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Pervez Hoodbhoy is a prominent Pakistani nuclear physicist, mathematician, and educator, known for his work in the field of physics as well as his advocacy for secularism, rationalism, and social justice. He has served as a professor at the Pakistan Institute of Engineering and Applied Sciences (PIEAS) and has been involved in various educational reforms in Pakistan.

As of my last update in October 2023, Syed Tajammul Hussain may refer to a specific individual or could be a common name in certain cultures, particularly in South Asia. Without additional context, it's challenging to provide precise information about who or what Syed Tajammul Hussain refers to.

Zia Mian is a prominent Pakistani-American physicist and a co-director of the Princeton University Program on Science and Global Security. His research primarily focuses on nuclear physics, with an emphasis on the implications of nuclear weapons for international security and arms control. Mian is known for his work on nuclear policy and his advocacy for non-proliferation.

"Former bodies of water" refers to areas that were once filled with water but are now dry or have undergone significant changes leading to their current state. This term can apply to various geological features, including: 1. **Dry Lake Beds (Playas)**: Flat areas that were once lakes but have dried up, often leaving behind salt flats or sediment.

Marine Isotope Stage 11 (MIS 11) is a specific period in Earth's climatic history that occurred between approximately 400,000 and 420,000 years ago, during the Late Pleistocene epoch. It is characterized by a relatively warm interglacial period, which is part of a series of alternating glacial and interglacial stages documented in the paleoclimatic record.

Fixed-target experiments are a type of experimental setup commonly used in particle physics, nuclear physics, and other fields of physics to study the interactions of particles. In these experiments, a beam of particles (such as protons, electrons, or heavy ions) is directed towards a stationary target, which is usually made of a material like hydrogen, carbon, or other elements. The target is "fixed" in place, as opposed to "collider" experiments, where two beams collide head-on.

Upset welding is a type of resistance welding process used to join two metal parts together by generating heat through the resistance of the materials. In upset welding, two workpieces are brought together under pressure. An electric current is passed through the interface of the materials, causing localized heating at the contact point due to electrical resistance. Once the materials reach their melting temperature, they are upset (compressed) further to create a solid bond as the molten area cools and solidifies.

The Q-Krawtchouk polynomials are a set of orthogonal polynomials that generalize the Krawtchouk polynomials, which themselves are a class of discrete orthogonal polynomials. The Krawtchouk polynomials arise in combinatorial settings and are connected to binomial distributions, while the Q-Krawtchouk polynomials introduce a parameter \( q \) that allows for further generalization. ### Definition and Properties 1.

Q-Meixner polynomials are a class of orthogonal polynomials that generalize the classical Meixner polynomials. They are typically associated with specific probability distributions, particularly in the context of q-calculus, which is a branch of mathematics dealing with q-series and q-orthogonal polynomials. Meixner polynomials arise in probability theory, especially in relation to certain types of random walks and discrete distributions.

The Q-Meixner–Pollaczek polynomials are a family of orthogonal polynomials that arise in the context of certain special functions and quantum mechanics. They are a generalization of both the Meixner and Pollaczek polynomials and are associated with q-analogues, which are modifications of classic mathematical structures that depend on a parameter \( q \).

Quantum \( q \)-Krawtchouk polynomials are a family of orthogonal polynomials that can be seen as a \( q \)-analogue of the classical Krawtchouk polynomials. They arise in various areas of mathematics, particularly in the theory of quantum groups, representation theory, and combinatorial analysis. ### Definitions and Properties 1.

Rogers polynomials are a family of orthogonal polynomials that arise in the context of approximation theory and special functions. They are closely related to the theory of orthogonal polynomials on the unit circle and have connections to various areas of mathematics, including combinatorics and number theory.

Sobolev orthogonal polynomials are a generalization of classical orthogonal polynomials that arise in the context of Sobolev spaces. In classical approximation theory, orthogonal polynomials, such as Legendre, Hermite, and Laguerre polynomials, are orthogonal with respect to a weight function over a given interval or domain. Sobolev orthogonal polynomials extend this concept by introducing a notion of orthogonality that involves both a weight function and derivatives.

Zernike polynomials are a set of orthogonal polynomials defined over a unit disk, which are commonly used in various fields such as optics, imaging science, and surface metrology. They are particularly useful for describing wavefronts and optical aberrations, as they provide a convenient mathematical framework for representing complex shapes and patterns.

Orthogonal coordinate systems are systems used to define a point in space using coordinates in such a way that the coordinate axes are perpendicular (orthogonal) to each other. In these systems, the position of a point is determined by a set of values, typically referred to as coordinates, which indicates its distance from the axes.

In geometry, the term "normal" can refer to several concepts, but it is most commonly used in relation to the idea of a line or vector that is perpendicular to a surface or another line. Here are a few contexts in which "normal" is used: 1. **Normal Vector:** In three-dimensional space, a normal vector to a surface at a given point is a vector that is perpendicular to the tangent plane of the surface at that point.

The term "perpendicular" refers to the relationship between two lines, segments, or planes that meet or intersect at a right angle (90 degrees). In two-dimensional geometry, if line segment \( AB \) is perpendicular to line segment \( CD \), it means they intersect at an angle of 90 degrees. In three-dimensional space, the concept extends similarly; for example, a line can be said to be perpendicular to a plane if it intersects the plane at a right angle.

Perpendicular distance refers to the shortest distance from a point to a line, plane, or a geometric shape. This distance is measured along a line that is perpendicular (at a 90-degree angle) to the surface or line in question. ### Key Points: - **From a Point to a Line**: The perpendicular distance from a point to a line is the length of the segment that connects the point to the line at a right angle.

Evan Tom Davies is not widely recognized as a prominent figure or concept in popular culture or academia as of my last knowledge update in October 2023. It is possible that he may be a private individual or a less well-known person in a specific context.

Thomas Jones was a mathematician primarily known for his contributions to the field of mathematics education and his work related to number theory. While there are several individuals with the same name, the most notable Thomas Jones in mathematics is often recognized for his writings and efforts in promoting mathematical understanding, particularly at a time when the field was evolving rapidly. He may not be as widely recognized as some of his contemporaries, but his influence on mathematics education has been acknowledged in academic circles.