## Sunday, August 5, 2018

### DNS Root Zone

The DNS root zone is the top-level DNS zone in the hierarchical namespace of the Domain Name System (DNS) of the Internet.
Since 2016, the root zone has been overseen by the Internet Corporation for Assigned Names and Numbers (ICANN) which delegate the management to a subsidiary acting as the Internet Assigned Numbers Authority (IANA). Distribution services are provided by Verisign. Prior to this, ICANN performed management responsibility under oversight of the National Telecommunications and Information Administration (NTIA), an agency of the United States Department of Commerce.
A combination of limits in the DNS definition and in certain protocols, namely the practical size of unfragmented User Datagram Protocol (UDP) packets, resulted in a practical maximum of 13 root name server addresses that can be accommodated in DNS name query responses. However the root zone is serviced by several hundred servers at over 130 locations in many countries.

The DNS root zone is served by thirteen root server clusters which are authoritative for queries to the top-level domains of the Internet. Thus, every name resolution either starts with a query to a root server or uses information that was once obtained from a root server.
The root servers clusters have the official names a.root-servers.net to m.root-servers.net. To resolve these names into addresses, a DNS resolver must first find an authoritative server for the net zone. To avoid this circular dependency, the address of at least one root server must be known for bootstrapping access to the DNS. For this purpose operating systems or DNS server or resolver software packages typically include a file with all addresses of the DNS root servers. Even if the IP addresses of some root servers change, at least one is needed to retrieve the current list of all name servers. This address file is called named.cache in the BIND name server reference implementation. The current official version is distributed by ICANN's InterNIC.
With the address of a single functioning root server, all other DNS information may be discovered recursively, and information about any domain name may be found.

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### Internet Assigned Numbers Authority

The Internet Assigned Numbers Authority (IANA) is a function of ICANN, a nonprofit private American corporation that oversees global IP address allocation, autonomous system number allocation, root zone management in the Domain Name System (DNS), media types, and other Internet Protocol-related symbols and Internet numbers.
Before ICANN was established primarily for this purpose in 1998, IANA was administered principally by Jon Postel at the Information Sciences Institute (ISI) of the University of Southern California (USC) situated at Marina Del Rey (Los Angeles), under a contract USC/ISI had with the United States Department of Defense, until ICANN was created to assume the responsibility under a United States Department of Commerce contract. Following ICANN's transition to a global multistakeholder governance model, the IANA functions were transferred to Public Technical Identifiers, an affiliate of ICANN.

In addition, five regional Internet registries delegate number resources to their customers, local Internet registries, Internet service providers, and end-user organizations. A local Internet registry is an organization that assigns parts of its allocation from a regional Internet registry to other customers. Most local Internet registries are also Internet service providers.

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### Internet Architecture Board

The Internet Architecture Board (IAB) is "a committee of the Internet Engineering Task Force (IETF) and an advisory body of the Internet Society (ISOC). Its responsibilities include architectural oversight of IETF activities, Internet Standards Process oversight and appeal, and the appointment of the Request for Comments (RFC) Editor. The IAB is also responsible for the management of the IETF protocol parameter registries."
The body which eventually became the IAB was created originally by the United States Department of Defense's Defense Advanced Research Projects Agency with the name Internet Configuration Control Board in 1979. Later, in 1983, the ICCB was reorganized by Dr. Barry Leiner, Vint Cerf's successor at DARPA, around a series of task forces considering different technical aspects of internetting. The re-organized group was named the Internet Activities Board. It finally became the Internet Architecture Board, under ISOC, during January 1992, as part of the Internet's transition from a U.S.-government entity to an international, public entity.
The IAB is responsible for:
• Providing architectural oversight of Internet protocols and procedures
• Liaising with other organizations on behalf of the Internet Engineering Task Force (IETF)
• Reviewing appeals of the Internet standards process
• Managing Internet standards documents (the RFC series) and protocol parameter value assignment
• Confirming the Chair of the IETF and the IETF Area Directors
• Selecting the Internet Research Task Force (IRTF) Chair
• Acting as a source of advice and guidance to the Internet Society.
In its work, the IAB strives to:
• Ensure that the Internet is a trusted medium of communication that provides a solid technical foundation for privacy and security, especially in light of pervasive surveillance,
• Establish the technical direction for an Internet that will enable billions more people to connect, support the vision for an Internet of Things, and allow mobile networks to flourish, while keeping the core capabilities that have been a foundation of the Internet’s success, and
• Promote the technical evolution of an open Internet without special controls, especially those which hinder trust in the network.
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The Internet Engineering Task Force (IETF) develops and promotes voluntary Internet standards, in particular the standards that comprise the Internet protocol suite (TCP/IP). It is an open standards organization, with no formal membership or membership requirements. All participants and managers are volunteers, though their work is usually funded by their employers or sponsors.
The IETF started out as an activity supported by the U.S. federal government, but since 1993 it has operated as a standards development function under the auspices of the Internet Society, an international membership-based non-profit organization.

The IETF is organized into a large number of working groups and informal discussion groups (BoFs, or Birds of a Feather), each dealing with a specific topic and operates in a bottom-up task creation mode, largely driven by these working groups. Each working group has an appointed chairperson (or sometimes several co-chairs), along with a charter that describes its focus, and what and when it is expected to produce. It is open to all who want to participate, and holds discussions on an open mailing list or at IETF meetings, where the entry fee in July 2014 was USD $650 per person. Midst 2018 the fees are: early bird$700, late payment $875, student$150 and a one day pass for \$375.
Rough consensus is the primary basis for decision making. There are no formal voting procedures. Because the majority of the IETF's work is done via mailing lists, meeting attendance is not required for contributors. Each working group is intended to complete work on its topic and then disband. In some cases, the WG will instead have its charter updated to take on new tasks as appropriate.

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### Cauchy–Kowalevski Theorem

In mathematics, the Cauchy–Kowalevski theorem (also written as the Cauchy–Kovalevskaya theorem) is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems. A special case was proven by Augustin Cauchy (1842), and the full result by Sophie Kovalevskaya (1875).

This theorem is about the existence of solutions to a system of m differential equations in n dimensions when the coefficients are analytic functions. The theorem and its proof are valid for analytic functions of either real or complex variables.
Let K denote either the fields of real or complex numbers, and let V = Km and W = Kn. Let A1, ..., An−1 be analytic functions defined on some neighbourhood of (0, 0) in V × W and taking values in the m × m matrices, and let b be an analytic function with values in V defined on the same neighbourhood. Then there is a neighbourhood of 0 in W on which the quasilinear Cauchy problem
${\displaystyle \partial _{x_{n}}f=A_{1}(x,f)\partial _{x_{1}}f+\cdots +A_{n-1}(x,f)\partial _{x_{n-1}}f+b(x,f)}$
with initial condition
${\displaystyle f(x)=0}$
on the hypersurface
${\displaystyle x_{n}=0}$
has a unique analytic solution ƒ : W → V near 0.
Lewy's example shows that the theorem is not valid for all smooth functions.
The theorem can also be stated in abstract (real or complex) vector spaces. Let V and W be finite-dimensional real or complex vector spaces, with n = dim W. Let A1, ..., An−1 be analytic functions with values in End (V) and b an analytic function with values in V, defined on some neighbourhood of (0, 0) in V × W. In this case, the same result holds.

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### Partial Differential Equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.

Partial differential equations (PDEs) are equations that involve rates of change with respect to continuous variables. The position of a rigid body is specified by six parameters, but the configuration of a fluid is given by the continuous distribution of several parameters, such as the temperature, pressure, and so forth. The dynamics for the rigid body take place in a finite-dimensional configuration space; the dynamics for the fluid occur in an infinite-dimensional configuration space. This distinction usually makes PDEs much harder to solve than ordinary differential equations (ODEs), but here again, there will be simple solutions for linear problems. Classic domains where PDEs are used include acoustics, fluid dynamics, electrodynamics, and heat transfer.

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### Vector Space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.
Euclidean vectors are an example of a vector space. They represent physical quantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector. In the same vein, but in a more geometric sense, vectors representing displacements in the plane or in three-dimensional space also form vector spaces. Vectors in vector spaces do not necessarily have to be arrow-like objects as they appear in the mentioned examples: vectors are regarded as abstract mathematical objects with particular properties, which in some cases can be visualized as arrows.
Vector spaces are the subject of linear algebra and are well characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. Infinite-dimensional vector spaces arise naturally in mathematical analysis, as function spaces, whose vectors are functions. These vector spaces are generally endowed with additional structure, which may be a topology, allowing the consideration of issues of proximity and continuity. Among these topologies, those that are defined by a norm or inner product are more commonly used, as having a notion of distance between two vectors. This is particularly the case of Banach spaces and Hilbert spaces, which are fundamental in mathematical analysis.

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