What's the purpose of root?
Square root
In mathematics, a square root of a number "a" is a number "y" such that ; in other words, a number "y" whose "square" (the result of multiplying the number by itself, or ) is "a". For example, 4 and −4 are square roots of 16 because .
Every nonnegative real number "a" has a unique nonnegative square root, called the "principal square root", which is denoted by , where √ is called the "radical sign" or "radix". For example, the principal square root of 9 is 3, which is denoted by = 3, because and 3 is nonnegative. The term (or number) whose square root is being considered is known as the "radicand". The radicand is the number or expression underneath the radical sign, in this example 9.
Graeffe's method
with roots
Root-finding algorithm
The methods for computing all roots may be used for computing real roots. However, it may be difficult to decide whether a root with a small imaginary part is real or not. Moreover, as the number of the real roots is, in the average, the logarithm of the degree, it a waste of computer resources, to compute the non-real roots when one is interested in real roots.
Philodendron
Philodendrons have both aerial and subterranean roots. The aerial roots occur in many shapes and sizes and originate from most of the plant's nodes or occasionally from an internode. The size and number of aerial roots per node depends on the presence of a suitable substrate for the roots to attach themselves. Aerial roots serve two primary purposes. They allow the philodendron to attach itself to a tree or other plant, and they allow it to collect water and nutrients. As such, the roots are divided morphologically into these two categories. Aerial roots used for attaching to trees tend to be shorter, more numerous, and sometimes have a layer of root hairs attached; those used for collecting water and nutrients tend to be thicker and longer. These feeder roots tend to attach flush with the substrate to which the philodendron is attached, and make their way directly downwards in search of soil. In general, feeder roots tend to show both positive hydrotropic and negative heliotropic behaviors. Characteristic of roots in philodendrons is the presence of a sclerotic hypodermis, which are cylindrical tubes inside the epidermis that can be one to five cells long. The cells that line the sclerotic hypodermis are elongated and tend to be hardened. Underneath the epidermis is a unique layer of cells in a pattern of long cells followed by short cells.
Radical symbol
Each positive real number has two square roots, one positive and the other negative. The square root symbol refers to the principal square root, which is the positive one. The two square roots of a negative number are both imaginary numbers, and the square root symbol refers to the principal square root, the one with positive imaginary part. For the definition of the principal square root of other complex numbers, see Square root#Principal square root of a complex number.
Root
The first root that comes from a plant is called the radicle. A root's four major functions are:
Root
Early root growth is one of the functions of the apical meristem located near the tip of the root. The meristem cells more or less continuously divide, producing more meristem, root cap cells (these are sacrificed to protect the meristem), and undifferentiated root cells. The latter become the primary tissues of the root, first undergoing elongation, a process that pushes the root tip forward in the growing medium. Gradually these cells differentiate and mature into specialized cells of the root tissues.
Nth root
Thus finding "n"th roots in the complex plane can be segmented into two steps. First, the magnitude of all the "n"th roots is the "n"th root of the magnitude of the original number. Second, the angle between the positive horizontal axis and a ray from the origin to one of the "n"th roots is formula_102, where formula_98 is the angle defined in the same way for the number whose root is being taken. Furthermore, all "n" of the "n"th roots are at equally spaced angles from each other.
Polynomial decomposition
gives the roots
Crown-to-root ratio
Crown-to-root-ratio is the ratio of the length of the part of a tooth that appears above the alveolar bone versus what lies below it. It is an important consideration in the diagnosis, treatment planning and restoration of teeth, one that hopefully guides the plan of treatment to the proper end result.
Root cause
A root cause is an initiating cause of either a condition or a causal chain that leads to an outcome or effect of interest. The term denotes the earliest, most basic, 'deepest', cause for a given behavior; most often a fault. The idea is that you can only see an error by its manifest signs. Those signs can be widespread, multitudinous, and convoluted, whereas the root cause leading to them often is a lot simpler.
Root system
Given a root system, select a set Δ of simple roots as in the preceding section. The vertices of the associated Dynkin diagram correspond to the roots in Δ. Edges are drawn between vectors as follows, according to the angles. (Note that the angle between simple roots is always at least 90 degrees.)
The term "directed edge" means that double and triple edges are marked with an arrow pointing toward the shorter vector. (Thinking of the arrow as a "greater than" sign makes it clear which way the arrow is supposed to point.)
Real-root isolation
For root isolation, one requires a procedure for counting the real roots of a polynomial in an interval without having to compute them, or, at least a procedure for deciding whether an interval contains zero, one or more roots. With such a decision procedure, one may work with a working list of intervals that may contain real roots. At the beginning, the list contains a single interval containing all roots of interest, generally the whole real line or its positive part. Then each interval of the list is divided into two smaller intervals. If one of the new intervals does not contains any root, it is removed from the list. If it contains one root, it is put in an output list of isolating intervals. Otherwise, it is kept in the working list for further divisions, and the process may continue until all roots are eventually isolated
Root-finding algorithm
Bracketing methods determine successively smaller intervals (brackets) that contain a root. When the interval is small enough, then a root has been found. They generally use the intermediate value theorem, which asserts that if a continuous function has values of opposite signs at the end points of an interval, then the function has at least one root in the interval. Therefore, they require to start with an interval such that the function takes opposite signs at the end points of the interval. However, in the case of polynomials there are other methods (Descartes' rule of signs, Budan's theorem and Sturm's theorem) for getting information on the number of roots in an interval. They lead to efficient algorithms for real-root isolation of polynomials, which ensure finding all real roots with a guaranteed accuracy.
Irrigation game
The definition of Márkus et al. 2011 is the following:
A "graph" is a pair formula_1, where the elements of formula_2 are called vertices or nodes, and formula_3 stands for the ordered pairs of vertices, called arcs or edges. A rooted tree is a graph in which any two vertices are connected by exactly one simple path, and one vertex has been designated the root, in which case the edges have a natural orientation, away from the root. The tree-order is the partial ordering on the vertices of a rooted tree with formula_4, if the unique path from the root to formula_5 passes through formula_6. For any formula_7 formula_8 means formula_9 is an edge between vertices formula_10 such that formula_4.
Cube root
In some contexts, particularly when the number whose cube root is to be taken is a real number, one of the cube roots (in this particular case the real one) is referred to as the "principal cube root", denoted with the radical sign . The cube root operation is associative with exponentiation and distributive with multiplication and division if considering only real numbers, but not always if considering complex numbers: for example, the cube of any cube root of 8 is 8, but the three cube roots of 8 are 8, −4 + 4"i", and −4 − 4"i".
Nepenthes distillatoria
The root draws up moisture from the earth which with the help of the sun's rays rises up into the plant itself and then flows down through the stems and nerves of the leaves into the natural utensil to be stored there until used for human needs. [translated from Latin in "Pitcher-Plants of Borneo"]
Root pressure
Root pressure is the transverse osmotic pressure within the cells of a root system that causes sap to rise through a plant stem to the leaves.
Root
The term root crops refers to any edible underground plant structure, but many root crops are actually stems, such as potato tubers. Edible roots include cassava, sweet potato, beet, carrot, rutabaga, turnip, parsnip, radish, yam and horseradish. Spices obtained from roots include sassafras, angelica, sarsaparilla and licorice.
On the Fourfold Root of the Principle of Sufficient Reason
In his Translator's Introduction to Schopenhauer's "The World as Will and Representation", E. F. J. Payne concisely summarized the "Fourfold Root".
Our knowing consciousness...is divisible solely into subject and object. To be object for the subject and to be our representation or mental picture are one and the same. All our representations are objects for the subject, and all objects of the subject are our representations. These stand to one another in a regulated connection which in form is determinable "a priori", and by virtue of this connection nothing existing by itself and independent, nothing single and detached, can become an object for us. ...The first aspect of this principle is that of becoming, where it appears as the law of causality and is applicable only to "changes". Thus if the cause is given, the effect must of necessity follow. The second aspect deals with concepts or abstract representations, which are themselves drawn from representations of intuitive perception, and here the principle of sufficient reason states that, if certain premises are given, the conclusion must follow. The third aspect of the principle is concerned with being in space and time, and shows that the existence of one relation inevitably implies the other, thus that the equality of the angles of a triangle necessarily implies the equality of its sides and "vice versa". Finally, the fourth aspect deals with actions, and the principle appears as the law of motivation, which states that a definite course of action inevitably ensues on a given character and motive.
Lateral root
Lateral roots extend horizontally from the primary root (radicle) and serve to anchor the plant securely into the soil. This branching of roots also contributes to water uptake, and facilitates the extraction of nutrients required for the growth and development of the plant.
Square root
The square root of a nonnegative number is used in the definition of Euclidean norm (and distance), as well as in generalizations such as Hilbert spaces. It defines an important concept of standard deviation used in probability theory and statistics. It has a major use in the formula for roots of a quadratic equation; quadratic fields and rings of quadratic integers, which are based on square roots, are important in algebra and have uses in geometry. Square roots frequently appear in mathematical formulas elsewhere, as well as in many physical laws.
Domestic pig
Rooting is an instinctual behavior in pigs that is characterized by a pig nudging its snout into something. Similar to a cat’s kneading, rooting is found comforting, first happens when they are born in order to obtain their mother’s milk, and can become a habitual, obsessive behavior which is most prominent in animals weaned too early. Often, pigs will root and dig into the ground to forage for food. Rooting is known to also be used as a means of communication.
Root (chord)
The fundamental bass ("basse fondamentale") is a concept proposed by Jean-Philippe Rameau, derived from the thoroughbass, to notate what would today be called the progression of chord roots rather than the actual lowest note found in the music, the bassline. From this Rameau formed rules for the progression of chords based on the intervals between their roots. Subsequently, the Viennese theory of tonal music has typically treated chordal roots as the defining feature of harmony.
Proto-Indo-European root
The onset and coda must contain at least one consonant; a root may not begin or end with the ablaut vowel. Consequently, the simplest roots have an onset and coda consisting of one consonant each. Such simple roots are common; examples are: 'to give', 'to bear', 'to put', 'to run', 'to eat', 'sharp', 'to tread', 'to sit', 'to clothe'. Roots can also have a more complex onset and coda, consisting of a consonant cluster (multiple consonants). These include: 'to breathe', 'red', 'to plough', 'straight', 'to bind', 'to freeze', 'to flow' and 'to sleep', 'to moisten'. The maximum number of consonants seems to be five, as in 'to twine'.
Nose ring (animal)
Rooting is the act of a pig nudging into something with its snout, such as into the dirt to unearth plants to eat. In some circumstances, owners of pigs may find this undesirable. Nose rings make rooting painful for the animal, although a ringed pig may still able to forage freely through leaf litter and surface vegetation. Pig nose-ringing may sometimes be required by local regulations, as when farm pigs are released into public woods to pannage (such as on the New Forest in southern England).
Root
The configuration of root systems serves to structurally support the plant, compete with other plants and for uptake of nutrients from the soil. Roots grow to specific conditions, which, if changed, can impede a plant's growth. For example, a root system that has developed in dry soil may not be as efficient in flooded soil, yet plants are able to adapt to other changes in the environment, such as seasonal changes.
.root
root is the name of a database record of the root zone in the Domain Name System of the Internet that was occasionally used as a diagnostic marker. Its presence demonstrated the root zone was not truncated upon loading by a root nameserver.
Root system of a semi-simple Lie algebra
The last two relations hold because formula_50 belongs to the root space formula_51, and more generally, formula_52 belongs to formula_53. But, as we shall see momentarily, if formula_13 and formula_55 are simple roots, then formula_56 is not a root if formula_57, so that formula_52 must be zero. To see that formula_56 is not a root, note that if formula_13 and formula_26 are distinct elements of formula_27, then formula_63 cannot be a root, for this would violate one of the defining properties of a base—that the expansion of a root in terms of the base cannot have both positive and negative coefficients. But then if formula_64 is the reflection associated to formula_13, we can easily calculate that 
Then since formula_63 is not a root, neither is formula_56.
Root-finding algorithm
The most widely used method for computing a root is Newton's method, which consists of the iterations of the computation of 
by starting from a well-chosen value formula_6
If is a polynomial, the computation is faster when using Horner rule for computing the polynomial and its derivative.
Root (chord)
In tertian harmonic theory, that is in a theory where chords can be considered stacks of third intervals (e.g. in common practice tonality), the root of a chord is the note on which the subsequent thirds are stacked. For instance, the root of a triad such as C Major is C, independently of the vertical order in which the three notes (C, E and G) are presented. A triad can be in three possible positions, a "root position" with the root in the bass (i.e., with the root as the lowest note, thus C, E, G or C, G, E, from lowest to highest notes), a first inversion, e.g. E, C, G or E, G, C (i.e., with the note which is a third interval above the root, E, as the lowest note) and a second inversion, e.g. G, C, E or G, E, C, in which the note that is a fifth interval above the root (G ) is the lowest note.
The Need for Roots
Obedience is defined as an essential need of the soul as long as it's the sort of obedience that arises from freely given consent to obey a given set of rules or the commands of a leader. Obedience motivated by a fear of penalties or a desire for reward is mere servility and of no value. The author writes that it's important that the social structure has a common goal, the essence of which can be grasped by all, so people can appreciate the purpose of the rules and orders.
Lawn aerator
Lawn aeration constitutes three things: controlling lawn thatch, and reducing soil compaction, making grass roots multiply. Aerating either by coring or spiking causes the roots to divide or sever apart. This is something rarely done naturally. By severing roots it makes the roots multiply. When roots multiply the blades multiply thereby keeping the lawn thick and rooting deeply. the holes become engorged with roots. Lawn thatch is a layer of dead organic tissue that can protect the lawn by moderating temperature and reducing evapotranspiration when it is a reasonable thickness, but too much thatch can limit soil oxygenation and reduce watering effectiveness. Soil compaction makes it difficult for grass to develop long roots and disturbs both natural rainwater and artificial irrigation.
Platycodon
In Korea, the plant as well as its root are referred to as (). The root, fresh or dried, is one of the most common vegetables. It is also one of the most frequent ingredients in bibimbap. Sometimes, rice is cooked with balloon flower root to make . Preparation of the root always involves soaking and washing (usually rubbing it with coarse sea salt and rinsing it multiple times), which gets rid of the bitter taste.
Ebb and flow
The film of water left around the roots during ebb has a high surface-to-mass ratio, which means that even as the roots absorb oxygen, its high surface area facilitates re-oxygenation, which can sustain the roots as long as their surfaces remain damp. The high oxygen content of water filmed in this way suppresses most harmful lifeforms, keeping the root zones disease free. In other types of hydroponics this function must be performed by cooling the solution to protect it from pythium, a form of water mold responsible for a condition called 'root rot', in which the outer cells of the roots die, turn brown and slough off when handled. Need for supplementary oxygenation using air pumps is also eliminated, which increases reliability and reduces complexity.
Shifting nth root algorithm
and
Phylogenetic tree
A rooted phylogenetic tree (see two graphics at top) is a directed tree with a unique node — the root — corresponding to the (usually imputed) most recent common ancestor of all the entities at the leaves of the tree. The root node does not have a parent node, but serves as the parent of all other nodes in the tree. The root is therefore a node of degree 2 while other internal nodes have a minimum degree of 3 (where "degree" here refers to the total number of incoming and outgoing edges).
Root test
the root test uses the number
Rooting (Android)
Rooting is often performed with the goal of overcoming limitations that carriers and hardware manufacturers put on some devices. Thus, rooting gives the ability (or permission) to alter or replace system applications and settings, run specialized applications ("apps") that require administrator-level permissions, or perform other operations that are otherwise inaccessible to a normal Android user. On Android, rooting can also facilitate the complete removal and replacement of the device's operating system, usually with a more recent release of its current operating system.
Root
The roots, or parts of roots, of many plant species have become specialized to serve adaptive purposes besides the two primary functions, described in the introduction.
Root directory
In a computer file system, and primarily used in the Unix and Unix-like operating systems, the root directory is the first or top-most directory in a hierarchy. It can be likened to the trunk of a tree, as the starting point where all branches originate from. The root file system is the file system contained on the same disk partition on which the root directory is located; it is the filesystem on top of which all other file systems are mounted as the system boots up.
Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power . Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform.
Nth root
The two square roots of a complex number are always negatives of each other. For example, the square roots of are and , and the square roots of are
If we express a complex number in polar form, then the square root can be obtained by taking the square root of the radius and halving the angle:
A "principal" root of a complex number may be chosen in various ways, for example
which introduces a branch cut in the complex plane along the positive real axis with the condition , or along the negative real axis with .
Root invasion
Root invasion is the incursion of plant roots with undesirable impacts.
Root hair
The root hairs are where most water absorption happens. They are long and so they can penetrate between soil particles, and prevent harmful bacterial organisms from entering the plant through the xylem vessels. They have a large surface area for absorption of water. Increasing root surface area aids plants to be more efficient in absorbing nutrients and establishing relationships with microbes.
Cross-section of root hair cell: a roughly rectangular shape with a long, thin tail extending to the right and a nucleus at the top left.
Water passes from the soil water to the root hair cell’s cytoplasm by osmosis. This happens because the soil water has a higher water potential than the root hair cell cytoplasm. The function of root hairs is to collect water and mineral nutrients present in the soil and take this solution up through the roots to the rest of the plant. As root hair cells do not carry out photosynthesis they do not contain chloroplasts.
Heart rot
Pruning focuses on removing dead or diseased branches with minimal damage done to the tree. Branches connect to the trunk and grow from the branch collar. While the branch itself may be dead, the branch collar is still healthy and resistant to disease. It is from the branch collar that a new limb will generate and grow, so it is important not to damage it while pruning. Make clean cuts at the base of branch adjacent to the branch collar. Small branch stubs(larger than three inches) will inhibit the growth process and provide fungi with ideal growth environments.
Tree rotation
The right rotation operation as shown in the adjacent image is performed with "Q" as the root and hence is a right rotation on, or rooted at, "Q". This operation results in a rotation of the tree in the clockwise direction. The inverse operation is the left rotation, which results in a movement in a counter-clockwise direction (the left rotation shown above is rooted at "P"). The key to understanding how a rotation functions is to understand its constraints. In particular the order of the leaves of the tree (when read left to right for example) cannot change (another way to think of it is that the order that the leaves would be visited in an in-order traversal must be the same after the operation as before). Another constraint is the main property of a binary search tree, namely that the right child is greater than the parent and the left child is less than the parent. Notice that the right child of a left child of the root of a sub-tree (for example node B in the diagram for the tree rooted at Q) can become the left child of the root, that itself becomes the right child of the "new" root in the rotated sub-tree, without violating either of those constraints. As you can see in the diagram, the order of the leaves doesn't change. The opposite operation also preserves the order and is the second kind of rotation.
Root system
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and representation theory of semisimple Lie algebras. Since Lie groups (and some analogues such as algebraic groups) and Lie algebras have become important in many parts of mathematics during the twentieth century, the apparently special nature of root systems belies the number of areas in which they are applied. Further, the classification scheme for root systems, by Dynkin diagrams, occurs in parts of mathematics with no overt connection to Lie theory (such as singularity theory). Finally, root systems are important for their own sake, as in spectral graph theory.
Root (linguistics)
The traditional definition allows roots to be either free morphemes or bound morphemes. Root morphemes are essential for affixation and compounds. However, in polysynthetic languages with very high levels of inflectional morphology, the term "root" is generally synonymous with "free morpheme". Many such languages have a very restricted number of morphemes that can stand alone as a word: Yup'ik, for instance, has no more than two thousand.
ITIL
Root-cause analysis is a formal problem-solving process and a critical component of Problem Management. Once a problem (or potential problem) has been identified, the root cause analysis process begins. The purpose of a root cause analysis is two-fold:Classic root-cause analysis methods include the 5-whys and "Ishikawa diagram" or fishbone diagram. Others have since developed more advanced root cause analysis methodologies, some with corresponding software applications.
Root trainer
A root pruning container is an aid to the cultivation of young plants and trees in nurseries. Many pot designs train the roots. One example is a truncated plastic cone in which a seedling is planted. There is a drainage hole at the bottom and the main tap root tends to grow towards this.
Swarm behaviour
Roots, in particular, display observable swarm behavior, growing in patterns that exceed the statistical threshold for random probability, and indicate the presence of communication between individual root apexes. The primary function of plant roots is the uptake of soil nutrients, and it is this purpose which drives swarm behavior. Plants growing in close proximity have adapted their growth to assure optimal nutrient availability. This is accomplished by growing in a direction that optimizes the distance between nearby roots, thereby increasing their chance of exploiting untapped nutrient reserves. The action of this behavior takes two forms: maximization of distance from, and repulsion by, neighboring root apexes. The transition zone of a root tip is largely responsible for monitoring for the presence of soil-borne hormones, signaling responsive growth patterns as appropriate. Plant responses are often complex, integrating multiple inputs to inform an autonomous response. Additional inputs that inform swarm growth includes light and gravity, both of which are also monitored in the transition zone of a root's apex. These forces act to inform any number of growing "main" roots, which exhibit their own independent releases of inhibitory chemicals to establish appropriate spacing, thereby contributing to a swarm behavior pattern. Horizontal growth of roots, whether in response to high mineral content in soil or due to stolon growth, produces branched growth that establish to also form their own, independent root swarms.
Tree (data structure)
The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its "root path"). This is commonly needed in the manipulation of the various self-balancing trees, AVL Trees in particular. The root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such are allowed) has height −1.
Root mucilage
Root mucilage is a part of a wider secrete from plant roots known as root exudate. Plant roots secrete a variety of organic molecules into the surrounding soil, such as proteins, enzymes, DNA, sugars and amino acids, which are the building blocks of life. This collective secretion is known as root exudate. This root exudate prevents root infection from bacteria and fungi, helps the roots to penetrate through the soil, and can create a micro-climate that is beneficial to the plant.
Cutting (plant)
It was known as early as 1935 that when indolyl-3-acetic acid (IAA), also known as auxin, is applied to the stem of root cuttings, there is an increase the average number of adventitious roots compared to cuttings that are not treated. Researchers also applied this compound to stems without leaves that normally would not have any root formation and found that auxin induced root formation, thus determining auxin is necessary for root formation. Identification of this hormone has been important to industries that rely on vegetative propagation, as it is sometimes applied to fresh cuttings to stimulate root growth.
Elementary mathematics
Roots are the opposite of exponents. The nth root of a number "x" (written formula_4) is a number "r" which when raised to the power "n" yields "x". That is,
where "n" is the "degree" of the root. A root of degree 2 is called a "square root" and a root of degree 3, a "cube root". Roots of higher degree are referred to by using ordinal numbers, as in "fourth root", "twentieth root", etc.
Root (linguistics)
This distinction between the word as a unit of speech and the root as a unit of meaning is even more important in the case of languages where roots have many different forms when used in actual words, as is the case in Semitic languages. In these, roots are formed by consonants alone, and speakers elaborate different words (belonging potentially to different parts of speech) from the root by inserting different vowels. For example, in Hebrew, the root gdl represents the idea of largeness, and from it we have gadol and gdola" (masculine and feminine forms of the adjective "big"), gadal "he grew", "higdil "he magnified" and "magdelet" "magnifier", along with many other words such as godel "size" and "migdal" "tower".
Nerve root
It is helpful to the administration of anti-inflammatory drugs. In the acute setting, the main goal is to restore proper mobility by not producing pain, individually selected physiotherapy. Surgery is used when other methods do not produce results.
Root directory
In UNIX-like operating systems, each process has its own idea of what the root directory is. For most processes this is the same as the system's actual root directory, but it can be changed by calling the chroot system call. This is typically done to create secluded environment to run software that requires legacy libraries and sometimes to simplify software installation and debugging. Chroot is not meant to be used for enhanced security as the processes inside can break out. FreeBSD offers a stronger jail() system call that enables operating-system-level virtualization and also serves security purposes to restrict which files a process may access to just a subset of the file system hierarchy.
Square root
The principal square root function "f"("x") = (usually just referred to as the "square root function") is a function that maps the set of nonnegative real numbers onto itself. In geometrical terms, the square root function maps the area of a square to its side length.
Shifting nth root algorithm
and let
Root (disambiguation)
Root or roots may also refer to:
Plant nutrition
The root, especially the root hair, is the essential organ for the uptake of nutrients. The structure and architecture of the root can alter the rate of nutrient uptake. Nutrient ions are transported to the center of the root, the stele, in order for the nutrients to reach the conducting tissues, xylem and phloem. The Casparian strip, a cell wall outside the stele but within the root, prevents passive flow of water and nutrients, helping to regulate the uptake of nutrients and water. Xylem moves water and mineral ions within the plant and phloem accounts for organic molecule transportation. Water potential plays a key role in a plant's nutrient uptake. If the water potential is more negative within the plant than the surrounding soils, the nutrients will move from the region of higher solute concentration—in the soil—to the area of lower solute concentration - in the plant.
Kudzu
For successful long-term control of kudzu, destroying the underground system, which can be extremely large and deep, is not necessary. Only killing or removing the kudzu root crown and all rooting runners is needed. The root crown is a fibrous knob of tissue that sits on top of the roots. Crowns form from multiple vine nodes that root to the ground, and range from pea- to basketball-sized. The older the crowns, the deeper they tend to be found in the ground. Nodes and crowns are the source of all kudzu vines, and roots cannot produce vines. If any portion of a root crown remains after attempted removal, the kudzu plant may grow back.
Root Force
Root Force is a biocentric, decentralized, international direct-action campaign devoted to "[dismantling] the system that is killing and enslaving [the] planet and its people." Its slogan is "Demolishing Colonialism At Its Foundations."
Proto-Indo-European nominals
The root indicates a basic concept, often a verb (e.g. 'give'), while the stem carries a more specific nominal meaning based on the combination of root and suffix (e.g. 'giver', 'gift'). Some roots seem to have no definable meaning, as in 'father'; and some stems cannot clearly be broken up into root and suffix altogether, as in 'bear'.
E. Merrill Root
Root's central philosophy was what he called "Essentialism". His intention was "... to make coherent and affirmative a certain philosophy, and American philosophy, and to do so in terms of art." He stated his philosophy thus:
"More and more as my life has matured, I have realized that by fundamental nature I am a conservative. I have realized that I wish to preserve the roots of life whence grow the blossoms and the fruits of life, and that I have become a genuine radical - i.e., one who works with the roots of life, laboring to set them more firmly and to nourish them more richly. I applaud fruitful change that comes from an enhancement and intensification of the last things that maintain their continuity with first things. But, as I see it, such change must be growth from within, so that you and I and our nation become ever more clearly, more richly, more truly, what we always "are", potentially in principle. Man is ever seeking novelty; God is forever and ever making things new. He does not make the seasons, nor the rose, nor the Labrador retriever, nor the lover nor the poet, "novel" - He makes them new. And because they are new in their fundamental being, they are vitally old; as tomorrow's sunrise will be the newest of dawns and the oldest of dawns, since it shone upon the Birthday of Creation."
Tuber
Root tubers are perennating organs, thickened roots that store nutrients over periods when the plant cannot actively grow, thus permitting survival from one year to the next. The massive enlargement of secondary roots typically represented by sweet potato ("Ipomoea batatas"), have the internal and external cell and tissue structures of a normal root, they produce adventitious roots and stems which again produce adventitious roots.
Root
When dissected, the arrangement of the cells in a root is root hair, epidermis, epiblem, cortex, endodermis, pericycle and, lastly, the vascular tissue in the centre of a root to transport the water absorbed by the root to other places of the plant.
Perhaps the most striking characteristic of roots (that makes it distinguishable from other plant organs such as stem-branches and leaves) is that, roots have an "endogenous" origin, i.e. it originates and develops from an inner layer of the mother axis (Such as Pericycle). Whereas Stem-branching and leaves (those develop as buds) are "exogenous", i.e. start to develop from the cortex, an outer layer.
Nth root
Any non-zero number, considered as complex number, has "n" different "complex roots of degree "n"" ("n"th roots), including those with zero imaginary part, i.e. any real roots. The root of "0" is zero for all degrees "n", since . In particular, if "n" is even and "x" is a positive real number, one of its "n"th roots is positive, one is negative, and the rest (when "n" > 2) are complex but not real; if "n" is even and "x" is a negative real, none of the "n"th roots is real. If "n" is odd and "x" is real, one "n"th root is real and has the same sign as "x", while the other ("n" − 1) roots are not real. Finally, if "x" is not real, then none of its "n"th roots is real.
Root test
The terms of this series would then be given by "a" = "c"("z" − "p"). One then applies the root test to the "a" as above. Note that sometimes a series like this is called a power series "around "p"", because the radius of convergence is the radius "R" of the largest interval or disc centred at "p" such that the series will converge for all points "z" strictly in the interior (convergence on the boundary of the interval or disc generally has to be checked separately). A corollary of the root test applied to such a power series is that the radius of convergence is exactly formula_9 taking care that we really mean ∞ if the denominator is 0.
Root-finding algorithm
When one root has been found, one may use Euclidean division for removing the factor from the polynomial. Computing a root of the resulting quotient, and repeating the process provides, in principle, a way for computing all roots. However, this iterative scheme is numerically unstable; the approximation errors accumulate during the successive factorizations, so that the last roots are determined with a polynomial that deviates widely from a factor of the original polynomial. To reduce this error, one may, for each root that is found, restart Newton's method with the original polynomial, and this approximate root as starting value.
Multiplicity (mathematics)
This definition generalizes the multiplicity of a root of a polynomial in the following way. The roots of a polynomial "f" are points on the affine line, which are the components of the algebraic set defined by the polynomial. The coordinate ring of this affine set is formula_1 where "K" is an algebraically closed field containing the coefficients of "f". If formula_2 is the factorization of "f", then the local ring of "R" at the prime ideal formula_3 is formula_4 This is a vector space over "K", which has the multiplicity formula_5 of the root as a dimension.
Rootstock
A rootstock is part of a plant, often an underground part, from which new above-ground growth can be produced. It could also be described as a stem with a well developed root system, to which a bud from another plant is grafted. It can refer to a rhizome or underground stem. In grafting, it refers to a plant, sometimes just a stump, which already has an established, healthy root system, onto which a cutting or a bud from another plant is grafted. In some cases, such as vines of grapes and other berries, cuttings may be used for rootstocks, the roots being established in nursery conditions before planting them out. The plant part grafted onto the rootstock is usually called the scion. The scion is the plant that has the properties that propagator desires above ground, including the photosynthetic activity and the fruit or decorative properties. The rootstock is selected for its interaction with the soil, providing the roots and the stem to support the new plant, obtaining the necessary soil water and minerals, and resisting the relevant pests and diseases. After a few weeks the tissues of the two parts will have grown together, eventually forming a single plant. After some years it may be difficult to detect the site of the graft although the product always contains the components of two genetically different plants.
Root
In vascular plants, the root is the organ of a plant that typically lies below the surface of the soil. Roots can also be aerial or aerating, that is,
growing up above the ground or especially above water. Furthermore, a stem normally occurring below ground is not exceptional either (see rhizome). Therefore, the root is best defined as the non-leaf, non-nodes bearing parts of the plant's body. However, important internal structural differences between stems and roots exist.
Root ball
A root ball is the main mass of roots at the base of a plant such as a shrub or tree. It is of particular significance in horticulture when plants are repotted or planted out in the ground. The quality and preparation of the root ball will determine how well the plant will survive this transplantation and then flourish in its new situation.
Cluster root
Cluster roots, also known as proteoid roots, are plant roots that form clusters of closely spaced short lateral rootlets. They may form a two- to five-centimetre-thick mat just beneath the leaf litter. They enhance nutrient uptake, possibly by chemically modifying the soil environment to improve nutrient solubilisation. As a result, plants with proteoid roots can grow in soil that is very low in nutrients, such as the phosphorus-deficient native soils of Australia.
Rational root theorem
The theorem is used in order to determine whether a polynomial has any rational roots, and if so to find them. Since the theorem gives constraints on the numerator and denominator of the fully reduced rational roots as being divisors of certain numbers, all possible combinations of divisors can be checked and either the rational roots will be found or it will be determined that there are none. If one or more are found, they can be factored out of the polynomial, resulting in a polynomial of lower degree whose roots are also roots of the original polynomial.
Nelumbo nucifera
The lotus root is used to add seasoning to food. Lotus root is a moderate calorie root vegetable (100 g of root-stem provides about 74 calories) and is composed of several vitamins, minerals, and nutrients: 83.80% water, 0.11% fat, 1.56% reducing sugar, 0.41% sucrose, 2.70% crude protein, 9.25% starch, 0.80% fiber, 0.10% ash and 0.06% calcium. 100 g of root provides 44 mg of vitamin C or 73% of daily recommended values (RDA).
Root cap
The purpose of the root cap is to enable downward growth of the root, with the root cap covering the sensitive tissue in the root. Also, the root cap enables geoperception or gravitropism. This allows the plant to grow downwards (with gravity) or upwards (against gravity).
Exponentiation
It is usual in mathematics to define as the principal value of the root, which is, conventionally, the th root whose argument has the smallest absolute value. When is a positive real number, this is coherent with the usual convention of defining as the unique positive real th root. On the other hand, when is a negative real number, and is an odd integer, the unique real th root is not one of the two th roots whose argument has the smallest absolute value. In this case, the meaning of may depend on the context, and some care may be needed for avoiding errors.
Root-finding algorithm
For finding all the roots, the oldest method is, when a root has been found, to divide the polynomial by , and restart iteratively the search of a root of the quotient polynomial. However, except for low degrees, this does not work well because of the numerical instability: Wilkinson's polynomial shows that a very small modification of one coefficient may change dramatically not only the value of the roots, but also their nature (real or complex). Also, even with a good approximation, when one evaluates a polynomial at an approximate root, one may get a result that is far to be close to zero. For example, if a polynomial of degree 20 (the degree of Wilkinson's polynomial) has a root close to 10, the derivative of the polynomial at the root may be of the order of formula_2 this implies that an error of formula_3 on the value of the root may produce a value of the polynomial at the approximate root that is of the order of formula_4
Aggadah
In terms of etymology, the cognate means "telling", while the Aramaic root אגד (as well as נגד, from which אגדה may arise) has the dual implication of “expanding” / “drawing out” and “binding” / “drawing in”. Correspondingly, the Aggadah may be seen as those teachings which communicate Rabbinic traditions to the reader, simultaneously expanding their understanding of the text, while strengthening their religious experience and spiritual connection. The root also has the meaning "flow", and here relates to the transmission of ideas.
Root race
The first aim of the Theosophical Society she founded is "To form a nucleus of the Universal Brotherhood of Humanity, without distinction of race, creed, sex, caste or colour", and her writings also include references emphasizing the unity of humanity: "all men have spiritually and physically the same origin" and that "mankind is essentially of one and the same essence".
Nepenthes
The root draws up moisture from the earth which with the help of the sun's rays rises up into the plant itself and then flows down through the stems and nerves of the leaves into the natural utensil to be stored there until used for human needs. [translated from Latin in "Pitcher-Plants of Borneo"]
Superuser
The name "root" may have originated because "root" is the only user account with permission to modify the root directory of a Unix system. This directory was originally considered to be root's home directory, but the UNIX Filesystem Hierarchy Standard now recommends that root's home be at /root."" The first process bootstrapped in a Unix-like system, usually called init, runs with root privileges. It spawns all other processes directly or indirectly, which inherit their parents' privileges. Only a process running as root is allowed to change its user ID to that of another user; once it's done so, there is no way back. Doing so is sometimes called "dropping root privileges" and is often done as a security measure to limit the damage from possible contamination of the process. Another case is login and other programs that ask users for credentials and in case of successful authentication allow them to run programs with privileges of their accounts.
Root system
Let "E" = R, and let Φ consist of all integer vectors in "E" of length together with all vectors of the form 2λ, where λ is an integer vector of length 1. The total number of roots is 2"n". One choice of simple roots is: α = e – e, for 1 ≤ i ≤ n – 1 (the above choice of simple roots for A), and the longer root α = 2e.
The reflection σ(α) = α + α, but σ(α) = α + 2α.
E8 (mathematics)
A set of simple roots for a root system Φ is a set of roots that form a basis for the Euclidean space spanned by Φ with the special property that each root has components with respect to this basis that are either all nonnegative or all nonpositive.
Real-root isolation
Real-root isolation is useful because usual root-finding algorithms for computing the real roots of a polynomial may produce some real roots, but, cannot generally certify having found all real roots. In particular, if such an algorithm does not find any root, one does not know whether it is because there is no real root. Some algorithms compute all complex roots, but, as there are generally much fewer real roots than complex roots, most of their computation time is generally spent for computing non-real roots (in the average, a polynomial of degree has complex roots, and only roots). Moreover, it may be difficult to distinguish the real roots from the non-real roots with small imaginary part (see the example of Wilkinson's polynomial in next section).
Square root of a matrix
giving the square root
Butcher group
A rooted tree is a graph with a distinguished node, called the "root", in which every other node is connected to the root by a unique path. If the root of a tree t is removed and the nodes connected to the original node by a single bond are taken as new roots, the tree t breaks up into rooted trees t, t, ... Reversing this process a new tree t = [t, t, ...] can be constructed by joining the roots of the trees to a new common root. The number of nodes in a tree is denoted by |t|. A "heap-ordering" of a rooted tree t is an allocation of the numbers 1 through |t| to the nodes so that the numbers increase on any path going away from the root. Two heap orderings are "equivalent", if there is an automorphism of rooted trees mapping one of them on the other. The number of equivalence classes of heap-orderings on a particular tree is denoted by α(t) and can be computed using the Butcher's formula:
Proto-Indo-European root
Root extensions are additions of one or two sounds, often plosives, to the end of a root. These extensions do not seem to change the meaning of a root, and often lead to variant root forms across different descendants. The source and function of these extensions is not known.
Nth root
In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction:
Roots are particularly important in the theory of infinite series; the root test determines the radius of convergence of a power series. Roots can also be defined for complex numbers, and the complex roots of 1 (the roots of unity) play an important role in higher mathematics. Galois theory can be used to determine which algebraic numbers can be expressed using roots and to prove the Abel–Ruffini theorem, which states that a general polynomial equation of degree five or higher cannot be solved using roots alone; this result is also known as "the insolubility of the quintic".
Cutting (plant)
A plant cutting is a piece of a plant that is used in horticulture for vegetative (asexual) propagation. A piece of the stem or root of the source plant is placed in a suitable medium such as moist soil. If the conditions are suitable, the plant piece will begin to grow as a new plant independent of the parent, a process known as striking. A stem cutting produces new roots, and a root cutting produces new stems. Some plants can be grown from leaf pieces, called leaf cuttings, which produce both stems and roots. The scions used in grafting are also called cuttings.
Square root
and
Taproot
Taproots develop from the radicle of a seed, forming the primary root. It branches off to secondary roots, which in turn branch to form tertiary roots. These may further branch to form rootlets. For most plants species the radicle dies some time after seed germination, causing the development of a fibrous root system, which lacks a main downward-growing root. Most trees begin life with a taproot, but after one to a few years the main root system changes to a wide-spreading fibrous root system with mainly horizontal-growing surface roots and only a few vertical, deep-anchoring roots. A typical mature tree 30–50 m tall has a root system that extends horizontally in all directions as far as the tree is tall or more, but as much as 100% of the roots are in the top 50 cm of soil.
Root pressure
Root pressure is caused by active distribution of mineral nutrient ions into the root xylem. Without transpiration to carry the ions up the stem, they accumulate in the root xylem and lower the water potential. Water then diffuses from the soil into the root xylem due to osmosis. Root pressure is caused by this accumulation of water in the xylem pushing on the rigid cells. Root pressure provides a force, which pushes water up the stem, but it is not enough to account for the movement of water to leaves at the top of the tallest trees. The maximum root pressure measured in some plants can raise water only to 6.87 meters, and the tallest trees are over 100 meters tall.
Evolutionary history of plants
Roots are important to plants for two main reasons: Firstly, they provide anchorage to the substrate; more importantly, they provide a source of water and nutrients from the soil. Roots allowed plants to grow taller and faster.
The Need for Roots
A peasant's requirements include a strong need to own land, which is important for them to feel rooted. Boredom can be a problem as many peasants do the same work throughout their lives, starting from about age 14. Weil suggests a tradition should be established for peasant youths take a few months out for travel in their late teens, similar to the "tour de France" that used to exist for apprentice artisans. Those who desire it should also be able to return to education for a year or two.
Root cap
The root cap is a type of tissue at the tip of a plant root. It is also called calyptra. Root caps contain statocytes which are involved in gravity perception in plants. If the cap is carefully removed the root will grow randomly. The root cap protects the growing tip in plants. It secretes mucilage to ease the movement of the root through soil, and may also be involved in communication with the soil microbiota.
Radical symbol
In mathematics, the radical sign or radical symbol or root symbol is a symbol for the square root or higher-order root of a number. The square root of a number formula_1 is written as
while the formula_3th root of formula_1 is written as
It is also used for other meanings in more advanced mathematics, such as the radical of an ideal.