Maximum - definition of maximum by The Free Dictionary /maximum
maximum Also found in: , , , , .
max·i·mum
(măk′sə-məm)n. pl.
max·i·mums or
max·i·ma (-mə) 1. a.
The greatest possible quantity or degree.b.
The greatest quantity or degree the upper limit of variation.c.
The time or period during which the highest point or degree is attained.2.
An upper limit permitted by law or other authority.3.
Astronomy a.
The moment when a variable star is most brilliant.b.
The magnitude of the star at such a moment.4.
Mathematics a.
The greatest value assumed by a function over a given interval.b.
The largest number in a set.adj.1.
Having or being the greatest quantity or the highest degree that has been or can be attained: maximum temperature.2.
Of, relating to, or making up a maximum: a maximum number in a series.[Latin, from
neuter of maximus, greatest; see
in .]maximum (ˈmæksɪməm) n, pl -mums or -ma (-mə) 1. the greatest possible amount, degree, etc2. the highest value of a variable quantity3.
(Mathematics) maths a. a value of a function that is greater than any neighbouring valueb. a stationary point on a curve at which the tangent changes from a positive value on the left of this point to a negative value on the right. Compare 4c. the largest number in a set4.
(Astronomy) astronomy a. the time at which the brightness of a variable star has its greatest valueb. the magnitude of the star at that timeadj5. of, being, or showing a maximum or maximumsAbbreviation: max [C18: from Latin: greatest (the neuter form used as noun), from magnus great]max•i•mum
(ˈmaek sə məm)
-mums, -ma (-mə), adj.
the highest amount, value, or degree attained or attainable.
an upper limit allowed by law or regulation.
the value of a mathematical function at a certain point in its domain, which is greater than or equal to the values at all other points in the immediate vicinity of the point.
the point in the domain at which a maximum occurs.
being the greatest or highest attainable or attained.
[;40; & Latin, from maximus, superlative of magnus great]
max′i•mum•ly, adv.
max·i·mum (măk′sə-məm) Plural
The greatest known or greatest possible number, measure, quantity, or degree.2.
Mathematics
The greatest value of a function, if it has such a value.
Noun1.maximum - the largest possible quantity &,
- the most extreme poss "voltage peak",
- an indefinite quantity that is above the average in size or magnitude,
- the smallest possible quantity2.maximum - the grea "he tried his utmost", , , ,
- the greatest possible "what he did was beyond the bounds of acceptable behavior"; "to the limit of his ability"3.maximum - the point on a curve where the tangent changes from positive on the left to negative on the right - as far as something can go - the point on a curve where the tangent changes from negative on the left to positive on the rightAdj.1.maximum - the greatest or most compl "maximal expansion"; "maximum pressure",
- "needed to enforce minimal standards"; "her grades were minimal"; "minimum wage"; "a minimal charge for the service"maximumadjective1. , , , , , , ,
The maximum height for a fence here is 2 metres. greatest , , noun1. , , , , , , ,
The law provides for a maximum of two years in prison. top , maximumnoun1. The greatest quantity or highest degree attainable:, , , , .Idiom: ne plus ultra.2. The greatest amount or number allowed:, , .adjectiveGreatest in quantity or highest in degree that has been or can be attained:, , , , , .
maximum [ˈmæksɪməm]A. ADJ [amount, temperature, speed, load, efficiency] → for maximum benefit, use once a week → para
for maximum effect → para
to use sth to maximum effect →
maximum expenditure →
m a maximum security prison/hospital → una /un
maximum sentence →
f B. N (maximums or maxima (pl)) →
m20 kilos is the maximum → el
son 20 at the maximum → , up to a maximum of ?20 → hasta 20
to the maximum → C. ADV → you should drink two cups of coffee a day maximum →
maximum [ˈmæksɪməm] adj [speed] → (e), The maximum speed is 100 km/h → La
à l'heure., La
à l'heure. [number] → (e), the maximum amount → la , la
[efficiency, enjoyment] → (e),
[sentence, penalty] → (e),
n [maxima] (pl) →
mthe maximum → a maximum of two years → un
de deux to do sth to the maximum (= to the full) →
adv (= at the most) six weeks maximum → six
maximum adj attr → ; size, height, costs, length → ; maximum amount (= money) →
m; maximum penalty/sentence → H?chststrafe f; maximum fine →
; maximum credible accident →
m; for maximum effect → um die
zu ; they capitalized on our mistakes to maximum effect → sie haben unsere
; he scored maximum points → er hat die
; a maximum speed of … → eine
von …; we are producing at maximum speed → wir
; five is the maximum number allowed in a taxi →
dürfen in ein ; maximum security wing/prison →
m → /-gef?ngnis nt n pl &-s or maxima& →
nt; up to a maximum of ?8 →
? 8; temperatures reached a maximum of 34° → die
34°; is that the maximum you can offer? → ist das Ihr
?; ?20 at the maximum →
20 ; my salary is now at its maximum → ich bin
; to exploit something to the maximum →
adv (= at the most) → ; drink two cups of coffee a day maximum →
pro maximum [ˈmæksɪməm]1. n (maxima or maximums (pl)) → 2. adj → massimo/amaximum ('m?ksim?m)
adjective greatest. This requires maximum effort / the maximum amount of effort. maksimum
максимален
maximální
maksimaalne
maksimaalinen
najve?i stupanj
maximális
did?iausias, maksimalus
maksimāls
h?yeste ?? ????? ???
maximálny
maksimalen
maksimalan
h?gst, st?rst, maximi-
en büyük;
максимальний
noun – plurals 'maximums, ~'maxima (-m?)
the greatest number or quantity or the highest point or degree. Two hundred an hour is the maximum we can produce. maksimum
????? ???????
максимум
das Maximum
det h?jeste
(το) μ?γιστο, το μ?ξιμουμ
??????? ?????
??????????, ???????? ?????????
??????, ??????
najve?a koli?ina
did?iausias kiekis, maksimumas
???????????
en büyük de?er
最大數，最大量，最大程度
максимум; найвищий ступ?нь
??????? ????? ?????
l??ng c?c ??i
最大数，最大量，最大值
màxim maximum →
maximální, maximum maksimal, maksimum ,
maksimi, maksimi-
maksimalan, maksimum
最大の, 最大限 ??, ??? ,
maximal, maximum ???????????, ?????? ,
l??ng t?i ?a, t?i ?a , max·i·mum, maximala., sup. máximo. maximum adj & n (pl -mums) máximo
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In the long history of the world, only a few generations have been granted the role of defending freedom in its hour of maximum I do not shrink from this responsibility. by
He assigned a height of 11,400 feet to the maximum elevations, and reduced the mean of the different altitudes to little more than 2,400 feet. by
in four days, and will reach its maximum intensity twenty-seven hours after inception. by
▲maximum▼
For webmasters:在数学里minimum和minimal有啥区别吗？
boyd's convex optimization的2.6.3节，分不清楚他说的minimum element和minimal element都是啥...
按投票排序
一张图让你明白：============================================================================================================按照
的建议做一点补充说明：1、集合 X 上的偏序 ≤ 是指满足以下条件的二元关系：(i) 对任意 x∈X，x≤x；(ii) 对任意 x,y∈X，若 x≤y，y≤x，则 x=y；(iii) 对任意 x,y,z∈X，若 x≤y，y≤z，则 x≤z。2、上面的图分别表示一个偏序集，图中的小圆圈表示偏序集中的点，连线表示大小关系。3、如果两个相邻的点之间有连线，则下面的点&上面的点（x&y 的意思是 x≤y 且 x≠y）。4、对于不相邻的点，其大小关系由 1(iii) 决定（如果可以比较大小的话）。5、如果两个点之间没有连线，或者虽然有间接的连线但不符合 1(iii) 所述情形，则不能比较大小。6、maximum 的意思是“最大”，表示该偏序集中其他的点都比它小；maximal 的意思是“极大”，表示该偏序集中没有比它更大的点，即该偏序集中的其他点要么比它小，要么和它不能比较大小。minimum 和 minimal 的意思同理。7、注意与中文微积分教材中函数的最值与极值区分。函数的最大值/最小值是指在整个定义域上的最大值/最小值；而函数的极大值/极小值是指“局部最大值/局部最小值”，即极大值/极小值是在它的某个邻域内的最大值/最小值。
如果版本没错的话，请退回去看 2.4.2 节，配合图 2.17 中的例子。维基看 ，，简单来说（忽略相等情况）minimal：没有比他小的。minimum：别的都比他大。在偏序集合中，这两者是不一样的，因为偏序集合中不是任意两个元素都可以比较。==似乎贴图之后还是有人误解，发现主要干扰是高等数学时学的「极小值」「最小值」。首先， 贴的是一个偏序集的 Hasse diagram，不要理解为能级图！建议加上箭头，拓扑上做个调整，消除「等级高低」的印象……：函数的「极小值」对应的英语是 local minimum，不是 minimal。 minimal element 是偏序集合中的概念，汉译「极小元」。minimum 译为「最小元」。：偏序集合可能同时有最小元 minimum 和极小元 minimal，最小元不一定存在。的第二个图中就没有所谓的「偏序最小」。而「局部最小」「极小值」见前段。
minimum 最小值。minimal极小值。。。。。最值和极值的区别。
minimum是最小值minimal是极小值我想有点高等数学基础的都懂吧顶一下
英语都怎么学的？？
局部和全局Physiology & Psychology:
Performance Benchmarks -- Maximal Oxygen Uptake
Introduction to maximal oxygen
uptake (VO2 max)
Because cross country skiing engages
about all of the major muscle groups in the body, cross country skiing is
an excellent method of training for physical fitness and dynamic muscular
endurance. For the same reason, top cross country skiers generally have exceedingly
high maximal oxygen uptakes (VO2 max). Maximal Oxygen Uptake (units are liters
per minute) is predominately a function of cardiac output, or how much blood
the heart can pump. Therefore, maximal oxygen uptake has a "central limitation".
Cardiac output is a function of stroke volume, the amount of blood the heart
pumps in one beat. The stroke volume is determined by the end diastolic volume
(how much blood your heart can accommodate) and end systolic volume (how completely
it can empty). Both the end diastolic and end systolic volumes are a result
of the number, size, and the strength of the muscle fibers (left ventricular
mass and maximal contractility), how large the blood volume (preload) is,
how much the arteries can dilate, (afterload) and the size of the pericardium.
The pericardium is a non-elastic sack around the heart that may limit maximum
filling. The lungs could also be a limiting factor in cases of disease, altitude,
or possibly at very high work loads.
Maximal Oxygen Uptake
Oxygen consumption is considered
the standard for measuring the physiological intensity of exercise. If heart
rate is the tachometer, then oxygen consumption is how much gas per mile you're
burning to achieve a certain speed. In cross-country skiing, success is largely
dependent on the body's oxygen uptake ability. The more oxygen that can be
delivered to the working muscles, the greater the energy supply, and the faster
the body can travel over distance.
Elite cross-country skiers
are considered the most powerful in oxygen uptake capacity. This is
partly due to genetics, but those genes are the foundation on which
the athlete builds an aerobic powerhouse over many years of training
in a sport that demands the highest aerobic output.
Exercise science has determined
that you achieve specific training adaptations by exercising at various intensities
or percent-ages of VO2 max. Oxygen uptake capacity is measured directly, however,
only in the sports physiology laboratory with expensive equipment by qualified
professionals to which few of us have ready access. Fortunately, research
has shown a reliable relationship between oxygen consumption and heart rate
(beats per minute) for monitoring intensity during training. The methods for
calculating intensity levels by heart rate, described later in this chapter,
produce results that accurately correspond with relative percentages of VO
Remember that in each stage of
the training plan, the amount and type of exercise you do will determine how
fit and race ready your body will become. The physiological effects of each
training intensity will dictate the amount of each training component scheduled
during a given training cycle. For example, low-intensity over distance training
sessions are most effective if the intensity is between 55 and 65 percent
of VO2 max. This develops aerobic energy pathways and improves capillary density
in muscle tissue, proliferation of muscle cell mitochondria, oxidative enzyme
activity, and fat substrate mobilization and utilization in the muscle cells.
Concurrently, intervals and race/pace sessions, when planned appropriately,
are best accomplished at an intensity at or slightly below the anaerobic threshold
Cross-country skiing and VO2 max
Since more muscle groups generally
are engaged in skiing than in walking (the use of the arms to pull and push
on the ski-poles), the overall energy expenditure involved in transporting
the body on skis from one place to another may be as high as, or higher than,
the energy expenditure when moving the body the same distance on foot.
Liters/minute is the
absolute value of maximal oxygen uptake (example: 6.2 liters). Milliliters
(ml) per kilogram (kg) per minute (min) is the relative value (example:
6.2 liters = 6200 ml/75 kg = 82 ml/kg/min).
A maximal oxygen uptake
of 7.4 liters/minute has been reported in a Finnish cross-country
skier, Mieto. Also reported is 94 ml oxygen uptake kg/min for a
male O 75 ml/kg/min for a female skier.
The efficiency of skiing is illustrated
by the following examples:
A good skier covered 30 km
on a snow-covered lake in 1 hr 20 min (speed 6.25 m/s).
The 1996 time in the Swedish
Vasa race, 86 km (with some 30,000 participants), was 3 hrs 49 min (average
speed 6.23 m/s). The terrain is relatively flat.
In the Olympic Games in 1994
the 50 km winner finished after 1hr 50 min 55 sec (average speed 7.51 m/s).
For comparison, the best time in track running 10,000 m gives a speed of
6.34 m/s, and for marathon about 42.2 km, 5.65 m/s.
It is thus clear that skiing, even
at submaximal speeds, requires a high aerobic work capacity. Accordingly,
most elite cross-country skiers have maximal oxygen uptakes of 5.5 liters/min
or more (in excess of 80 ml/ kg/ min), with a maximum of 94 ml obtained in
an Olympic Champion (15 km race), an extremely high aerobic power. The corresponding
figures for the top Swedish female cross-country skiers are 3.5 to 4.4 liters/
min or 70 to 75 ml/ kg/ min. This is shown in the graph.
Look at swimming and compare it
with cross country skiing. For swimming, men (68%) and women (60%) have a
much lower VO2 max than cross country skiers, men (90%) and women (70%).
Dr. Norman (a Canadian biomechanist),
based on film data collected during the 1988 Olympics in Canmore, Calgary
estimated that:
For a man, skiing on flat terrain
at a pace to win an Olympic medal required 75 milliliters of oxygen per
kilogram of body weight, per minute.
Uphill skiing, during the first
20 minutes, required 110 milliliters per kilogram of body weight per minute
of energy output.
These estimates imply that energy
must come from sources other than aerobic metabolism, since no athlete has
a sufficiently high oxygen uptake and that recovery (restoration of homeostasis)
must take place during high levels of work. This requires the highest values
for maximal oxygen uptake, a tremendous ability to buffer the byproducts of
the anaerobic metabolism quickly, and large glycogen stores. We should design
training fully to develop these qualities in each athlete. Said another way,
not only must peak energy production be extremely high, but beyond any recorded
level of aerobic power for humans.
The debt must be repaid while sustaining
near maximal levels of oxidative metabolism. You can see in the graph, that
during the first twenty minutes of cross country skiing, the maximal oxygen
uptake is as high as 130%. After two hours, cross country skiers utilized
80% of their VO2 max during a 50 km race!
U.S. Olympic cross country skiers
compared to Swedish cross country skiers
It is clear that a high maximal
oxygen uptake is critical for high level cross country skiing.. Cross country
skiers need a big engine (aerobic power). Once an athlete has this basic ability
other parameters become much more important. The minimum VO2 max range we
believe necessary to achieve for international success is 5.5 liters per minute
for men, and 3.5 liters per minute for women.
Swedish studies indicate that
male athletes who never progressed beyond National Team nomination were in
the 5-5.3 liter per minute range. Those qualifying for Olympic and World Championship
Teams were in-the 5.6-5.8 liter per minute range, and medalists were in the
6-6.2 liter per minute range.
In general, Olympic Gold Medal
winners have a V02 max no lower than 6 liters per minute for men, and 4 liters
per minute for women.
The graph above shows maximal oxygen
uptake values for top American and Swedish men and women from the 1970's,
while the values for the U.S. cross country skiers are in a very high range,
our average values were 6-9% lower than our Swedish competitors. In an individual
it is unlikely that this difference would be significant, but as average values
for a large group, it shows us that we were slightly behind in this area at
that time.
Among elite male long distance
runners and cross country skiers, the highest VO2 max value recorded
for a male is from a champion Norwegian cross country skier who had
a VO2 max of 94 ml/kg/min. The highest value recorded for a female
is 74 ml/kg/min in a Russian cross country skier. In contrast, poorly
conditioned adults may have values below 20ml/kg/min!
U.S. Cross Country Ski Team Field
The method used by the U.S. Cross
Country Ski Team can be done completely in the field, and is specific to each
training activity. The test is used to determine the intensity needed for
the U.S. cross country ski team members to improve maximum oxygen uptake.
What you need to conduct the field
test while roller skiing:
An accurately measured constant
grade of 1 kilometer, approximately 3-4 minutes, and at a grade of 5-1 0%.
A heart rate monitor with a
To run a thorough test, 10-12 steady
runs up the hill will be necessary (minimum of 6-8). The first run should
start at an intensity corresponding to Low Intensity 1. During each run the
skiers should try to maintain the pace as steadily as possible. The pace is
increased each run by 5-10 heart beats, and subsequent runs are done until
the skier reaches maximum pace and intensity.
The coach times each run, and later
calculates speed for each run. The heart rates for the last minute of each
run are averaged and graphed according to speed. When graphed, the heart rate
will go up linearly relative to speed. The Conconi Point, or maximal steady
state, is determined by the inflection point in the graph. The inflection
point in the graph is caused by a decrease in the rate of increase in the
heart rate or a break in the linear slope of the curve.
Other methods for systematic increases
in speed during the test can be done, such as pacing on a bike with a computer
It is recommended that testing
on foot be done on 5-10% grade. By the nature of ski training most skiers
cannot run fast enough on the flat to complete the test and still be taxed
cardiovascularly. By doing it uphill, the test eliminates the need to be a
particularly good foot runner.
Initial testing with this method
should be carried out for foot running, roller skiing-classical and free-style,
to determined if there is a significant difference. Once this is determined,
one test every two to three weeks is all that is necessary.
To determine training intensities
based upon Conconi Test.
30-50k race
Sample Training
Zones for an athlete with a Conconi Point of 175.
<font color="#5
<font color="#5-145
<font color="#5
<font color="#5-170
<font color="#5
<font color="#0-180
<font color="#5
or Long Race Average
<font color="#5+10
<font color="#5
or Short Race Average
Estimate your maximal oxygen uptake (VO2 max).
You'll find various formulas and calculators on the following pages:
When you are finished with the above pages, close the window to return to the Olympics Sport and Science Site.
1998, Montana State University-Bozeman