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Cubic Mean
The cubic mean (written as \bar_\mathrm) is a specific instance of the generalized mean with p=3. Definition For n real numbers x_i \in \mathbb R the cubic mean is defined as: : \bar_\mathrm = \sqrt = \sqrt For example, the cubic mean of two numbers is: :\sqrt /math>. Applications The cubic mean is used to predict the life expectancy of machine parts. The cubic mean wind speed has been used a measure of local potential for wind energy. The cubic mean is also used in biology to measure the mean dimensions of spherical bacteria (cocci) and of larger animals that are approximately spheroidal in shape. In this case using the conventional arithmetic mean In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results fr ... will not give an accurate result because the size of a spherica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Generalized Mean
In mathematics, generalised means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means (arithmetic mean, arithmetic, geometric mean, geometric, and harmonic mean, harmonic means). Definition If is a non-zero real number, and x_1, \dots, x_n are positive real numbers, then the generalized mean or power mean with exponent of these positive real numbers is M_p(x_1,\dots,x_n) = \left( \frac \sum_^n x_i^p \right)^ . (See Norm (mathematics)#p-norm, -norm). For we set it equal to the geometric mean (which is the limit of means with exponents approaching zero, as proved below): M_0(x_1, \dots, x_n) = \left(\prod_^n x_i\right)^ . Furthermore, for a sequence of positive weights we define the weighted power mean as M_p(x_1,\dots,x_n) = \left(\frac \right)^ and when , it is equal to the weighted geometric mean: M_0(x_1,\dots,x_n) = \left(\prod_^n x_i^\right)^ . The unweight ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fatigue (material)
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of the fracture surface. The crack will continue to grow until it reaches a critical size, which occurs when the stress intensity factor of the crack exceeds the fracture toughness of the material, producing rapid propagation and typically complete fracture of the structure. Fatigue has traditionally been associated with the failure of metal components which led to the term metal fatigue. In the nineteenth century, the sudden failing of metal railway axles was thought to be caused by the metal crystallising because of the brittle appearance of the fracture surface, but this has since been disproved. Most materials, such as composites, plastics and ceramics, seem to experience some sort of fatigue-related failure. To aid in predicting the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Wind Energy
Wind power is the use of wind energy to generate useful work. Historically, wind power was used by sails, windmills and windpumps, but today it is mostly used to generate electricity. This article deals only with wind power for electricity generation. Today, wind power is generated almost completely using wind turbines, generally grouped into wind farms and connected to the electrical grid. In 2024, wind supplied over 2,494 TWh of electricity, which was 8.1% of world electricity. With about 100 GW added during 2021, mostly in China and the United States, global installed wind power capacity exceeded 800 GW. 30 countries generated more than a tenth of their electricity from wind power in 2024 and wind generation has nearly tripled since 2015. To help meet the Paris Agreement goals to limit climate change, analysts say it should expand much faster – by over 1% of electricity generation per year. Wind power is considered a sustainable, renewable energy source, and has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Biology
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and distribution of life. Central to biology are five fundamental themes: the cell (biology), cell as the basic unit of life, genes and heredity as the basis of inheritance, evolution as the driver of biological diversity, energy transformation for sustaining life processes, and the maintenance of internal stability (homeostasis). Biology examines life across multiple biological organisation, levels of organization, from molecules and cells to organisms, populations, and ecosystems. Subdisciplines include molecular biology, physiology, ecology, evolutionary biology, developmental biology, and systematics, among others. Each of these fields applies a range of methods to investigate biological phenomena, including scientific method, observation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bacteria
Bacteria (; : bacterium) are ubiquitous, mostly free-living organisms often consisting of one Cell (biology), biological cell. They constitute a large domain (biology), domain of Prokaryote, prokaryotic microorganisms. Typically a few micrometres in length, bacteria were among the first life forms to appear on Earth, and are present in most of its habitats. Bacteria inhabit the air, soil, water, Hot spring, acidic hot springs, radioactive waste, and the deep biosphere of Earth's crust. Bacteria play a vital role in many stages of the nutrient cycle by recycling nutrients and the nitrogen fixation, fixation of nitrogen from the Earth's atmosphere, atmosphere. The nutrient cycle includes the decomposition of cadaver, dead bodies; bacteria are responsible for the putrefaction stage in this process. In the biological communities surrounding hydrothermal vents and cold seeps, extremophile bacteria provide the nutrients needed to sustain life by converting dissolved compounds, suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cocci
Bacterial cellular morphologies are the shapes that are characteristic of various types of bacteria and often key to their identification. Their direct examination under a light microscope enables the classification of these bacteria (and archaea). Generally, the basic morphologies are spheres (coccus) and round-ended cylinders or rod shaped (bacillus). But, there are also other morphologies such as helically twisted cylinders (example '' Spirochetes''), cylinders curved in one plane (selenomonads) and unusual morphologies (the square, flat box-shaped cells of the Archaean genus '' Haloquadratum)''. Other arrangements include pairs, tetrads, clusters, chains and palisades. Types Coccus A coccus (plural ''cocci'', from the Latin ''coccinus'' (scarlet) and derived from the Greek ''kokkos'' (berry)), is any microorganism (usually bacteria) whose overall shape is spherical or nearly spherical. Coccus refers to the shape of the bacteria and can contain multiple genera, such as sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Stillwater, Oklahoma
Stillwater is the tenth-largest city in the U.S. state of Oklahoma, and the county seat of Payne County, Oklahoma, Payne County. It is located in north-central Oklahoma at the intersection of U.S. Route 177#Oklahoma, U.S. Route 177 and Oklahoma State Highway 51, State Highway 51. As of the 2020 census, the city population was 48,394. The Stillwater Micropolitan Statistical Area had a population of 78,399 according to the 2012 census estimate. Stillwater was part of the first Land Rush of 1889, Oklahoma Land Run held on April 22, 1889, when the Unassigned Lands were opened for settlement and became the core of the new Oklahoma Territory. The city charter was adopted on August 24, 1889, and operates under a Council–manager government, council-manager government system. Stillwater has a diverse economy with a foundation in aerospace, agribusiness, biotechnology, optoelectronics, printing and publishing, and software and standard manufacturing. Stillwater is home to the main campus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a Survey (statistics), survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric mean, geometric and harmonic mean, harmonic. Arithmetic means are also frequently used in economics, anthropology, history, and almost every other academic field to some extent. For example, per capita income is the arithmetic average of the income of a nation's Human population, population. While the arithmetic mean is often used to report central tendency, central tendencies, it is not a robust statistic: it is greatly influenced by outliers (Value (mathematics), values much larger or smaller than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
