Yishan Road station is a station on the Shanghai Metro network, specifically located on Line 9. It is situated in the Minhang District of Shanghai, China. The station serves as a vital transportation hub for residents and commuters in the area, providing access to various destinations within the city. Like many metro stations, it features facilities to enhance passenger convenience, including ticketing services, waiting areas, and connections to other transport options.

Zhaojiabang Road Station is an underground station on Line 7 of the Shanghai Metro system. Located in the Xuhui District of Shanghai, China, it serves as an important transit point for passengers traveling through the area. The station features modern amenities and facilities to accommodate commuters. It was opened for service in December 2009 and is part of the expansion of the Shanghai Metro to enhance public transportation in the city. The station's name reflects its location on Zhaojiabang Road.

"Castrovalva" is a lithograph created by the Dutch artist M.C. Escher in 1964. The artwork depicts a fictional, impossible city that showcases Escher's fascination with architectural design and mathematical concepts. The image features a complex arrangement of staircases and buildings that seem to defy the laws of physics and perspective, creating an intriguing visual puzzle for the viewer.

A strangelet is a hypothetical type of exotic matter that is composed of strange quarks. In particle physics, quarks are elementary particles and fundamental constituents of matter. There are six flavors of quarks: up, down, charm, strange, top, and bottom. Normally, matter is made up of up and down quarks (e.g., protons and neutrons).

A conjecture is an educated guess or a proposition that is put forward based on limited evidence, which has not yet been proven or disproven. In mathematics and science, conjectures arise from observations or patterns that suggest a certain conclusion, but they need formal proof or experimental validation to be accepted as a theorem or law.

Cousin primes are pairs of prime numbers that differ by four. In mathematical terms, if \( p \) and \( q \) are prime numbers and \( q = p + 4 \), then \( (p, q) \) is a cousin prime pair.

The Inverse Galois Problem is a central question in the field of algebra, particularly in the area of field theory and algebraic geometry. It seeks to determine whether every finite group can be represented as the Galois group of some field extension of the rational numbers \(\mathbb{Q}\) or more generally, of some base field.

Artin's conjecture on primitive roots is a conjecture in number theory proposed by Emil Artin in 1927. It concerns the existence of primitive roots modulo primes and more generally, modulo any integer.

Carmichael's totient function conjecture is a mathematical conjecture related to the properties of the Euler's totient function, denoted as \(\varphi(n)\). The conjecture is named after the mathematician Robert Carmichael. The conjecture states that for any integer \( n \) greater than \( 1 \), the inequality \[ \varphi(n) < n \] holds true, which is indeed true for all integers \( n > 1 \).

The Berlekamp–Zassenhaus algorithm is a method in computational algebraic geometry and number theory, primarily used for factoring multivariate polynomials over finite fields. It is particularly well-known for its application in coding theory and cryptography. The algorithm is a combination of the Berlekamp algorithm for univariate polynomials and the Zassenhaus algorithm for more general multivariate cases.

Hermite's problem, named after the French mathematician Charles Hermite, refers to an important question in the theory of numbers that concerns the representation of numbers as sums of squares. Specifically, the problem seeks to establish conditions under which a natural number can be expressed as a sum of squares of integers. One of the notable results related to Hermite's problem is a theorem concerning the number of ways a given positive integer can be expressed as a sum of two squares.

Lemoine's conjecture, also known as the "Lemoine's problem" or "Lemoine's hypothesis," is a statement in number theory that relates to the representation of numbers as sums of prime numbers. Specifically, it posits that every odd integer greater than 5 can be expressed as the sum of an odd prime and an even prime (which can only be 2).

Leopoldt's conjecture is a conjecture in the field of number theory, particularly concerning \( p \)-adic numbers and the study of class fields. Specifically, it deals with the behavior of abelian extensions of number fields in relation to their \( p \)-adic completions and \( p \)-adic class groups.

Frans Michel Penning (1894-1973) was a Dutch physicist known for his contributions to the field of atomic and molecular physics. He is particularly recognized for his work on the study of Penning traps, a type of device used to trap ions using electromagnetic fields. This technique is widely used in mass spectrometry and quantum computing research.

Oppermann's conjecture, proposed by mathematician Frank Oppermann in 2012, is a conjecture about the existence of certain types of prime numbers known as "twin primes." Specifically, it suggests that for every positive integer \( n \), there exists a prime number \( p \) such that both \( p \) and \( p + n \) are primes.

In algebraic number theory, supersingular primes are particularly interesting as they relate to the study of elliptic curves and the behavior of their reduction modulo prime numbers. Specifically, a prime \( p \) is called **supersingular** for an elliptic curve \( E \) over the finite field \( \mathbb{F}_p \) if the reduced curve \( E \mod p \) has a specific structure that makes it "supersingular.

Twin primes are pairs of prime numbers that have a difference of two. In other words, if \( p \) and \( p+2 \) are both prime numbers, then they are considered twin primes. For example, (3, 5), (11, 13), and (17, 19) are all pairs of twin primes. The concept of twin primes is an interesting area of study in number theory.

Vacuum gauges are instruments used to measure the pressure of gases in a vacuum system. They are essential for applications where low-pressure measurements are critical, such as in vacuum chambers, scientific research, manufacturing processes, and various industrial applications. There are several types of vacuum gauges, each designed to operate in different pressure ranges and to measure vacuum levels in different ways.

A cold cathode refers to a type of electron source used in vacuum tubes and some types of display technologies (like cold cathode fluorescent lamps, or CCFLs) where electrons are emitted from a cathode without the need for significant heating. This is in contrast to hot cathodes, where the cathode is heated to facilitate electron emission through thermionic emission. In a cold cathode, the electron emission is typically achieved through processes such as field emission or Schottky emission.

Outer space is the vast, seemingly infinite expanse that exists beyond the Earth’s atmosphere. It is the region of the universe where there is a near vacuum, meaning it has very low density and pressure compared to the conditions we experience on Earth. Here are some key characteristics and features of outer space: 1. **Vacuum**: Outer space is largely a vacuum, which means it has very few particles, including air, atoms, and molecules.