Coffee preparationCoffee preparation is the process of turning coffee beans into liquid coffee. While the particular steps vary with the type of coffee and with the raw materials, the process includes four basic steps: raw coffee beans must be roasted, the roasted coffee beans must then be ground, and the ground coffee must then be mixed with hot or cold water (depending on the method of brewing) for a specific time (brewed), the liquid coffee extraction must be separated from the used grounds, and finally, if desired, the extracted coffee is combined with other elements of the desired beverage, such as sweeteners, dairy products, dairy alternatives, or toppings (such as shaved chocolate).
Compact spaceIn mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact.
Drip coffeeDrip coffee is made by pouring hot water onto ground coffee beans, allowing it to brew. There are several methods for doing this, including using a filter. Terms used for the resulting coffee often reflect the method used, such as drip-brewed coffee, filtered coffee, or immersion-brewed coffee in general. Manually brewed drip coffee is typically referred to as pour-over coffee. Water seeps through the ground coffee, absorbing its constituent chemical compounds, and then passes through a filter.
CoffeeCoffee is a beverage prepared from roasted coffee beans. Darkly colored, bitter, and slightly acidic, coffee has a stimulating effect on humans, primarily due to its caffeine content. It has the highest sales in the world market for hot drinks. The seeds of the Coffea plant's fruits are separated to produce unroasted green coffee beans. The beans are roasted and then ground into fine particles that are typically steeped in hot water before being filtered out, producing a cup of coffee.
Locally compact spaceIn topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely, it is a topological space in which every point has a compact neighborhood. In mathematical analysis locally compact spaces that are Hausdorff are of particular interest; they are abbreviated as LCH spaces. Let X be a topological space. Most commonly X is called locally compact if every point x of X has a compact neighbourhood, i.
Σ-compact spaceIn mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces. A space is said to be σ-locally compact if it is both σ-compact and (weakly) locally compact. That terminology can be somewhat confusing as it does not fit the usual pattern of σ-(property) meaning a countable union of spaces satisfying (property); that's why such spaces are more commonly referred to explicitly as σ-compact (weakly) locally compact, which is also equivalent to being exhaustible by compact sets.
Coffee substituteCoffee substitutes are non-coffee products, usually without caffeine, that are used to imitate coffee. Coffee substitutes can be used for medical, economic and religious reasons, or simply because coffee is not readily available. Roasted grain beverages are common substitutes for coffee. In World War II, acorns were used to make coffee, as were roasted chicory and grain. Postum, a bran and molasses beverage, also became a popular coffee substitute during this time.
Relatively compact subspaceIn mathematics, a relatively compact subspace (or relatively compact subset, or precompact subset) Y of a topological space X is a subset whose closure is compact. Every subset of a compact topological space is relatively compact (since a closed subset of a compact space is compact). And in an arbitrary topological space every subset of a relatively compact set is relatively compact. Every compact subset of a Hausdorff space is relatively compact.
Coffee roastingRoasting coffee transforms the chemical and physical properties of green coffee beans into roasted coffee products. The roasting process is what produces the characteristic flavor of coffee by causing the green coffee beans to change in taste. Unroasted beans contain similar if not higher levels of acids, protein, sugars, and caffeine as those that have been roasted, but lack the taste of roasted coffee beans due to the Maillard and other chemical reactions that occur during roasting.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Compact convergenceIn mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology. Let be a topological space and be a metric space. A sequence of functions is said to converge compactly as to some function if, for every compact set , uniformly on as . This means that for all compact , If and with their usual topologies, with , then converges compactly to the constant function with value 0, but not uniformly.
Countably compact spaceIn mathematics a topological space is called countably compact if every countable open cover has a finite subcover. A topological space X is called countably compact if it satisfies any of the following equivalent conditions: (1) Every countable open cover of X has a finite subcover. (2) Every infinite set A in X has an ω-accumulation point in X. (3) Every sequence in X has an accumulation point in X. (4) Every countable family of closed subsets of X with an empty intersection has a finite subfamily with an empty intersection.
Bowman's capsuleBowman's capsule (or the Bowman capsule, capsula glomeruli, or glomerular capsule) is a cup-like sac at the beginning of the tubular component of a nephron in the mammalian kidney that performs the first step in the filtration of blood to form urine. A glomerulus is enclosed in the sac. Fluids from blood in the glomerulus are collected in the Bowman's capsule. Outside the capsule, there are two "poles": The vascular pole is the side with the afferent arteriole and efferent arteriole.
MaterialMaterial is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geological origin or biological function. Materials science is the study of materials, their properties and their applications. Raw materials can be processed in different ways to influence their properties, by purification, shaping or the introduction of other materials.
Coffea arabicaCoffea arabica (əˈræbɪkə), also known as the Arabic coffee, is a species of flowering plant in the coffee and madder family Rubiaceae. It is believed to be the first species of coffee to have been cultivated and is currently the dominant cultivar, representing about 60% of global production. Coffee produced from the less acidic, more bitter, and more highly caffeinated robusta bean (C. canephora) makes up most of the remaining coffee production. The natural populations of Coffea arabica are restricted to the forests of South Ethiopia and Yemen.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Materials scienceMaterials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials science stem from the Age of Enlightenment, when researchers began to use analytical thinking from chemistry, physics, and engineering to understand ancient, phenomenological observations in metallurgy and mineralogy. Materials science still incorporates elements of physics, chemistry, and engineering.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Comma-separated valuesComma-separated values (CSV) is a format that uses commas to separate values. A CSV file stores tabular data (numbers and text) in plain text, where each line of the file typically represents one data record. Each record consists of the same number of fields, and these are separated by commas in the CSV file. If the field delimiter itself may appear within a field, fields can be surrounded with quotation marks . The CSV file format is one type of delimiter-separated file format.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
