Primes, Modular Arithmetic, and Public Key Cryptography
(April 15, 2004)
Every cipher we have worked with up to this point has been what is called a symmetric key cipher, in that the key with which you encipher a plaintext message is the same as the key with which you decipher a ciphertext message. As we have discussed from time to time, this leads to several problems. One of these is that, somehow, two people who want to use such a system must privately and secretly agree on a secret key. This is quite difficult if they are a long distance apart (it requires either a trusted courier or an expensive trip), and is wholly impractical if there is a whole network of people (for example, an army) who need to communicate. Even the sophisticated Enigma machine required secret keys. In fact, it was exactly the key distribution problem that led to the initial successful attacks on the Enigma machine.
However, in the late 1970’s, several people came up with a remarkable new way to solve the Continue reading
Mutations in mtDNA D-loop region of mtDNA in various tissues of Papuan individuals
Johnson Siallagan,1 Agnes Maryuni,1 Jukwati,2 Rosye H. R. Tanjung3 and Yohanis Ngili1, Der Pharmacia Lettre, 2016, 8 (14):73-79
1 Department of Chemistry, Faculty of Mathematics and Natural Science, University of Cenderawasih, Jayapur a, Indonesia. 2 Study Program of Chemistry, Faculty of Teacher Training and Education, University of Cenderawasih, Jayapura, Indonesia. 3 Department of Biology, Faculty of Mathematics and Natural Sciences, University of Cenderawasih, Jayapura, Indonesia.
High mutation rate of mtDNA causes the difference in the nucleotide sequence of mtDNA between individual (high degree of polymorphism). At the mtDNA there are areas that do not encode controller (noncoding region), which is known by the local displacement loop (D-loop), which has two areas with high variations which hypervariable region I (HVR1) and hypervariable region II (HVR2). But there is no information on whether the nucleotide sequence of mtDNA D-loop is the same for the different cells in certain individuals. The purpose of this study to obtain nucleotide sequence information area mtDNA D-loop different cells on each individual to five individuals with different ages. Stages of research performed includes preparation of template mtDNA by way of cell lysis. Amplification fragments of mtDNA D-loop with the method of Polymerase Chain Reaction (PCR) using the primers M1 and HV2R. Continue reading
a structure in replicating circular DNA.
Synonym(s): displacement loop
Farlex Partner Medical Dictionary
A Box – A highly conserved (i.e., the DNA nucleotide sequence is similar among many eukaryotic species) region located between base pairs +10 and +20 “upstream” on the tRNA gene, which have the dual role of encoding functional tRNA and promoting tRNA transcription, and acting as a site of receptive protein binding.
Segen’s Medical Dictionary.
A simplified drawing illustrating D-loops forming on the sense strand of DNA isolated during transcription of RNA. The double-helical nature of the DNA–DNA portions is omitted in this drawing.
This article is about DNA structure. For the loop of RNA that forms the end of the D arm of a transfer RNA molecule, see D arm. [Below]
In molecular biology, a displacement loop or D-loop is a DNA structure where the two strands of a double-stranded DNA Continue reading
Prime Arithmetic Progression
An arithmetic progression of primes is a set of primes of the form for fixed and and consecutive , i.e., . For example, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 is a 10-term arithmetic progression of primes with difference 210.
It had long been conjectured that there exist arbitrarily long sequences of primes in arithmetic progression (Guy 1994). As early as 1770, Lagrange and Waring investigated how large the common difference of an arithmetic progression of primes must be. In 1923, Hardy and Littlewood (1923) made a very general conjecture known as the k-tuple conjecture about the distribution of prime constellations, which includes the hypothesis that there exist infinitely long prime arithmetic progressions as a special case. Important additional theoretical progress was subsequently made by van der Corput (1939), who proved than there are infinitely many triples of primes in arithmetic progression, and Heath-Brown (1981), who proved that there are infinitely many four-term progressions consisting of three primes and a number that is either a prime or semiprime. Continue reading
Top 20 Arithmetic Progression of Primes
by Chris Caldwell
The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection’s home page. This page is about one of those forms.
Definitions and Notes
Are there infinitely many primes in most arithmetic progressions? Certainly not if the common difference has a prime factor in common with one of the terms (for example: 6, 9, 12, 15, …). In 1837, Dirichlet proved that in all other cases the answer was yes:
- Dirichlet’s Theorem on Primes in Arithmetic Progressions
- If a and b are relatively prime positive integers, then the arithmetic progression a, a+b, a+2b, a+3b, … contains infinitely many primes.
BASIC PRINCIPLES of non-contact temperature measurement
By Optris 
1. Physical principles
2. Emissivity and temperature measurement
3. Optics, sighting techniques and electronics
4. Infrared thermometers and applications
5. Infrared cameras and applications
- Physical principles
With our eyes we see the world in visible light. Although visible light makes up only a small part of the radiation spectrum, the invisible light covers most of the remaining spectral range. The radiation of invisible light carries much more additional information.
Discovery of the infrared radiation
Searching for new optical material, William Herschel accidentally rediscovered the infrared radiation in 1800. He blackened the tip of a sensitive mercury thermometer and used it as measuring system to test the heating properties of different colors of the spectrum, which were directed to a tabletop by having beams of light shine through a glass prism. With this, he tested the heating of different colors of the Continue reading
A thermographic camera (infrared camera or thermal imaging camera) is a device that forms an image using infrared radiation, similar to a common camera that forms an image using visible light. Instead of the 400–700 nanometre range of the visible light camera, infrared cameras operate in wavelengths as long as 14,000 nm (14 µm). Their use is called thermography.
Theory of operation
Infrared energy is just one part of the electromagnetic spectrum, which encompasses radiation from gamma rays, x-rays, ultra violet, a thin region of visible light, infrared, terahertz waves, microwaves, and radio waves. These are all related and differentiated in the length of their wave (wavelength). All objects emit a certain amount of black body radiation as a function of their temperatures.
Generally speaking, the higher an object’s temperature, the more infrared radiation is emitted as black-body radiation. A special camera can detect this radiation in a way similar to the way an ordinary Continue reading