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Hook point types
Hook points are also described relative to their offset from the hook shank. A kerbed hook point is offset to the left, a straight point has no offset and a reversed point is offset to the right.
Hook points are commonly referred to by these names: needle point, rolled-in, hollow, spear, beak, mini-b... | Fish hook | Wikipedia | 473 | 989954 | https://en.wikipedia.org/wiki/Fish%20hook | Technology | Hunting and fishing | null | vital_articles |
Some hooks, such as the traditional Japanese Tenkara hooks, lack any opening for the line to be threaded, and are thus eyeless. Eyeless hooks instead have a widened "spade end" to help snelling the line onto the shank without slipping.
Size
There are no internationally recognized standards for hooks and thus size i... | Fish hook | Wikipedia | 230 | 989954 | https://en.wikipedia.org/wiki/Fish%20hook | Technology | Hunting and fishing | null | vital_articles |
Mental health encompasses emotional, psychological, and social well-being, influencing cognition, perception, and behavior. According to the World Health Organization (WHO), it is a "state of well-being in which the individual realizes his or her abilities, can cope with the normal stresses of life, can work productive... | Mental health | Wikipedia | 498 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
In the mid-19th century, William Sweetser was the first to coin the term mental hygiene, which can be seen as the precursor to contemporary approaches to work on promoting positive mental health. Isaac Ray, the fourth president of the American Psychiatric Association and one of its founders, further defined mental hygi... | Mental health | Wikipedia | 470 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Deinstitutionalization and transinstitutionalization
When US government-run hospitals were accused of violating human rights, advocates pushed for deinstitutionalization: the replacement of federal mental hospitals for community mental health services. The closure of state-provisioned psychiatric hospitals was enforce... | Mental health | Wikipedia | 311 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Other critics of state deinstitutionalization argue that this was simply a transition to "transinstitutionalization", or the idea that prisons and state-provisioned hospitals are interdependent. In other words, patients become inmates. This draws on the Penrose Hypothesis of 1939, which theorized that there was an inve... | Mental health | Wikipedia | 455 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Mental illnesses are more common than cancer, diabetes, or heart disease. As of 2021, over 22 percent of all Americans over the age of 18 meet the criteria for having a mental illness. Evidence suggests that 970 million people worldwide have a mental disorder. Major depression ranks third among the top 10 leading cause... | Mental health | Wikipedia | 500 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
The tripartite model of mental well-being views mental well-being as encompassing three components of emotional well-being, social well-being, and psychological well-being. Emotional well-being is defined as having high levels of positive emotions, whereas social and psychological well-being are defined as the presence... | Mental health | Wikipedia | 236 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
In the United States alone, in 2021, at least roughly 17.5% of the population (ages 18 and older) were recorded as having a mental illness. The comparison between reports and statistics of mental health issues in newer generations (18–25 years old to 26–49 years old) and the older generation (50 years or older) signifi... | Mental health | Wikipedia | 505 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Refugees and immigrants experience psychosocial stressors after resettlement. These include discrimination, lack of economic stability, and social isolation causing emotional distress. For example, Not far into the 1900s, campaigns targeting Japanese immigrants were being formed that inhibited their ability to particip... | Mental health | Wikipedia | 455 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Many mental health professionals are beginning to, or already understand, the importance of competency in religious diversity and spirituality, or the lack thereof. They are also partaking in cultural training to better understand which interventions work best for these different groups of people. The American Psycholo... | Mental health | Wikipedia | 503 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Social work in mental health, also called psychiatric social work, is a process where an individual in a setting is helped to attain freedom from overlapping internal and external problems (social and economic situations, family and other relationships, the physical and organizational environment, psychiatric symptoms,... | Mental health | Wikipedia | 455 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Biological factors
According to the National Institute of Health Curriculum Supplement Series book, most scientists believe that changes in neurotransmitters can cause mental illnesses. In the section "The Biology of Mental Illnesses" the issue is explained in detail, "...there may be disruptions in the neurotransmitt... | Mental health | Wikipedia | 386 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Emotional mental disorders are a leading cause of disabilities worldwide. Investigating the degree and severity of untreated emotional mental disorders throughout the world is a top priority of the World Mental Health (WMH) survey initiative, which was created in 1998 by the World Health Organization (WHO). "Neuropsych... | Mental health | Wikipedia | 419 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
The coordinated surveys on emotional mental health disorders, their severity, and treatments were implemented in the aforementioned countries. These surveys assessed the frequency, types, and adequacy of mental health service use in 17 countries in which WMH surveys are complete. The WMH also examined unmet needs for t... | Mental health | Wikipedia | 457 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
"The terms mental health promotion and prevention have often been confused. Promotion is defined as intervening to optimize positive mental health by addressing determinants of positive mental health (i.e. protective factors) before a specific mental health problem has been identified, with the ultimate goal of improvi... | Mental health | Wikipedia | 497 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
Additionally, social media is becoming a resource for prevention. In 2004, the Mental Health Services Act began to fund marketing initiatives to educate the public on mental health. This California-based project is working to combat the negative perception with mental health and reduce the stigma associated with it. Wh... | Mental health | Wikipedia | 104 | 990505 | https://en.wikipedia.org/wiki/Mental%20health | Biology and health sciences | Health, fitness, and medicine | null | vital_articles |
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidea... | Norm (mathematics) | Wikipedia | 498 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
Suppose that and are two norms (or seminorms) on a vector space Then and are called equivalent, if there exist two positive real constants and such that for every vector
The relation " is equivalent to " is reflexive, symmetric ( implies ), and transitive and thus defines an equivalence relation on the set of ... | Norm (mathematics) | Wikipedia | 466 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
The Euclidean norm is by far the most commonly used norm on but there are other norms on this vector space as will be shown below.
However, all these norms are equivalent in the sense that they all define the same topology on finite-dimensional spaces.
The inner product of two vectors of a Euclidean vector space is t... | Norm (mathematics) | Wikipedia | 503 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
The set of vectors whose 1-norm is a given constant forms the surface of a cross polytope, which has dimension equal to the dimension of the vector space minus 1.
The Taxicab norm is also called the norm. The distance derived from this norm is called the Manhattan distance or distance.
The 1-norm is simply the sum o... | Norm (mathematics) | Wikipedia | 509 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
In general, the value of the norm is dependent on the spectrum of : For a vector with a Euclidean norm of one, the value of is bounded from below and above by the smallest and largest absolute eigenvalues of respectively, where the bounds are achieved if coincides with the corresponding (normalized) eigenvectors. B... | Norm (mathematics) | Wikipedia | 356 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
In signal processing and statistics, David Donoho referred to the zero "norm" with quotation marks.
Following Donoho's notation, the zero "norm" of is simply the number of non-zero coordinates of or the Hamming distance of the vector from zero.
When this "norm" is localized to a bounded set, it is the limit of -norms... | Norm (mathematics) | Wikipedia | 507 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
All the above formulas also yield norms on without modification.
There are also norms on spaces of matrices (with real or complex entries), the so-called matrix norms.
In abstract algebra
Let be a finite extension of a field of inseparable degree and let have algebraic closure If the distinct embeddings of a... | Norm (mathematics) | Wikipedia | 512 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
In terms of the vector space, the seminorm defines a topology on the space, and this is a Hausdorff topology precisely when the seminorm can distinguish between distinct vectors, which is again equivalent to the seminorm being a norm. The topology thus defined (by either a norm or a seminorm) can be understood either i... | Norm (mathematics) | Wikipedia | 460 | 990534 | https://en.wikipedia.org/wiki/Norm%20%28mathematics%29 | Mathematics | Linear algebra | null | vital_articles |
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynam... | Dynamical systems theory | Wikipedia | 496 | 990632 | https://en.wikipedia.org/wiki/Dynamical%20systems%20theory | Mathematics | Other | null | vital_articles |
Even simple nonlinear dynamical systems often exhibit seemingly random behavior that has been called chaos. The branch of dynamical systems that deals with the clean definition and investigation of chaos is called chaos theory.
History
The concept of dynamical systems theory has its origins in Newtonian mechanics. Th... | Dynamical systems theory | Wikipedia | 511 | 990632 | https://en.wikipedia.org/wiki/Dynamical%20systems%20theory | Mathematics | Other | null | vital_articles |
Related fields
Arithmetic dynamics
Arithmetic dynamics is a field that emerged in the 1990s that amalgamates two areas of mathematics, dynamical systems and number theory. Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the stu... | Dynamical systems theory | Wikipedia | 446 | 990632 | https://en.wikipedia.org/wiki/Dynamical%20systems%20theory | Mathematics | Other | null | vital_articles |
Functional analysis
Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon them. It has its historical roots in the study of functional spaces, in particular transformations of functions, such as the Fourier transform, as well... | Dynamical systems theory | Wikipedia | 420 | 990632 | https://en.wikipedia.org/wiki/Dynamical%20systems%20theory | Mathematics | Other | null | vital_articles |
In biomechanics
In sports biomechanics, dynamical systems theory has emerged in the movement sciences as a viable framework for modeling athletic performance and efficiency. It comes as no surprise, since dynamical systems theory has its roots in Analytical mechanics. From psychophysiological perspective, the human mo... | Dynamical systems theory | Wikipedia | 461 | 990632 | https://en.wikipedia.org/wiki/Dynamical%20systems%20theory | Mathematics | Other | null | vital_articles |
Further, since the middle of the 1990s cognitive science, oriented towards a system theoretical connectionism, has increasingly adopted the methods from (nonlinear) “Dynamic Systems Theory (DST)“. A variety of neurosymbolic cognitive neuroarchitectures in modern connectionism, considering their mathematical structural ... | Dynamical systems theory | Wikipedia | 258 | 990632 | https://en.wikipedia.org/wiki/Dynamical%20systems%20theory | Mathematics | Other | null | vital_articles |
A sol is a colloidal suspension made out of tiny solid particles in a continuous liquid medium. Sols are stable, so that they do not settle down when left undisturbed, and exhibit the Tyndall effect, which is the scattering of light by the particles in the colloid. The size of the particles can vary from 1 nm - 100 nm.... | Sol (colloid) | Wikipedia | 261 | 991054 | https://en.wikipedia.org/wiki/Sol%20%28colloid%29 | Physical sciences | Mixture | Chemistry | vital_articles |
Rodenticides are chemicals made and sold for the purpose of killing rodents. While commonly referred to as "rat poison", rodenticides are also used to kill mice, woodchucks, chipmunks, porcupines, nutria, beavers, and voles.
Some rodenticides are lethal after one exposure while others require more than one. Rodents ar... | Rodenticide | Wikipedia | 446 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
First-generation rodenticidal anticoagulants generally have shorter elimination half-lives, require higher concentrations (usually between 0.005% and 0.1%) and consecutive intake over days in order to accumulate the lethal dose, and are less toxic than second-generation agents.
Second-generation anticoagulant rodentic... | Rodenticide | Wikipedia | 426 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
Metal phosphides have been used as a means of killing rodents and are considered single-dose fast acting rodenticides (death occurs commonly within 1–3 days after single bait ingestion). A bait consisting of food and a phosphide (usually zinc phosphide) is left where the rodents can eat it. The acid in the digestive sy... | Rodenticide | Wikipedia | 478 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
The tablets or pellets (usually aluminium, calcium or magnesium phosphide for fumigation/gassing) may also contain other chemicals which evolve ammonia, which helps reduce the potential for spontaneous combustion or explosion of the phosphine gas.
Metal phosphides do not accumulate in the tissues of poisoned animals, ... | Rodenticide | Wikipedia | 223 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
Cholecalciferol (vitamin D3) and ergocalciferol (vitamin D2) are used as rodenticides. They are toxic to rodents for the same reason they are important to humans: they affect calcium and phosphate homeostasis in the body. Vitamins D are essential in minute quantities (few IUs per kilogram body weight daily, only a frac... | Rodenticide | Wikipedia | 479 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
|title=Efficacy of Cholecalciferol Baits for Pocket Gopher Control and Possible Effects on Non-Target Rodents in Pacific Northwest Forests |url=https://naldc.nal.usda.gov/download/39036/PDF |conference=Vertebrate Pest Conference (2006) |publisher=USDA |quote= 0.15% cholecalciferol bait appears to have application for p... | Rodenticide | Wikipedia | 234 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
There is an important feature of calciferols toxicology, that they are synergistic with anticoagulant toxicant. In other words, mixtures of anticoagulants and calciferols in same bait are more toxic than a sum of toxicities of the anticoagulant and the calciferol in the bait, so that a massive hypercalcemic effect can ... | Rodenticide | Wikipedia | 306 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
The Merck Veterinary Manual states the following:
Although this rodenticide [cholecalciferol] was introduced with claims that it was less toxic to nontarget species than to rodents, clinical experience has shown that rodenticides containing cholecalciferol are a significant health threat to dogs and cats. Cholecalcifer... | Rodenticide | Wikipedia | 302 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
Other chemical poisons include:
ANTU (α-naphthylthiourea; specific against Brown rat, Rattus norvegicus'')
Arsenic trioxide
Barium carbonate (sometimes called Witherite)
Chloralose (a narcotic prodrug)
Crimidine (inhibits metabolism of vitamin B6)
1,3-Difluoro-2-propanol ("Gliftor")
Endrin (organochlorine insecticide, ... | Rodenticide | Wikipedia | 494 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
Inert gas killing of burrowing pest animals is another method with no impact on scavenging wildlife. One such method has been commercialized and sold under the brand name Rat Ice.
Non-target issues
Secondary poisoning and risks to wildlife
One of the potential problems when using rodenticides is that dead or weakene... | Rodenticide | Wikipedia | 384 | 991169 | https://en.wikipedia.org/wiki/Rodenticide | Technology | Pest and disease control | null | vital_articles |
A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article presents rules and ... | Divisibility rule | Wikipedia | 505 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Divisibility by 3 or 9
First, take any number (for this example it will be 492) and add together each digit in the number (4 + 9 + 2 = 15). Then take that sum (15) and determine if it is divisible by 3. The original number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).
Adding t... | Divisibility rule | Wikipedia | 476 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Alternatively, one can just add half of the last digit to the penultimate digit (or the remaining number). If that number is an even natural number, the original number is divisible by 4
Also, one can simply divide the number by 2, and then check the result to find if it is divisible by 2. If it is, the original numb... | Divisibility rule | Wikipedia | 472 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
If the last digit in the number is 5, then the result will be the remaining digits multiplied by two, plus one. For example, the number 125 ends in a 5, so take the remaining digits (12), multiply them by two (12 × 2 = 24), then add one (24 + 1 = 25). The result is the same as the result of 125 divided by 5 (125/5=25... | Divisibility rule | Wikipedia | 446 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Divisibility by 7
Divisibility by 7 can be tested by a recursive method. A number of the form 10x + y is divisible by 7 if and only if x − 2y is divisible by 7. In other words, subtract twice the last digit from the number formed by the remaining digits. Continue to do this until a number is obtained for which it is ... | Divisibility rule | Wikipedia | 365 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
A more complicated algorithm for testing divisibility by 7 uses the fact that 100 ≡ 1, 101 ≡ 3, 102 ≡ 2, 103 ≡ 6, 104 ≡ 4, 105 ≡ 5, 106 ≡ 1, ... (mod 7). Take each digit of the number (371) in reverse order (173), multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers ... | Divisibility rule | Wikipedia | 251 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
The simplification goes as follows:
Take for instance the number 371
Change all occurrences of 7, 8 or 9 into 0, 1 and 2, respectively. In this example, we get: 301. This second step may be skipped, except for the left most digit, but following it may facilitate calculations later on.
Now convert the first digit (3) in... | Divisibility rule | Wikipedia | 492 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Now we have a number smaller than 7, and this number (4) is the remainder of dividing 186/7. So 186 minus 4, which is 182, must be a multiple of 7.
Note: The reason why this works is that if we have: a+b=c and b is a multiple of any given number n, then a and c will necessarily produce the same remainder when divided ... | Divisibility rule | Wikipedia | 482 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Vedic method of divisibility by osculation
Divisibility by seven can be tested by multiplication by the Ekhādika. Convert the divisor seven to the nines family by multiplying by seven. 7×7=49. Add one, drop the units digit and, take the 5, the Ekhādika, as the multiplier. Start on the right. Multiply by 5, add the prod... | Divisibility rule | Wikipedia | 468 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
001 001 = 1,001 / 7 = 143
010 010 = 10,010 / 7 = 1,430
011 011 = 11,011 / 7 = 1,573
100 100 = 100,100 / 7 = 14,300
101 101 = 101,101 / 7 = 14,443
110 110 = 110,110 / 7 = 15,730
01 01 01 = 10,101 / 7 = 1,443
10 10 10 = 101,010 / 7 = 14,430
111,111 / 7 = 15,873
222,222 / 7 = 31,746
999,999 / 7 = 142,857
576... | Divisibility rule | Wikipedia | 482 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
22,862,420 − (999,999 × 22) = 22,862,420 − 21,999,978 -> 862,420 + 22 = 862,442
862,442 -> 862 − 442 (Step B) = 420 -> 42 − (0×2) (Step A) = 42 YES
This allows adding and subtracting alternating sets of three digits to determine divisibility by seven. Understanding these patterns allows you to quickly calculate ... | Divisibility rule | Wikipedia | 493 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Find remainder of 1036125837 divided by 7
1×3 + 0 = 3
3×3 + 3 = 12 remainder 5
5×3 + 6 = 21 remainder 0
0×3 + 1 = 1
1×3 + 2 = 5
5×3 + 5 = 20 remainder 6
6×3 + 8 = 26 remainder 5
5×3 + 3 = 18 remainder 4
4×3 + 7 = 19 remainder 5
Answer is 5
Finding remainder of a number when divided by 7
7 − (1, 3, 2, −1, −3... | Divisibility rule | Wikipedia | 393 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
This method uses 1, −3, 2 pattern on the digit pairs. That is, the divisibility of any number by seven can be tested by first separating the number into digit pairs, and then applying the algorithm on three digit pairs (six digits). When the number is smaller than six digits, then fill zero's to the right side until th... | Divisibility rule | Wikipedia | 382 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Separate the number into digit pairs starting from the ones place. Prepend the number with 0 to complete the final pair if required.
Calculate the remainders left by each digit pair on dividing by 7.
Multiply the remainders with the appropriate multiplier from the sequence 1, 2, 4, 1, 2, 4, ... : the remainder from t... | Divisibility rule | Wikipedia | 479 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Multiply the right most digit of the number with the left most number in the sequence shown above and the second right most digit to the second left most digit of the number in the sequence. The cycle goes on.
Example: What is the remainder when 321 is divided by 13?
Using the first sequence,
Ans: 1 × 1 + 2 × −3 + 3 ... | Divisibility rule | Wikipedia | 436 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
A composite divisor may also have a rule formed using the same procedure as for a prime divisor, given below, with the caveat that the manipulations involved may not introduce any factor which is present in the divisor. For instance, one cannot make a rule for 14 that involves multiplying the equation by 7. This is n... | Divisibility rule | Wikipedia | 503 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
For example, to determine whether 913 = 10 × 91 + 3 is divisible by 11, find that m = (11 × 9 + 1) ÷ 10 = 10. Then mq + t = 10 × 3 + 91 = 121; this is divisible by 11 (with quotient 11), so 913 is also divisible by 11. As another example, to determine whether 689 = 10 × 68 + 9 is divisible by 53, find that m = (53 × 3 ... | Divisibility rule | Wikipedia | 486 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
Using 11 as an example, 11 divides 11 = 10 + 1. That means . For the higher powers of 10, they are congruent to 1 for even powers and congruent to −1 for odd powers:
Like the previous case, we can substitute powers of 10 with congruent values:
which is also the difference between the sum of digits at odd positi... | Divisibility rule | Wikipedia | 460 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
This section will illustrate the basic method; all the rules can be derived following the same procedure. The following requires a basic grounding in modular arithmetic; for divisibility other than by 2's and 5's the proofs rest on the basic fact that 10 mod m is invertible if 10 and m are relatively prime.
For 2n or ... | Divisibility rule | Wikipedia | 154 | 991210 | https://en.wikipedia.org/wiki/Divisibility%20rule | Mathematics | Basics | null | vital_articles |
An acidity function is a measure of the acidity of a medium or solvent system, usually expressed in terms of its ability to donate protons to (or accept protons from) a solute (Brønsted acidity). The pH scale is by far the most commonly used acidity function, and is ideal for dilute aqueous solutions. Other acidity fun... | Acidity function | Wikipedia | 276 | 10851309 | https://en.wikipedia.org/wiki/Acidity%20function | Physical sciences | Concepts | Chemistry | vital_articles |
Comparison of acidity functions with aqueous acidity
In dilute aqueous solution, the predominant acid species is the hydrated hydrogen ion H3O+ (or more accurately [H(OH2)n]+). In this case H0 and H− are equivalent to pH values determined by the buffer equation or Henderson-Hasselbalch equation.
However, an H0 value of... | Acidity function | Wikipedia | 314 | 10851309 | https://en.wikipedia.org/wiki/Acidity%20function | Physical sciences | Concepts | Chemistry | vital_articles |
A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which itself was a rediscovery of Allan Marquand's 1881 logical diagram (aka. Marquand diagram). It is also useful for unde... | Karnaugh map | Wikipedia | 485 | 10854684 | https://en.wikipedia.org/wiki/Karnaugh%20map | Mathematics | Mathematical logic | null | vital_articles |
Following are two different notations describing the same function in unsimplified Boolean algebra, using the Boolean variables , , , and their inverses.
where are the minterms to map (i.e., rows that have output 1 in the truth table).
where are the maxterms to map (i.e., rows that have output 0 in the truth tab... | Karnaugh map | Wikipedia | 493 | 10854684 | https://en.wikipedia.org/wiki/Karnaugh%20map | Mathematics | Mathematical logic | null | vital_articles |
The grid is toroidally connected, which means that rectangular groups can wrap across the edges (see picture). Cells on the extreme right are actually 'adjacent' to those on the far left, in the sense that the corresponding input values only differ by one bit; similarly, so are those at the very top and those at the bo... | Karnaugh map | Wikipedia | 463 | 10854684 | https://en.wikipedia.org/wiki/Karnaugh%20map | Mathematics | Mathematical logic | null | vital_articles |
Karnaugh maps also allow easier minimizations of functions whose truth tables include "don't care" conditions. A "don't care" condition is a combination of inputs for which the designer doesn't care what the output is. Therefore, "don't care" conditions can either be included in or excluded from any rectangular group, ... | Karnaugh map | Wikipedia | 506 | 10854684 | https://en.wikipedia.org/wiki/Karnaugh%20map | Mathematics | Mathematical logic | null | vital_articles |
Whether glitches will actually occur depends on the physical nature of the implementation, and whether we need to worry about it depends on the application. In clocked logic, it is enough that the logic settles on the desired value in time to meet the timing deadline. In our example, we are not considering clocked logi... | Karnaugh map | Wikipedia | 471 | 10854684 | https://en.wikipedia.org/wiki/Karnaugh%20map | Mathematics | Mathematical logic | null | vital_articles |
Related graphical minimization methods include:
Marquand diagram (1881) by Allan Marquand (1853–1924)
Veitch chart (1952) by Edward W. Veitch (1924–2013)
Svoboda chart (1956) by Antonín Svoboda (1907–1980)
Mahoney map (M-map, designation numbers, 1963) by Matthew V. Mahoney (a reflection-symmetrical extension of Ka... | Karnaugh map | Wikipedia | 245 | 10854684 | https://en.wikipedia.org/wiki/Karnaugh%20map | Mathematics | Mathematical logic | null | vital_articles |
Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing. The result is an equation for the Gibbs free energy change for mixing a polymer with a solvent. Altho... | Flory–Huggins solution theory | Wikipedia | 497 | 3010589 | https://en.wikipedia.org/wiki/Flory%E2%80%93Huggins%20solution%20theory | Physical sciences | Thermodynamics | Chemistry | vital_articles |
For a random walk on a lattice we can calculate the entropy change (the increase in spatial uncertainty) as a result of mixing solute and solvent.
where is the Boltzmann constant. Define the lattice volume fractions and
These are also the probabilities that a given lattice site, chosen at random, is occupied by... | Flory–Huggins solution theory | Wikipedia | 456 | 3010589 | https://en.wikipedia.org/wiki/Flory%E2%80%93Huggins%20solution%20theory | Physical sciences | Thermodynamics | Chemistry | vital_articles |
In the most general case the interaction and the ensuing mixing parameter, , is a free energy parameter, thus including an entropic component. This means that aside to the regular mixing entropy there is another entropic contribution from the interaction between solvent and monomer. This contribution is sometimes very... | Flory–Huggins solution theory | Wikipedia | 458 | 3010589 | https://en.wikipedia.org/wiki/Flory%E2%80%93Huggins%20solution%20theory | Physical sciences | Thermodynamics | Chemistry | vital_articles |
As in the case for dilute polymer solutions, the first two terms on the right-hand side represent the entropy of mixing. For large polymers of and these terms are negligibly small. This implies that for a stable mixture to exist , so for polymers A and B to blend their segments must attract one another.
Limitations ... | Flory–Huggins solution theory | Wikipedia | 446 | 3010589 | https://en.wikipedia.org/wiki/Flory%E2%80%93Huggins%20solution%20theory | Physical sciences | Thermodynamics | Chemistry | vital_articles |
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is t... | Euler method | Wikipedia | 482 | 3011098 | https://en.wikipedia.org/wiki/Euler%20method | Mathematics | Differential equations | null | vital_articles |
The value of is an approximation of the solution at time , i.e., . The Euler method is explicit, i.e. the solution is an explicit function of for .
Higher-order process
While the Euler method integrates a first-order ODE, any ODE of order can be represented as a system of first-order ODEs. When given the ODE of o... | Euler method | Wikipedia | 464 | 3011098 | https://en.wikipedia.org/wiki/Euler%20method | Mathematics | Differential equations | null | vital_articles |
The conclusion of this computation is that . The exact solution of the differential equation is , so . Although the approximation of the Euler method was not very precise in this specific case, particularly due to a large value step size , its behaviour is qualitatively correct as the figure shows.
Using other step si... | Euler method | Wikipedia | 496 | 3011098 | https://en.wikipedia.org/wiki/Euler%20method | Mathematics | Differential equations | null | vital_articles |
Higher-order example
For this third-order example, assume that the following information is given:
From this we can isolate y''' to get the equation:
Using that we can get the solution for :And using the solution for , we can get the solution for :We can continue this process using the same formula as long as necess... | Euler method | Wikipedia | 512 | 3011098 | https://en.wikipedia.org/wiki/Euler%20method | Mathematics | Differential equations | null | vital_articles |
In the above expressions for the error, the second derivative of the unknown exact solution can be replaced by an expression involving the right-hand side of the differential equation. Indeed, it follows from the equation that
Global truncation error
The global truncation error is the error at a fixed time , after h... | Euler method | Wikipedia | 501 | 3011098 | https://en.wikipedia.org/wiki/Euler%20method | Mathematics | Differential equations | null | vital_articles |
If the Euler method is applied to the linear equation , then the numerical solution is unstable if the product is outside the region
illustrated on the right. This region is called the (linear) stability region. In the example, , so if then which is outside the stability region, and thus the numerical solution is u... | Euler method | Wikipedia | 490 | 3011098 | https://en.wikipedia.org/wiki/Euler%20method | Mathematics | Differential equations | null | vital_articles |
In popular culture
In the film Hidden Figures, Katherine Goble resorts to the Euler method in calculating the re-entry of astronaut John Glenn from Earth orbit. | Euler method | Wikipedia | 32 | 3011098 | https://en.wikipedia.org/wiki/Euler%20method | Mathematics | Differential equations | null | vital_articles |
Florigens (or flowering hormone) are proteins capable of inducing flowering time in angiosperms. The prototypical florigen is encoded by the FT gene and its orthologs in Arabidopsis and other plants. Florigens are produced in the leaves, and act in the shoot apical meristem of buds and growing tips.
Mechanism
For a ... | Florigen | Wikipedia | 475 | 3011436 | https://en.wikipedia.org/wiki/Florigen | Biology and health sciences | Plant hormone | Biology | vital_articles |
This ebb-and-flow of flowering in plants is essentially controlled by an internal clock known as the endogenous oscillator. It is thought that these internal pacemakers "are regulated by the interaction of four sets of genes expressed in the dawn, morning, afternoon, and evening hours [and that] light may augment the a... | Florigen | Wikipedia | 480 | 3011436 | https://en.wikipedia.org/wiki/Florigen | Biology and health sciences | Plant hormone | Biology | vital_articles |
Flowering
Florigen is a systemically mobile signal that is synthesized in leaves and the transported via the phloem to the shoot apical meristem (SAM) where it initiates flowering. In Arabidopsis, the FLOWERING LOCUS T (FT) genes encode for the flowering hormone and in rice the hormone is encoded by Hd3a genes thereby ... | Florigen | Wikipedia | 505 | 3011436 | https://en.wikipedia.org/wiki/Florigen | Biology and health sciences | Plant hormone | Biology | vital_articles |
Research history
Florigen was first described by Soviet Armenian plant physiologist Mikhail Chailakhyan, who in 1937 demonstrated that floral induction can be transmitted through a graft from an induced plant to one that has not been induced to flower. Anton Lang showed that several long-day plants and biennials could ... | Florigen | Wikipedia | 460 | 3011436 | https://en.wikipedia.org/wiki/Florigen | Biology and health sciences | Plant hormone | Biology | vital_articles |
Triggers of gene transcription
There are three genes involved in clock-controlled flowering pathway, GIGANTEA (GI), CONSTANS (CO), and FLOWERING LOCUS T (FT). Constant overexpression of GI from the Cauliflower mosaic virus 35S promoter causes early flowering under short day so an increase in GI mRNA expression induces... | Florigen | Wikipedia | 394 | 3011436 | https://en.wikipedia.org/wiki/Florigen | Biology and health sciences | Plant hormone | Biology | vital_articles |
Many types of glucose tests exist and they can be used to estimate blood sugar levels at a given time or, over a longer period of time, to obtain average levels or to see how fast the body is able to normalize changed glucose levels. Eating food for example leads to elevated blood sugar levels. In healthy people, these... | Glucose test | Wikipedia | 413 | 3012322 | https://en.wikipedia.org/wiki/Glucose%20test | Biology and health sciences | Diagnostics | Health | vital_articles |
High blood sugar may indicate
gestational diabetes. This temporary form of diabetes appears during pregnancy, and with glucose-controlling medication or insulin symptoms can be improved.
type 1 and type 2 diabetes or prediabetes. If diagnosed with diabetes, regular glucose tests can help manage or maintain conditions... | Glucose test | Wikipedia | 464 | 3012322 | https://en.wikipedia.org/wiki/Glucose%20test | Biology and health sciences | Diagnostics | Health | vital_articles |
The Rheic Ocean (; ) was an ocean which separated two major paleocontinents, Gondwana and Laurussia (Laurentia-Baltica-Avalonia). One of the principal oceans of the Paleozoic, its sutures today stretch from Mexico to Turkey and its closure resulted in the assembly of the supercontinent Pangaea and the formation of th... | Rheic Ocean | Wikipedia | 495 | 3012682 | https://en.wikipedia.org/wiki/Rheic%20Ocean | Physical sciences | Paleogeography | Earth science | vital_articles |
The closure of the Rheic began in the Early Devonian and was completed in the Mississippian when Gondwana and Laurentia collided to form Pangaea. This closure resulted in the largest collisional orogen of the Palaeozoic: the Variscan and Alleghanian orogens between Gondwana's West African margin and southern Baltica an... | Rheic Ocean | Wikipedia | 271 | 3012682 | https://en.wikipedia.org/wiki/Rheic%20Ocean | Physical sciences | Paleogeography | Earth science | vital_articles |
Teleosauridae is a family of extinct typically marine crocodylomorphs similar to the modern gharial that lived during the Jurassic period. Teleosaurids were thalattosuchians closely related to the fully aquatic metriorhynchoids, but were less adapted to an open-ocean, pelagic lifestyle. The family was originally coined... | Teleosauridae | Wikipedia | 477 | 5508267 | https://en.wikipedia.org/wiki/Teleosauridae | Biology and health sciences | Other prehistoric archosaurs | Animals | vital_articles |
Palaeobiology
Teleosaurids were originally regarded as marine analogues to modern gharials, as they both typically share long, tubular snouts and narrow teeth. However, differences in the jaws, teeth, and skeleton of different teleosaurids suggest that they were more ecologically diverse than this. Earlier teleosaurid... | Teleosauridae | Wikipedia | 234 | 5508267 | https://en.wikipedia.org/wiki/Teleosauridae | Biology and health sciences | Other prehistoric archosaurs | Animals | vital_articles |
The Lygaeidae are a family in the Hemiptera (true bugs), with more than 110 genera in four subfamilies. The family is commonly referred to as seed bugs, and less commonly, milkweed bugs, or ground bugs. Many species feed on seeds, some on sap or seed pods, others are omnivores and a few, such as the wekiu bug, are ins... | Lygaeidae | Wikipedia | 484 | 5512111 | https://en.wikipedia.org/wiki/Lygaeidae | Biology and health sciences | Hemiptera (true bugs) | Animals | vital_articles |
The Egyptian mongoose (Herpestes ichneumon), also known as ichneumon (), is a mongoose species native to the tropical and subtropical grasslands, savannas, and shrublands of Africa and around the Mediterranean Basin in North Africa, the Middle East and the Iberian Peninsula. Whether it is introduced or native to the Ib... | Egyptian mongoose | Wikipedia | 497 | 5512223 | https://en.wikipedia.org/wiki/Egyptian%20mongoose | Biology and health sciences | Other carnivora | Animals | vital_articles |
In Sudan, it is present in the vicinity of human settlements along the Rahad River and in Dinder National Park. It was also recorded in the Dinder–Alatash protected area complex during surveys between 2015 and 2018. In Ethiopia, the Egyptian mongoose was recorded at elevations of in the Ethiopian Highlands.
In Senega... | Egyptian mongoose | Wikipedia | 428 | 5512223 | https://en.wikipedia.org/wiki/Egyptian%20mongoose | Biology and health sciences | Other carnivora | Animals | vital_articles |
It preys on rodents, fish, birds, reptiles, amphibians, and insects. It also feeds on fruit and eggs. To crack eggs open, it throws them between its legs against a rock or wall.
In Doñana National Park, 30 Egyptian mongooses were radio-tracked in 1985 and their faeces collected. These samples contained remains of Europ... | Egyptian mongoose | Wikipedia | 372 | 5512223 | https://en.wikipedia.org/wiki/Egyptian%20mongoose | Biology and health sciences | Other carnivora | Animals | vital_articles |
Reproduction
Captive males and females reach sexual maturity at the age of two years. In Doñana National Park, courtship and mating happens in spring between February and June. Two to three pups are born between mid April and mid August after a gestation of 11 weeks. They are hairless at first, and open their eyes aft... | Egyptian mongoose | Wikipedia | 145 | 5512223 | https://en.wikipedia.org/wiki/Egyptian%20mongoose | Biology and health sciences | Other carnivora | Animals | vital_articles |
Taxonomy
In 1758, Carl Linnaeus described an Egyptian mongoose from the area of the Nile River in Egypt in his work Systema Naturae and gave it the scientific name Viverra ichneumon.
H. i. ichneumon (Linnaeus, 1758) is the nominate subspecies. The following zoological specimen were described between the late 18th centu... | Egyptian mongoose | Wikipedia | 501 | 5512223 | https://en.wikipedia.org/wiki/Egyptian%20mongoose | Biology and health sciences | Other carnivora | Animals | vital_articles |
Mummified remains of four Egyptian mongooses were excavated in the catacombs of Anubis at Saqqara during works started in 2009.
At the cemetery of Beni Hasan, an Egyptian mongoose on a leash is depicted in the tomb of Baqet I dating to the Eleventh Dynasty of Egypt.
The American poet John Greenleaf Whittier wrote a poe... | Egyptian mongoose | Wikipedia | 179 | 5512223 | https://en.wikipedia.org/wiki/Egyptian%20mongoose | Biology and health sciences | Other carnivora | Animals | vital_articles |
Toxicodendron vernicifluum (formerly Rhus verniciflua), also known by the common name Chinese lacquer tree, is an Asian tree species of genus Toxicodendron native to China and the Indian subcontinent, and cultivated in regions of China, Japan and Korea. Other common names include Japanese lacquer tree, Japanese sumac, ... | Toxicodendron vernicifluum | Wikipedia | 411 | 5512913 | https://en.wikipedia.org/wiki/Toxicodendron%20vernicifluum | Biology and health sciences | Sapindales | Plants | vital_articles |
Products coated with lacquer are recognizable by an extremely durable and glossy finish. Lacquer has many uses; some common applications include tableware, musical instruments, fountain pens, jewelry, and bows for archery. There are various types of lacquerware. The cinnabar-red is highly regarded. Unpigmented lacquer ... | Toxicodendron vernicifluum | Wikipedia | 288 | 5512913 | https://en.wikipedia.org/wiki/Toxicodendron%20vernicifluum | Biology and health sciences | Sapindales | Plants | vital_articles |
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