Linear molecular geometryThe linear molecular geometry describes the geometry around a central atom bonded to two other atoms (or ligands) placed at a bond angle of 180°. Linear organic molecules, such as acetylene (), are often described by invoking sp orbital hybridization for their carbon centers. According to the VSEPR model (Valence Shell Electron Pair Repulsion model), linear geometry occurs at central atoms with two bonded atoms and zero or three lone pairs ( or ) in the AXE notation.
AntimatroidIn mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included.
Shell USAShell USA, Inc. (formerly Shell Oil Company, Inc.) is the United States-based wholly owned subsidiary of Shell plc, a UK-based transnational corporation "oil major" which is amongst the largest oil companies in the world. Approximately 18,000 Shell employees are based in the U.S. Its U.S. headquarters are in Houston, Texas. Shell USA, including its consolidated companies and its share in equity companies, is one of America's largest oil and natural gas producers, natural gas marketers, fuel marketers and petrochemical manufacturers.
TopologyIn mathematics, topology (from the Greek words τόπος, and λόγος) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity.
Path integral formulationThe path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.
Separation of variablesIn mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. A differential equation for the unknown will be separable if it can be written in the form where and are given functions. This is perhaps more transparent when written using as: So now as long as h(y) ≠ 0, we can rearrange terms to obtain: where the two variables x and y have been separated.
Shell plcShell plc is a British multinational oil and gas company headquartered in London, England. Shell is a public limited company with a primary listing on the London Stock Exchange (LSE) and secondary listings on Euronext Amsterdam and the New York Stock Exchange. A core component of Big Oil, Shell is the second largest investor-owned oil and gas company in the world by revenue (after ExxonMobil), and among the world's largest companies out of any industry.
Data analysisData analysis is the process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively.
Wave equationThe (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields - as they occur in classical physics - such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media.
On shell and off shellIn physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called "on the mass shell" or simply more often on shell; while those that do not are called "off the mass shell", or off shell. In quantum field theory, virtual particles are termed off shell because they do not satisfy the energy–momentum relation; real exchange particles do satisfy this relation and are termed on shell (mass shell).
