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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...
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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.
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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 ...
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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...
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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...
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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...
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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.
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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...
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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).
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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...
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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...
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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...
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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 (...
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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 ⊊....
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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)).
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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...
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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).
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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
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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...
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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.
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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.
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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.
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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...
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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.
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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...
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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.
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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...
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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...
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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...
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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.
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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 ...
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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.
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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.
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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...
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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...
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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...
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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.
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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...
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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...
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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.
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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...
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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...
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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...
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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.
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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 ...
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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.
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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...
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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...
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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...
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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...
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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...
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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...
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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 ...
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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...
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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.
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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...
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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.
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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...
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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...
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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.
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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. ...
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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.
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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 ...
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