搜索内容

包含标签:hdd 的文章
  • crimboi[22] 你什么拓扑?
    教程

    crimboi[22] 你什么拓扑?

    funny problem from model theory problem sheet 题面 Let L be a countable language, T a theory. Let c_1,c_2,... be new constants, L'=L\cup\lbrace c_1,...\rbrace, and let X be the set of all complete theories of L' with T\subset t. Enumerate the L' se……
    HDD 2024年11月15日
  • crimboi[21] 模仿大赛
    教程

    crimboi[21] 模仿大赛

    Rotman algebraic topology上的题, 个人认为出的非常好, 极大增进了读者对\pi_1(S^1)计算过程的理解. 题面 A group G which is also a topology space is called a topological group if \mu:G\times G\to G:(x,y)\mapsto xy and i:G\to G:x\mapsto x^{-1} are contin……
    HDD 2024年9月14日
  • crimboi[20] 泛函分析心犯寒
    教程

    crimboi[20] 泛函分析心犯寒

    Dieudonne的题, 真实难度不好说, 回顾一下发现其实挺简单的. 题面 Let E be a Hilbert space, F a dense linear subspace of E, distinct from E. (For example E space of l^2 sum of a suitable countable linear independent set and F space of finite sum of thi……
    HDD 2024年8月1日
  • 小科普之Principal Ideal Domain is not necessarily Euclidean Domain
    教程

    小科普之Principal Ideal Domain is not necessarily Euclidean Domain

    It's a well known fact that Euclidean domains are principal ideal domain by taking the element in a certain ideal with smallest \varphi value. Yet the converse is false, and one counterexample just lies among our familiar algebraic integer rings, \……
    HDD 2024年7月10日
  • crimboi[19] 吃屎绕大弯
    教程

    crimboi[19] 吃屎绕大弯

    题目背景 为证一个非零吃大师 题面 Assuming AC, prove that for a integral domain R, if any nonzero prime ideal P contains a nonzero prime (p), R is UFD. 先想再看提示哦 提示 Let S be the set of elements that are prime factori……
    HDD 2024年7月6日
  • 微科普之Necessary and sufficient condition for a sequence to be graphic
    教程

    微科普之Necessary and sufficient condition for a sequence to be graphic

    This proof is due to Choudum. A sequence of nonnegative integers (d_1,...,d_n) is called graphic if there is a simple graph G with V(G)=\lbrace v_1,...,v_n\rbrace and d(v_i)=d_i. It's very easy to show that if a nonincreasing sequence, i.e. d_1\ge ……
    HDD 2024年6月29日
  • [indiscipline][2] 初中不等式
    教程

    [indiscipline][2] 初中不等式

    飞机上半昏迷状态下以为无法调整, 暴力算出来的搞笑解答. 非常具有统计色彩 (nod) 题面 A simple graph G is called complete k-partite if there's a partion of V(G): A_1,..., A_k s.t. for all i there's no edge with both vertices in A_i , and for any v\in A……
    HDD 2024年6月28日
  • 中科普之alternating group is simple for n>=5
    教程

    中科普之alternating group is simple for n>=5

    It's a well-known fact that the alternating groups, A_n, are simple for n\neq 4, with small cases like A_1, A_2, A_3 very easy to verify. Yet most proofs of n\geq 5, including Hungerford's, relies heavily on 'magical' permutation composition, which……
    HDD 2024年6月5日
  • 小科普之epimorphism in Grp is surjective
    教程

    小科普之epimorphism in Grp is surjective

    This proof is due to Arturo Magidin. In category theory, as we don't consider the 'internal structure' of objects, many properties of maps are defined in an abstract way using interaction with other morphisms. 'Epimorphism' is such an analog of sur……
    HDD 2024年5月18日
  • crimboy[18] 复分析...
    题&解

    crimboy[18] 复分析...

    题目背景 证明连续性时缩放水平哈哈了(sweatgrinning) 题面 f is a nonconstant holomorphic function on a region \Omega_1 and g is defined on f(\Omega_1). Prove that if h=g\circ f is holomorphic, then so is g. 先想再看提示哦 提……
    HDD 2024年4月29日