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The surfaces of the premaxillae are rugose with the edges elevated above the body of the bone, suggesting that a keratinous shield would have been supported by the rugosities at the tip of the snout. Along the interpremaxillary suture, the area where the two premaxillae meet, the surface is smooth, giving the paired ru... | Kaprosuchus | Wikipedia | 393 | 25139347 | https://en.wikipedia.org/wiki/Kaprosuchus | Biology and health sciences | Prehistoric crocodiles | Animals |
PaleobiologyKaprosuchus was once thought to have been a primarily if not exclusively terrestrial predator. Evidence for this behavior includes the positioning of the orbits laterally and somewhat anteriorly, which suggests an overlap in vision. This is unlike many other neosuchians, including extant crocodilians, in wh... | Kaprosuchus | Wikipedia | 357 | 25139347 | https://en.wikipedia.org/wiki/Kaprosuchus | Biology and health sciences | Prehistoric crocodiles | Animals |
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets.
A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used. To extend this process to v... | Ordinal number | Wikipedia | 462 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
When dealing with infinite sets, however, one has to distinguish between the notion of size, which leads to cardinal numbers, and the notion of position, which leads to the ordinal numbers described here. This is because while any set has only one size (its cardinality), there are many nonisomorphic well-orderings of a... | Ordinal number | Wikipedia | 477 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Perhaps a clearer intuition of ordinals can be formed by examining a first few of them: as mentioned above, they start with the natural numbers, 0, 1, 2, 3, 4, 5, ... After all natural numbers comes the first infinite ordinal, ω, and after that come ω+1, ω+2, ω+3, and so on. (Exactly what addition means will be defin... | Ordinal number | Wikipedia | 463 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
It is inappropriate to distinguish between two well-ordered sets if they only differ in the "labeling of their elements", or more formally: if the elements of the first set can be paired off with the elements of the second set such that if one element is smaller than another in the first set, then the partner of the fi... | Ordinal number | Wikipedia | 464 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
The original definition of ordinal numbers, found for example in the Principia Mathematica, defines the order type of a well-ordering as the set of all well-orderings similar (order-isomorphic) to that well-ordering: in other words, an ordinal number is genuinely an equivalence class of well-ordered sets. This definit... | Ordinal number | Wikipedia | 429 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Furthermore, the elements of every ordinal are ordinals themselves. Given two ordinals S and T, S is an element of T if and only if S is a proper subset of T. Moreover, either S is an element of T, or T is an element of S, or they are equal. So every set of ordinals is totally ordered. Further, every set of ordinals is... | Ordinal number | Wikipedia | 430 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Transfinite sequence
If α is any ordinal and X is a set, an α-indexed sequence of elements of X is a function from α to X. This concept, a transfinite sequence (if α is infinite) or ordinal-indexed sequence, is a generalization of the concept of a sequence. An ordinary sequence corresponds to the case α = ω, while a f... | Ordinal number | Wikipedia | 378 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Here is an example of definition by transfinite recursion on the ordinals (more will be given later): define function F by letting F(α) be the smallest ordinal not in the set , that is, the set consisting of all F(β) for . This definition assumes the F(β) known in the very process of defining F; this apparent vicious c... | Ordinal number | Wikipedia | 508 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Another way of defining a limit ordinal is to say that α is a limit ordinal if and only if:
There is an ordinal less than α and whenever ζ is an ordinal less than α, then there exists an ordinal ξ such that ζ < ξ < α.
So in the following sequence:
0, 1, 2, ..., ω, ω+1
ω is a limit ordinal because for any smaller ... | Ordinal number | Wikipedia | 355 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Any well-ordered set is similar (order-isomorphic) to a unique ordinal number ; in other words, its elements can be indexed in increasing fashion by the ordinals less than . This applies, in particular, to any set of ordinals: any set of ordinals is naturally indexed by the ordinals less than some . The same holds, w... | Ordinal number | Wikipedia | 403 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
A class of ordinals is said to be unbounded, or cofinal, when given any ordinal , there is a in such that (then the class must be a proper class, i.e., it cannot be a set). It is said to be closed when the limit of a sequence of ordinals in the class is again in the class: or, equivalently, when the indexing (clas... | Ordinal number | Wikipedia | 502 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Rather than formulating these definitions for (proper) classes of ordinals, one can formulate them for sets of ordinals below a given ordinal : A subset of a limit ordinal is said to be unbounded (or cofinal) under provided any ordinal less than is less than some ordinal in the set. More generally, one can call a ... | Ordinal number | Wikipedia | 390 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Each ordinal associates with one cardinal, its cardinality. If there is a bijection between two ordinals (e.g. and ), then they associate with the same cardinal. Any well-ordered set having an ordinal as its order-type has the same cardinality as that ordinal. The least ordinal associated with a given cardinal is call... | Ordinal number | Wikipedia | 333 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
The α-th infinite initial ordinal is written , it is always a limit ordinal. Its cardinality is written . For example, the cardinality of ω0 = ω is , which is also the cardinality of ω2 or ε0 (all are countable ordinals). So ω can be identified with , except that the notation is used when writing cardinals, and ω wh... | Ordinal number | Wikipedia | 423 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
An ordinal that is equal to its cofinality is called regular and it is always an initial ordinal. Any limit of regular ordinals is a limit of initial ordinals and thus is also initial even if it is not regular, which it usually is not. If the Axiom of Choice, then is regular for each α. In this case, the ordinals 0... | Ordinal number | Wikipedia | 488 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Any ordinal number can be made into a topological space by endowing it with the order topology; this topology is discrete if and only if it is less than or equal to ω. A subset of ω + 1 is open in the order topology if and only if either it is cofinite or it does not contain ω as an element.
See the Topology and ordin... | Ordinal number | Wikipedia | 465 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
Cantor's second theorem becomes: If is countable, then there is a countable ordinal α such that . Its proof uses proof by contradiction. Let be countable, and assume there is no such α. This assumption produces two cases.
Case 1: is non-empty for all countable β. Since there are uncountably many of these pairwise ... | Ordinal number | Wikipedia | 430 | 26547932 | https://en.wikipedia.org/wiki/Ordinal%20number | Mathematics | Set theory | null |
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
The concept of a limit of a sequence is further generali... | Limit (mathematics) | Wikipedia | 512 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
Real numbers
The expression 0.999... should be interpreted as the limit of the sequence 0.9, 0.99, 0.999, ... and so on. This sequence can be rigorously shown to have the limit 1, and therefore this expression is meaningfully interpreted as having the value 1.
Formally, suppose is a sequence of real numbers. When t... | Limit (mathematics) | Wikipedia | 456 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
A sequence with is called unbounded, a definition equally valid for sequences in the complex numbers, or in any metric space. Sequences which do not tend to infinity are called bounded. Sequences which do not tend to positive infinity are called bounded above, while those which do not tend to negative infinity are bo... | Limit (mathematics) | Wikipedia | 512 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
Many different notions of convergence can be defined on function spaces. This is sometimes dependent on the regularity of the space. Prominent examples of function spaces with some notion of convergence are Lp spaces and Sobolev space.
In functions
Suppose is a real-valued function and is a real number. Intuitivel... | Limit (mathematics) | Wikipedia | 512 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
In these expressions, the infinity is normally considered to be signed ( or ) and corresponds to a one-sided limit of the reciprocal. A two-sided infinite limit can be defined, but an author would explicitly write to be clear.
It is also possible to define the notion of "tending to infinity" in the value of ,
Again... | Limit (mathematics) | Wikipedia | 485 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
Limit set of a trajectory
This notion is used in dynamical systems, to study limits of trajectories. Defining a trajectory to be a function , the point is thought of as the "position" of the trajectory at "time" . The limit set of a trajectory is defined as follows. To any sequence of increasing times , there is an a... | Limit (mathematics) | Wikipedia | 491 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
Often is thought of as a complex number, and a suitable notion of convergence of complex sequences is needed. The set of values of for which the series sum converges is a circle, with its radius known as the radius of convergence.
Continuity of a function at a point
The definition of continuity at a point is given ... | Limit (mathematics) | Wikipedia | 495 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
In real analysis, for the more concrete case of real-valued functions defined on a subset , that is, , a continuous function may also be defined as a function which is continuous at every point of its domain.
Limit points
In topology, limits are used to define limit points of a subset of a topological space, which in... | Limit (mathematics) | Wikipedia | 509 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
A metric space in which every Cauchy sequence is also convergent, that is, Cauchy sequences are equivalent to convergent sequences, is known as a complete metric space.
One reason Cauchy sequences can be "easier to work with" than convergent sequences is that they are a property of the sequence alone, while convergen... | Limit (mathematics) | Wikipedia | 303 | 26551602 | https://en.wikipedia.org/wiki/Limit%20%28mathematics%29 | Mathematics | Analysis | null |
The harbor (or harbour) seal (Phoca vitulina), also known as the common seal, is a true seal found along temperate and Arctic marine coastlines of the Northern Hemisphere. The most widely distributed species of pinniped (walruses, eared seals, and true seals), they are found in coastal waters of the northern Atlantic a... | Harbor seal | Wikipedia | 454 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
There are an estimated 350,000–500,000 harbor seals worldwide. While the population is not threatened as a whole, the Greenland, Hokkaidō and Baltic Sea populations are exceptions. Local populations have been reduced or eliminated through disease (especially the phocine distemper virus) and conflict with humans, both u... | Harbor seal | Wikipedia | 482 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
Considerable scientific inquiry has been carried out by the Marine Mammal Center and other research organizations beginning in the 1980s regarding the incidence and transmission of diseases in harbor seals in the wild, including analysis of phocine herpesvirus. In San Francisco Bay, some harbor seals are fully or part... | Harbor seal | Wikipedia | 200 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
Atlantic Coast
Historically, the range of the harbor seal extended from the mouth of the St. Lawrence River and Greenland to the sandy beaches of North Carolina, a distance of well over a thousand miles (greater than 1600 km) Evidence of their presence in these areas is consistent with both the fossil record as well a... | Harbor seal | Wikipedia | 379 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
As of 2020, however, the seals have returned. They never were extirpated from Canada and certain pockets of the Maine coast, and thus an important mother population was created from whence the species could reclaim the home of their ancestors. Currently, they are sighted as far south as the barrier islands of North Car... | Harbor seal | Wikipedia | 431 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
Harbor seals prefer to frequent familiar resting sites. They may spend several days at sea and travel up to 50 km in search of feeding grounds, and will also swim more than a hundred miles upstream into fresh water in large rivers in search of migratory fish like shad and likely salmon. Resting sites may be both rugged... | Harbor seal | Wikipedia | 426 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
Birthing of pups occurs annually on shore. The timing of the pupping season varies with location, occurring in February for populations in lower latitudes, and as late as July in the subarctic zone. The mothers are the sole providers of care, with lactation lasting 24 days. The single pups are born well developed, capa... | Harbor seal | Wikipedia | 346 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
Notable individuals
Andre, rescued and trained by his owner Harry Goodridge, he became an iconic figure in his hometown of Rockport, Maine.
Hoover, also rescued from a Maine harbor. Hoover became famous for his ability to imitate human speech, something not observed in any other mammal.
Popeye, the official seal of ... | Harbor seal | Wikipedia | 190 | 26555929 | https://en.wikipedia.org/wiki/Harbor%20seal | Biology and health sciences | Pinnipeds | Animals |
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-defined interface and behavior and can be invoked multiple times.
Callable units provide a powerful programming tool. The primary purpose is to allow for the decompositi... | Function (computer programming) | Wikipedia | 408 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
The idea of a callable unit was initially conceived by John Mauchly and Kathleen Antonelli during their work on ENIAC and recorded in a January 1947 Harvard symposium on "Preparation of Problems for EDVAC-type Machines." Maurice Wilkes, David Wheeler, and Stanley Gill are generally credited with the formal invention of... | Function (computer programming) | Wikipedia | 412 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
Some very early computers and microprocessors, such as the IBM 1620, the Intel 4004 and Intel 8008, and the PIC microcontrollers, have a single-instruction subroutine call that uses a dedicated hardware stack to store return addresses—such hardware supports only a few levels of subroutine nesting, but can support recur... | Function (computer programming) | Wikipedia | 474 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
Libraries
Even with this cumbersome approach, subroutines proved very useful. They allowed the use of the same code in many different programs. Memory was a very scarce resource on early computers, and subroutines allowed significant savings in the size of programs.
Many early computers loaded the program instructions... | Function (computer programming) | Wikipedia | 505 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
to call a subroutine called MYSUB from the main program. The subroutine would be coded as
MYSUB NOP (Storage for MYSUB's return address.)
AA ... (Start of MYSUB's body.)
...
JMP MYSUB,I (Returns to the calling program.)
The JSB instruction placed the address of the NEXT instruction (namely, BB)... | Function (computer programming) | Wikipedia | 474 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
The call stack is usually implemented as a contiguous area of memory. It is an arbitrary design choice whether the bottom of the stack is the lowest or highest address within this area, so that the stack may grow forwards or backwards in memory; however, many architectures chose the latter.
Some designs, notably some ... | Function (computer programming) | Wikipedia | 449 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
This overhead is most obvious and objectionable in leaf procedures or leaf functions, which return without making any procedure calls themselves. To reduce that overhead, many modern compilers try to delay the use of a call stack until it is really needed. For example, the call of a procedure P may store the return add... | Function (computer programming) | Wikipedia | 505 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
If declared to return a value, a call can be embedded in an expression in order to consume the return value. For example, a square root callable unit might be called like y = sqrt(x).
A callable unit that does not return a value is called as a stand-alone statement like print("hello"). This syntax can also be used for... | Function (computer programming) | Wikipedia | 491 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
If supported by the language, a callable may call itself, causing its execution to suspend while another nested execution of the same callable executes. Recursion is a useful means to simplify some complex algorithms and break down complex problems. Recursive languages provide a new copy of local variables on each call... | Function (computer programming) | Wikipedia | 491 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
Some languages support overloading allow multiple callables with the same name in the same scope, but operating on different types of input. Consider the square root function applied to real number, complex number and matrix input. The algorithm for each type of input is different, and the return value may have a diff... | Function (computer programming) | Wikipedia | 491 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
Most modern languages support exceptions which allows for exceptional control flow that pops the call stack until an exception handler is found to handle the condition.
Languages that do not support exceptions can use the return value to indicate success or failure of a call. Another approach is to use a well-known lo... | Function (computer programming) | Wikipedia | 499 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
Inlining eliminates calls for particular callables. The compiler replaces each call with the compiled code of the callable. Not only does this avoid the call overhead, but it also allows the compiler to optimize code of the caller more effectively by taking into account the context and arguments at that call. Inlining,... | Function (computer programming) | Wikipedia | 504 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
With respect to naming, many developers name a callable with a phrase starting with a verb when it does a certain task, with an adjective when it makes an inquiry, and with a noun when it is used to substitute variables.
Some programmers suggest that a callable should perform exactly one task, and if it performs more ... | Function (computer programming) | Wikipedia | 510 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
Each parameter has a data type that can be specified, but if not, defaults to Object for later versions based on .NET and variant for VB6.
VB supports parameter passing conventions by value and by reference via the keywords ByVal and ByRef, respectively.
Unless ByRef is specified, an argument is passed ByVal. Therefo... | Function (computer programming) | Wikipedia | 501 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
void addTwo(int *pi) {
*pi += 2;
}
This function has a side-effect modifies the value passed by address to the input value plus 2. It could be called for variable v as addTwo(&v) where the ampersand (&) tells the compiler to pass the address of a variable. Giving v is 5 before the call, it will be 7 after.
void ... | Function (computer programming) | Wikipedia | 487 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
In the procedural interpretation of logic programs, logical implications behave as goal-reduction procedures. A rule (or clause) of the form:
A :- B
which has the logical reading:
A if B
behaves as a procedure that reduces goals that unify with A to subgoals that are instances ofB.
Consider, for example, the Prol... | Function (computer programming) | Wikipedia | 291 | 32177451 | https://en.wikipedia.org/wiki/Function%20%28computer%20programming%29 | Technology | Software development: General | null |
Rainfed agriculture is a type of farming that relies on rainfall for water. It provides much of the food consumed by poor communities in developing countries. E.g., rainfed agriculture accounts for more than 95% of farmed land in sub-Saharan Africa, 90% in Latin America, 75% in the Near East and North Africa, 65% in Ea... | Rainfed agriculture | Wikipedia | 504 | 33775893 | https://en.wikipedia.org/wiki/Rainfed%20agriculture | Technology | Agriculture_2 | null |
The importance of rainfed agriculture varies regionally, but it produces most food for poor communities in developing countries. In sub-Saharan Africa, more than 95% of the farmed land is rainfed, while the corresponding figure for Latin America is almost 90%, for South Asia about 60%, for East Asia 65%, and for the Ne... | Rainfed agriculture | Wikipedia | 344 | 33775893 | https://en.wikipedia.org/wiki/Rainfed%20agriculture | Technology | Agriculture_2 | null |
A spectrometer () is a scientific instrument used to separate and measure spectral components of a physical phenomenon. Spectrometer is a broad term often used to describe instruments that measure a continuous variable of a phenomenon where the spectral components are somehow mixed. In visible light a spectrometer can ... | Spectrometer | Wikipedia | 498 | 45311025 | https://en.wikipedia.org/wiki/Spectrometer | Technology | Measuring instruments | null |
Some forms of spectroscopy involve analysis of electron energy rather than photon energy. X-ray photoelectron spectroscopy is an example.
Mass spectrometer
A mass spectrometer is an analytical instrument that is used to identify the amount and type of chemicals present in a sample by measuring the mass-to-charge rati... | Spectrometer | Wikipedia | 454 | 45311025 | https://en.wikipedia.org/wiki/Spectrometer | Technology | Measuring instruments | null |
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus)... | Ricci calculus | Wikipedia | 464 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
Applications
Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning... | Ricci calculus | Wikipedia | 433 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
For example, in 3-D Euclidean space and using Cartesian coordinates; the coordinate vector shows a direct correspondence between the subscripts 1, 2, 3 and the labels , , . In the expression , is interpreted as an index ranging over the values 1, 2, 3, while the , , subscripts are only labels, not variables. In the ... | Ricci calculus | Wikipedia | 480 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
The number of each upper and lower indices of a tensor gives its type: a tensor with upper and lower indices is said to be of type , or to be a type- tensor.
The number of indices of a tensor, regardless of variance, is called the degree of the tensor (alternatively, its valence, order or rank, although rank is ambi... | Ricci calculus | Wikipedia | 466 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
This table summarizes how the manipulation of covariant and contravariant indices fit in with invariance under a passive transformation between bases, with the components of each basis set in terms of the other reflected in the first column. The barred indices refer to the final coordinate system after the transformati... | Ricci calculus | Wikipedia | 476 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
In the first replacement, replaced and replaced everywhere, so the expression still has the same meaning. In the second, did not fully replace , and did not fully replace (incidentally, the contraction on the index became a tensor product), which is entirely inconsistent for reasons shown next.
Indices are the... | Ricci calculus | Wikipedia | 492 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
Indices are not part of the symmetrization when they are:
not on the same level, for example;
within the parentheses and between vertical bars (i.e. |⋅⋅⋅|), modifying the previous example;
Here the and indices are symmetrized, is not.
Antisymmetric or alternating part of tensor
Square brackets, [ ], around ... | Ricci calculus | Wikipedia | 363 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
While most of the expressions of the Ricci calculus are valid for arbitrary bases, the expressions involving partial derivatives of tensor components with respect to coordinates apply only with a coordinate basis: a basis that is defined through differentiation with respect to the coordinates. Coordinates are typicall... | Ricci calculus | Wikipedia | 470 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
The components of this derivative of a tensor field transform covariantly, and hence form another tensor field, despite subexpressions (the partial derivative and the connection coefficients) separately not transforming covariantly.
This derivative is characterized by the product rule:
Connection types
A Koszul con... | Ricci calculus | Wikipedia | 470 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
The Kronecker delta is one of the family of generalized Kronecker deltas. The generalized Kronecker delta of degree may be defined in terms of the Kronecker delta by (a common definition includes an additional multiplier of on the right):
and acts as an antisymmetrizer on indices:
Torsion tensor
An affine conn... | Ricci calculus | Wikipedia | 263 | 35456546 | https://en.wikipedia.org/wiki/Ricci%20calculus | Mathematics | Multivariable and vector calculus | null |
Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processing, scientific visualization, algorithms and systems to extract or extrapolate knowledge and insights from potentially noisy, structured, or unstructured data.
Data science also integrates domai... | Data science | Wikipedia | 438 | 35458904 | https://en.wikipedia.org/wiki/Data%20science | Physical sciences | Science basics | Basics and measurement |
Relationship to statistics
Many statisticians, including Nate Silver, have argued that data science is not a new field, but rather another name for statistics. Others argue that data science is distinct from statistics because it focuses on problems and techniques unique to digital data. Vasant Dhar writes that statis... | Data science | Wikipedia | 474 | 35458904 | https://en.wikipedia.org/wiki/Data%20science | Physical sciences | Science basics | Basics and measurement |
Modern usage
In 2012, technologists Thomas H. Davenport and DJ Patil declared "Data Scientist: The Sexiest Job of the 21st Century", a catchphrase that was picked up even by major-city newspapers like the New York Times and the Boston Globe. A decade later, they reaffirmed it, stating that "the job is more in demand t... | Data science | Wikipedia | 426 | 35458904 | https://en.wikipedia.org/wiki/Data%20science | Physical sciences | Science basics | Basics and measurement |
Data analysis typically involves working with smaller, structured datasets to answer specific questions or solve specific problems. This can involve tasks such as data cleaning, data visualization, and exploratory data analysis to gain insights into the data and develop hypotheses about relationships between variables.... | Data science | Wikipedia | 490 | 35458904 | https://en.wikipedia.org/wiki/Data%20science | Physical sciences | Science basics | Basics and measurement |
Data Science as an Academic Discipline
As illustrated in the previous sections, there is substantially some considerable differences between data science, data analysis and statistics. Consequently, just like statistics grew into an independent field from applied mathematics, similarly data science has emerged as an i... | Data science | Wikipedia | 347 | 35458904 | https://en.wikipedia.org/wiki/Data%20science | Physical sciences | Science basics | Basics and measurement |
A stone slab is a big stone, flat and relatively thin, often of rectangular or almost rectangular form. They are generally used for paving floors, for covering walls or as headstones.
In dolmens
Most dolmen constructions were built using stone slabs of big dimensions. Their architecture often includes a corridor of a... | Stone slab | Wikipedia | 504 | 52134207 | https://en.wikipedia.org/wiki/Stone%20slab | Technology | Building materials | null |
A pyramidal or "hipped" stone slab, sometimes surmounting another base or fuller sarcophagus is a design seen across all continents as most organic debris will fall off of this and overgrowth from moss, grass and akin lowest-level plants. Examples are the graves of Sir John Whittaker Ellis and of the 1st Baron Cozens-... | Stone slab | Wikipedia | 487 | 52134207 | https://en.wikipedia.org/wiki/Stone%20slab | Technology | Building materials | null |
The term "slab" in toponyms
From the term slab and its derivatives, there are many toponyms among them. | Stone slab | Wikipedia | 26 | 52134207 | https://en.wikipedia.org/wiki/Stone%20slab | Technology | Building materials | null |
A mechanical filter is a signal processing filter usually used in place of an electronic filter at radio frequencies. Its purpose is the same as that of a normal electronic filter: to pass a range of signal frequencies, but to block others. The filter acts on mechanical vibrations which are the analogue of the electr... | Mechanical filter | Wikipedia | 497 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
The elements of a passive linear electrical network consist of inductors, capacitors and resistors which have the properties of inductance, elastance (inverse capacitance) and resistance, respectively. The mechanical counterparts of these properties are, respectively, mass, stiffness and damping. In most electronic fil... | Mechanical filter | Wikipedia | 495 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Any mechanical component will unavoidably possess both mass and stiffness. This translates in electrical terms to an LC circuit, that is, a circuit consisting of an inductor and a capacitor, hence mechanical components are resonators and are often used as such. It is still possible to represent inductors and capacitors... | Mechanical filter | Wikipedia | 480 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Mechanical equivalent circuits
Once the basics of electrical network analysis began to be established, it was not long before the ideas of complex impedance and filter design theories were carried over into mechanics by analogy. Kennelly, who was also responsible for introducing complex impedance, and Webster were the ... | Mechanical filter | Wikipedia | 383 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
An early application of these new theoretical tools was in phonographic sound reproduction. A recurring problem with early phonograph designs was that mechanical resonances in the pickup and sound transmission mechanism caused excessively large peaks and troughs in the frequency response, resulting in poor sound qualit... | Mechanical filter | Wikipedia | 294 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Harrison used Campbell's image filter theory, which was the most advanced filter theory available at the time. In this theory, filter design is viewed essentially as an impedance matching problem. More advanced filter theory was brought to bear on this problem by Norton in 1929 at Bell Labs. Norton followed the same ge... | Mechanical filter | Wikipedia | 346 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Volume production
Modern mechanical filters for intermediate frequency (IF) applications were first investigated by Robert Adler of Zenith Electronics who built a 455 kHz filter in 1946. The idea was taken up by Collins Radio Company who started the first volume production of mechanical filters from the 1950s onwards. ... | Mechanical filter | Wikipedia | 511 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
The usual magnetostrictive materials used for the transducer are either ferrite or compressed powdered iron. Mechanical filter designs often have the resonators coupled with steel or nickel-iron wires, but on some designs, especially older ones, nickel wire may be used for the input and output rods. This is because it ... | Mechanical filter | Wikipedia | 501 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Another kind of piezoelectric transducer has the piezoelectric material sandwiched in longitudinally, usually into the resonator itself. This kind is good for torsional vibration modes and is called a torsional transducer.
As miniaturized by using thin film manufacturing methods piezoelectric resonators are called thi... | Mechanical filter | Wikipedia | 512 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Resonator modes
It is usually possible for a mechanical part to vibrate in a number of different modes, however the design will be based on a particular vibrational mode and the designer will take steps to try to restrict the resonance to this mode. As well as the straightforward longitudinal mode some others which ar... | Mechanical filter | Wikipedia | 216 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
There are a great many combinations of resonators and transducers that can be used to construct a mechanical filter. A selection of some of these is shown in the diagrams. Figure 6 shows a filter using disc flexural resonators and magnetostrictive transducers. The transducer drives the centre of the first resonator, ca... | Mechanical filter | Wikipedia | 477 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
The frequency response behaviour of all mechanical filters can be expressed as an equivalent electrical circuit using the impedance analogy described above. An example of this is shown in figure 8b which is the equivalent circuit of the mechanical filter of figure 8a. Elements on the electrical side, such as the induct... | Mechanical filter | Wikipedia | 496 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
An example of such a design is shown in figure 10a. The resonators are disc flexural resonators similar to those shown in figure 6, except that these are energised from an edge, leading to vibration in the fundamental flexural mode with a node in the centre, whereas the figure 6 design is energised in the centre leadin... | Mechanical filter | Wikipedia | 449 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
The method of coupling between non-adjacent resonators is not limited to mechanical filters. It can be applied to other filter formats and the general term for this class is cross-coupled filter. For instance, channels can be cut between cavity resonators, mutual inductance can be used with discrete component filters,... | Mechanical filter | Wikipedia | 479 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Adjustment
The precision applications in which mechanical filters are used require that the resonators are accurately adjusted to the specified resonance frequency. This is known as trimming and usually involves a mechanical machining process. In most filter designs, this can be difficult to do once the resonators ha... | Mechanical filter | Wikipedia | 429 | 25154546 | https://en.wikipedia.org/wiki/Mechanical%20filter | Technology | Signal processing | null |
Stomatosuchidae is an extinct family of neosuchian crocodylomorphs. It is defined as the most inclusive clade containing Stomatosuchus inermis but not Notosuchus terrestris, Simosuchus clarki, Araripesuchus gomesii, Baurusuchus pachecoi, Peirosaurus torminni, or Crocodylus niloticus. Two genera are known to belong to S... | Stomatosuchidae | Wikipedia | 480 | 25156868 | https://en.wikipedia.org/wiki/Stomatosuchidae | Biology and health sciences | Prehistoric crocodiles | Animals |
In electronics, flip-flops and latches are circuits that have two stable states that can store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will output its state (often along with its logical complement too). It is the basic s... | Flip-flop (electronics) | Wikipedia | 411 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
The first electronic latch was invented in 1918 by the British physicists William Eccles and F. W. Jordan. It was initially called the Eccles–Jordan trigger circuit and consisted of two active elements (vacuum tubes). The design was used in the 1943 British Colossus codebreaking computer and such circuits and their tra... | Flip-flop (electronics) | Wikipedia | 436 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
Clocked flip-flops are specially designed for synchronous systems; such devices ignore their inputs except at the transition of a dedicated clock signal (known as clocking, pulsing, or strobing). Clocking causes the flip-flop either to change or to retain its output signal based upon the values of the input signals at ... | Flip-flop (electronics) | Wikipedia | 505 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
The SR NOR latch consists of two parallel NOR gates where the output of each NOR is also fanned out into one input of the other NOR, as shown in the figure.
We call these output-to-input connections feedback inputs, or simply feedbacks.
The remaining inputs we will use as control inputs as explained above.
Notice that ... | Flip-flop (electronics) | Wikipedia | 450 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
{| class="wikitable" style="text-align:center;"
|+ SR latch operation
|-
! colspan="4" | Characteristic table
! colspan="4" | Excitation table
|-
! S !! R !! Qnext !! Action
! Q !! Qnext !! S !! R
|-
| 0 || 0 || Q || Hold state
| 0 || 0 || 0 ||
|-
| 0 || 1 || 0 || Reset
| 0 || 1 || 1 || 0
|-
| 1 || 0 || 1 || Set
| 1 |... | Flip-flop (electronics) | Wikipedia | 455 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
The circuit shown below is a basic NAND latch. The inputs are also generally designated and for Set and Reset respectively. Because the NAND inputs must normally be logic 1 to avoid affecting the latching action, the inputs are considered to be inverted in this circuit (or active low).
The circuit uses the same feed... | Flip-flop (electronics) | Wikipedia | 429 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
The SR AND-OR latch is easier to understand, because both gates can be explained in isolation, again with the control view of AND and OR from above. When neither S or R is set, then both the OR gate and the AND gate are in "hold mode", i.e., they let the input through, their output is the input from the feedback loop. ... | Flip-flop (electronics) | Wikipedia | 509 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
Gated latches and conditional transparency
Latches are designed to be transparent. That is, input signal changes cause immediate changes in output. Additional logic can be added to a transparent latch to make it non-transparent or opaque when another input (an "enable" input) is not asserted. When several transparent l... | Flip-flop (electronics) | Wikipedia | 364 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
Gated D latch
This latch exploits the fact that, in the two active input combinations (01 and 10) of a gated SR latch, R is the complement of S. The input NAND stage converts the two D input states (0 and 1) to these two input combinations for the next latch by inverting the data input signal. The low state of the ena... | Flip-flop (electronics) | Wikipedia | 379 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
Designers looked for alternatives. A successful alternative is the Earle latch. It requires only a single data input, and its output takes a constant two gate delays. In addition, the two gate levels of the Earle latch can, in some cases, be merged with the last two gate levels of the circuits driving the latch because... | Flip-flop (electronics) | Wikipedia | 469 | 32186638 | https://en.wikipedia.org/wiki/Flip-flop%20%28electronics%29 | Technology | Digital logic | null |
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