(ii)と(iii)がどうしてこうなるのか分かりません お願いします

b. [1+] Let t(n) be the number of total partitions of n, as defined in Exam- ple 5.2.5. Let g(n) have the same meaning as in Exercise 5.26. Deduce from (a) that g(n) = 2"t(n) for n >1. c. [2+] Give a simple combinatorial proof of (b). 5,37. a. [2+] Let 1=D po(x), pi(x), be a sequence of polynomials (with coeffi- cients in some field K of characteristic O0), with deg pn=n for all nE N. Show that the following four conditions are equivalent: ) Pn(x + y) =DE>o (") Pe(x)pnーk(y), for all n eN. (i) There exists a power series f(u)=aju+azu'+ E K [[u]] such that と P(x)- un expxf(u). (5.110) n! n>0 仮定 NOTE: The hypothesis that deg pPn=nimplies that aj ¥ 0. () E20 Pa(x) = (E>0 Pn(1)). (iv) There exists a linear operator Q on the vector space K[x] of all poly- nomials in x, with the following properties: ●Ox is a nonzero constant ●Qis a shift-invariant operator, i.e., for all aeK,Qcommutes with the shift operator E4 defined by E® p(x)=D p(x +a). ● We have Qpn(x) =D npn-1(x) for all n e P. NOTE: A sequence po, Pi, .. . of polynomials satisfying the above con- ditions is said to be of binomial tvpe. The operator Q is called a delta

この画像が何を主張しているのか教えてください🙏

GLOPE DEITY {CHAIST SALVATIUN FAITH Cont nig rnley 「p G00 「VRGIN BIRTH Jesus Christ ATONEMEN CROSS BL00D This is the kind of bridge they'd have us cross."" 細長い部分の文字:BIBLW WRITTEN BY MAN/ EDUCATION/ SALVATION BY WORKS/ NATURAL BIRTH/ NO HELL/ EVOLUTION ブロックの中の文字:INFALLIBLE WORD OF GOD/ CROSS/ VIRGIN BIRTH/ ATONEMENT BY BLOOD/DEITY OF CHRIST/OTHERFOUNDATION CAN NO MAN LAY/JESUS CHRIST/ SALVATION BY FAITH VFALLIBLE

間違えが10個あります。 教えてください。

On July, a Japanese friend named Toshi and I decided to climb Kitadake, who is Japan's second highest mountain. Knowing this wouldn't be easy 1I started training. I went jogging and swimming regularly to trying and prepare and was feeling fit and ready at the end of July. At the beginning of August, the number of Corona cases was increasing so unfortunately we had to change our plans. Toshi doesn't want to catch the bus from Kofu to the Suothern Alps because of the risk of Corona infection, so we stayed in Shizuoka prefecture. Yanbushi was a mountain, 2014 meters high. It is not far from Umegashima, which is famous for it's hot springs. Instead of Kitadake, we climbed Yanbushi. In August 10, we woke up early and drove to the starting point. It was the day after a typhoon had passed and a beautifull, clear morning in Shizuoka city. However when we arrived, it was very cloudy and it was raining lightly. After a three and a half hour climb we arrived at the summit. It rained most of the way but it wasn't so bad under the trees and actually kept us cool. It was a challenging and rewarding experience. Ithink exploring nature is a fun, healthy and interesting way to spent your free time. T have included a photo of my climb.

英検準1級の英作文の添削をお願いします。 Points Construction costs Effect local people Spending by visitors The environment

Date No. Topic: Is it a good idea tar local govegnments to build touist sires, Such as theme parks and museums? I think it is nota good idea for local (3 governments to build touriT sites, sach as theme parks and museums. I have two reasons 7 to support my opinion in fems of construction Costs and the envinanmant. fist, bilding taurist sites Cost alot. For erample, local garernents shodd buy vast soil To bild taurist sies. Maay loal (6 govemments do net have rmuch raeonty because they have a lot of a things to 'de for local peple, so it is diffi ault to bil tourist sites. (2 Secende it is not good for the environment. If tourist sits are bilt, the envionmert would be boken down such as 破増さんら deferestation. I think proterting the_ environment is more inportant ? than building tarist sites. For these reasons, local goverments should not build tovist sites. la a

英検準1級の英作文の添削をお願いします。

Dat: No. Topic. Ague discgre There, sthould be stricter censership of the Intenet ar I I agree with the idea that there should be stricter censorship of the Intemet.I have two reasons to support my opinion in Terws of 14 secwity and viclence. First, the Intenet secarity shauld be high quality. Many people Contuse the Internet Virus these days, o the Internet secmrity have to be enbanced to protect the computer from virus. It is important for people To use the Compiter mae Contoctabdly. Secand. the rurdber of ballying is incensing on the Intemet For esample, o person is bullied on twirer by Bullying pople do not be krowm their name Tn public. other people いじめト々 Jepanere government have to make a new law to purish these people, For these reasons, consorshipothe Internet should be strit.

量子力学・ハイゼンベルクの交換相互作用についての問題です。 参考書を参考に(あ)〜(え)まで解いてみたのですが、考え方はあっていますか？ また、(お)以降の解説をお願いします。ブロッホの定理やフーリエ変換はどのように効いてくるのでしょうか？

III. 以下の文章のあ き の枠内に当てはまる数式や記号を答えよ。 ヘ =1として,スピン角運動量1/2をもつ三つのスピンが,互いに相互作用している系を考え る。スピン演算子を$, S,, $, とすると,系のハミルトニアンは次のように与えられる。 自=-J(S, S+ S,. S。+ $。. S.), J>0. ここでも番目(;= 1,2,3) のスピンのz,9, z 方向成分をそれぞれ好,S, S とする。スピン演算 子の間には (S, SY] = iS}, [SF, SY] = 0などの交換関係が成り立つ、自) = E\d) を満たす。 固有エネルギーEとエネルギー固有状態|)を求めたい。 全スピン角運動量 Shot = $, + $2+S。を使うとハミルトニアンは次のように書き直すことが できる。 自= - + JC, 定数C= あ 'tot このことから基底状態のエネルギー固有値は 時の固有値は S= +1/2, -1/2 のニつであり,これらに相当する1スピン状態をそれぞれ↑。 ↓と記すと,3スピン状態は,|S{ S S3) = |M1),| t)などのように表すことができる。独 立な3スピン状態は全部で 具体的にエネルギー固有状態をあらわしてみよう。 まず基底状態のうちで Sto = St+ Sz + Sg が最大の状態は |S S; Sg) ちに書き下すことができる。 つぎにエネルギー固有状態のうちで Sie = 1/2 のものを求めたい,ハミルトニアンと交換可 能な演算子はハミルトニアンと同時固有状態をもつことを利用する.このような演算子の一つ にスピンをRIS; S; S) = |S; S; S;)のように巡回置換する演算子良がある。-iとなるこ とと,周期系におけるブロッホの定理やフーリエ変換を思い出すと,Rと St。と自の同時固有 状態は適切な定数A(複素数も含む)を用いて い である。 う 種類あり,規格直交基底をなす。にれらの線形結合の形で え のように直 三 る(「4)+A|)+ ^°| +t) V3 と表せることが分かる。Aの取り得る値をすべて列挙すると 底状態となるのは A- か 以上の結果からすでに二つ基底状態が得られた。残りの基底状態を列挙すると, お となる.このうちで,基 の場合である。 き と なる。

(5)以外を教えていただきたいです。 名詞構文・無生物主語の単元です。 よろしくお願いします。

1 1[]から適当な語を選び, 必要ならば形を変えて( )に入れなさい。各1回のみ使用可。 A )of the theory of evolution started a new era in history. resign ) surprised all the people in Japan. accepT ) of the project.complete (1) The ( (2) The prime minister's ( (3) There was a big party after the ( (4) I made a (soeak) in Chinese for the first time, and the audience understood me. (5) Agatha Christie is a famous mystery (writer). (6) My mother always takesa (walk) in order to lose weight. [ resign / speak / write / accept / walik / complete ]

逆行列を求める問題です。 答えがなく分からないので教えていただきたいです。

1 2 -1 3. (1) B= -2 -3 4 の逆行列を求めよ。 2 4 -1 1B| - 3+ 16+ & - よって Bの逆行刻 B-'はる在し 6-16+4= 9 fo (2) (1) の結果を用いて, 次の連立方程式を解け。 + 2y - 2 = 2 -2c - 3y + 4z = = -2 2c + 4y - 2 = 4

The term "global warming" is specific to temperature rise on the surface of our planet, while "climate change" can be used as a catch-all... 続きを読む

1から9までを埋めなければならないのですが、質問の意味もよくわからず…。どなたか質問の意味と解き方を教えて頂けると助かります…！

Vocabulary skills: Collocations Read the text. Then find verbs that collocate with the words and phrases below. Write the infinitive of each verb. KEY VOCABULARY SKILLS STUDY SHEET 7, PAGE 164 The Duke of Edinburgh’'s Award The Duke of Edinburgh's Award (known as the DofE) began in the U.K. in 1956. It gives young people from all backgrounds an opportunity to experience challenge and adventure, acquire new skills, and make new friends. Each year, participants between the ages of 14 and 24 complete many hours of voluntary community work. There are three levels: Bronze, Silver, and Gold. Each one requires increasing commitment, so you can choose which level is best for you. There are four sections at Bronze and Silver level, and five at Gold. These sections combine practical, cultural, and adventurous activities. Achieving a Duke of Edinburgh's Award helps young people to develop a sense of responsibility, and promotes values of persistence, commitment, and enterprise. It has a lasting impact on young people's behavior, skils, and life chances. In 1988, the DofE was expanded to become international. These days, over 635,000 participants around the world are achieving a DofE at any one time. Since the DofE began, Over six million young people in over 123 countries have taken part, and it continues to grow in popularity. 1 an appointment / small talk / progress success / your goals / independence dark / older / crops 2 4 a course / a form / an exercise someone a chance / a talk / feedback 5 awareness / growth / competition a qualification / knowledge / a reputation for something a problem / dificulty / something at first hand a friendship / a taste for something / an idea 6 7 8 9 Predicting Look at the title of the information sheet you’re going to read. Discus with a partner what. think you'll read about. Gnbal Youth Service Day