# Carly

Carly who dances on a stomach of the Siva

Carly (काली, Kālī) is a goddess of the Hinduism. The name "a black person" or will (woman form of Carla meaning "time, black") of "time" [1]. The goddess of the fight to like blood and a massacre. It is one of them of the wife of Shiva and is called the Carly mer (black mother). I am considered to be one of the furious aspects of God princess Davy (マハーデーヴィー) of Shiva. Similarly of パールヴァティー which is Durga which is a furious aspect of Davy and the benevolent aspect that is gentle for objection is alias said, but it is thought that was the godhood that these goddesses are different each formerly [2]. Sound copying by the kanji 迦利 [3].

## Iconographic Buddhist image

It is black from head to foot and has three eyes and four arms and opens the cakra and drips a tongue having a long it from the mouth which bared a tusk, and be accompanied, and the necklace which I tied a skeleton to a freshly-severed head to is expressed with the figure which decorated the waist with the hands and feet which I cut. It may be described in the figure with 10 faces and six - ten arms by the pictures.

## Story

When goddess Durga fought against the military of アスラ of brothers called シュムバ, ニシュムバ with a Shakta according to "デーヴィーマーハートミャ" considered to be a sacred book, I appear from the sum of the goddess dyed black, and it is said that I massacred アスラ by anger. By the fight with ラクタヴィージャ of アスラ which made the other self from one's bloodshed, I breathed all the blood as well as bloodshed exhaustively and defeated it. Because the earth seemed to break into the excessive intensity into pieces when Carly intoxicated by victory began to dance, Siva lay in the step and had to weaken the shock. Frequently, what is described in a figure dancing on a stomach of the husband Siva comes from this.

## Faith

It is a massacre and a symbol of the destruction and is understood that 習合 did nature of native God led by south India. It is Indian popular God believed in altogether, but the faith in the Bengal district in particular is ardent, and the memorial service that did a goat for sacrifice is performed every morning even now at the car re-gath temple in Kolkata. In addition, it was a believer of Carly who was eager in Indian teacher of religion, person of mystery Rama Krishna.

タギー said to have existed in India until the mid-19th century was the secret society which believed in Carly and was as a doctrine by murder.

## Source

 [Help]
1. In ^ Kazuo Matsumura, flat wisteria Kikuko, Satoshi Yamada compilation "cultural history encyclopedia Hakusuisha, 2013 of God" page 167 (clause of "Carly", Tamaki Watanabe writing).
2. In ^ Mizuho Okita "Indian goddess small encyclopedia" "Asia goddess perfection" Atsuhiko Yoshida, Kazuo Matsumura compilation, Aoto Corporation, 2011, it is 408 pages, 416-418 pages.
3. ^ Tamotsu Sato "consideration Heibonsha Publishers Ltd. 〈 Heibonsha Publishers Ltd. library 〉, 155 pages of the gods cultural history of the esoteric Buddhism", page 242. [Page number required]

## Allied item

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# Losey Louise

 Losey Louise
Player information
Full name Rosie Ruiz Vivas
Nationality The United States of America
Item Marathon
The date of birth 1953
Birth place Republic of Cuba Havana
Place of residence The United States of AmericaFloridaWest Palm Beach
Personal best Marathon: Two hours 31 minutes 56 seconds (in 1980, is disqualified later)
Editing

Losey Louise (Rosie Ruiz Vivas, 1953 -) is a former track-and-field athlete of the United States of America. She reached the goal with the first place in the part of the Boston marathon girl held in 1980, but championship was canceled saying that there was an illegal act later.

## Pre-half life

I was born in Havana in 1953 and emigrated to Miami with a family in 1962 [1]. In youth, wanted to be an actress [1]; [2]. I moved in New York in the early 1970s and worked as a trader of the metal business. I participate in Empire City marathon as the first marathon and, on October 21, 1979, set eleventh place and two hours 56 minutes 29 seconds to be record in the part of the female athlete and get a participation in Boston marathon qualification in the next year [3].

## Boston marathon

On April 21, 1980, Louise cut the goal tape of the part of the Boston marathon girl by a record of two hours 31 minutes 56 seconds. And this record greatly exceeded a Boston marathon girl record (two hours 35 minutes 15 seconds) that Joan ベノイト gave in the last year and entered the third place in history in women marathon history at the time [4]; [5] [6].

However, "championship" of Louise was haunted by a doubt from the first. I won the championship at the part of consecutive boys by the same Boston marathon for 1978 through 3, and building Rodgers (en:Bill Rodgers (athlete)) who carried out four times of championships stated that there was not the memory that saw a figure of Louise during a race in which scene in total [5]. According to Rodgers, a question came back for his having asked "your split time" と after a race adversely saying it was in "split time" [3]. Other witnesses were not drenched with sweat about her state at the time of the goal without being out of breath although I finished running the distance that had a long marathon race and pointed out that I had no cracking down on at all to muscle femor for the marathon contestant who set record of such a world level. Louise underwent an examination of the heart rate later. As a result, the heart rate at rest was greatly apart from 50 heart rates that a most women marathon player showed with 76 at rest with it numerical value less than it [1].

In addition, it was exceptional that Louise that just began marathon 18 months ago showed shortening of the record from the Empire City marathon that was the first marathon for a little less than 25 minutes in a period in only a half year [4]. Though it was the back of the severe race, a tiring state was not seen in Louise. For the question of the reporter, I answered it that it was, "I used one cup of willpower to get up this morning" [7].

There was not the human being with the memorizing that saw Louise that ran through a race in a serious thing above all. Canadian Jacqueline Garaud approved as a true champion thought after disqualification of Louise that oneself ran with the first place of the female athlete all the time [2]; [4]. Besides, the figure of race Louise was not recorded except the half-mile [8] part in the course last to a photograph and a video picture at all without remembering that Louise passed watchmen who were in all checkpoints of the marathon course as a player of the girl first place either [4].

It was the testimony of two Harvardians who witnessed that she jumped out from the large audience who it remained until a goal to have become the conclusive evidence for Louise, and was by the roadside at a point of 800m and started running. In the Empire City marathon that Louise participated in first soon, testimony of woman photographer Susan Morrow (Susan Morrow) whom I rode on with the Louise person who took a subway was provided afterwards. Morrow after Empire City marathon with Louise was not able to come into contact, but knew a doubt about by Boston marathon and the news of the championship deprivation, and decided testimony. After having met Louise that gave its name when it was the participant who got injured, and retired according to Morrow in the inside of car of the subway, I seemed to walk together to the neighborhood of goal point of the marathon for two people. After I was sent to the relief place, Louise has got a participation in Boston marathon qualification because the administration volunteer of the race mistook her for a finisher [3]. The executive committee of the Empire City marathon began an investigation about this situation originally, but was not able to discover the evidence that Louise arrived at near the goal point. Based on this and other evidence, ) who acted as a practice chairperson declared disqualification as the thing that Louise did not run the whole distance in a race in 1979 in the founders of the Empire City marathon in those days [1].

In the same week, association of track and field of Boston treated Louise as disqualification, too. As a result, it is admitted with a champion in two hours 34 minutes 28 seconds when Jacqueline Garaud becomes the part best record of the girl by Boston marathon at the time, and American patty Catalano (en:Patti Catalano) [9] will move up in the second place in the best record of the United States women marathon player for two hours 35 minutes eight seconds at the time [10].

After Boston marathon was finished, the commendation ceremony of Garaud who became a true champion was performed after it passed more than one week. After having jogged at the distance of 20 yards [11], Garaud cut goal tape. The prize medal conferred on Garaud was one size bigger than a medal given in Louise and was size same as a medal conferred on a boy [12]. In addition, Garaud is chosen as "grand Marshal" equal to the honorary winner of the race in Boston marathon carried out in 2005, and it is allowed to cut goal tape by a memory ceremony.

## The post

The Boston marathon and other marathon meet establishes some preventive measures against illegal acts and, as a result of this disgraceful affair, reaches it at the present. In these preventive measures, a system confirming that I introduce large-scale monitoring and RFID with the video picture, and a runner passes various checkpoints electronically is included.

According to the recent news, Louise acted as the accounts person in charge in West Palm Beach of Florida. At that point, the return of the Boston marathon prize medal refuses after continuing still insisting that ran the whole distance by two marathon [3]; [4].

## Footnote

1. ^ a b c d Scorecard. Sports Illustrated November 7, 2010 reading. (English)
2. 175-177 pages of ^ a b "marathon 100 episodes."
3. ^ a b c d Rosie's Run The Eagle-Tribune November 7, 2010 reading. (English)
4. ^ a b c d e Mass Moments: Rosie Ruiz Steals Boston Marathon Massachusetts Foundation for the Humanities November 13, 2010 reading. (English)
5. ^ a b Rosie Ruiz Wins the Boston Marathon Museum of Hoaxes November 13, 2010 reading. (English)
6. ^ Mastery and Mystery Sports Illustrated (April 28, 1980) November 13, 2010 reading. (English)
7. ^ The top 50 sporting scandals (Times London August 8, 2007) November 7, 2010 reading. (English)
8. ^ 804.672m.
9. I gave "patty Lions" (Patti Lyons) of the maiden name at the time of ^.
10. ^ Rosie Ruiz Tries To Steal the Boston Marathon. Running Times, 1980-07-01 November 7, 2010 reading. (English)
11. ^ 18.288m.
12. After the race of ^ 1980, I am changed to the medal of the man and woman size.

## Outside link

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# Kaori Kodaira

 Kaori KodairaKaori Kodaira
Basic information
Nationality Japan
The date of birth 1990April 13(26 years old)
Hometown Chino-shi, Nagano
Roman letters Kaori Kodaira
Height 170cm
The weight 62 kg
Blood type Type B
Player information
Nickname Face
Position WS/L
Higher finger 217cm
The dominant hand The right
Spikes 297cm
I display a template

Kaori Kodaira (こだいらかおり, woman, April 13, 1990 -) is a Japanese former volleyball player. I belonged to V Premier League, Toray Arrows.

## Origin

NaganoChino-shiA native place. I begin volleyball than the fifth grade at an elementary school under the influence of the mom valley whom mother worked as.

At the time of a junior high student, I achieve championship as a member of the Nagano all-star team with a JOC cup with Saki Minemura (teammate of existing Toray). At the time of the Tokai University Mitaka attendance at school, I shine with guidance best 16 for the 39th new year high valley participation [1]. I contributed to a youth championship runner up in Asia in the 14th in 2008.

In April, 2009, it is entered the company by Toray Arrows. A proud play is receiving and states, "I want to be defeated by nobody". In the 61st black eagle flag meeting of May, 2012, I contributed to a team runner up, and I was elected by best 6 [2].

In September, 2012, I was picked by the representative from Japan member of the third Asian Cup girl meeting [3].

I played an active part in offense and defense as a regular in 2012/13V Premier League and greatly contributed to a runner up.

I was converted from 2013/14 season by a sweeper and played an active part. Retirement was announced on May 29, 2015 [4].

## Ball career

• All-Japan representative 2012

## Receiving a prize career

• 2012 - 61st black eagle flag meeting best 6

## Personal results

The personal results in the V Premier League regular round as follows [6].

Season Position Participation Attack Block Serve Reception Point count Remarks
Game Set At bats Score Decision rate Effect rate Decision /set At bats Ace Goal average Effect rate Receive; a number The success rate
2009/10 Toray 18 12 3 2 66.7% % 0 0.00 17 0 0.00% 5.9% 5 80.0% 2
2010/11 26 28 1 0 0.0% % 0 0.00 40 2 5.00% 7.8% 6 100.0% 2
2011/12 18 19 4 0 0.0% % 0 0.00 17 0 0.00% 4.4% 7 71.4% 0
2012/13 28 107 802 273 34.0% % 45 0.42 277 7 2.53% 8.7% 521 68.5% 325
2013/14 28 118 0 0 0.0% % 0 0.00 0 0 0.00% 0.0% 525 62.9% 0
2014/15 21 76 0 0 0.0% % 0 0.00 0 0 0.0% 0.0% 0 0.0% 0

## References

• 37 pages of watching monthly volleyball January, 2012 issue extra edition V league guidebooks

## Footnote

1. High school valley EXPRESS. of the ^ 39th new year "Spring hero & heroine girl edition". April 30, 2012 reading.
2. Association of ^ Japan volleyball. "The 61st black eagle flag all-Japan man and woman selection volleyball meeting special commendation player". May 7, 2012 reading.
3. Association of ^ Japan volleyball. "The third Asian Cup girl meeting all-Japan member". September 5, 2012 reading.
4. ^ Toray Arrows. "About a voluntary retirement of Kaori Kodaira". May 29, 2015 reading.
5. ^ http://www.nagano-np.co.jp/modules/news/article.php?storyid=13152
6. ^ V league mechanism. "Results according to the player". March 20, 2015 reading.

## Outside link

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# Hibiya nonfiction III

"Hibiya nonfiction III"
Live DVD of Base Ball Bear
Release
Label EMI Records Japan
Chart best order
Base Ball Bear chronological table
 10th Anniversary tour(This Is The)Base Ball Bear part.2 "Live new breathing" (2012) Hibiya nonfiction III (2013) It is Vol. 3 about "band B" for pictureHibiya nonfiction V - LIVE BY THE C2 ... (2016)
I display a template

"Hibiya nonfiction III" (crack shop nonfiction three) is the third piece live DVD of Base Ball Bear.

## Commentary

• I picturized a design of series live "Hibiya nonfiction III" (June 15, 2013 @ Hibi Yano University of Foreign Studies concert hall) constructed mainly on the request high rank music from a fan added up after a national tour.
• Release simultaneous with 16th single "/senkou hanabi where a fanfare sounds" like.
• Two kinds of simultaneous release of a complete production-limited board (5,000 sets-limited) and the normal board. A bonus disk is attached to the limited board other than sleeve case specifications.
• "The extremely strange improvising live performance that I recorded it only for this privilege idly and took down" was the first arrival and was presented a special CD when I purchased it with "/senkou hanabi where a fanfare sounded" like at a target store.
• Furthermore, a universal music store original privilege "2014 BBB original calendar" was presented by the first arrival in addition to a special CD when I purchased it at the same time in a universal music store.

## Collecting music

### DISC-1

1. BREEEEZE GIRL
2. PERFECT BLUE
3. GIRL FRIEND
4. 17 years old
5. Relations of boyfriend her
6. アイノシタイ
7. I love it
8. BOYS MAY CRY
9. short hair
10. You are nonfiction
11. SIMAITAI
12. Condition of the midsummer
13. yoakemae
14. Tabibito In The Dark
15. part.2 which wants to become the sea
16. LOVE MATHEMATICS
17. HIGH COLOR TIMES (Enc.)
18. After a festival (Enc.)
19. changes (Double-Enc.)

### DISC-2 (only as for the complete production-limited board a bonus disk)

• 2009.06.27 "Hibiya nonfiction" @ Hibi Yano University of Foreign Studies concert hall
1. image club
2. Timing to a labyrinth
3. I want you to notice
4. BREEEEZE GIRL
5. HIGH COLOR TIMES
• 2010.06.19 "Hibiya nonfiction part.2" @ Hibi Yano University of Foreign Studies concert hall
1. Lemon squash sense
2. ELECTRIC SUMMER
• 2010.06.20 "Hibiya nonfiction part.2" @ Hibi Yano University of Foreign Studies concert hall
1. SCHOOL GIRL FANTASY

## Complete production-limited board privilege contents

• Camera finder style sleeve case specifications
• An entering "fortune" sound bonus disk by the member is attached
• Special photobook enclosure
• Spring of 2014 tour DVD buyer limitation, the first advance reservation information enclosure

This article is taken from the Japanese Wikipedia Hibiya nonfiction III

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Wikipedia and Tranpedia does not guarantee the accuracy of this document. See our disclaimer for more information.

In addition, Tranpedia is simply not responsible for any show is only by translating the writings of foreign licenses that are compatible with CC-BY-SA license information.

# C0 semigroup

The C0- semigroup (C0- はんぐん British: C0-semigroup) in the field of the mathematics or the strong continuation one parameter semigroup is one generalization of the exponential function. I am given the solution of the differential equation that a linear fixed number coefficient in the バナッハ space is the way it goes by strong continuation semigroup so that the solution of the differential equation that it is the way it goes to assume the linear scalar fixed number a coefficient gives it in an exponential function. The differential equation in such バナッハ space appears, for example, in a field of a ) and the partial differential equation.

The strong continuation semigroup is expression of semigroup (R+,+) on consecutive バナッハ space X in strong operator phase formally. Therefore, as for the strong continuation semigroup, it may be said that it is continuous expression of the very special semigroup rather than semigroup when I say closely.

## Definition

バナッハ space ${\displaystyle X}$  The representation that meets the next property with the upper strong continuation semigroup ${\displaystyle T:\mathbb {R} _{+}\to L(X)}$  It is with a saw:

1. ${\displaystyle T(0)=I}$ ,${\displaystyle X}$  Upper 恒等作用素)
2. ${\displaystyle \forall t,s\geq 0:\ T(t+s)=T(t)T(s)}$
3. ${\displaystyle \forall x_{0}\in X:\ T(t)x_{0}-x_{0} \to 0}$ , as ${\displaystyle t\downarrow 0}$ .

Two axioms of the beginning are algebraic things,${\displaystyle T}$  But, it is semigroup${\displaystyle \mathbb {R} _{+},+}$ I mean that it is expression of). The last axiom is topologic and represents it ${\displaystyle T}$  But, I mean that it is continuation in strong operator phase.

## Simple example

I assume A existence world operator on バナッハ space X. Then,

${\displaystyle T(t)={\rm {e}}^{At}:=\sum _{k=0}^{\infty }{\frac {A^{k}}{k!}}t^{k}}$

It is は 強連続半群 (I really continue in ). On the contrary, existence boarder-line type operator A that I can write in the upper form in any same consecutive semigroup by all means exists [1]. Particularly, alignment operator A which I can write in the upper form in any strong continuation semigroup by all means exists if X is limited dimensional バナッハ space [2].

## Infinitesimal generation operator

Infinitesimal generation operator A of strong continuation semigroup T

${\displaystyle A\,x=\lim _{t\downarrow 0}{\frac {1}{t}}\,(T(t)-I)\,x}$

It is defined によって (when the limit of the right side exists). Domain D(A) of A is a meeting consisting of x ∈ X where there is such a limit. D(A) is a linear subspace, and A is linear on the domain [3]. A is not necessarily existence world, but it is shut, and the domain is dense again in X [4].

Strong continuation semigroup T with generation operator A is often expressed using sign eAt. This scale adapts to the scale for the function of the operator defined through a line exponential function and a Pan-function calculation (e.g., a spectrum theorem).

## Issue of abstract Cauchy

I think about the issue of following abstract Cauchy:

${\displaystyle u'(t)=Au(t),~~~u(0)=x.}$

A assumes it a shut operator on バナッハ space X here and assumes it x ∈ X. With two concepts following in the solution of this problem:

• Continuous function u: which can differentiate it [0, ∞] the thing meeting the initial condition that satisfy u(t) ∈ D(A) for all t≥0 in → X and was given is called the classic solution of the upper Cauchy problem.
• Continuous function u: [0, ∞] in → X
${\displaystyle \int _{0}^{t}u(s)\,ds\in D(A){\text{ and }}A\int _{0}^{t}u(s)\,ds=u(t)-x}$

The thing satisfying を is called a soft solution of the issue of big Cauchy.

All classic solutions are soft solutions. A necessary and sufficient condition for a soft solution to be a classic solution is that it is continuous differentiability [5].

The next theorem relates to the abstract issue of Cauchy and relations of the strong continuation semigroup.

I assume theorem [6] A a shut operator on バナッハ space X. The following claims are the equivalent:

1. For all x ∈ X, there is merely one soft solution for the issue of abstract Cauchy.
2. Operator A generates a certain strong continuation semigroup.
3. The レゾルベント set of A is not empty, and, for all xD(A), there is an only horn classic solution for the issue of abstract Cauchy.

When these claims are concluded, the solution of the issue of Cauchy is given by u(t) = T(t)x. But T is strong continuation semigroup generated by A.

## Generation theorem

When mostly I was given a certain linear operator A, in conjunction with the issue of Cauchy, it is in a problem it a generation bare となるかどうかという point of the strong continuation semigroup. The theorem becoming the answer to this problem is called a generation theorem. One perfect characterization about the operator which generated strong continuation semigroup was given by a theorem of fin - Yoshida. In addition, I was given the condition that it was easy to confirm it by a theorem of roux mer - Philips more practically while being important.

## Special kind of the semigroup

### The same consecutive semigroup

If tT(t) is consecutive mapping from [0, ∞] to L(X), strong continuation semigroup T is told to be the same continuation.

It is generation bare は of the same consecutive semigroup, existence world operator [1].

### The semigroup that can differentiate it

A certain t0 where T(t0)X ⊂ D(A) (as the condition that or is it and the equivalent for all t≥t0 T(t)XD(A)) is established in strong continuation semigroup T > If 0 exists, I am called when I can differentiate it for an end. In addition, it is all t > I am called when I can differentiate it promptly if T(t)XD(A) is established for 0.

All analysis semigroup can differentiate it promptly.

The characterization that is one equivalent in the issue of Cauchy is the following thing: A necessary and sufficient condition for strong continuation semigroup generated by A to be able to differentiate it for an end is that t1≥0 which there is which becomes when solution u of the issue of abstract Cauchy can differentiate it on (t1, ∞) for all xX exists. It is if I can choose t1 to become zero when such a semigroup can differentiate it promptly.

### Compact semigroup

A certain t0 where T(t0) becomes the compact operator in strong continuation semigroup T > If 0 exists; for an end called the compact ([7] that this condition is the equivalent with T(t) being compact for all t≥t0). It is all t > If T(t) is a compact operator, I am called for 0 when such a semigroup is compact promptly.

### Norm consecutive semigroup

If t0≥0 which there is where tT(t) becomes the consecutive representation from (t0, ∞) to L(X) exists, the strong continuation semigroup is called it for an end when it is norm continuation. I am called if I can choose t0 as zero when such a semigroup is norm continuation promptly.

For the semigroup which is norm continuation, in tT(t), it should be noted consecutive things in t = 0 promptly (the semigroup becomes the same continuation if it is continuation).

Analysis semigroup, the semigroup which can differentiate it (for an end), semigroup compact (for an end) are all norm consecutive semigroup for an end [8].

## Stability

### Index stability

The growth upper limit of semigroup T is the fixed number

${\displaystyle \omega _{0}=\lim _{t\downarrow 0}{\frac {1}{t}}\log T(t) }$

It is defined によって. This number

${\displaystyle T(t) \leq Me^{\omega t}}$

But, because is given as the lower limit of real number ω which there is fixed number M (≥1) established for all t≥0; such; call it, and do.

All the conditions to give next are the equivalent [9]:

1. For all t≥0 ${\displaystyle T(t) \leq M{\rm {e}}^{-\omega t}}$  But, established M,ω>0 exists.
2. Growth upper limit ω 0 <0 is minus number.
3. The semigroup converges to zero in ). In other words,${\displaystyle \lim _{t\to \infty} T(t) =0}$  となる.
4. ${\displaystyle T(t_{0}) <1}$  であるようなある t0 > 0 exists.
5. t1 where a spectrum radius of T(t1) becomes smaller than 1 closely > 0 exists.
6. For all x ∈ X ${\displaystyle \int _{0}^{\infty} T(t)x ^{p}\,dt<\infty}$  となるような p ∈ [1, ∞] exists.
7. For all p ∈ [1, ∞] and xX,${\displaystyle \int _{0}^{\infty} T(t)x ^{p}\,dt<\infty}$  But, it is established.

It is said that the semigroup meeting the condition that is these equivalent is index stability or the same stability (in the related documents, one of three conditions of the upper beginning is often treated as a definition). It is known that a condition of Lp is index stability and the equivalent as a theorem of ダツコ - ペジー.

When X is Hilbert space, the following different condition about the generation natural レゾルベント operator also becomes index stability and the equivalent of the semigroup: All complex number λ with an equilateral real part belongs to レゾルベント set of A, and, as for the レゾルベント operator, it is in the right half plane in same existence world. In other words, (λI-A)-1 is Hardy space ${\displaystyle H^{\infty }(\mathbb {C} _{+};L(X))}$  に belongs [10]. This is called a theorem of gear heart - pulse.

The spectrum upper limit of operator A is the fixed number

${\displaystyle s(A):=\sup {\rm {Re}}\lambda :\lambda \in \sigma (A)}$

It is defined として. But it is a spectrum of A ${\displaystyle \sigma (A)}$  But, I assume it s(A) = - ∞ when it is empty.

In the growth upper limit and the spectrum upper limit of the semigroup, I have a relationship called s(A)≤ω0(T) [11]. s(A) The example becoming <ω0(T) is seen by some documents [12]. T is said to meet a spectrum decision growth condition (spectral determined growth condition) if it is s(A) =ω0(T). The norm consecutive semigroup meets a spectrum decision growth condition for an end [13]. From this, the condition that is index stability and the equivalent of those semigroup is provided again:

• The necessary and sufficient condition for norm consecutive semigroup to be index stability for an end is s(A) It is <0.

Because it is norm continuation, compact semigroup, the semigroup which can differentiate it for an end, analysis semigroup and the same consecutive semigroup meet a spectrum decision growth condition for an end for an end.

### Strong stability

Strong continuation semigroup T for all xX ${\displaystyle \lim _{t\to \infty} T(t)x =0}$  But, or strong stability is called if established if asymptotically stable.

The index stability means strong stability, but the reverse is not generally satisfied when X is an infinite dimension (if X is a limited dimension, the reverse is established).

The sufficient condition for strong stability to speak next called the theorem of the アレンド - Bhatti - リュビッヒ - phone [14]:

1. T is existence world. A certain M≥1 exists and ${\displaystyle T(t) \leq M}$  But, it is managed.
2. A does not have a ) on the empty axis.
3. The spectrum of A located on the empty axis is a countable unit.

であるなら, T are strong stability.

These conditions are simplified as follows if X is recursive: T is strong stability if T is existence world, and A does not have eigenvalue on the empty axis, and the spectrum of A on the empty axis is a countable unit.

## Explanatory note

1. ^ a b Engel and Nagel Theorem I.3.7
2. ^ Engel and Nagel Theorem I.2.9
3. ^ Partington (2004) page 23
4. ^ Partington (2004) page 24
5. ^ Arendt et. al. Proposition 3.1.2
6. ^ Arendt et. al. Theorem 3.1.12
7. ^ Engel and Nagel Lemma II.4.22
8. ^ Engel and Nagel (diagram II.4.26)
9. ^ Engel and Nagel Section V.1.b
10. ^ Engel and Nagel Theorem V.1.11
11. ^ Engel and Nagel Proposition IV2.2
12. ^ Engel and Nagel Section IV.2.7, Luo et. al. Example 3.6
13. ^ Engel and Nagel Corollary 4.3.11
14. ^ Arendt and Batty, Lyubich and Phong

## References

• Hille, E.; Phillips, R. S. (1975). Functional Analysis and Semi-Groups. American Mathematical Society.
• Curtain, R. F.; Zwart, H. J. (1995). An introduction to infinite dimensional linear systems theory. Springer Verlag.
• Davies, E. B. (1980). One-parameter semigroups. L.M.S. monographs. Academic Press. ISBN 0-12-206280-9.
• Engel, Klaus-Jochen; Nagel, Rainer (2000), One-parameter semigroups for linear evolution equations, Springer
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