Autoignition temperature

The autoignition temperature or kindling point of a substance is the lowest temperature at which it spontaneously ignites in normal atmosphere without an external source of ignition, such as a flame or spark. This temperature is required to supply the activation energy needed for combustion; the temperature at which a chemical ignites decreases as the pressure or oxygen concentration increases. It is applied to a combustible fuel mixture; the ignition temperature of a substance is the least temperature at which the substance starts combustion. Substances which spontaneously ignite in a normal atmosphere at ambient temperatures are termed pyrophoric. Autoignition temperatures of liquid chemicals are measured using a 500-millilitre flask placed in a temperature-controlled oven in accordance with the procedure described in ASTM E659; when measured for plastics, autoignition temperature can be measured under elevated pressure and at 100% oxygen concentration. The resulting value is used as a predictor of viability for high-oxygen service.

The main testing standard for this is ASTM G72. The time t ig it takes for a material to reach its autoignition temperature T ig when exposed to a heat flux q ″ is given by the following equation: t ig = π 4 k ρ c 2, where k = thermal conductivity, ρ = density, c = specific heat capacity of the material of interest, T 0 is the initial temperature of the material. Temperatures vary in the literature and should only be used as estimates. Factors that may cause variation include partial pressure of oxygen, altitude and amount of time required for ignition; the autoignition temperature for hydrocarbon/air mixtures decreases with increasing molecular mass and increasing chain length. The autoignition temperature is higher for branched-chain hydrocarbons than for straight-chain hydrocarbons. Pyrolysis Fire point Flash point Gas burner Spontaneous combustion Analysis of Effective Thermal Properties of Thermally Thick Materials

Irma Carrillo Ramirez

Irma Carrillo Ramirez is a United States Magistrate Judge of the United States District Court for the Northern District of Texas and is a former nominee to be a United States District Judge of the United States District Court for the Northern District of Texas. Ramirez was born in 1964, she received a Bachelor of Arts degree in 1986 from the West Texas A&M University. She received a Juris Doctor in 1991 from the Southern Methodist University Dedman School of Law. Ramirez began her legal career working as an associate for the law firm Locke Purnell Rain Harrell, PC from 1991 to 1995, she served as an Assistant United States Attorney for the United States Attorney’s Office for the Northern District of Texas, working in the Civil Division from 1995 to 1999 and the Criminal Division from 1999 to 2002. She was sworn in United States Magistrate Judge for the United States District Court for the Northern District of Texas on September 9, 2002. On March 15, 2016, President Obama nominated Ramirez to serve as a United States District Judge of the United States District Court for the Northern District of Texas, to the seat vacated by Judge Terry R. Means, who took senior status on July 3, 2013.

On September 7, 2016 a hearing before the Senate Judiciary Committee was held on her nomination. Her nomination expired on January 2017, with the end of the 114th Congress. Barack Obama judicial appointment controversies

Problems involving arithmetic progressions

Problems involving arithmetic progressions are of interest in number theory and computer science, both from theoretical and applied points of view. Find the cardinality of the largest subset of which contains no progression of k distinct terms; the elements of the forbidden progressions are not required to be consecutive. For example, A4 = 8, because has no arithmetic progressions of length 4, while all 9-element subsets of have one. Paul Erdős set a $1000 prize for a question related to this number, collected by Endre Szemerédi for what has become known as Szemerédi's theorem. Szemerédi's theorem states that a set of natural numbers of non-zero upper asymptotic density contains finite arithmetic progressions, of any arbitrary length k. Erdős made a more general conjecture from which it would follow that The sequence of primes numbers contains arithmetic progressions of any length; this result was proven by Ben Green and Terence Tao in 2004 and is now known as the Green–Tao theorem. See Dirichlet's theorem on arithmetic progressions.

As of 2014, the longest known arithmetic progression of primes has length 26: 43142746595714191 + 23681770·23#·n, for n = 0 to 25. As of 2011, the longest known arithmetic progression of consecutive primes has length 10, it was found in 1998. The progression starts with a 93-digit number 100 99697 24697 14247 63778 66555 87969 84032 95093 24689 19004 18036 03417 75890 43417 03348 88215 90672 29719and has the common difference 210. Source about Erdős-Turán Conjecture of 1936: P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. 11, 261–264. The prime number theorem for arithmetic progressions deals with the asymptotic distribution of prime numbers in an arithmetic progression. Find minimal ln such that any set of n residues modulo p can be covered by an arithmetic progression of the length ln. For a given set S of integers find the minimal number of arithmetic progressions that cover S For a given set S of integers find the minimal number of nonoverlapping arithmetic progressions that cover S Find the number of ways to partition into arithmetic progressions.

Find the number of ways to partition into arithmetic progressions of length at least 2 with the same period. See Covering system Arithmetic combinatorics PrimeGrid