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The Brown–Gibson model is a theoretical framework used in the field of economic geography and regional science to analyze and understand the dynamics of technological change and innovation diffusion. Developed by economists William Brown and James Gibson, the model focuses on the spatial aspects of economic activities, particularly how innovations spread across geographic areas and influence regional development.

The Buckmaster equation is a concept from the field of combustion and flame dynamics, specifically relating to turbulent flame behavior in gases. It is named after the researcher who derived it. The equation represents a relationship involving various physical parameters that influence the behavior of turbulent flames, particularly the balance between the production and consumption of reactants in a turbulent flow. The Buckmaster equation typically includes terms that account for: - The unburned fuel and oxidizer concentrations.

Mathematical programming with equilibrium constraints (MPEC) is a type of optimization problem that involves finding an optimal solution while satisfying certain equilibrium conditions, which are often described by complementarity conditions or variational inequalities. MPECs are particularly useful in areas where the decision-making process is influenced by equilibrium relationships, such as economics, engineering, and operations research.

The term "Shekel function" may refer to a specific mathematical function used in optimization problems, particularly within the field of benchmark functions for testing optimization algorithms. The Shekel function is often utilized to evaluate the performance of such algorithms due to its well-defined characteristics, including having multiple local minima.

The term "small control property" is often discussed in the context of functional analysis and operator theory. It pertains to a specific characteristic of certain types of Banach spaces or functional spaces. A space is said to have the small control property if, roughly speaking, every bounded linear operator from this space into a Hilbert space can be approximated by finite-rank operators in a certain way.

Symlet is a family of wavelets used in signal processing and data analysis. They are a type of wavelet that was developed as a modification of the Daubechies wavelets, which are known for their compact support and orthogonality properties. Symlets are specifically designed to be symmetrical (or nearly symmetrical) and have better symmetry properties than the original Daubechies wavelets, making them particularly useful for certain applications, especially in image processing and denoising.

Transfinite interpolation is a mathematical technique used to create a continuous surface or function that passes through a given set of points, typically in a multidimensional space. It extends the concept of interpolation beyond finite-dimensional spaces to infinite-dimensional or higher-dimensional contexts. The technique is particularly useful in the context of geometric modeling, computer graphics, and numerical analysis. The key idea is to define a function that satisfies certain properties at specified boundary points (or control points) while allowing for continuity and smoothness in the interpolation.

The Estevez–Mansfield–Clarkson (EMC) equation is a mathematical model used in the study of fluid dynamics, particularly in relation to phase transitions and nonlinear waves in fluids. It describes the behavior of a particular type of nonlinear dispersion relation that can arise in various physical contexts. The equation itself arises from the combination of several principles in fluid dynamics and can incorporate aspects such as nonlinearity, dispersion, and potentially compressibility or other effects depending on the specific application.

Finite Element Exterior Calculus (FEEC) is a mathematical framework that unifies the finite element method (FEM) with the theory of differential forms and exterior calculus. It provides a systematic way to analyze and construct finite element methods for a variety of problems in applied mathematics, physics, and engineering, particularly those described by differential equations of a geometrical or physical nature. ### Key Concepts 1.

An M-spline, or Modified spline, is a type of spline function used in numerical analysis and computer graphics for interpolation and approximation of data points. Splines, in general, are piecewise-defined functions that can provide smooth curves, connecting a series of points. M-splines are characterized by certain properties that make them particularly useful in various applications. **Key features of M-splines include:** 1.

Quantitative marketing research is a systematic investigation that primarily focuses on obtaining quantifiable data and analyzing it using statistical and mathematical methods. This type of research is designed to collect numerical data that can be transformed into usable statistics, allowing marketers to identify patterns, measure variables, and assess relationships among various factors. ### Key Characteristics of Quantitative Marketing Research: 1. **Objective Measurement**: It seeks to quantify behaviors, opinions, and other defined variables, allowing for objective analysis rather than subjective judgment.

A risk score is a numerical value that quantifies the likelihood or severity of a specific risk associated with an individual, entity, or situation. It is often used in various fields such as finance, healthcare, insurance, and security to assess risk levels and make informed decisions. The score is typically derived from a set of variables or parameters that have been statistically analyzed to predict outcomes based on historical data.

Kushyar Gilani (also spelled as Khoshiyar Gilani) was a notable Persian astronomer and mathematician who lived in the 11th century. He played a significant role in the development of astronomical theories and practices during the Islamic Golden Age. Gilani is best known for his contributions to the field of astronomy, particularly for his work on star catalogs and astronomical tables.

Lakkoju Sanjeevaraya Sarma, often simply referred to as Sanjeevaraya Sarma, is an Indian mathematician known for his contributions to mathematics, specifically in the areas of number theory and combinatorics. He has been recognized for his work in popularizing mathematics and his efforts in education and research.

Li Guoping could refer to various individuals, as it is a common Chinese name. Without additional context, it's difficult to determine exactly who you are asking about.

Narayana Pandita, also known as Narayana Pandit or simply Narayana, was a notable Indian mathematician and scholar who lived during the 14th century. He is best known for his contributions to combinatorics and number theory. One of his most famous works is the "Ganita Kaumudi," which is a comprehensive treatise on arithmetic, geometry, and combinatorial mathematics.

Ning Cai is a prominent engineer and academic known for her contributions to the field of electrical engineering and computer science. She has been involved in various research areas, including machine learning, data analytics, and optimization methods. Dr. Cai has published numerous papers in reputable journals and has participated in several conferences, contributing to advancements in her field.

Nobushige Kurokawa is a notable figure in the field of mathematics, particularly known for his contributions to algebraic geometry and related areas. In addition to his research work, he may have also been involved in education or mentorship within the mathematical community.

The Poincaré and the Three-Body Problem refers to a significant area of research in dynamical systems and celestial mechanics. The "three-body problem" itself is a classic problem in physics and mathematics that seeks to understand the motion of three celestial bodies under their mutual gravitational attraction. ### The Three-Body Problem The three-body problem asks how three bodies, such as stars or planets, will move in space given their initial positions and velocities.

Geometrically and materially nonlinear analysis with imperfections is a complex approach used in structural engineering and applied mechanics to study how structures respond when subjected to loads. This type of analysis accounts for both the nonlinear behavior of materials and the geometric changes that occur in structures, as well as any imperfections that might influence their performance. Let’s break down these components: ### 1.