24.1.9

An Overview of Distributed PostgreSQL Architectures | Crunchy Data Blog

Marco just joined Crunchy Data and he reflects on his career in distributed systems in this post. He provides an overview of several options for approaching distributed Postgres workloads and the pros and cons of each approach.

https://www.crunchydata.com/blog/an-overview-of-distributed-postgresql-architectures

Tensor Network algorithms

canonical isomorphism

Universal property

In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for defining some objects independently from the method chosen for constructing them. For example, the definitions of the integers from the natural numbers, of the rational numbers from the integers, of the real numbers from the rational numbers, and of polynomial rings from the field of their coefficients can all be done in terms of universal properties. In particular, the concept of universal property allows a simple proof that all constructions of real numbers are equivalent: it suffices to prove that they satisfy the same universal property.

https://en.wikipedia.org/wiki/Universal_property

环同态

在环论或抽象代数中，环同态是指两个环R與S之间的映射f保持两个环的加法与乘法运算。

https://zh.wikipedia.org/wiki/环同态

什么是张量？(What are tensors?)

向量 = vector 向量空间 = vector space 两个向量空间 U, V 之间的线性变换，可以用 matrix 表示。如果 U 的维数是 m，V 的维数是 n，则 $T: U \rightarrow V$ 的矩阵形式是 $m \times n$。矩...

https://geniferology.blogspot.com/2015/03/what-are-tensors.html

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环同态的种类[编辑]

双射的环同态称为环同构。

定义域与值域相同的环同态称为环自同态。

在环范畴中，单射的环同态与单同态是相等的：如果f:R→S是单同态而不是单射，则它把某个r1和r2映射到S的同一个元素。考虑从Z[x]到R的两个映射g1和g2，分别把x映射到r1和r2；f o g1和f o g2是相等的，但由于f是单同态，这是不可能的。

然而，在环范畴中，满射的环同态与满同态是非常不同的。例如，Z ⊆ Q是满同态，但不是满射。

ideal subring理想子环简称理想 吸收律（absorption property）

主理想整环（principal ideal domain，PID）

环的局部化：分式域/商域（field of fractions/field of quotients）

环同态（ring homomorphism）与环同构（ring isomorphism）

【抽象代数】8. 理想、商环与环同态基本定理

前言以下内容可以与3. 正规子群、商群、群同态基本定理中的内容进行类比。下一篇将介绍极大理想与素理想，以及环直积的相关概念。8.1 理想理想设 R 是环， I 是 R 的子环，如果对于 \forall i \in I,\forall r \…

https://zhuanlan.zhihu.com/p/183883772

如果环同态是单射，则称为单同态；如果是满射，则称为满同态，此时称为同态像；如果是双射，则称为环同构，同构的环有相同的结构。域的同态与同构可以类似定义。

环同构定理：https://math.fandom.com/zh/wiki/环同构定理?variant=zh-sg

Ofgem

https://www.ofgem.gov.uk/

The Office of Gas and Electricity Markets (Ofgem) regulates the monopoly companies which run the gas and electricity networks. It takes decisions on price controls and enforcement, acting in the interests of consumers and helping the industries to achieve environmental improvements.
Ofgem is a non-ministerial department. https://www.gov.uk/government/organisations/ofgem#:~:text=The Office of Gas and,the gas and electricity networks.

EDF, Octopus and Scottish Power

https://www.mirror.co.uk/money/major-change-millions-energy-customers-31833423

Stanford University scientists have demonstrated that the use of transcranial magnetic stimulation—using a magnetic coil to zap particular regions of the brain—enhances someone's ability to be hypnotized.

Zapping your brain with magnets makes it easier to hypnotize you, research shows

Hypnosis has great potential to help people manage pain, control habits, overcome phobias, and manage a variety of other neurological and psychiatric challenges.The trick is that some people are more…