abstraction Layers , like DirectX , the AWE and GUS range became obsolete. DirectX, WDM and, now more commonly, ASIO , deliver high-quality sampled audio irrespective of hardware brand.
There was also a split off from the sample based trackers taking advantage of the OPL2 and OPL3 chips of the Sound Blaster series. All Sound Tracker was able to combine both the FM synthesis of the OPL chips and the sample based synthesis of the EMU-8000 chips in the Sound Blaster AWE series of cards as well as MIDI output to any additional hardware of choice.
Jeskola Buzz is a modular music studio developed from 1997 to 2000 for Microsoft Windows using a tracker as its sequencer where the sounds were produced by virtual machines (Buzzmachines) such as signal generators, synthesizer emulators, drum computers, samplers, effects and control machines, that where connected in a modular setup. Each machine would have its own tracker, drum machines would use a tracker-like drum pattern editor and effect and control machines could be automated tracker-like via tables of parameters.
Tracker music could be found in computer games of the late 1990s and early 2000s, such as the Unreal series , Deus Ex , Crusader: No Remorse , Jazz Jackrabbit and Uplink . Some of the early Amiga trackers such as Protracker (1990) and OctaMED have received various updates, mostly for porting to other platforms. Protracker having resumed development in 2004, with plans for releasing version 5 to Windows and AmigaOS , but only version 4.0 beta 2 for AmigaOS has been released.
During 2007, Renoise (PC, 2002) and OpenMPT (PC, 1997) were presented in Computer Music Magazine as professional and inexpensive alternative to other music production software. [ 7 ]
Modern trackers include, but not limited to Deflemask, [ 8 ] FamiTracker, [ 9 ] VGM Music Maker, [ 10 ] Furnace [ 11 ] (which currently is the only tracker allowing multiple sound chips from multiple systems to be played simultaneously (for example, Commodore 64 and PC-98 together.)), and SunVox [ 12 ] (Music Tracker with modular synth engine and a free form, dynamic length pattern timeline system)
The earliest trackers existed to get closer to the hardware of a given machine, allowing memory-light playback of music ideal for games and similar programs. [ 13 ] Keeping in theme with this philosophy, a few "hardware trackers" have emerged: specialized hardware designed specifically to host tracker software, in turn designed to exploit the hardware of the machine. These hardware trackers are largely inspired by LittleSoundDJ, [ 14 ] [ 15 ] a tracker created for the original Game Boy .
The first such hardware tracker released was the NerdSeq in 2018, a hybrid tracker-sequencer for Eurorack systems. As a module of said system, it cannot be used alone, and the "tracker" portion of the device is simply used as an interface to sequence , while the hardware is used to handle sampling and other functions.
The first standalone hardware tracker released was the Polyend Tracker in 2020, a USB -powered device with all the functions of a software tracker. It was met with mostly positive critical reception, [ 16 ] [ 17 ] with critics citing a modest price point, standalone all-in-one capability, and intuitive controls. In 2021, DirtyWave released the M8 Tracker, a portable tracker that is more heavily inspired by Little Sound DJ . [ 18 ]
There are several elements common to any tracker program: samples, notes, effects, tracks (or channels), patterns, and orders.
A sample is a small digital sound file of an instrument, voice, or other sound effect. Most trackers allow a part of the sample to be looped, simulating a sustain of a note.
A note designates the frequency at which the sample is played back. By increasing or decreasing the playback speed of a digital sample, the pitch is raised or lowered, simulating instrumental notes (e.g., C, C#, D, etc.).
An effect is a special function applied to a particular note. These effects are then applied during playback through either hardware or software. Common tracker effects include volume, portamento , vibrato , retrigger , and arpeggio .
A track (or channel) is a space where one sample is played back at a time. Whereas the original Amiga trackers only provided four tracks, the hardware limit, modern trackers can mix a virtually unlimited number of channels into one sound stream through software mixing. Tracks have a fixed number of "rows" on which notes and effects can be placed (most trackers lay out tracks in a vertical fashion). Tracks typically contain 64 rows and 16 beats, although the beats, rows and tempo can be increased or decreased to the composer's taste.
A basic drum set could thus be arranged by putting a bass drum at rows 0, 4, 8, 12 etc. of one track and putting some hi hat at rows 2, 6, 10, 14 etc. of a second track. Of course, bass and hats could be interleaved on the same track, if the samples are short enough. If not, the previous sample is usually stopped when the next one begins. Some modern trackers simulate polyphony in a single track by setting the "new note action" of each instrument to cut, continue, fade out, or release , opening new mixing channels as necessary.
A pattern is a group of simultaneously played tracks that represents a full section of the song. A pattern usually represents an even number of measures of music composition.
An order is part of a sequence of patterns that defines the layout of a song. Patterns can be repeated across multiple orders to save tracking time and file space.
There are also some tracker-like programs that utilize tracker-style sequencing schemes, while using real-time sound synthesis instead of samples. Many of these programs are designed for creating music for a particular synthesizer chip such as the OPL chips of the Adlib and SoundBlaster sound cards, or the sound chips of classic home computers.
Tracker music is typically stored in module files where the song data and samples are encapsulated in a single file. Several module file formats are supported by popular audio players . Well-known formats include MOD , MED , S3M , XM and IT . Many of these formats can also be imported into existing trackers, allowing to view arrangement, instrumentation and the use of effect commands. This also makes the self-teaching of music composition using trackers easier and allows to extract instruments for later use in own songs, which was very common. [ 19 ] | https://en.wikipedia.org/wiki/List_of_music_trackers |
Music visualization or music visualisation , a feature found in electronic music visualizers and media player software , generates animated imagery based on a piece of music . The imagery is usually generated and rendered in real time and in a way synchronized with the music as it is played.
Visualization techniques range from simple ones (e.g., a simulation of an oscilloscope display) to elaborate ones, which often include a number of composited effects. The changes in the music's loudness and frequency spectrum are among the properties used as input to the visualization.
Effective music visualization aims to attain a high degree of visual correlation between a musical track's spectral characteristics such as frequency and amplitude and the objects or components of the visual image being rendered and displayed.
Music visualization can be defined, in contrast to previous existing pre-generated music plus visualization combinations (as for example music videos ), by its characteristic as being real-time generated. Another possible distinction is seen by some in the ability of some music visualization systems (such as Geiss' MilkDrop ) to create different visualizations for each song or audio every time the program is run, in contrast to other forms of music visualization (such as music videos or a laser lighting display ) which always show the same visualization. Music visualization may be achieved in a 2D or a 3D coordinate system where up to six dimensions can be modified, the 4th, 5th and 6th dimensions being color, intensity and transparency.
The first electronic music visualizer was the Atari Video Music introduced by Atari Inc. in 1977, and designed by the initiator of the home version of Pong , Robert Brown. The idea was to create a visual exploration that could be implemented into a Hi-Fi stereo system. [ 1 ] In the United Kingdom music visualization was first pioneered by Fred Judd .
Music and audio players were available on early home computers, with some possessing visualization features, such as Sound to Light Generator (1985, Infinite Software), which used the ZX Spectrum 's cassette player. [ 2 ] The 1984 movie Electric Dreams prominently made use of a music visualizer, although as a pre-generated effect, rather than calculated in real-time .
For PC / DOS , one of the first modern music visualization programs was the open-source , multi-platform Cthugha , written in 1993. In the 1990s, the emerging demo and tracker music scene pioneered real-time techniques for music visualization on the PC platform; resulting examples are Cubic player (1994), Inertia Player (1995) or in general their real-time generated Demos . [ 3 ] [ 4 ]
Subsequently, PC computer music visualization became widespread in the mid to late 1990s as applications such as Winamp (1997), Audion (1999), and SoundJam (2000). By 1999, there were several dozen freeware non-trivial music visualizers in distribution. In particular, MilkDrop (2001) and its predecessor "geiss-plugin" (1998) by Ryan Geiss , G-Force by Andy O'Meara , and AVS (2000) by Nullsoft became popular music visualizations. AVS is part of Winamp and has been recently open-sourced , [ 5 ] and G-Force was licensed for use in iTunes [ 6 ] and Windows Media Center [ citation needed ] and is presently the flagship product for Andy O'Meara's software startup company, SoundSpectrum. In 2008, iTunes added the "Magnetosphere" visualizer created by The Barbarian Group . [ 7 ]
There have been applications of electronic music visualization in order to enhance the music listening experience for deaf and hard of hearing people . Richard Burn, a PhD candidate at Birmingham City University , as of 2015, is researching a device that displays detailed visual feedback from electronic instruments . These visuals will provide information on the specifics of what is being played, such as the pitch and the harmonics of the sound. This allows deaf musicians to better understand what notes they are playing, which enables them to create music in a new way. [ 8 ]
Researchers from the National University of Singapore have also created a device that seeks to enhance musical experiences for deaf people. This technology combines a music display and haptic chair that integrates sound qualities from music into vibrations and visual images that correlate with the specific qualities found within the music. The visual display shows various shapes that change size, color, and brightness in correlation with the music. Combining this visual display with a haptic chair that vibrates along with the music aims to give a more all-around experience of music to those hard of hearing. [ 9 ]
Music visualization can also be used in education of deaf students. The Cooper Union in New York City is using music visualization to teach deaf children about sound. They have developed an interactive light studio in the American Sign Language and English Lower School in New York City. This consists of an interactive wall display that shows digital output created by sound and music. Children can trigger the playing of instruments with their movement, and they can watch the visual feedback from this music. They are also able to view a "talking flower" wall, in which each flower can transform sound into light based on the specific frequencies of the sounds. [ 10 ] | https://en.wikipedia.org/wiki/List_of_music_visualization_software |
This is a list of plant genera that engage in myco-heterotrophic relationships with fungi . It does not include the fungi that are parasitized by these plants.
Burmanniaceae ( Dioscoreales )
Corsiaceae ( Liliales )
Iridaceae , formerly Geosiridaceae ( Asparagales )
Orchidaceae ( Asparagales )
This list concerns only the species that are leafless or are losing photosynthetic function.
Petrosaviaceae , also called Melanthiaceae ( Petrosaviales )
Triuridaceae ( Pandanales ), including Lacandoniaceae
Ericaceae ( Ericales )
Gentianaceae ( Gentianales )
Polygalaceae ( Fabales ) | https://en.wikipedia.org/wiki/List_of_myco-heterotrophic_genera |
This is a list of named alloys grouped alphabetically by the metal with the highest percentage. Within these headings, the alloys are also grouped alphabetically. Some of the main alloying elements are optionally listed after the alloy names.
Aluminium also forms complex metallic alloys , like β–Al–Mg, ξ'–Al–Pd–Mn, and T–Al 3 Mn.
Most iron alloys are steels , with carbon as a major alloying element. | https://en.wikipedia.org/wiki/List_of_named_alloys |
Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that have received specific names, area by area. | https://en.wikipedia.org/wiki/List_of_named_differential_equations |
This list of prefectural route of Japan contains every national route in Japan. | https://en.wikipedia.org/wiki/List_of_national_highways_of_Japan |
Natural phenols and polyphenols are a class of natural aromatic organic compounds with molecular formulas in which one or more hydroxy groups are attached directly to the benzene ring , generally formed from C, H and O. [ 1 ]
The entries are sorted by mass. | https://en.wikipedia.org/wiki/List_of_natural_phenols_and_polyphenols_molecular_formulas |
This is a list of protocol stack architectures. A protocol stack is a suite of complementary communications protocols in a computer network or a computer bus system. | https://en.wikipedia.org/wiki/List_of_network_protocol_stacks |
This article lists protocols , categorized by the nearest layer in the Open Systems Interconnection model . This list is not exclusive to only the OSI protocol family . Many of these protocols are originally based on the Internet Protocol Suite (TCP/IP) and other models and they often do not fit neatly into OSI layers.
This layer, presentation Layer and application layer are combined in TCP/IP model . | https://en.wikipedia.org/wiki/List_of_network_protocols_(OSI_model) |
Network theory is an area of applied mathematics .
This page is a list of network theory topics . | https://en.wikipedia.org/wiki/List_of_network_theory_topics |
Related articles are SAN and NAS . | https://en.wikipedia.org/wiki/List_of_networked_storage_hardware_platforms |
Neuroimaging software is used to study the structure and function of the brain. To see an NIH Blueprint for Neuroscience Research funded clearinghouse of many of these software applications, as well as hardware, etc. go to the NITRC web site. | https://en.wikipedia.org/wiki/List_of_neuroimaging_software |
A number of online neuroscience databases are available which provide information regarding gene expression , neurons , macroscopic brain structure, and neurological or psychiatric disorders. Some databases contain descriptive and numerical data, some to brain function, others offer access to 'raw' imaging data, such as postmortem brain sections or 3D MRI and fMRI images. Some focus on the human brain, others on non-human.
As the number of databases that seek to disseminate information about the structure, development and function of the brain has grown, so has the need to collate these resources themselves. As a result, there now exist databases of neuroscience databases, some of which reach over 3000 entries. [ 1 ] | https://en.wikipedia.org/wiki/List_of_neuroscience_databases |
Neurosteroids are natural and synthetic steroids that are active on the mammalian nervous system through receptors other than steroid hormone receptors . It includes inhibitory , excitatory , and neurotrophic neurosteroids as well as pheromones and vomeropherines . In contrast to steroid hormones , neurosteroids have rapid, non- genomic effects through interactions with membrane steroid receptors and can quickly influence central nervous system function.
The following are proneurosteroids:
The following are proneurosteroids:
The following are proneurosteroids:
The following are proneurosteroids: | https://en.wikipedia.org/wiki/List_of_neurosteroids |
Neutron stars are the collapsed cores of supergiant stars. [ 1 ] They are created as a result of supernovas and gravitational collapse, [ 2 ] and are the second-smallest and densest class of stellar objects. [ 3 ] In the cores of these stars, protons and electrons combine to form neutrons. [ 2 ] Neutron stars can be classified as pulsars if they are magnetized , if they rotate , and if they emit beams of electromagnetic radiation out of their magnetic poles . [ 4 ] They may include soft gamma repeaters (SGR) and radio-quiet neutron stars , as well as pulsars such as radio pulsars , recycled pulsars , low mass X-ray pulsars, and accretion-powered pulsars . A notable grouping of neutron stars includes the Magnificent Seven . | https://en.wikipedia.org/wiki/List_of_neutron_stars |
The Nobel Prize in Chemistry ( Swedish : Nobelpriset i kemi ) is awarded annually by the Royal Swedish Academy of Sciences to scientists who have made outstanding contributions in chemistry . [ 1 ] It is one of the five Nobel Prizes which were established by the will of Alfred Nobel in 1895. [ 2 ]
Every year, the Royal Swedish Academy of Sciences sends out forms, which amount to a personal and exclusive invitation, to about three thousand selected individuals to invite them to submit nominations. The names of the nominees are never publicly announced, and neither are they told that they have been considered for the Prize. Nomination records are strictly sealed for fifty years. Currently, the nominations for the years 1901 to 1970 are publicly available. Despite the annual sending of invitations, the prize was not awarded in eight years (1916, 1917, 1919, 1924, 1933, 1940–42) and have been delayed for a year nine times (1914, 1918, 1920, 1921, 1925, 1927, 1938, 1943, 1944).
From 1901 to 1970, there have been 641 scientists nominated for the prize, 79 of which were awarded either jointly or individually. 18 more scientists from these nominees were awarded after 1970 and Frederick Sanger was awarded second time on 1980. Of only 15 women nominees, three were awarded. The first woman to be nominated was Marie Skłodowska Curie . She was nominated on 1911 by Swedish scientist Svante Arrhenius and French mathematician Gaston Darboux and eventually won the prize on the same year. She is the only woman to win twice the Nobel Prize: Physics (1903) and Chemistry (1911). [ 3 ] Besides 27 and 13 scientists from these nominees won the prizes in Physiology or Medicine and in Physics (including one woman more) correspondingly (including years after 1970). Only one company has been nominated, the Geigy SA for the year 1947.
Despite the long list of nominated noteworthy chemists, physicists and engineers, there have still been other scientists who were overlooked for the prize in chemistry such as Per Teodor Cleve , Jannik Petersen Bjerrum , Ellen Swallow Richards , Alice Ball , Vladimir Palladin , Sergey Reformatsky , Prafulla Chandra Ray , Alexey Favorsky , Rosalind Franklin and Joseph Edward Mayer .
In addition, nominations of 21 scientists and four corporations more were declared invalid by the Nobel Committee.
Nominees are published 50 years later so 1973 nominees should be published in 2024. | https://en.wikipedia.org/wiki/List_of_nominees_for_the_Nobel_Prize_in_Chemistry |
Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area of interest. | https://en.wikipedia.org/wiki/List_of_nonlinear_ordinary_differential_equations |
See also Nonlinear partial differential equation , List of partial differential equation topics and List of nonlinear ordinary differential equations .
( ∂ f i ∂ t ) c o l l = ∑ j = 1 n ∬ g i j I i j ( g i j , Ω ) [ f i ′ f j ′ − f i f j ] d Ω d 3 p ′ {\displaystyle \left({\frac {\partial f_{i}}{\partial t}}\right)_{\mathrm {coll} }=\sum _{j=1}^{n}\iint g_{ij}I_{ij}(g_{ij},\Omega )[f'_{i}f'_{j}-f_{i}f_{j}]\,d\Omega \,d^{3}\mathbf {p'} }
+ mass conservation: ∂ ρ ∂ t + ∂ ( ρ v i ) ∂ x i = 0 {\displaystyle {\frac {\partial \rho }{\partial t}}+{\frac {\partial \left(\rho \,v_{i}\right)}{\partial x_{i}}}=0} + an equation of state to relate p and ρ , e.g. for an incompressible flow : ∂ v i ∂ x i = 0 {\displaystyle {\frac {\partial v_{i}}{\partial x_{i}}}=0}
S W Z ( γ ) = − 1 48 π 2 ∫ B 3 d 3 y ε i j k K ( γ − 1 ∂ γ ∂ y i , [ γ − 1 ∂ γ ∂ y j , γ − 1 ∂ γ ∂ y k ] ) {\displaystyle S^{\mathrm {W} Z}(\gamma )=-\,{\frac {1}{48\pi ^{2}}}\int _{B^{3}}d^{3}y\,\varepsilon ^{ijk}{\mathcal {K}}\left(\gamma ^{-1}\,{\frac {\partial \gamma }{\partial y^{i}}}\,,\,\left[\gamma ^{-1}\,{\frac {\partial \gamma }{\partial y^{j}}}\,,\,\gamma ^{-1}\,{\frac {\partial \gamma }{\partial y^{k}}}\right]\right)} | https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations |
The purpose of this annotated list is to provide a chronological, consolidated list of nonmetal monographs , which could enable the interested reader to further trace classification approaches in this area. Those marked with a ▲ classify these 14 elements as nonmetals: H, N; O, S; the 4 stable halogens; and the 6 naturally occurring noble gases. | https://en.wikipedia.org/wiki/List_of_nonmetal_monographs |
This is a list of topics in number theory . See also:
See list of algebraic number theory topics
Note: Computational number theory is also known as algorithmic number theory.
see also List of random number generators . | https://en.wikipedia.org/wiki/List_of_number_theory_topics |
This is a list of numerical analysis topics .
Error analysis (mathematics)
Numerical linear algebra — study of numerical algorithms for linear algebra problems
Eigenvalue algorithm — a numerical algorithm for locating the eigenvalues of a matrix
Interpolation — construct a function going through some given data points
Polynomial interpolation — interpolation by polynomials
Spline interpolation — interpolation by piecewise polynomials
Trigonometric interpolation — interpolation by trigonometric polynomials
Approximation theory
Root-finding algorithm — algorithms for solving the equation f ( x ) = 0
Mathematical optimization — algorithm for finding maxima or minima of a given function
Linear programming (also treats integer programming ) — objective function and constraints are linear
Convex optimization
Nonlinear programming — the most general optimization problem in the usual framework
Optimal control
Infinite-dimensional optimization
Numerical integration — the numerical evaluation of an integral
Numerical methods for ordinary differential equations — the numerical solution of ordinary differential equations (ODEs)
Numerical partial differential equations — the numerical solution of partial differential equations (PDEs)
Finite difference method — based on approximating differential operators with difference operators
Finite element method — based on a discretization of the space of solutions gradient discretisation method — based on both the discretization of the solution and of its gradient
For a large list of software, see the list of numerical-analysis software . | https://en.wikipedia.org/wiki/List_of_numerical_analysis_topics |
This is a list of well-known object–relational mapping software. | https://en.wikipedia.org/wiki/List_of_object–relational_mapping_software |
This is a list of observatory codes ( IAU codes or MPC codes ) published by the Minor Planet Center . [ 1 ] For a detailed description, see observations of small Solar System bodies .
bla de Vallbona | https://en.wikipedia.org/wiki/List_of_observatory_codes |
The following is a list of astronomical observatory software . | https://en.wikipedia.org/wiki/List_of_observatory_software |
This is a list of oceanography institutions and programs worldwide. Oceanographic institutions and programs are broadly defined as places where scientific research is carried out relating to oceanography. This list is organized geographically. Some oceanographic institutions are standalone programs, such as non-governmental organizations or government-funded agencies. Other oceanographic institutions are departments within colleges and universities. While oceanographic research happens at many other departments at other colleges and universities, such as Biology and Geology departments, this list focuses on larger departments and large research centers specifically devoted to oceanography and marine science. Aquaria are not listed here.
Brazilian national programs:
Brazilian universities with oceanography departments or institutes:
Colombian national programs:
Colombian universities with oceanography programs:
Indian national programs:
Indian universities with oceanography programs:
Central:
Eastern:
Northern:
Southern:
Western:
National agencies and non-profit organizations:
Universities with oceanography programs:
Northeast:
Southeast:
Gulf Coast:
West Coast:
Inland and Great Lakes: | https://en.wikipedia.org/wiki/List_of_oceanographic_institutions_and_programs |
In computing , an office suite is a collection of productivity software usually containing at least a word processor , spreadsheet and a presentation program . There are many different brands and types of office suites. | https://en.wikipedia.org/wiki/List_of_office_suites |
This is a list of people reported to have fathered a child at or after 75 years of age. These claims have not necessarily been verified.
According to a 1969 study, there is a decrease in sperm concentration as men age. The study reported that 90% of seminiferous tubules in men in their 20s and 30s contained spermatids , whereas men in their 40s and 50s had spermatids in 50% of their seminiferous tubules. In the study, only 10% of seminiferous tubules from men aged > 80 years contained spermatids. [ 1 ] [ 2 ] In a random international sample of 11,548 men confirmed to be biological fathers by DNA paternity testing, the oldest father was found to be 66 years old at the birth of his child; the ratio of DNA-confirmed versus DNA-rejected paternity tests around that age is in agreement with the notion of general male infertility greater than age 65–66. [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/List_of_oldest_fathers |
Inspired by the terms genome and genomics , other words to describe complete biological datasets, mostly sets of biomolecules originating from one organism , have been coined with the suffix -ome and - omics . Some of these terms are related to each other in a hierarchical fashion. For example, the genome contains the ORFeome , which gives rise to the transcriptome , which is translated to the proteome . Other terms are overlapping and refer to the structure and/or function of a subset of proteins (e.g. glycome , kinome ).
An omicist is a scientist who studies omeomics, cataloging all the “omics” subfields. [ 1 ]
Omics.org is a Wiki that collects and alphabetically lists all the known "omes" and "omics." [ 2 ]
For the sake of clarity, some topics are listed more than once. | https://en.wikipedia.org/wiki/List_of_omics_topics_in_biology |
This is a list of online digital musical document libraries . Each source listed below offers access to collections of digitized music documents (typically originating from printed or manuscript musical sources). They may contain scanned images, fully encoded scores, or encodings designed for music playback (e.g., via MIDI ). Some (e.g., KernScores) are adapted for music analysis.
Approximately 3,500 popular vocal and instrumental titles from the 1830s to the end of the century. Contains catalog descriptions and digital images of the individual pieces.
Sheet music published in California between 1852 and 1900, along with related materials such as a San Francisco publisher's catalog of 1872, programs, songsheets, advertisements, and photographs. Images of every printed page of sheet music from eleven locations have been scanned at 400 dpi, in color where indicated.
Sheet music, primarily vocal music of American imprint, dating from the 18th century to the present, with most titles in the period 1840–1950.
Printable sheet music primarily for singers and voice teachers—most downloadable. Emphasis on standard classical and traditional repertoire. IPA transcriptions available for every German, French, Italian and Latin song in the index. Supplementary information on more than 250 songs.
Largely from and about Washington State and the Pacific Northwest.
Johann Sebastian Bach's autograph manuscripts and original parts. Advanced search options. High-resolution scans. Also contains Bach's copies of works by other composers.
Comprises at least 90% of extant Bach manuscripts worldwide. Funding provided by the Deutsche Forschungsgemeinschaft and others.
Links more than 6,100 documents on 37,300 coloured high-quality scans, 1,600 audio files (including music examples and audio letters), and 7,600 text files.
Downloadable color images.
Sheet music in the Brazilian National Digital Library.
Printed materials range from the 16th to the 20th Century.
RGB tiff images with a resolution of 1,200 dpi (photos) or 400 dpi (autographs, letters, prints, etc.).
Medieval-era manuscripts written during the reign of Alfonso X "El Sabio" (1221–1284). One of the largest collections of monophonic (solo) songs from the Middle Ages. The To Codex contains roughly the first 100 cantigas, the E Codex all of the cantigas. Illuminations may be found in the E Codex with every 10th cantiga.
The largest single holding of cello music–related materials in the world, including annotated sheet music (manuscript and published), monographs, serials, audio/video recordings, personal papers, and artifacts associated with noted cellists.
Sheet music for popular tunes dating as far back as 1865. Items are scanned at 600 dpi and saved as a TIFF files.
AHRC-funded research project containing music files viewable on-site or as downloads. Most of the music consists of chamber music and concertos for string instruments, edited and annotated by such players as Ferdinand David, Friedrich Grützmacher, and Joseph Joachim.
All of the first impressions of Chopin's first editions.
Scores of early printed editions of Chopin's music works published before 1881, of which 74 are works with opus number and 11 are without.
Publicly editable library of public domain music in standardized, machine-parsable formats such as MusicXML, MuseScore, Sibelius, and Finale. Largest public, centralized repository of fully digitized CPP scores.
Rare and unusual publications of music for string quartet.
Manuscripts from the medieval codices in the Abbey library of St. Gallen. Downloadable colour PDFs and XML files.
High-quality early music scores. Online corpus of electronic editions and associated software tools.
Published in eScholarship, the collection includes digital, open access scores.
Images of medieval polyphonic music manuscripts from approximately 800 to 1600. Includes detailed information for all known sources of European polyphonic music (almost entirely vocal), high-resolution colour TIFF images, and links to external images available at other sites.
First and early editions and manuscripts from the 18th and early 19th centuries by J.S. Bach and Bach family members, Mozart, Schubert and other composers. Multiple versions of 19th-century opera scores, seminal works of musical modernism, and music of the Second Viennese School.
Metadata and scanned facsimiles of items in the Düben collection of musical manuscripts and prints from the 17th and early 18th centuries.
Medieval and early modern manuscripts from several Swiss libraries, including the Abbey Library of St. Galla.
Digitised images of over 320 volumes of 16th-century anthologies of printed music, from holdings at the British Library, made available for non-commercial use under JISC's Open Education User Licence.
From the late 18th century to the early 20th century.
Early printed and manuscript scores of the French composer and music publisher Ignaz Pleyel (1757–1831). Includes arrangements of large orchestral works published within the composer's lifetime.
Sheet music and open-source sheet music cataloging software.
Public domain music scores (720,000) and recordings (79,000), including some contemporary composers.
Sheet music for popular songs and piano compositions, mostly 1890–1920.
Rare 17th- and 18th-century scores of operas, ballets, and compilations by the French composer Jean-Baptiste Lully and his sons.
Autograph manuscripts, sketches, engravers' proofs, and first editions.
Scanned graphical music scores (separated by movement), with manually corrected OMR data:
One book of music from Rare Book Room, which contains digitized books of many types.
Laborde Chansonnier – ca. 1470 – Unknown, (author) – France – Library of Congress, Music Division
American popular music spanning the years 1780–1980.
Patriotic and parlour songs, piano pieces, sacred music, and novelty numbers published from before 1900 to 1920. Includes Canadian imprints and music by Canadians or about Canada published anywhere in the world.
19th and early 20th-century American sheet music drawn from the Rare Book, Manuscript, and Special Collections Library at Duke University.
Historical sheet music registered for copyright, including more than 15,000 registered during the years 1820–1860 and more than 47,000 during the years 1870–1885. Includes popular songs, operatic arias, piano music, sacred and secular choral music, solo instrumental music, method books and instructional materials, and music for band and orchestra.
Representative examples documenting the history of Western music from the medieval period through the modern era, including many complete works.
Four complete manuscripts, a gradual, and three antiphonals.
Graphical Scores and originating data [ 1 ] for:
Music made and played by Australians, most published before 1930. Medium-resolution scans. PDFs available.
Manuscript musical scores dating from the 17th through 19th centuries—mostly 17th and 18th century operas, opera excerpts, and other vocal music.
High-quality images and descriptions of music manuscripts.
Music scores by Brazilian composers.
Musical text and critical commentaries of the entire Neue Mozart-Ausgabe.
Public domain music scores provided by the user community in MusicXML format.
Bibliographic information and digital facsimiles for selected collections of manuscript codices, texts, documents, papers, and leaves held by the University of Pennsylvania's Rare Book & Manuscript Library in the Kislak Center for Special Collections, Rare Books, and Manuscripts, as well as those privately owned by Lawrence J. Schoenberg (C53, WG56).
Colour photos, not downloadable.
Searchable database of over 1.2 million historical musical sources, with a focus on the period between 1600 and 1850. When available, links are included to digitized items in the holding institution's repository.
Open collection of digitized sheet music, using the Open Archives Initiative: Protocol for Metadata Harvesting (OAI:PMH).
Collections Indexed:
Public domain scores and books.
Letters from and to the composer, violinist and conductor Louis Spohr
Lute music available in EPS, PDF, MIDI, or TAB format.
Prints and editions of Victoria, Morales, and some other Spanish composers.
Traditional and folk music from around the world. Includes downloadable PDF scores and MIDI backing tracks for many of the songs.
Colour JPEGs of Renaissance manuscripts.
Music from the 9th to 15th centuries.
Emphasis on 18th-century French opera. | https://en.wikipedia.org/wiki/List_of_online_digital_musical_document_libraries |
This is a list of open-source hardware projects, including computer systems and components, cameras, radio, telephony, science education, machines and tools, robotics, renewable energy , home automation, medical and biotech, automotive, prototyping, test equipment, and musical instruments.
Hardware that uses closed source components | https://en.wikipedia.org/wiki/List_of_open-source_hardware |
This is a list of open-source hardware projects, including computer systems and components, cameras, radio, telephony, science education, machines and tools, robotics, renewable energy , home automation, medical and biotech, automotive, prototyping, test equipment, and musical instruments.
Hardware that uses closed source components | https://en.wikipedia.org/wiki/List_of_open-source_hardware_projects |
The following is a list of notable software packages and applications licensed under an open-source license or in the public domain for use in the health care industry.
Source: [ 57 ] | https://en.wikipedia.org/wiki/List_of_open-source_health_software |
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