text:
#### 题目列表

Megalimpet is a nationwide owner of office space. ?They have major office buildings in the downtowns of several cities in the 48 lower states, and rent this space to individual companies. ?Megalimpet office spaces vary from small office to large suites, and every space has custom-designed wall-to-wall carpeting. ?The carpet in several Megalimpet facilities needed replacing. ?The winning bid for the nationwide carpet replacement was submitted by Bathyderm Carpet Company (BCC). ?The bid contract involves all delivery costs, all installation, and any ongoing maintenance and upkeep while the carpet is under the three-year warranty. ?Both BCC executives and independent consultants they hired felt BCC would be able to perform all these services for far less than their bid price; these circumstances would allow BCC to reap a considerable profit.
Which of the following, if true, most calls in question the argument that BCC will make a large profit from this contract with Megalimpet?
Self-pollinating plants carry several advantages over those plants that are non–self-pollinating. For one, self-pollinating plants still produce the same number of seeds during drought conditions, when the number of insects-which aid in the spread of seeds of non–self-pollinating plants-is low. Self-pollinating plants are also able to thrive in a greater variety of climates. Nonetheless, the number of self-pollinating plants in the world is much lower than that of non–self-pollinating plants.
Which of the following, if true, could account for the discrepancy described in the paragraph above?
In an effort to recruit the most qualified educators, New Way Education has begun to canvas for potential teachers in top-ranked universities throughout the country. Those students who show interest in becoming teachers are put through rigorous training that includes a final test, in which students must effectively teach a 15-minute mock classroom to a team of New Way Education trainers. Therefore, those who are selected to teach at New Way Education are some of the best educators in the industry and will create a positive learning experience for students in their classrooms.
Which of the following is an assumption on which the argument rests?
The rate of health complications of patients on intravenous (IV) therapy at a particular hospital were higher than usual. ?Government inspectors found that the typical IV solutions used in this hospital had somewhat high concentrations of sodium and potassium, which were raising patients' blood pressure and taxing their kidneys. ?The government inspectors mandated lowering the sodium and potassium in these IV preparations, and threatened with a possible government fine. ?In compliance, the hospital lowered the sodium and potassium levels in the IV solutions to the correct levels. ?Nevertheless, patients on IV therapy at that hospital continued to have a high rate of health complications.
Which of the following, if true, most helps to explain why acting on the government inspectors' recommendations failed to achieve its goal?
Freudianism sits alongside Marxism and Darwinism in the pantheon of modern theories held to be so revelatory that they not only gained the adherence of Western intelligentsia but shaped the broader culture. During the first half of the twentieth century, an air of intrigue and mystery hovered around Freuds newly anointed practitioners: psychotherapists. They occupied a strange universe, speaking in a language so incomprehensible but seemingly authoritative that it alternately awed and scared the average man on the street. Psychotherapy is no longer an intellectual movement today as it once was. But in the form of modern professional "caring," it has assumed a new role, which is to provide a peculiar sort of substitute friendship - what we might call "artificial friendship" - for lonely people in a lonely age.

To understand why this occurred and what it means for American culture, one must study the fractious history of the mental health field over the last six decades. It is a complicated story, with a staggering variety of terms, schools, leaders, and techniques, so any overview must necessarily leave out many important details. But from even just a synopsis of the conflicts that gave rise to todays culture of psychotherapy - battles over who would hold the truest title to physician of the mind, tensions between scientists and clinicians, academics and professionals, elites and the public - we can see more clearly how psychotherapy has profoundly shaped the American conception of what happiness is and how we can achieve it.
In the context in which it appears fractious most nearly means
In the mid-1970s, Walter Alvarez, a geologist, was studying Earths polarity. It had recently been learned that the orientation of the planets magnetic field reverses, so that every so often, in effect, south becomes north and vice versa. Alvarez and some colleagues had found that a certain formation of pinkish limestone in Italy, known as the scaglia rossa, recorded these occasional reversals. The limestone also contained the fossilized remains of millions of tiny sea creatures called foraminifera. Alvarez became interested in a thin layer of clay in the limestone that seemed to have been laid down around the end of the Cretaceous Period. Below the layer, certain species of foraminifera-or forams, for short-were preserved. In the clay layer, there were no forams. Above the layer, the earlier species disappeared and new forams appeared. Having been taught the uniformitarian view, which held that any apparent extinctions throughout geological time resulted from the incompleteness of the fossil record rather than an actual extinction, Alvarez was not sure what to make of the lacuna in geological time corresponding to the missing foraminifera, because the change looked very abrupt.

Had Walter Alvarez not asked his father, the Nobel Prize-winning physicist Luis Alvarez, how long the clay had taken to deposit, the younger Alvarez may not have thought to use iridium, an element rarely found on earth but more plentiful in meteorites, to answer this question. Iridium, in the form of microscopic grains of cosmic dust, is constantly raining down on the planet. The Alvarezes reasoned that if the clay layer had taken a significant amount of time to deposit, it would contain detectable levels of iridium. The results were startling: far too much iridium had shown up. The Alvarez hypothesis, as it became known, was that everything-not just the clay layer-could be explained by a single event: a six-mile-wide asteroid had slammed into Earth, killing off not only the forams but also the dinosaurs and all the other organisms that went extinct at the end of the Cretaceous period.
Proponents of the uniformitarian view would most likely argue that
The average size of marine life that washes up on the shore of the Japanese island Ryukyu is smaller than the average size that washes up on the Western coast of Australia. Giant squid have recently been found washed up on the shores of Ryukyu as well as the Western coast of Australia. It can be concluded that the average size of the giant squids on the shore Ryukyu must be less than that of giant squids washed up on the shores of Western Australia.
The argument above can be attacked on the grounds that it does which of the following?
An unknown simian virus recently killed off nearly half the human population of a remote jungle town. Because the disease spread at an alarming rate-victims usually exhibited signs within 8 hours of exposure, and many died within 36 hours-the simian virus, if an outbreak occurs again, is likely to cause more deaths than has any other previous virus.
Which of the following pieces of information most effectively calls into question the validity of the conclusion?
The US Constitution established both gold and silver as the basis of US currency: that is to say, it established a bimetallic standard for currency. This remained in place for about a century, until the Coinage Act of 1873, which embraced a "gold only" standard, a monometallic standard, effectively dropping silver as the basis of currency. Over the next several decades, advocates of bimetallism and advocates of the "gold only" standard fiercely debated.

The "gold only" advocates, such as William McKinley, argued that shifts in the relative value of the two precious metals could lead to wild fluctuations in the values of currency in a bimetallic system. Early in the United States history, Alexander Hamilton had tried to fix the gold-silver exchange rate by fiat, but of course, such restraints only inhibit the natural development of a free market.

Unemployment was high in the depression caused by the Panic of 1893, and many argued that these economic challenges had been triggered by abandoning bimetallism. One of the more prominent advocates of bimetallism was William Jennings Bryant: indeed, bimetallism was the very center of his presidential campaigns in 1896 and 1900, both of which he lost to McKinley. Bryant articulated the popular view that a "gold only" standard limited the money supply, and thus favored those who were already quite wealthy, against the interests of working people of all professions. He famously expressed this argument in his "Cross of Gold" speech at the 1896 Democratic National Convention, in which he argued that continuing the "gold only" standard would "crucify" the honest laboring classes on a "cross of gold."

Despite the eloquence of Bryant's arguments, history strongly favored the "gold-only" standard. The argument that increasing the money supply would lead to greater prosperity strikes us now as na?ve: of course, we now understand that increasing the monetary supply can lead to runaway inflation, which hurts everyone. Furthermore, gold did not remain as limited as the advocates of bimetallism imagined. In the 1890s, scientists discovered a cyanide process that allowed workers to extract pure gold from much lower grade ore, thus significantly increasing domestic gold production. Additionally, the discovery of two immense gold deposits in South Africa substantially increased world gold supply. Thus, the "gold only" standard allowed for ample currency, and even robust prosperity in the 1920s, so bimetallism died a quiet death.
It can be inferred from the passage that the author believes that government attempts to control exchange rates
The problem with treating the five-paragraph essay form as a relatively benign aid to clarity is that like any habit it is very hard to break. Students who can not break the habit remain handicapped because five-paragraph form runs counter to virtually all of the values and attitudes that they need in order to grow as writers and thinkers-such as respect for complexity, tolerance of uncertainty, and the willingness to test and complicate rather than just assert ideas. The form actually discourages thinking by conditioning writers to be afraid of looking closely at evidence. If they look too closely, they might find something that does not fit, at which point the prefabricated organizational scheme falls apart. But it is precisely the something-that-doesnt-seem-to-fit, the thing writers call a "complication" that triggers good ideas.
In the context in which it appears "conditioning" most nearly means
1 2 ... 16 17 18 19 20 21 22 ... 54 55

25000 +道题目

140本备考书籍


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# Deriving a conservation law using the divergence theorem

Problem:

Material scientists have discovered a new fluid property called "radost" that is carried along with a fluid as it moves from one place to the next (just like a fluid's mass or momentum). Let ##r(x,y,z,t)## be the amount of radost/unit mass in a fluid. Let ##\rho(x,y,z,t)## be the mass density of the fluid. Let ##\vec{v}(x,y,z,t)## be the velocity vector of the fluid. Use the divergence theorem to derive a conservation law for radost.

Attempt at a Solution:

We did an example like this in class, but for conserving mass, so it was a little different. What we ended up with was the following expression $$\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho \vec{v})=0$$

We started by writing, $$dM=\rho dV$$ Thus, $$M=\int_V \rho dV$$ Then we applied the divergence theorem and that was basically it.

I'm just kind of confused how to start this one.

Office_Shredder
Staff Emeritus

format: plain


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# Ultraproduct is Well-Defined

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## Theorem

Definition:Ultraproduct is well-defined.

More specificly, following the definitions on Definition:Ultraproduct,

we are going to prove that:

(1) $f^\mathcal M$ is well-defined
(2) $R^\mathcal M$ is well-defined

## Proof

First of all, we need to prove

### Lemma

Following the definitions on Definition:Ultraproduct

$\left(m_{k, i}\right)_\mathcal U = \left(m'_{k, i}\right)_\mathcal U$, $k = 1, \dotsc, n$
$\left\{ i : \left({m_{1, i}, \dots, m_{n, i} }\right) = \left({m'_{1, i}, \dots, m'_{n, i} }\right) \right \} \in \mathcal U$

### Proof

Let

$I_k := \left\{ i \in I : m_{k, i} = m'_{k, i} \right\}$
$I^* := \left\{ i : \left({m_{1, i}, \dots, m_{n, i} }\right) = \left({m'_{1, i}, \dots, m'_{n, i} }\right) \right \}= \displaystyle \bigcap^n_{k = 1} I_k$

Suppose

$\left(m_{k, i}\right)_\mathcal U = \left(m'_{k, i}\right)_\mathcal U$ for $k = 1, \dotsc, n$

we have

$I_k \in \mathcal U$ for $k = 1, \dotsc, n$

Since $\mathcal U$ is closed under intersection

$I^* \in \mathcal U$

On the other hand, suppose

$I^* \in \mathcal U$

Since $\mathcal U$ is upward-closed

$I_k \in \mathcal U$ for $k = 1, \dotsc, n$

Therefore

$\left(m_{k, i}\right)_\mathcal U = \left(m'_{k, i}\right)_\mathcal U$

$\blacksquare$

### Proposition 1

The definition of $f^\mathcal M$ is consistent.

i.e. for $\left(m_{k, i}\right)_\mathcal U = \left(m'_{k, i}\right)_\mathcal U$, $k = 1, \dotsc, n$

$\left(f^{\mathcal M_i}\left(m_{1, i}, \dots, m_{n, i}\right)\right)_\mathcal U = \left(f^{\mathcal M_i}\left(m'_{1, i}, \dots, m'_{n, i}\right)\right)_\mathcal U$

### Proof

Firstly note that:

$\{i : f^{\mathcal M_i}\left(m_{1, i}, \dots, m_{n, i}\right) = f^{\mathcal M_i}\left(m'_{1, i}, \dots, m'_{n, i}\right) \} \supseteq \{i : \left(m_{1, i}, \dots, m_{n, i}\right) = \left(m'_{1, i}, \dots, m'_{n, i}\right) \}$

and by $\mathcal U$ is an ultrafilter on $I$, we have

$\{i : \left(m_{1, i}, \dots, m_{n, i}\right) = \left(m'_{1, i}, \dots, m'_{n, i}\right) \} \in \mathcal U$

implies

$\{i : f^{\mathcal M_i}\left(m_{1, i}, \dots, m_{n, i}\right) = f^{\mathcal M_i}\left(m'_{1, i}, \dots, m'_{n, i}\right) \} \in \mathcal U$

Therefore,

$\left(m_{k, i}\right)_\mathcal U = \left(m'_{k, i}\right)_\mathcal U$, $k = 1, \dotsc, n$, by #Lemma, which is equvalent to $\{i : \left(m_{1, i}, \dots, m_{n, i}\right) = \left(m'_{1, i}, \dots, m'_{n, i}\right) \} \in \mathcal U$

implies

$\left(f^{\mathcal M_i}\left(m_{1, i}, \dots, m_{n, i}\right)\right)_\mathcal U = \left(f^{\mathcal M_i}\left(m'_{1, i}, \dots, m'_{n, i}\right)\right)_\mathcal U$

$\blacksquare$

### Proposition 2

The definition of $R^\mathcal M$ is consistent.

i.e. for $\left(m_{k, i}\right)_\mathcal U = \left(m'_{k, i}\right)_\mathcal U$, $k = 1, \dotsc, n$

$\left\{i \in I: \left({m_{1, i}, \dots, m_{n, i} }\right) \in R^\mathcal M_i\right\} \in \mathcal U$
$\left\{i \in I: \left({m'_{1, i}, \dots, m'_{n, i} }\right) \in R^\mathcal M_i\right\} \in \mathcal U$

### Proof

Let

$S := \left\{i \in I: \left({m_{1, i}, \dots, m_{n, i} }\right) \in R^\mathcal M_i\right\}$
$S' := \left\{i \in I: \left({m'_{1, i}, \dots, m'_{n, i} }\right) \in R^\mathcal M_i\right\}$
$I^* := \left\{ i : \left({m_{1, i}, \dots, m_{n, i} }\right) = \left({m'_{1, i}, \dots, m'_{n, i} }\right) \right \}$
$T := I^* \cap S$
$T' := I^* \cap S'$

As #Lemma implies

$I^* \in \mathcal U$

therefore

$S \in \mathcal U$ implies $T \in \mathcal U$

Note that

$\left({m_{1, i}, \dots, m_{n, i} }\right) = \left({m'_{1, i}, \dots, m'_{n, i} }\right)$ for $i \in I^*$

we have

$T = T'$

Hence

$T' \in \mathcal U$

and

$S' \in \mathcal U$ since $S' \supseteq T'$

So far we have proved

$S \in \mathcal U$ implies $S' \in \mathcal U$

By symmetry,

$S' \in \mathcal U$ implies $S \in \mathcal U$

$\blacksquare$


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# Attack speed

## Redirected from Attack Speed

2,292pages on
this wiki

Attack speed (often shortened as AS or ASPD) is the frequency of a champion's basic attacks. They are measured and displayed as attacks per second.

• Attack speed cannot be increased beyond 2.5 attacks per second (or 1 attack every two fifths of a second, or 0.4 seconds).
• bypasses this limit (up to 5.00 attack per second).

Attack speed bonuses (from items or abilities, etc.) are in percent. The bonus is a percentage of the champions base attack speed. Therefore, champions with higher base attack speed benefit more from attack speed increases. Like all stats, one's attack speed can be increased via leveling up, items, runes, masteries, buffs, and abilities. Some items and abilities (only those two) decrease enemy attack speed.

## Calculations

### Base attack speed

Every champion's base attack speed (ASbase) is calculated using a hidden variable called attack delay,[1] which ranges from −0.10 to 0.08. (ASbase) is the total number shown at level 1 without runes, masteries, etc. It is represented this way throughout the wiki.

$${\it AS}_{\rm base} = {0.625 \over 1 + {\it attack\ delay}}$$

### Bonus attack speed sources

• Champions gain AS% at each level, not including level 1. This amount ranges from roughly 0% to 4% and depends on the champion. This amount depends on the level through the Statistics growth formula.
• Items
• Champion abilities
• Masteries
• Attack Speed runes

Example: grants +50% attack speed and also grants +50% attack speed, so the champion gains +100% in total.

Notes:

• Final attack speed cannot go above the cap of 2.5 attacks per second.
• Many in-game tooltip percentages (such as runes) have been rounded, so results may be slightly different unless the precise numbers are known.

### Example

• Calculating base attack speed:
• attack delay is −0.04.
• $${0.625 \over (1 - 0.04)} = {0.625 \over 0.96} = 0.651041\overline6$$. This is base attack speed, seen at level 1 (without runes, masteries, etc).
• The number seen in game is rounded to 3 decimal places: 0.651.
• Calculating "bonus attack speed":
• Every time levels up, he gains bonus AS% based on percentage growth ($$3.22\%$$) and his level through the Statistics growth formula.
• At level 18 he has gained $$3.22\% \times({7 \over 400}\times(18^2-1)+{267\over400}\times(18-1))=54.74\%$$ as bonus AS%.
• At 18 he has maxed increasing his attack speed by 30%.
• Let's say he has the mastery up to 4%.
• Let's also say he has : +50%.
• All together he has: $$54.74\% + 30\% + 4\% + 50\% = 138.74\%$$ bonus AS% or 1.3874 bonus AS as a decimal.
• Final calculation:
\begin{align} & {0.625 \over 0.96} + ({{0.625 \over 0.96} \times 138.74\%}) \\ =& 0.651041\overline6 + ({0.651041 \times 138.74\%}) \\ \approx & 1.55429 \end{align}
• In game, the number will be shown as: 1.554.

## Increasing attack speed

### Items

• : Unique Passive: Your heals and shields on another unit grant them 15% attack speed and 30 magic damage on-hit for 6 seconds

. +40 ability power, +100% base mana regeneration, +10% cooldown reduction. Unique Passive: +8% movement speed.
2200
.
• : +30% attack speed

. Unique Passive – Enhanced Movement: +45 movement speed.
1100
.
• : +40% attack speed

, +25 attack damage, +10% life steal. Unique Passive: Basic attacks deal 6% of the target's current health as physical damage (60 max vs. minions). Unique Active: Deals 10% of target champion's maximum health (min. 100) as physical damage, heals for the same amount and steals 25% of the target's movement speed for 3 seconds (90 second cooldown) (550 range).
3400
.
• : +12% attack speed

.
300
.
• : Passive: Basic attacks grant +8% attack speed, +3 attack damage, and +4 ability power for 5 seconds (stacks up to 8 times, melee attacks grant 2 stacks). While you have 8 stacks, you gain Guinsoo's Rage

. +30 attack damage, +40 ability power. Unique Passive – Guinsoo's Rage: Basic attack deal 20 + (15% bonus AD) + (7.5% AP) bonus on-hit magic damage to the target and nearby units in a 385 range area of effect.
2800
.
• : +15% attack speed

. Passive: Moving and attacking will make an attack Energized. Unique Passive – Energized Strike: Your Energized attacks deal 30 bonus magic damage on hit.
750
.
• : Unique Passive – Lifegrip: When Lifeline triggers, gain +25% attack speed, +10% spell vamp, and +10% life steal until out of combat

. +55 attack damage, +50 magic resist, +10 armor penetration. Unique Passive – Lifeline: Upon taking magic damage that would reduce health below 30%, grants a shield that absorbs 300 + (100% bonus MR) magic damage for 5 seconds (90 second cooldown).
3250
.
• : +50% attack speed

, +80 ability power. Unique Passive: +20% cooldown reduction. Unique Passive: Basic attacks deal 15 + (15% AP) bonus magic damage on hit.
3000
.
• : +45% attack speed

, +30% critical strike chance, +5% movement speed. Unique Passive – Spectral Waltz: While within 500 units of an enemy champion you can see, +7% movement speed and you can move through units. Unique Passive – Lament: The last champion hit deals 12% less damage to you (ends after 10 seconds of not hitting).
2800
.
• : +30% attack speed

, +30% critical strike chance, +7% movement speed. Passive: Moving and attacking will make an attack Energized. Unique Passive – Firecannon: Your Energized attacks gain 35% bonus range (+150 range maximum) and deal 50 – 200 bonus magic damage on hit.
2600
.
• : +25% attack speed

. Unique Passive: Basic attacks deal an additional 15 physical damage on hit.
1000
.
• : +40% attack speed

, +30% critical strike chance, +7% movement speed. Unique Passive: When basic attacking, bolts are fire at up to 2 ennemies near the target, each dealing 25% AD physical damage. Bolts can critically strike and apply on hit effects. Unique Passive: Basic attacks deal an additional 15 physical damage on hit.
2600
.
• : +35% attack speed

, +30% critical strike chance, +5% movement speed. Passive – Energize: Moving and using basic attacks Energize you. When fully Energized, gain Shiv Lightning. Unique Passive – Shiv Lightning: Your next basic attack (on-hit) deals 30 – 100 bonus magic damage, increased to 66 – 220 against minions, that can spark to up to 4 additional nearby units.
2600
.
• : +50% attack speed

. Unique Passive: +10% cooldown reduction.
1200
.
• : +15% attack speed

, +250 health, +25 attack damage, +20% critical strike chance, +10% cooldown reduction, +5% movement speed, +250 mana. Unique Passive – Rage: Basic attacks grant 20 movement speed for 2 seconds on hit. Minion, monster, and champion kills grant 60 movement speed for 2 seconds. This movement speed bonus is halved for ranged champions. Unique Passive – Spellblade: After using an ability, the next basic attack deals 200% base AD bonus physical damage (1.5 second cooldown).
3800
.
• : +40% attack speed

, +40 magic resistance. Unique Passive: Your basic attacks deal 40 bonus magic damage. Unique Passive: Your basic attacks steal 5 magic resistance of the target for 5 seconds (stacks up to 5 times).
2800
.
• : Unique Active: Grants +20% movement speed and +40% attack speed for 6 seconds (45 second cooldown)

. +65 attack damage, +10% cooldown reduction. Unique Passive: +20 armor penetration.
3200
.
• : +15% attack speed

, +20% critical strike chance, +5% movement speed.
1300
.

#### Variable Availability

• TC : +50% attack speed

, +45 magic resist, +10% cooldown reduction. Unique Active – Quicksilver: Removes all debuffs from your champion. Melee champions also gain +50% movement speed for 1 second (90 second cooldown).
2700
.
• ST : +40% attack speed

, +30 + (Devourer stacks) on-hit magic damage. Unique Passive – Devouring: Scoring a takedown (kill or assist) on a champion or large monster will grant 1 Devourer stack, 5 Devourer stacks for epic monsters, and 2 Devourer stacks for the Rift Scuttler. While stacking your Devourer, you are accompanied by a Ghost Dog who will grow with stacks. At 30 stacks, the Ghost Dog merges with the wielder and the Devourer transforms into .
1400
.
• C : +15% attack speed

, +16 attack damage. Unique Passive – Prospector: +150 health.
950
.
• ST : +40% attack speed

, + 60 on-hit magic damage. Unique Passive – Phantom Hit: Every other basic attack will trigger a phantom attack that triggers all on hit effect a second time. Ranged champions trigger this every fourth attack.
1400
.

### Champion abilities

Note: Only the attack speed buff effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.

• passively increases his attack speed by 0.6 - 1.1 (based on level)% for every 2% in the Blood Well.
• increases his attack speed by 40 / 50 / 60% for 12 seconds.
• increases his attack speed by 30 / 38 / 46 / 54 / 62% for 5 seconds.
• passively grants Diana 20% bonus attack speed.
• increases his attack speed by 20 / 25 / 30 / 35 / 40% for 3 seconds.
• increases the attack speed of herself and her Spiderlings by 60 / 80 / 100 / 120 / 140% for 3 seconds.
• increases her attack speed by 60 / 75 / 90 / 105 / 120% for 3 seconds after attacking with .
• passively increases his attack speed by 10% whenever he hits a target with any of his abilities. This bonus lasts for 6 seconds and stacks up to 5 times.
• increases the attack speed of allied champions it passes through by 20 / 25 / 30 / 35 / 40% for 5 seconds.
• increases her attack speed by 50% for her 2 next basic attacks.
• increases his attack speed by (5.5 × Gnar's level) % when in .
• increases his attack speed by 20 / 30 / 40 / 50 / 60% for 3 seconds.
• passively increases his attack speed by 10 / 13 / 16 / 19 / 22%. When activated, it throws a flag that increases nearby allied champions and his own attack speed by the same amount.
• causes his basic attacks to increase his attack speed by 4 - 14 (based on level)%. This bonus lasts for 2.5 seconds and stacks up to six times.
• increases his attack speed to 2.5 for three basic attacks.
• causes her basic attacks to grant bonus attack speed for 2.5 seconds, stacking up to three times (up to 30 / 40 / 50 / 60 / 70%).
• passively increases his attack speed by 15 / 20 / 25 / 30 / 35%, and, upon activation and for 6 seconds, double his total attack speed.
• increases the attack speed by 40% of his next two 2 autoattacks within the next three seconds after casting an ability.
• increases his attack speed by 30 / 55 / 80% for 10 seconds. Kills and assists extends the duration by 4 second.
• increases her attack speed by 20 / 30 / 40 / 50 / 60% for 6 seconds.
• increases her or an allied unit's attack speed by 20 / 30 / 40 / 50 / 60% for 7 seconds.
• passively grants himself 20 / 25 / 30 / 35 / 40% attack speed. Upon activation, it summons a spell shield for 1.5 seconds, if the shield successfully blocks a spell, the attack speed bonus is doubled for 5 seconds.
• increases an allied unit's and his own attack speed by 25 / 30 / 35 / 40 / 45% for 12 seconds.
• passively increases his attack speed by 1% per 1% health he is missing.
• increases his attack speed by 40 / 50 / 60 / 70 / 80% for 6 seconds.
• increases Quinn's attack speed by 20 / 25 / 30 / 35 / 40% for 3 seconds when she attacks a target marked by .
• passively grants her 20 / 40 / 60% bonus attack speed.
• increases his attack speed by bonus 47 + (3 × Rengar's level) % for 5 seconds
• passively grants her 40 / 60 / 80% attack speed while is active.
• increases his attack speed by 20 / 40 / 60 / 80% for 3 seconds after leaving his stealth state.
• increases her attack speed by 30 / 50 / 70 / 90 / 110% for 5 seconds.
• coats the target location with ice for 8 seconds, while on this area, Trundle increases his attack speed by 20 / 35 / 50 / 65 / 80%.
• passively increases his attack speed by 10 / 15 / 20 / 25 / 30%.
• increases his attack speed by 30 / 40 / 50 / 60 / 70% for up to 5 seconds after revealing himself.
• increases his attack speed by 10% upon switching stances. This bonus lasts for 5 seconds and stacks up to 3 times.
• increases his attack speed by 30 / 40 / 50 / 60 / 70% for 5 seconds on activation.
• increases attack speed by 20% for 3 seconds on minion kills, while a champion kill/assist will grant 40% for 6 seconds.
• will increase Vi's attack speed by 30 / 35 / 40 / 45 / 50% for 4 seconds after attacking the same target 3 times.
• passively causes his auto attacks to increase his attack speed by 8 / 11 / 14 / 17 / 20%. This bonus stacks up to 3 times and lasts for 4 seconds.
• increases his attack speed by 40 / 50 / 60 / 70 / 80% and half of that amount to nearby allied champions for 6 seconds.
• increases his attack speed by 30 / 35 / 40 / 45 / 50% after hitting a target with this skill.
• increases his attack speed by 40 / 50 / 60 / 70 / 80% for 5 seconds.

### Masteries

• increases your champion's attack speed by 0.8 / 1.6 / 2.4 / 3.2 / 4%.

### Runes

Name Type Tier 1 (Lesser) Tier 2 (Normal) Tier 3 (Greater)
Attack Speed Mark

0.94 %

5

1.32 %

165

1.7 %

410

Seal

X X 0.76 %

410

Glyph

X X 0.64 %

410

Quintessence

2.52 %

15

3.51 %

100

4.5 %

1025

## Reducing attack speed

Note: Attack speed reductions stack multiplicatively and take percentages off the final attack speed value after all bonus attack speed has been factored in.

### Items

• : Unique Aura: Reduces the attack speed of nearby enemies by 15%.
• : Unique Passive – Cold Steel: If you are hit by a basic attack, you slow the attacker's attack speed by 15% for 1 second.
• : Unique Passive – Cold Steel: If you are hit by a basic attack, you slow the attacker's attack speed by 15% for 1 second.

### Summoner Spells

• : Active: Exhausts target enemy champion, reducing their movement speed and attack speed by 30%, their armor and magic resist by 10, and their damage dealt by 40% for 2.5 seconds.

### Champion abilities

Note: Only the attack speed reduction effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.

• slows affected units' attack speed by 20% for 1 second.
• slows affected enemy champion's attack speed by 50% for 1.5 seconds.
• slows affected units' attack speed by 30 / 35 / 40 / 45 / 50% for 3 seconds.
• reduces an enemy unit's attack speed by 17.5% plus an additional 1.5 / 3 / 4.5 / 6 / 7.5% per second for 5 seconds.
• slows the attack speed of all nearby enemy units by 25% while channeling for 3 seconds.
• reduces an enemy unit's attack speed by 25% for 3 seconds.

## Notes

(bonus attack speed only) is the only ability that directly scales with a champion's attack speed statistic. Many other abilities can scale indirectly (for example, through the flat cooldown reduction per attack with ).

## List of champions' attack speed

The highest and lowest base attack speed champions
Champion Level Top 5 champions Bottom 5 champions
Level 1 1. 0.694 AS 1. 0.481 AS
1.
1.
1.
1.
2. 0.69 AS 2. 0.568 AS
2.
3. 0.679 AS 3. 0.571 AS
3.
3.
3.
3.
3.
4. 0.672 AS 4. 0.579 AS
4.
5. 0.67 AS 5. 0.601 AS
5.
5.
5.
Level 18 1. 1.105 AS 1. 0.678 AS
2. 1.089 AS 2. 0.712 AS
3. 1.087 AS 3. 0.717 AS
4. 1.07 AS 4. 0.731 AS
5. 1.06 AS 5. 0.731 AS
5.
5.

## Trivia

[Last updated 27/02/2016 on patch 6.4]

The most attack speed a champion can reach at level 1 with 500  and without any ally is 2.155. This is only possible with .

Relevant mathematics:
Base AS = 0.625
Bonus AS = 9 × 1.7 + 9 × 0.64 + 9 × 0.76 + 3 × 4.5 + 4 + 12 + 15 = 72.4%
Total AS = (0.625 × 1.724) × 2 = 2.155

With the same set-up, but with 4 level 1 allies (, , , and ) the most attack speed a champion can reach at level 1 with 500  is 3.2175. This is only achievable with .

• will cast on (+20% AS for 5 seconds)
• will cast on (+20% AS for 7 seconds)
• will cast on (+25% AS for 12 seconds)
• will cast close to (+20% AS for 6 seconds)
Relevant mathematics:
Base AS = 0.625
Bonus AS = 9 × 1.7 + 9 × 0.64 + 9 × 0.76 + 3 × 4.5 + 4 + 12 + 15 + 20 + 20 + 25 + 20 = 157.4%
Total AS = (0.625 × 2.574) × 2 = 3.2175

With no particular context, requires to have at least 300% bonus AS in order to reach the 5.00 attack speed cap.

Relevant mathematics:
Total AS = (0.625 × X) × 2 = 5.00
X = (5.00 ÷ 2) ÷ 0.625
X = 2.5 ÷ 0.625
X = 4 or 300%


text:
# Two Dimensional Array In C Pdf

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Multidimensional Arrays in C++ Revisited: Dealing with Large Arrays If you have a large multidimensional array in C++, you probably don't want to store all your data on the stack. Below is a program to check whether a matrix is sparse or not. For an n-element one-. It is a collection of data elements of same data type arranged in rows and columns (that is, in two dimensions). In C programming an array can have two, three, or even ten or more dimensions. rarray - multidimensional array class template. In the example below you can see how to convert an array into JSON string. You can think of such an array as a grid where the elements are arranged in rows and columns. Similarly, you can delete a row using the delete() method. File upload progressor. Multidimensional arrays are sometimes called _____ Arrays. 1) When both dimensions are available. Moreover, in the example above, aand bcould be multidimensional arrays of the same shape, or a scalar and an array, or even two arrays of with different shapes, provided that the smaller array is “expandable” to the shape of the larger in such a way that the resulting broadcast is unambiguous. I have seen that post but it isn't 100% clear. From the evolution of C 60 internal patterns with decreasing temperature, we conclude that there is an ordered rotational motion of the two-dimensional C 60 array, as in the case of bulk C 60. This is Java Programming Section with Multiple Choice Questions on Java Arrays. obtains it’s sorted position. Individual variables are accessed by their position within each dimension. to represent individual variables. In this paper a two dimensional array of antenna-coupled microbolometers is demonstrated as an area receiver. Following are different ways to create a 2D array on heap (or dynamically allocate a 2D array). To put it another way, numbers is an array of int arrays. Suppose we are solving for a zero (root) of f(x): f(x) = 0 for an arbitrary (but di erentiable) function f, and we have a guess x. One just starts with the array name, followed by ()between which are the indices separated by ,. The OutputArr must be a dynamic array. That is, you need to produce such an array. #43 Multidimensional Arrays In this video will look at multi-dimensional arrays. 3 AdvancedArray Techniques Shifting Values in an Array Arrays of Objects Command-Line Arguments 7. More practice on 2D array data type. And here's an array of two rows and four columns: {1,2,3,4;5,6,7,8}. Hi, I have a unique requirement in which I need to create a 2 dimensional java array in Peoplecode and pass it as a parameter to a custom Java class. C allows for arrays of two or more dimensions. Hopefully this makes sense too!. Result: The program creates a 2x2 string array and then prints out all 4 elements (with no loops). First Back TOC One-Dimensional Arrays Prev Next Last 10. 3TranslationTables 8. And hence I decided to make a video just to talk briefly about the concept of 2D Arrays in C or 2-dimensional arrays in C with the help of a real-life example. However, to work with multi-level data, we have to use the Multi-Dimensional Array. A two- dimensional (2D) array is an array of arrays. For a 2-dimensional array, you can let the compiler figure out how many items the array uses. Arrays take vectors in the form of input and use the values in the dim parameter for creating an array. However, now two indexes are needed to specify a cell. The C equivalent of the previous method is passing the array by pointer. C program to merge two arrays into another array. int n [ ] = { 2,3,15,8,48,13 }; In this case, we are declaring and assigning values to the array at the same time. perform on such a multidimensional array. an array containing all variable as a pointer variable. So how can I change it to handle multi-dimentional arrays? I have to do this with multiple files so bubble sort, histogram, and the main are all separate. Chapter 18: Miscellaneous C Features. Array uses an integer value index to access a specific element. Any element of the array can be accessed by. For instance, they could be all String variables or all Integer variables. Consider the following example, where we have deleted a row from a 2-dimensional array:. More On 2D Array Manipulation Part 3 1. 4 Multidimensional Arrays (Optional) Rectangular Two-Dimensional Arrays Jagged Arrays 7. @inproceedings{Poher2008MicroLEDAA, title={Micro-LED arrays: a tool for two-dimensional neuron stimulation}, author={Vincent Poher and Nir Grossman and Gordon T. Two Dimensional Arrays 2 2D Arrays in Java Arrays with multiple dimensions may be declared and used int[][] mat = new int[3][4]; the number of pairs of square brackets indicates the dimension of the array. Two-Dimensional Arrays A two-dimensional array is a collection of data of the same type that is structured in two dimensions. Cell Array Functions cell Creates cell array. Protein nanostructures have the potential to give greater geometric control and shape variability. D) First in first out. One Dimensional Array All Programs. So, for example, integer, dimension(5,5) :: a sets up a storage space with 25 integer locations. Order and number of columns to be sorted as well as column sort order can vary from case to case. Now we have discussed two types of pointers, * and **. A two dimension array is commonly known as a table (a spreadsheet like Excel is a two dimension array). However, arrays can have more than one dimension. How? By taking on the management of the array indexing arithmetic yourself. 2 One-Dimensional Arrays A one-dimensional array is a list of related variables. Introduction to Programming in C Department of Computer Science and Engineering Lecture No. The benchmarks are provided, comparing the implementation with standard C-style arrays and Boost multi_array [2]. The program output is also shown below. A PHP array is a variable that stores more than one piece of related data in a single variable. So, a two-dimensional array is an array of arrays. Multidimensional arrays are also known as array of arrays. nrow , ncol , and dim provide ways of accessing the dimensions of an array. Is a list of related values, all having the same data type,that's stored with a single group name. • all arrays are of type double and are column vectors in n-space # n (i. parallel arrays d. Some texts refer to these two values with the nomenclature rvalue (right value, pronounced "are value") and lvalue (left value, pronounced "el. This is unlike languages like C or FORTRAN, which allows Java array to have rows of varying length i. Classes define types of data structures and the functions that operate on those data structures. Add a passenger to the flight. C programming language allows multidimensional arrays. plot3D: Tools for plotting 3-D and 2-D data. Currently, Scratch does not support multidimensional arrays. • Examples: • Lab book of multiple readings over several days • Periodic table. A variable such as gradeTable is a reference to a 2D array object. An item in the array. In C programming, you can create an array of arrays. Two Dimensional Arrays, C++ Tutorial. type arrayName [ x ][ y ]; Where type can be any valid C data type and arrayName will be a valid C identifier. Calculate average & percentage 3. For example, the following table that describes the distances between the cities can be represented using a two-dimensional array. At the end of this post we will also share the link of last years class 12 Sample papers. The data in multidimensional array is stored in a tabular form as shown in the diagram below: This array has total 2*3 = 6 elements. Multidimensional arrays. multidimensional array in c pdf. A two dimensional array has the same number of columns in all the rows. However, arrays can have more than one dimension. I want to create a two-dimensional array (people by var), so I need a 10x5 array. Each cell can hold a value (as with a 1D array). Especially, when it comes to game applications. Multi-dimensional array representation in memory Syntax to declare two-dimensional array type array_name[row-size][col-size]; type is a valid C data type. The core data structure in numpy is the ndarray (short for n-dimensional array). On the same lines you can also create three or more dimensional arrays. one-dimensional arrays b. A PHP array is a variable that stores more than one piece of related data in a single variable. iv Contents Cell Arrays. An example of this type of array is a chess board — a grid of 8 rows and 8 columns. array_name is any valid C / C++ identifier name that obeys the same rule for the identifier naming. • One dimension array has one column. The Two Dimensional Array in C language is nothing but an Array of Arrays. multidimensional array in c pdf. The previous examples involved one dimensional arrays, equivalent to a single row or column of values. The C++ programming language allows programmers to separate program-specific datatypes through the use of classes. // Two-dimensional array. Manipulating 2D array elements. For an mXn matrix, formula for the same can be written as. You can use a two-dimensional array to represent a matrix or a table. In other words, two arrays are equal if they contain the same elements in the same order. They are used to store data in a tabular manner. Aluminum-based micro fin arrays were replicated at room temperature, and the fabrication process is one with high throughput and low cost. rarray is open-source, and is released under the MIT license. The array can hold 12 elements. 4 Multidimensional Arrays (Optional) Rectangular Two-Dimensional Arrays Jagged Arrays 7. Arrays are using for store similar data types grouping as a single unit. Chapter9 Multidimensional arrays Lessonpage9-1. Strings as arrays: In C, the abstract idea of a string is implemented with just an array of characters. 2D Array Exercise Objectives: Practice using two dimensional arrays to input and output data in a tabular format. Find largest element in array 7. In this topic, we will discuss 2-Dimensional (2D) arrays in C Programming Language. Following one standard method, we used the Gaussian neighborhood function that takes the following form: where c and i specify two nodes, d(c, i) specifies the physical distance between the two nodes in the array, and σ(t) specifies the time-dependent SD of the Gaussian. To declare a two-dimensional integer array of size [x][y], you would write something as follows −. Two-dimensional (2D) metal halide perovskites have shown great potential in high performance optoelectronic applications due to their intrinsic quantum well structure, enhanced moisture- and photo-stability. A two dimensional array has the same number of columns in all the rows. Though you can declare a single 64. Plot the graph, name and find point on the graph d. (10) can be then rewritten as: (11) K m, 2 D d × d ′ c t = ∑ r u, n u ∈ c t d × d K m r u + log 2 n u where r u are the different square arrays in the partition {c t} d×d of the matrix c t and n u the multiplicity of r u, that is the number of repetitions of d × d-length patches or square arrays found in c t. What you have set up is an array of arrays. The present invention may be used with electronic warfare systems such as with a four-channel AN/ALR-67(V)3 radar warning receiver to provide accurate angle of arrival data. CountDigit. Consider the following matrix. You can use a two-dimensional array to represent a matrix or a table. The latest release version is 2. A two dimension array is commonly known as a table (a spreadsheet like Excel is a two dimension array). Advantages: 1. This program will help to understand the working of for loop, array, if statement and random numbers. Unfortunately, there is still no effective method to produce large-size 2D hybrid perovskite single c. Bottom-up fabrication of such arrays with specific orientation of nanoparticles remains a challenge. 1) Using fprintf( ) with arrays: If you only specify one formatting command, all elements of an array will be printed on a single row (even multidimensional arrays). An array is a collection of variables that are of similar data types and are alluded by a common name. And suppose you have to set elements of the main diagonal equal to 1 (that is, those elements a[i][j] for which i==j), to set elements above than that diagonal equal to 0, and to set elements below that diagonal equal to 2. Multidimensional arrays are also known as array of arrays. 1WhyWeNeedArrays 8. That is, you need to produce such an array. Here we can create single or multidimensional arrays to hold values in different scenarios. Chapter 7 Multidimensional Arrays 7. A multi-dimension array is declared as follows: string[,] mutliDimStringArray; A multi-dimensional array can be fixed-sized or dynamic sized. ) … 2,1 2,0 1,C-1 … 1,1 1,0 0,C-1 … 0,2 0,1 0,0 This is cell 0 of a 1D array. Chapter 25: Variable-Length Argument Lists. Solve the global equation system. To do this, when declaring the array, precede the name of the array with an asterisk. As we see earlier, we can store a set of characters or a string in a single dimensional array. The memory allocated to an array is consecutive. (likedim(x,2)). It allows to store the elements in any dimensional array - supports multidimensional array. However, optical components nowadays are rather bulky. For instance, you can create a matrix of zeros with dimensions N by M with the following code:. The subproduct outputs of each of the T two-dimensional arrays are summed together to produce the full product. On the same lines you can also create three or more dimensional arrays. (10) can be then rewritten as: (11) K m, 2 D d × d ′ c t = ∑ r u, n u ∈ c t d × d K m r u + log 2 n u where r u are the different square arrays in the partition {c t} d×d of the matrix c t and n u the multiplicity of r u, that is the number of repetitions of d × d-length patches or square arrays found in c t. Following are different ways to create a 2D array on heap (or dynamically allocate a 2D array). That is, you need to produce such an array. C) Last in last out. This array has total 2*2*2 = 8 elements. A PHP array is a variable that stores more than one piece of related data in a single variable. Array variable has a type and a valid Java identifier i. Class 12 Computer Science Notes (C++) with Assignments. This is unlike languages like C or FORTRAN, which allows Java array to have rows of varying length i. For instance, they could be all String variables or all Integer variables. A two dimensional aperture has application in many systems in the radio, microwave, visible and x-ray bands of the electromagnetic spectrum as well as the 10 Hz (underwater acoustics) to 10 MHz (medical imaging) bands in the acoustic spectr um. What is displayed when code corresponding to the following pseudocode is executed? Declare Numbers[12] Of Integers For K = 0 Step 1 to 2 Set Numbers[3 * K. C Program to Insert an element in an Array. Coherent emission has been generated by two‐dimensional arrays of SIS Josephson junctions and detected in a junction coupled to the array through a dc‐blocking capacitor. An array is a table of values, called elements. If the data is linear, we can use the One Dimensional Array. Multidimensionalarrays Activity9-1-1Declaringandcreatingtwo-dimensionalarrays Question 1. A two-dimensional (2D) array is an array of arrays. So, for example, integer, dimension(5,5) :: a sets up a storage space with 25 integer locations. In a matrix, the two dimensions are represented by rows and columns. They are used to store data in a tabular manner. Each entry in the array represents an element a i,j of the matrix and is accessed by the two indices i and j. Question 2. If you want to add another dimension, just add another comma and another number: Dim MyArray(5, 4, 6) As Integer Dim MyArray(1 To 5, 1 To 4, 1 To 6) As Integer. This function counts the number of digit letters in the. The buffer interface is documented in Buffer Protocol. This paper presents a two-dimensional phased array antenna consisting of. If it were a 3-dimensional array, you should use 3 for loops. Three- and four-dimensional arrays have their place. To access an integer element in this multidimensional array, one would use. generalized reduction: For a two-way array, A[+,] gives sums over rows, and A[,+] gives sums over columns. To create a one-dimensional array, execute the following steps. Two-dimensional arrays. A two dimensional aperture has application in many systems in the radio, microwave, visible and x-ray bands of the electromagnetic spectrum as well as the 10 Hz (underwater acoustics) to 10 MHz (medical imaging) bands in the acoustic spectr um. How to declare a One-Dimensional arrays ?. You can delete an element within a one-dimensional ARRAY and a row or column within a TWO-DIMENSIONAL ARRAY. Fast download. Two-dimensional arrays are objects. It can hold a maximum of 12 elements. This function counts the number of digit letters in the. Class 12 Computer Science Notes (C++) with Assignments. This creates a rectangular array - each row has the same number of columns. Chapter9 Multidimensional arrays Lessonpage9-1. Although the example uses a two-dimensional string array, the information can also be applied to a one-dimensional string array or a multidimensional string array. A Simple 2D array example //***** // TwoDArray. For example, if an array variable is declared as s[10], then it ranges from 0 to 9. In this post , lets have a look at getting the number of elements in the multi-dimentional array in C#. ind = 1:8; sz = [2 2 2]; Specify three output arguments when using ind2sub to return the row, column, and page subscripts for the 2-by-2-by-2 array. From the previous article Java Array Basics, we understand that an array is like a container that can hold a certain number of values. Valid C/C++ data type. The arrays that have too few dimensions can have their NumPy shapes prepended with a dimension of length 1 to satisfy property #2. The equilibrium ~0 is called a saddle point, and it is. For multi-line arrays on the other hand the trailing comma is commonly used, as it allows easier addition of new elements at the end. The main difference between 1D and 2D array is that the 1D array represents multiple data items as a list while 2D array represents multiple data items as a table consisting of rows and columns. Chapter 21: Pointer Allocation Strategies. You can even make a three dimensional array, though you probably won't need to. The Two Dimensional Array in C language is nothing but an Array of Arrays. More practice on 2D array data type. Near-field enhancement and sub-wavelength imaging properties of a system comprising a coupled pair of two-dimensional arrays of resonant nanospheres are studied. So how can I change it to handle multi-dimentional arrays? I have to do this with multiple files so bubble sort, histogram, and the main are all separate. The main topic of our discussion is the difference between One-dimension and Two-Dimension array. The benchmarks are provided, comparing the implementation with standard C-style arrays and Boost multi_array [2]. Index starts from 0 and goes till N-1 (where N is the size of array). A two-dimensional array is, in essence, a list of one. Sample 51221: Pass a multidimensional array to a C function from the SAS® system Overview This Sample describes a way to use SAS to call a C function that has an array parameter that is multidimensional. B, B +4, B +8, B +12, and so on, and in general, element array[k] is at address B +12k. The dimension with three or more called multi dimensional arrays. , the address of k. Ex: int a[2][3]={0,0,0,1,1,1}; initializes the elements of the first row to zero and the second. Solve the global equation system. In C, multidimensional arrays can be initialized in different number of ways. For example, to access the author (index position 1 of the second dimension) of the book located at index position 2 of the first dimension in our multidimensional array: System. Arrays can have more than one dimension. , they broadcast. The coordinates of any point on the xy -plane are determined. Christodoulou, and M. The resulting pointer is not itself an array, and it does not carry any information about the length of the array from which it was derived. , 4, 5] and [9, 7, 4] are enclosed in square brackets to make a two-dimensional list. Each entry in the array represents an element a i,j of the matrix and is accessed by the two indices i and j. Order and number of columns to be sorted as well as column sort order can vary from case to case. DNA has been used as a nano building material since the 1980s. Two-Dimensional Arrays A two-dimensional array is a collection of data of the same type that is structured in two dimensions. El Zooghby, C. The detector junction exhibits Shapiro steps at frequencies corresponding to the voltage across single array junctions and ranging from 60 to 210 GHz. PDF Download. You can think this array as table with 3 rows and each row has 4 columns as shown below. FUN: the function to be applied: see ‘Details’. Types of arrays in C, Array in PDF, Two Dimensional array in C, Array Initialization in C, Learn Him Self Arrays in C Arrays a kind of data structure that can store a fixed-size sequential collection of elements of the same type. Two-Dimensional Arrays in C. (See the previous memory layout again. 2-66 Creating Cell Arrays. 2CollectingInputDatainArrays 8. The present invention may be used with electronic warfare systems such as with a four-channel AN/ALR-67(V)3 radar warning receiver to provide accurate angle of arrival data. An array is a collection of variables that are of similar data types and are alluded by a common name. In this post , lets have a look at getting the number of elements in the multi-dimentional array in C#. Delete a row. The OutputArr must be a dynamic array. For example: int val = a[2][3]; Types of arrays in C, Array in PDF, Two Dimensional array in C, Array Initialization in C, Learn Him Self. The detector junction exhibits Shapiro steps at frequencies corresponding to the voltage across single array junctions and ranging from 60 to 210 GHz. How? By taking on the management of the array indexing arithmetic yourself. Two-dimensional arrays. Here we can create single or multidimensional arrays to hold values in different scenarios. It is a header-only implementation that uses templates, which allows most compilers to generate fast code. For dosimetric plan verification, the expected two‐dimensional distribution of the array signals is calculated via convolution of the planned dose distribution, obtained from the treatment planning system, with the two‐dimensional response function of a single chamber. Additional beam pattern in between those shown in Figure 2(b) can also be generated. 1 Introduction Thus far, you have used one-dimensional arrays to model linear collections of elements. An array is defined in a very. 2f' , x) fprintf(' '). In this next exercise, we'll set up a 2-D array. Web browser screens are two dimensional, as are spreadsheets, printed pages, and images. array pdf example two dimensional c++ in program. In this section we briefly examine the use of two-dimensional arrays to represent two-dimensional structures such as screen bitmaps or nxm matrices of integers.


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# What is the limiting distribution of local minima of n mod i, for i up to $\sqrt{n}$, as $n \rightarrow \infty$?

### The sequence n mod i

Consider the sequence n mod i for i=1...$\sqrt{n}$. If we draw the sequence as an xy-plot, we get a dense triangle (since n mod i < i). More precisely, the limiting density of the figure is uniform across the allowable triangle (I think you can prove this using Weyl's equidistribution criterion).

### Local minima of the sequence

Now suppose we take only local minima of the sequence. If we do this, we get what look like dense triangles (beware: slowly loading!), with some outliers between the triangles. One explanation goes like this: $n \mod i = i \cdot frac(n/i)$; if i is increased or decreased by 1, the change will be roughly $i \cdot frac(n/i^2)$; so a local minimum must always lie below $i \cdot sfrac(n/i^2)$ (sfrac is the distance to the closest integer). This accounts for the 'triangles' (enumerate over the integer closest to $n/i^2$ and its direction). Outliers are explained by our approximation being especially bad when $sfrac(n/i^2)$ is small.

What is the limiting density (if any) of this sequence? How many outliers are there, asymptotically?

In order to make the question of density meaningful, we need to normalize the axes through division by $\sqrt{n}$. The weight of each point should be $1/\sqrt{n}$.

### Further iterations

The process of taking local minima can be iterated. Local maxima can also be mixed. Using reasoning similar to the above, one can come up with equations for the limiting curves, which conform with experimental data. The equations can be found in the pdf linked to above.

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# Tropical homological algebra

Has anyone out there thought about homological algebra over the tropical semifield $\mathbb{T}$? For example, I'm interested in the Hochschild homology and cyclic homology of tropical algebras, if this can be made to make sense.

 Perhaps I should add some motivation. Topologists and geometric group theorists have been interested in the moduli space of metric graphs for at least 25 years now, mainly because of its appearance as a classifying space for automorphism groups of free groups. This space turns out to have a second identity as the moduli space of tropical curves, and people in tropical geometry tell me that it should probably in fact carry the structure of a tropical orbifold.

This means that, in addition to homological invariants built from (sheaves of) continuous of PL functions on the space (containing essentially the information of rational homotopy), one can try to build and study homological invariants made from the tropical structure sheaf. I'm interested in what sort of geometric information these invariants might carry. Is there perhaps some new information hiding in here?

It is always exciting when one finds that an object one has known for many years turns out to have a hidden new structure.

Following Zoran's comment, it looks like Durov has constructed, among many other things, a model category structure on complexes of modules over $\mathbb{T}$. This means that, in principle, something like homological algebra can be done. But it's a different matter to explicitly develop homological algebra.

So, to expand on my original question, here are some explicit questions.

1. What is a tropical chain complex?

2. Is there an explicit tropical analogue of the usual Hochschild chain complex and does it compute the correct derived functor?

3. Ordinary Hochschild homology carries a Gerstenhaber algebra structure. Is there an analogous structure on a tropical Hochschild homology?

4. Same questions for cyclic homology.

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Durov in his thesis arxiv.org/abs/0704.2030 develops (cf. chapter 10) nonabelian homological algebra for "generalized algebraic geometry" which, as special cases, includes a variant of the geometry over a field of one element, tropical geometry and an algebraic version of Arakelov geometry. –  Zoran Skoda Feb 10 '11 at 14:01
Zoran, since this question is more or less of a "yes or no" type, your comment would make a fine answer. –  S. Carnahan Feb 10 '11 at 15:58
An interesting couple of question along these lines is: 1. can one interpret the Baker-Norine rank of a linear system on a metric graph as the rank of a tropical module? 2. are there higher cohomology analogs of the Baker-Norine rank. The Baker-Norine rank makes sense from the point of view of deformation theory, but there should be a way of doing tropical homological algebra to make it natural. –  Eric Katz Feb 15 '11 at 19:55

Your question has two parts - the main question, existence of tropical homotopical algebra, seems to be nicely resolved by Zoran's answer. The questions about Hochschild homology though are rather context independently true - I am not familiar with the Durov story, but assuming he provides a symmetric monoidal model category (and hence symmetric monoidal $\infty$-category) that should suffice. Given an algebra object $A$ in any symmetric monoidal $\infty$-category, we can define its Hochschild homology and cohomology, as self-tor and ext as bimodules (see e.g. here - note that what I'm referring to as the homology and cohomology corresponds to the chain level versions of these notions, not the cohomology groups). The former has an $S^1$ action, with invariants giving cyclic homology, and can be calculated by a version of the cyclic bar construction. Regarding the Gerstenhaber structure on Hochschild COhomology, again the answer is yes by a general form of the Deligne conjecture (see Lurie's Higher Algebra - the part that until last week was called DAG VI..) - there's an $E_2$ structure on the Hochschild cohomology. In fact if your algebra $A$ is separable (dualizable as $A$-bimodule) one obtains the full structure of a framed two-dimensional topological field theory (via Lurie's Cobordism Hypothesis theorem), which includes all these operations and many more. (The Hochschild homology and cohomology are assigned to the circle with two different framings in this story.)