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25ccae254ce83a52101c3dcceb87f9436afe7fae | mills is a marine biologist. in 2006 mills | mills is a marine biologist. in 2006 mills started work with national institute of water and atmospheric research taihoro nukurangi (niwa). in 2014 she became collections manager of the niwa invertebrate collection. this role heads a small team and is responsible for over 300,000 of preserved marine invertebrates speci... | wikipedia |
8c87c4d0a17f10ad191b71d3b5ad7bfae56e3173 | mills qualified with a master in science from | mills qualified with a master in science from otago university in 2006. her thesis is: benthic macrofauna assemblages of fragmented seagrass (zostera capricorni) beds in two southern new zealand inlets. | wikipedia |
aa046e9628887e705266b421c9fdb70dbf691062 | mills grew up in the united kingdom. she | mills grew up in the united kingdom. she knew from a young age she wanted to be a marine biologist. mills family moved to dunedin in the south island of new zealand when she was a teenager, and she went on to study at otago university. | wikipedia |
c10b0b6ac32a99051b620fc4820cd293c265028f | victoria sadie mills is a new zealand marine | victoria sadie mills is a new zealand marine biologist and an invertebrate collection manager at new zealand's national institute of water and atmospheric research. mills specialises in the taxonomy of ophiuroidea and has written a book titled extraordinary echinoderms : a guide to the echinoderms of new zealand. | wikipedia |
2c96d8251e5bbad168552935289ff0d431964505 | justin brian melton, popularly known as quickmelt, mouse, | justin brian melton, popularly known as quickmelt, mouse, the flying minion, and minion, is a filipino-american former professional basketball player. he was drafted 13th overall by the san mig coffee mixers in the 2013 pba draft. | wikipedia |
f6d531df8640f427fdb94189aa25d28d2b12f51e | on december 24, 2021, after only playing three | on december 24, 2021, after only playing three games for the dyip, melton was traded to the blackwater bossing for ed daquioag. melton became an unrestricted free agent on february 1, 2023. shortly after, he retired from professional basketball. | wikipedia |
6ca91e64a94790c3ec27d50961a1c8fa920d6840 | he shocked the whole pba, by winning the | he shocked the whole pba, by winning the 2014 pba all-star weekend slam dunk contest held in the mall of asia arena. he and rey guevarra had a head-to-head matchup on that battle, they have been tied for three rounds on the championship round, at last, they have been declared co-champions, because the process is going ... | wikipedia |
63d0f8107a7894290a9340da0f3878792451aa03 | melton was picked 13th overall by the mixers | melton was picked 13th overall by the mixers in the 2013 pba draft. melton was noticed as one of the most athletic players in his draft class, and he showcased that athleticism very fast with his teammates. though measured at just 5-foot-9 in socks, melton finished with several rim-rattling slams during practice. his e... | wikipedia |
acd56de794c4ade05c70f3dd60b4477666115bae | melton studied and played basketball on a full | melton studied and played basketball on a full scholarship at mount olive college, in mount olive, north carolina where he was very successful. justin was a very tough player in college and was the leader and motor of the team for the last 3 seasons. he is extremely athletic can finish strong at the rim. he shot over 4... | wikipedia |
a48d524461dc5cf46c80a31ee308d171a5901564 | justin melton played high school basketball at tabb | justin melton played high school basketball at tabb high school in yorktown, virginia. after playing one year of junior varsity basketball, melton played three years of varsity basketball, capturing bay rivers district 1st team honors in his junior and senior seasons. in his senior season, he was awarded bay rivers dis... | wikipedia |
18739e3b3ee41fb974084bd2d6d2bc1eb232cb1f | justin brian melton (born april 7, 1987), popularly | justin brian melton (born april 7, 1987), popularly known as quickmelt, mouse, the flying minion, and minion, is a filipino-american former professional basketball player. he was drafted 13th overall by the san mig coffee mixers in the 2013 pba draft. | wikipedia |
f37fed9febc19cec862fb4e7b4008899e092085e | in computational complexity theory, the time hierarchy theorems | in computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on turing machines. informally, these theorems say that given more time, a turing machine can solve more problems. for example, there are problems that can be solved with n2 time but not n time, where... | wikipedia |
4e780b9bbeb2963908fbca61a57dfe39bf5a2d4c | in computational complexity theory, the time hierarchy theorems | if g(n) is a time-constructible function, and f(n+1) = o(g(n)), then the analogous theorems for space are the space hierarchy theorems. a similar theorem is not known for time-bounded probabilistic complexity classes, unless the class also has one bit of advice. | wikipedia |
e83ff87f87a72b072b9a544a4a706980532d8b7d | thus, a constant-factor increase in the time bound | thus, a constant-factor increase in the time bound allows for solving more problems, in contrast with the situation for turing machines (see linear speedup theorem). moreover, ben-amram proved that, in the above models, for f of polynomial growth rate (but more than linear), it is the case that for all ε > 0 {\displays... | wikipedia |
e2f3489afbb8f947d714ba0bbfc2623c766853be | if f (n) is a time-constructible function, then | if f (n) is a time-constructible function, then there exists a decision problem which cannot be solved in worst-case deterministic time f (n) but can be solved in worst-case time af (n) for some constant a (dependent on f). | wikipedia |
fefd44dc30492903e17050657b442e275dc78d69 | the gap of approximately log f (n) {\displaystyle | the gap of approximately log f (n) {\displaystyle \log f(n)} between the lower and upper time bound in the hierarchy theorem can be traced to the efficiency of the device used in the proof, namely a universal program that maintains a step-count. this can be done more efficiently on certain computational models. the sha... | wikipedia |
070adbf9ad3c3e961d68a25fe8c5fdcc8f529435 | however, the time hierarchy theorems provide no means | however, the time hierarchy theorems provide no means to relate deterministic and non-deterministic complexity, or time and space complexity, so they cast no light on the great unsolved questions of computational complexity theory: whether p and np, np and pspace, pspace and exptime, or exptime and nexptime are equal o... | wikipedia |
645a8210d824e80874f55620ade49383c96edddc | the theorem also guarantees that there are problems | the theorem also guarantees that there are problems in p requiring arbitrarily large exponents to solve; in other words, p does not collapse to dtime (n) for any fixed k. for example, there are problems solvable in n time but not n time. this is one argument against cobham's thesis, the convention that p is a practical... | wikipedia |
96817822cc216378a7f9b0cac10308933b849b19 | for example, p ⊊ e x p t | for example, p ⊊ e x p t i m e {\displaystyle {\mathsf {p}}\subsetneq {\mathsf {exptime}}} since p ⊆ d t i m e (2 n) ⊊ d t i m e (2 2 n) ⊆ e x p t i m e {\displaystyle {\mathsf {p}}\subseteq {\mathsf {dtime}}(2^{n})\subsetneq {\mathsf {dtime}}(2^{2n})\subseteq {\mathsf {exptime}}}. indeed, d t i m e (2 n) ⊆ d t i m e (... | wikipedia |
6fbbf63ce94942160833f02154f6799df49b675d | the time hierarchy theorems guarantee that the deterministic | the time hierarchy theorems guarantee that the deterministic and non-deterministic versions of the exponential hierarchy are genuine hierarchies: in other words p ⊊ exptime ⊊ 2-exp ⊊... and np ⊊ nexptime ⊊ 2-nexp ⊊.... | wikipedia |
d81c4761de105ae786a684d276fd41cd177a547d | if g (n) is a time-constructible function, and | if g (n) is a time-constructible function, and f (n +1) = o (g (n)), then there exists a decision problem which cannot be solved in non-deterministic time f (n) but can be solved in non-deterministic time g (n). in other words, the complexity class ntime (f (n)) is a strict subset of ntime (g (n)). | wikipedia |
f0bdcd6fa787214366f2832b70751ec7f90243c0 | we use this k to construct another machine, | we use this k to construct another machine, n, which takes a machine description and runs k on the tuple (,), ie. m is simulated on its own code by k, and then n accepts if k rejects, and rejects if k accepts. if n is the length of the input to n, then m (the length of the input to k) is twice n plus some delimiter sym... | wikipedia |
75994430be026bfd2a87a9a292b96dbc14ae3d53 | we know that we can decide membership of | we know that we can decide membership of h by way of a deterministic turing machine r, that simulates m for f (x) steps by first calculating f (| x |) and then writing out a row of 0s of that length, and then using this row of 0s as a "clock" or "counter" to simulate m for at most that many steps. at each step, the sim... | wikipedia |
a95fe0732760c71371b3da99ba07026165898020 | we include here a proof of a weaker | we include here a proof of a weaker result, namely that dtime (f (n)) is a strict subset of dtime (f (2 n + 1)), as it is simpler but illustrates the proof idea. see the bottom of this section for information on how to extend the proof to f (n)log f (n). | wikipedia |
1648f4be744659b0f5472a9ade720669c2aa3cbb | time hierarchy theorem. if f (n) is a | time hierarchy theorem. if f (n) is a time-constructible function, then there exists a decision problem which cannot be solved in worst-case deterministic time o (f (n)) but can be solved in worst-case deterministic time o (f (n)log f (n)). thus | wikipedia |
978c1f5f990b7fa0d836c1edf3f76948cbc366f7 | we need to prove that some time class | we need to prove that some time class time (g (n)) is strictly larger than some time class time (f (n)). we do this by constructing a machine which cannot be in time (f (n)), by diagonalization. we then show that the machine is in time (g (n)), using a simulator machine. | wikipedia |
b64a20562195e8a7e2fd230353749bc146978cec | both theorems use the notion of a time-constructible | both theorems use the notion of a time-constructible function. a function f: n → n {\displaystyle f:\mathbb {n} \rightarrow \mathbb {n} } is time-constructible if there exists a deterministic turing machine such that for every n ∈ n {\displaystyle n\in \mathbb {n} }, if the machine is started with an input of n ones, i... | wikipedia |
69437625555c076394d7ef838c2f5738b5b2481b | the time hierarchy theorem for nondeterministic turing machines | the time hierarchy theorem for nondeterministic turing machines was originally proven by stephen cook in 1972. it was improved to its current form via a complex proof by joel seiferas, michael fischer, and albert meyer in 1978. finally in 1983, stanislav Žák achieved the same result with the simple proof taught today. ... | wikipedia |
9f4ca42c71c1db2230d12773a67a234b0ca7e010 | in particular, this shows that d t i | in particular, this shows that d t i m e (n a) ⊊ d t i m e (n b) {\displaystyle {\mathsf {dtime}}(n^{a})\subsetneq {\mathsf {dtime}}(n^{b})} if and only if a < b {\displaystyle a<b}, so we have an infinite time hierarchy. | wikipedia |
a7009c1abd1cbe6a3711384b5623d4068e38f5fd | where dtime (f (n)) denotes the complexity class | where dtime (f (n)) denotes the complexity class of decision problems solvable in time o (f (n)). the left-hand class involves little o notation, referring to the set of decision problems solvable in asymptotically less than f (n) time. | wikipedia |
46605d0d6807a8b5907c987a177febeb4a16dbc9 | the time hierarchy theorem for deterministic multi-tape turing | the time hierarchy theorem for deterministic multi-tape turing machines was first proven by richard e. stearns and juris hartmanis in 1965. it was improved a year later when f. c. hennie and richard e. stearns improved the efficiency of the universal turing machine. consequent to the theorem, for every deterministic ti... | wikipedia |
638e02785b1f523c1fea58710942bcd7ca2fc355 | in computational complexity theory, the time hierarchy theorems | in computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on turing machines. informally, these theorems say that given more time, a turing machine can solve more problems. for example, there are problems that can be solved with n time but not n time, where ... | wikipedia |
82768cc231c66950df411505f59ee605ee1bb99a | the nokia lumia 930 is a high-end smartphone | the nokia lumia 930 is a high-end smartphone developed by nokia that shipped with microsoft's windows phone 8.1 operating system. it was announced on april 2, 2014 at microsoft build 2014 and was released in april 2014 as nokia's flagship. it is the last high-end nokia-branded lumia device and succeeded by the microsof... | wikipedia |
e4cc1b33b1061e413efc113acd3cdd1adec94966 | a significant number of lumia 930 users have | a significant number of lumia 930 users have reported an issue with the operation of the audio microphones, where handsfree calls and video recordings have very low audio levels. this has been confirmed to be caused by a motherboard fault. there have been a number of reports of this being a software issue introduced wi... | wikipedia |
07521d89838d62c7d06e5e6fe37fc7991f500847 | the lumia 930 has a 5.0-inch amoled display, | the lumia 930 has a 5.0-inch amoled display, quad-core 2.2 ghz krait 400 qualcomm snapdragon 800 processor, 2 gb of ram and 32 gb of internal storage. the phone has a 2420 mah li-ion battery, 20 mp rear camera and 1.2 mp front-facing camera. it is available in orange, green, white, black and gold. | wikipedia |
f02d5d6a77e5026d12a614814e54de4f6d8d988b | neither the 930 nor the icon have the | neither the 930 nor the icon have the glance feature, which displays the time and other selectable information on the display of an otherwise sleeping phone. while other contemporary nokia smartphones have glance, the 930 and icon do not because their displays lack the necessary "display memory" feature. | wikipedia |
8afeda58180218aaad9ac0df12aa2fccfc24d37b | the nokia lumia icon, which is exclusive to | the nokia lumia icon, which is exclusive to verizon wireless in the united states, is essentially a derivative of the lumia 930. the two versions share a common design and specifications; the only hardware difference is that the 930 is equipped with gsm radios and available as both carrier-locked and unlocked versions,... | wikipedia |
b06b1919a4e2a321fbbbd7774067ae7881e86d26 | the nokia lumia 930 (codenamed martini) is a | the nokia lumia 930 (codenamed martini) is a high-end smartphone developed by nokia that shipped with microsoft's windows phone 8.1 operating system. it was announced on april 2, 2014 at microsoft build 2014 and was released in april 2014 as nokia's (and later microsoft mobile 's) flagship. it is the last high-end noki... | wikipedia |
7252a6f1f7795ccdec547787e634d3873de76234 | wolfgang grodd is a german neuroradiologist and professor | wolfgang grodd is a german neuroradiologist and professor emeritus of the university hospital at the university of tübingen. he is known for his scientific works on the development and application of structural and functional magnetic resonance imaging in metabolic diseases, sensorimotor representation, language produc... | wikipedia |
12ae7c7814d673a41f259f2007a318f441659892 | for his scientific research activity, grodd was awarded | for his scientific research activity, grodd was awarded the "kurt-decker award" of the german society for neuroradiology in 1988, 1989, 1992 and in 1998. in 1989 the german society for neurotraumatology honored him for his outstanding scientific work. | wikipedia |
1899b2441f08108441aca040420145c89fe561d6 | in 1987, he initially moved to the department | in 1987, he initially moved to the department of neuroradiology at the university of tübingen as a consultant, where he worked as a senior physician from 1991 to 1995. in 1991, he habilitated in the field of radiology/neuroradiology on the topic of experimental and clinical investigations of volume-selective proton spe... | wikipedia |
4e35f3480b689ddeab4bf67b3b60a0dea1638539 | after serving as a temporary soldier in the | after serving as a temporary soldier in the german army from 1959 to 1964 and training as an electronics technician, w. grodd obtained his abitur (high school diploma) in 1968 at westfalen kolleg in bielefeld and studied biology from 1968 to 1977 and medicine from 1974 to 1981 at the university of tübingen. from 1972 t... | wikipedia |
884cd09e2823ade2aa4d5886d9e909e14f23ae19 | wolfgang grodd (born 25 july 1942 in detmold) | wolfgang grodd (born 25 july 1942 in detmold) is a german neuroradiologist and professor emeritus of the university hospital at the university of tübingen. he is known for his scientific works on the development and application of structural and functional magnetic resonance imaging in metabolic diseases, sensorimotor ... | wikipedia |
cfee8d781295e1eaf5705609ce9de03bfed45042 | coulibaly's first goal for vfb stuttgart came in | coulibaly's first goal for vfb stuttgart came in a 3–1 home loss to bayern munich on 28 november 2020. on 12 december, he scored in a 5–1 away win against borussia dortmund at the westfalenstadion. | wikipedia |
d0f09d8dfc76658f446f2b2868e76f698308929e | on 2 july 2019, coulibaly signed for vfb | on 2 july 2019, coulibaly signed for vfb stuttgart on a four-year contract. he made his debut in the 2. bundesliga for the team on 20 october 2019 against holstein kiel. | wikipedia |
bf5091016ef0a03d8b6c9c2b53ed275746871fe8 | coulibaly is a product of the paris saint-germain | coulibaly is a product of the paris saint-germain youth academy. during the 2018–19 season, he played for the u19 side of the club, grabbing one goal and two assists in seven uefa youth league appearances. he left paris saint-germain in 2019, having not played any senior football in france. | wikipedia |
3940f182914eb3a474fbe646765048cab0cf5d19 | based upon work of the german mathematician leopold | based upon work of the german mathematician leopold löwenheim (1915) the norwegian logician thoralf skolem showed in 1922 that every consistent theory of first-order predicate calculus, such as set theory, has an at most countable model. however, cantor's theorem proves that there are uncountable sets. the root of this... | wikipedia |
32a6fe1d77f508b33e2b38b15fb5d81941503da5 | as with könig's paradox, this paradox cannot be | as with könig's paradox, this paradox cannot be formalized in axiomatic set theory because it requires the ability to tell whether a description applies to a particular set (or, equivalently, to tell whether a formula is actually the definition of a single set). | wikipedia |
67467a3a1bb6bcb720ce0a69179425eb1da4f95c | in the same year the french mathematician jules | in the same year the french mathematician jules richard used a variant of cantor's diagonal method to obtain another contradiction in naive set theory. consider the set a of all finite agglomerations of words. the set e of all finite definitions of real numbers is a subset of a. as a is countable, so is e. let p be the... | wikipedia |
a89c61ae5ef2b80ae8c434db6973120914092913 | this paradox is avoided in axiomatic set theory. | this paradox is avoided in axiomatic set theory. although it is possible to represent a proposition about a set as a set, by a system of codes known as gödel numbers, there is no formula φ (a, x) {\displaystyle \varphi (a,x)} in the language of set theory which holds exactly when a {\displaystyle a} is a code for a fin... | wikipedia |
a119f596c3d94e6da94b9b38531db42f834d8bb2 | in 1905, the hungarian mathematician julius könig published | in 1905, the hungarian mathematician julius könig published a paradox based on the fact that there are only countably many finite definitions. if we imagine the real numbers as a well-ordered set, those real numbers which can be finitely defined form a subset. hence in this well-order there should be a first real numbe... | wikipedia |
624954fbd8fb7528e8e0b7676878ae29cebf1408 | after all this, the version of the "set | after all this, the version of the "set of all sets" paradox conceived by bertrand russell in 1903 led to a serious crisis in set theory. russell recognized that the statement x = x is true for every set, and thus the set of all sets is defined by { x | x = x }. in 1906 he constructed several paradox sets, the most fam... | wikipedia |
bc7186d1b2ea9d7e85206c57809ba499765071f2 | by the end of the 19th century cantor | by the end of the 19th century cantor was aware of the non-existence of the set of all cardinal numbers and the set of all ordinal numbers. in letters to david hilbert and richard dedekind he wrote about inconsistent sets, the elements of which cannot be thought of as being all together, and he used this result to prov... | wikipedia |
848508ff74265117ec4db446fd34f6006dc441d7 | in 1897 the italian mathematician cesare burali-forti discovered | in 1897 the italian mathematician cesare burali-forti discovered that there is no set containing all ordinal numbers. as every ordinal number is defined by a set of smaller ordinal numbers, the well-ordered set Ω of all ordinal numbers (if it exists) fits the definition and is itself an ordinal. on the other hand, no o... | wikipedia |
5bb044216d3a50e6d2656d7135a57d85405a4f83 | for all its usefulness in resolving questions regarding | for all its usefulness in resolving questions regarding infinite sets, naive set theory has some fatal flaws. in particular, it is prey to logical paradoxes such as those exposed by russell's paradox. the discovery of these paradoxes revealed that not all sets which can be described in the language of naive set theory ... | wikipedia |
e960acb431f5d04d002ae42d747b8da0817fd8f8 | the paradox is further increased by the significance | the paradox is further increased by the significance of the removal sequence. if the balls are not removed in the sequence 1, 2, 3,... but in the sequence 1, 11, 21,... after one hour infinitely many balls populate the reservoir, although the same amount of material as before has been moved. | wikipedia |
9df484e4c1b84a1e79c7b88b72356d61d0388a0f | an increased version of this type of paradox | an increased version of this type of paradox shifts the infinitely remote finish to a finite time. fill a huge reservoir with balls enumerated by numbers 1 to 10 and take off ball number 1. then add the balls enumerated by numbers 11 to 20 and take off number 2. continue to add balls enumerated by numbers 10 n - 9 to 1... | wikipedia |
a0e3c0c1df878d2ca28bb07a2603599b19e5092c | tristram shandy, the hero of a novel by | tristram shandy, the hero of a novel by laurence sterne, writes his autobiography so conscientiously that it takes him one year to lay down the events of one day. if he is mortal he can never terminate; but if he lived forever then no part of his diary would remain unwritten, for to each day of his life a year devoted ... | wikipedia |
9bc22097cbbf7859beffbeefc256b162411d8df0 | in set theory, an infinite set is not | in set theory, an infinite set is not considered to be created by some mathematical process such as "adding one element" that is then carried out "an infinite number of times". instead, a particular infinite set (such as the set of all natural numbers) is said to already exist, "by fiat", as an assumption or an axiom. ... | wikipedia |
6800729b12bce605abf2f3d60af2ecc17934c8eb | however, the ability to well order any set | however, the ability to well order any set allows certain constructions to be performed that have been called paradoxical. one example is the banach–tarski paradox, a theorem widely considered to be nonintuitive. it states that it is possible to decompose a ball of a fixed radius into a finite number of pieces and then... | wikipedia |
bc0b99ea0aad83670d2288e979dfce55a65be22f | in 1904 ernst zermelo proved by means of | in 1904 ernst zermelo proved by means of the axiom of choice (which was introduced for this reason) that every set can be well-ordered. in 1963 paul j. cohen showed that in zermelo–fraenkel set theory without the axiom of choice it is not possible to prove the existence of a well-ordering of the real numbers. | wikipedia |
57c93475a1a41551a14ce3e615047b78ceaa406e | the evidence strongly suggests that cantor was quite | the evidence strongly suggests that cantor was quite confident in the result itself and that his comment to dedekind refers instead to his then-still-lingering concerns about the validity of his proof of it. nevertheless, cantor's remark would also serve nicely to express the surprise that so many mathematicians after ... | wikipedia |
0210b0db0aff6204e417a5db501e9cbacac1fc7f | "i see it but i don't believe," cantor | "i see it but i don't believe," cantor wrote to richard dedekind after proving that the set of points of a square has the same cardinality as that of the points on just an edge of the square: the cardinality of the continuum. | wikipedia |
cbd7201cfacfc3ad8b52e0d0a98b5850063ae0bb | by defining the notion of the size of | by defining the notion of the size of a set in terms of its cardinality, the issue can be settled. since there is a bijection between the two sets involved, this follows in fact directly from the definition of the cardinality of a set. | wikipedia |
c7f89ac80e89e05d6291b18b298c453204f492ea | before set theory was introduced, the notion of | before set theory was introduced, the notion of the size of a set had been problematic. it had been discussed by galileo galilei and bernard bolzano, among others. are there as many natural numbers as squares of natural numbers when measured by the method of enumeration? | wikipedia |
2cfd20200c98dca4efc2969306600ae8824a5f56 | instead of relying on ambiguous descriptions such as | instead of relying on ambiguous descriptions such as "that which cannot be enlarged" or "increasing without bound", set theory provides definitions for the term infinite set to give an unambiguous meaning to phrases such as "the set of all natural numbers is infinite". just as for finite sets, the theory makes further ... | wikipedia |
dca857eb03196adec75c227a5e999313ef6986e4 | by forming all subsets of a set s | by forming all subsets of a set s (all possible choices of its elements), we obtain the power set p (s). georg cantor proved that the power set is always larger than the set, i.e., | p (s)| > | s |. a special case of cantor's theorem proves that the set of all real numbers r cannot be enumerated by natural numbers. r i... | wikipedia |
e3005287df90239fc167eb81bfd63968034484cc | there is a natural ordering on the ordinals, | there is a natural ordering on the ordinals, which is itself a well-ordering. given any ordinal α, one can consider the set of all ordinals less than α. this set turns out to have ordinal number α. this observation is used for a different way of introducing the ordinals, in which an ordinal is equated with the set of a... | wikipedia |
11e46671ce512160486fc3d008bcc75e29336c1e | ordinal numbers can be defined with the same | ordinal numbers can be defined with the same method used for cardinal numbers. define two well-ordered sets to have the same order type by: there exists a bijection between the two sets respecting the order: smaller elements are mapped to smaller elements. then an ordinal number is, by definition, a class consisting of... | wikipedia |
ae3b1732e411eba57674ee91b3e6fc437fdfb949 | besides the cardinality, which describes the size of | besides the cardinality, which describes the size of a set, ordered sets also form a subject of set theory. the axiom of choice guarantees that every set can be well-ordered, which means that a total order can be imposed on its elements such that every nonempty subset has a first element with respect to that order. the... | wikipedia |
ff500ad8b02b5210792a0129689ddc31d74ce26b | cardinal numbers can be defined as follows. define | cardinal numbers can be defined as follows. define two sets to have the same size by: there exists a bijection between the two sets (a one-to-one correspondence between the elements). then a cardinal number is, by definition, a class consisting of all sets of the same size. to have the same size is an equivalence relat... | wikipedia |
c9f17390caf23e99ccbf3e20745c3cd06d10916c | set theory as conceived by georg cantor assumes | set theory as conceived by georg cantor assumes the existence of infinite sets. as this assumption cannot be proved from first principles it has been introduced into axiomatic set theory by the axiom of infinity, which asserts the existence of the set n of natural numbers. every infinite set which can be enumerated by ... | wikipedia |
180fe46ab56c4d592ff93a48471389fbc65cb339 | pakistan civil aviation authority football club, commonly referred | pakistan civil aviation authority football club, commonly referred as pcaa or caa, serves as the football section of pakistan civil aviation authority. it is based in karachi. the club used to compete in the pakistan premier league. the club regularly participates in the pff national challenge cup. | wikipedia |
5e5d10b69df061600f5a92167198cfdec0b243c7 | aviation authority won promotion after winning the play-off | aviation authority won promotion after winning the play-off against asia ghee mills. on 28 september 2018, aviation authority played their first top-flight match against newly promoted sui southern gas, a 0–0 draw. aviation authority's first loss of the season was against national bank in the second match day on 1 octo... | wikipedia |
5842920d24f11cd98b472a8edad73e42fa5a45ef | civil aviation authority played their first game on | civil aviation authority played their first game on 28 april 2018 against sindh government press in the opening match at all brothers football stadium, karachi. the aviation authority won 3–1. on 2 may 2018, aviation authority did a major upset after defeating six times and defending champions, khan research laboratori... | wikipedia |
332e695e51f85e436afb23fdaeddb2b1d311aab2 | the club was formed in 2017, before the | the club was formed in 2017, before the start of 2018 national challenge cup, along with pakistan petroleum and asia ghee mills. all the clubs were formed to take part in first ever football tournament in pakistan since 2016 pff cup. | wikipedia |
180fe46ab56c4d592ff93a48471389fbc65cb339 | pakistan civil aviation authority football club, commonly referred | pakistan civil aviation authority football club, commonly referred as pcaa or caa, serves as the football section of pakistan civil aviation authority. it is based in karachi. the club used to compete in the pakistan premier league. the club regularly participates in the pff national challenge cup. | wikipedia |
0feb44b757b486221c0c093666911dff77acf805 | the volvo b9l is a fully low-floor single-decker | the volvo b9l is a fully low-floor single-decker bus chassis constructed by volvo buses from 2005 until 2013, replacing the volvo b7l and volvo b10l. an articulated model, known as the volvo b9la, is also available. it was superseded by the volvo b5lh in europe. the engine is mounted vertically on the rear left overhan... | wikipedia |
5e6e43c1562ad61498783ce70a11538f3898458f | the volvo b9l is a fully low-floor single-decker | by weichai wp7.270e50 or shanghai diesel engine sc9df260q5 designed and manufactured domestically. in greece, specifically in thessaloniki, the local operator oasth introduced 44 b9las in 2007 (851-894) and in 2010 20 b9ls were introduced and additionally 20 more b9las (901-920), all constructed by elvo. eventually in... | wikipedia |
9d4e84684df7a40a2db7e4c4e71bc841aa2f7148 | in greece, specifically in thessaloniki, the local operator | in greece, specifically in thessaloniki, the local operator oasth introduced 44 b9las in 2007 (851-894) and in 2010 20 b9ls were introduced and additionally 20 more b9las (901-920), all constructed by elvo. eventually in 2019-2023 the 44 b9las from 2007 were mostly withdrawn due to serious chassis defects (except for t... | wikipedia |
f8b2809a6ca00d6e295771796aa39432d96abdb3 | in mainland china, volvo b9l chassis is bodied | in mainland china, volvo b9l chassis is bodied with volvo 7900 three-door bodywork manufactured by shanghai sunwin bus, a joint venture of saic group and volvo bus, assembly named swb6128v8lf. the d9b engine is replaced by weichai wp7.270e50 or shanghai diesel engine sc9df260q5 designed and manufactured domestically. | wikipedia |
a52545765d5a287695829378da87378ab5fc21a4 | large orders for b9ls were placed in malmö, | large orders for b9ls were placed in malmö, where they form the majority of the fleet, as well as in stockholm, kristianstad, and Örebro. despite this overall sales of the b9l were poor, especially outside of sweden, with many operators instead preferring the existing b7rle or new b9s. outside of europe, comfortdelgro ... | wikipedia |
9234804e417253c0f8a385693c33018ca30509cb | additionally, the b9l reintroduced cng engines, an option | additionally, the b9l reintroduced cng engines, an option unavailable in its predecessor, the b7l. these versions replaced much older predecessor, the b10l. it was the last low-floor bus chassis from volvo to be available with such option. | wikipedia |
34639a837ef9805e4024cf16c6ca79176269658f | the engine is mounted vertically on the rear | the engine is mounted vertically on the rear left overhang of the chassis similarly to with the b7l, allowing b9ls to be low-floor throughout the whole length of the bus due to a lack of underfloor equipment. the volvo b9l is available as an integral bus bodied by volvo (7500/7700/7900) or as a chassis only, with bodie... | wikipedia |
290990fa771413a2dca4fc900292017da3782ff1 | the volvo b9l (also known as the volvo | the volvo b9l (also known as the volvo 7500, volvo 7700 or volvo 7900 for integral models) is a fully low-floor single-decker bus chassis constructed by volvo buses from 2005 until 2013, replacing the volvo b7l and volvo b10l. an articulated model, known as the volvo b9la, is also available. it was superseded by the vo... | wikipedia |
bc9d4b463642a887522fe0441126d08b45a754ff | marjorie ann hoy was an american entomologist and | marjorie ann hoy was an american entomologist and geneticist known for her work using integrated pest management (ipm) and biological control in agriculture. she was professor and eminent scholar at the university of florida, fellow of the royal entomological society of london, the american association for the advancem... | wikipedia |
d69cec9bb316839e4d1397a0974ea90f70e64785 | hoy was born in kansas city, kansas, in | hoy was born in kansas city, kansas, in 1941. she earned her ba at the university of kansas in 1963, and completed her m.s. (1966) and phd (1972) at the university of california, berkeley. she was research entomologist at the connecticut agricultural experiment station (1973–1974) and u.s. forest service northeast fore... | wikipedia |
a2acf342af18af1df65f87079f6b1e18bee8c08e | hoy was known as a pioneer in using | hoy was known as a pioneer in using genetic engineering to reduce the impact of agricultural pests, including developing pesticide resistant predators to control populations of destructive pests in areas where pesticides are applied. her books include the textbook insect molecular genetics, the third edition of which w... | wikipedia |
80f64718a8077dccb3bc77c1c36420faa3879382 | marjorie ann hoy (19 may 1941 – 19 | marjorie ann hoy (19 may 1941 – 19 june 2020) was an american entomologist and geneticist known for her work using integrated pest management (ipm) and biological control in agriculture. she was professor and eminent scholar at the university of florida, fellow of the royal entomological society of london, the american... | wikipedia |
d0860ed44db4513dfd38cd7cc531d831241ebfae | in june 2016, work began on the construction | in june 2016, work began on the construction of a new station building at isahaya. the old station building, a timber structure in western style built in 1935, was noted for its role as a receiving station for relief trains carrying the injured from the atomic bomb at nagasaki. this would be replaced by a new building ... | wikipedia |
8d950889459d31cc6f4b0b5165b437049df7591f | on 24 march 1934, a track was opened | on 24 march 1934, a track was opened from isahaya to yue, known as the ariake nishi, as part of the development of an alternative route for the nagasaki main line along the coast of the ariake sea. by 1 december 1934, a link up was achieved between the ariake nishi line at yue and the ariake higashi line which had been... | wikipedia |
35c52ac449836ff626fe53a9b3a0e0918a1f46bc | when the kyushu railway was nationalized on 1 | when the kyushu railway was nationalized on 1 july 1907, japanese government railways (jgr) took over control of the station. on 12 october 1909, track from tosu through haiki, Ōmura, isahaya, nagayo to nagasaki was designated the nagasaki main line. | wikipedia |
e92278d89f9478a19935f61118fe4ca9d9cf2f4e | the private kyushu railway, had opened a track | the private kyushu railway, had opened a track from tosu to saga by 5 may 1895, and thereafter expanding southwards in phases, as part of the construction of a line to nagasaki. separately, a track was laid from urakami (then known as nagasaki) north to nagayo, which opened on 22 july 1897 as the terminus. on 27 novemb... | wikipedia |
f0edabdd8641fc8b498c71b9e56a67ed2bbc35cf | this station has a side platform for the | this station has a side platform for the shimabara railway line. the jr kyushu has 2 island platform serving four tracks. the nishi kyushu shinkansen has 2 side platforms serving two tracks, totaling to 7 tracks at this station. | wikipedia |
f7ef95a70f7af6e264433d8da4503c05ca6da63a | the station consists of three side platforms and | the station consists of three side platforms and two island platforms serving seven tracks. track/platform 0 is a dead-end siding which juts into the platform 1 (the side platform) and is used exclusively by the trains of the shimabara railway line. platform 2 is a second side platform serving track 2 while tracks 3 an... | wikipedia |
9fdd75b35fb9c18e27b6285667f10ea6a79be9e1 | the station is served by the jr nagasaki | the station is served by the jr nagasaki main line and is located 100.4 km from the starting point of the line at tosu. it is also the eastern terminus of the jr Ōmura line, 36.2 km from the starting point at haiki and the western terminus and starting point for the 43.2 kilometer third-sector shimabara railway line. t... | wikipedia |
a676f9cdd81d52dd73d598cb03608c8ad47ab68a | isahaya station (諫早駅, isahaya-eki) is a junction passenger | isahaya station (諫早駅, isahaya-eki) is a junction passenger railway station located in eishō-chō, isahaya, nagasaki, japan. it is owned by kyushu railway company (jr kyushu) and the third-sector shimabara railway company. | wikipedia |
b592c767de6639c0161b07bd64fc77f13a8e8574 | the station is on the ground level with | the station is on the ground level with two opposing unnumbered side platforms and two tracks. the two platforms are staggered, with the south platform slightly offset toward jindaicho and the north platform slightly offset toward taisho. the two platforms are connected by a level crossing (without barriers or alarms. ... | wikipedia |
93f58a687d714f0b10a8939ab764043418833359 | saigō station (西郷駅, saigō-eki) is a passenger railway | saigō station (西郷駅, saigō-eki) is a passenger railway station in located in mizuho neighborhood of the city of unzen, nagasaki. it is operated by third-sector railway company shimabara railway. | wikipedia |
11f523dc714e1c06f145bf3a1dcaa930b8a3d4af | ellis eugene vance was an american professional basketball | ellis eugene vance was an american professional basketball player. he played in the basketball association of america (baa) and national basketball association (nba) for the chicago stags and tri-cities blackhawks / milwaukee hawks. vance played college basketball for the illinois fighting illini where he led the team ... | wikipedia |
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