A vacuum flask, also known as a thermos, is an insulated container designed to keep liquids hot or cold for extended periods of time. It consists of two containers, one inside the other, with the space between them evacuated of air (creating a vacuum). This vacuum layer minimizes heat transfer by conduction or convection, helping to maintain the temperature of the contents.

A Wieferich prime is a special type of prime number that satisfies a particular congruence relation involving powers of 2.

The Wall–Sun–Sun prime is a special type of prime number that is defined in relation to a specific type of sequence known as the Fibonacci sequence. A Wall–Sun–Sun prime is a prime number that can be expressed in the form \( F_{k+1} - 1 \), where \( F_k \) is the \( k \)-th Fibonacci number.

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.

Metal vapor synthesis (MVS) is a technique used in materials science and chemistry to produce nanostructured materials, particularly metal clusters, nanoparticles, and thin films. The method typically involves the vaporization of a metal in a controlled environment, allowing for the formation of metal clusters through the cooling and subsequent condensation of the vaporized metal.

Manifold vacuum refers to the vacuum created in the intake manifold of an internal combustion engine when it is running. The intake manifold is the component that distributes the air and fuel mixture to the engine's cylinders. Here's a breakdown of the concept: 1. **Creation of Vacuum**: When the engine operates, the pistons move downward during the intake stroke, creating a negative pressure (vacuum) in the intake manifold.

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.

Newman's conjecture is a proposed mathematical conjecture concerning the distribution of the digits in the decimal expansion of the reciprocals of certain integers. More specifically, it relates to the behavior of the leading digits of the decimal expansion of the fractions formed by taking the reciprocal of integers. The conjecture states that for a given positive integer \( n \), the reciprocal \( \frac{1}{n} \) has a certain predictable pattern in the distribution of its leading digits.

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.

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).

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.

Hall's conjecture is a concept in combinatorics and graph theory, specifically related to the properties of perfect matchings in bipartite graphs. The conjecture states that a certain condition involving the size of subsets of one partition of a bipartite graph must hold for the graph to contain a perfect matching.

The Minimum Overlap Problem typically refers to a scenario in optimization and scheduling where the goal is to minimize the overlap of certain events, tasks, or processes. This concept can be applied in various fields such as computer science, operations research, and project management, among others. Here are a few specific contexts in which the Minimum Overlap Problem might arise: 1. **Scheduling Tasks**: When scheduling multiple tasks or jobs, it is often desirable to minimize the overlapping of their execution times.

A Fibonacci prime is a Fibonacci number that is also a prime number. The Fibonacci sequence is defined recursively, starting with the numbers 0 and 1, and each subsequent number is the sum of the two preceding ones.

The Erdős–Turán conjecture on additive bases is a famous conjecture in additive number theory, which is concerned with the representation of integers as sums of elements from specific sets, known as additive bases. Formally, the conjecture can be stated as follows: Let \( B \) be a set of integers.

The Elliott-Halberstam conjecture is a significant hypothesis in number theory, specifically in the field of analytic number theory, dealing with the distribution of prime numbers in arithmetic progressions. It was formulated by the mathematicians Paul Elliott and Harold Halberstam in the 1960s. The conjecture asserts that there is a specific form of "density" of primes in arithmetic progressions that can be used to improve results concerning the distribution of primes.

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.

Gillies' conjecture is a hypothesis in the field of number theory that relates to the distribution of powers of prime numbers. Specifically, it suggests that if you take any finite set of integers and consider their product, the resulting product is often composite. The conjecture posits that a certain rational expression, derived from the powers of prime numbers that comprise the integers in the set, will eventually yield a non-zero value under specific conditions.

The Casas-Alvero conjecture is a statement in algebraic geometry and commutative algebra concerning the properties of certain classes of varieties, and it addresses the relationship between numerical and geometric properties of projective varieties.

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 \( n > 1 \).