Scientific methodThe scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific method for additional detail.) It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation.
Phase-space formulationThe phase-space formulation of quantum mechanics places the position and momentum variables on equal footing in phase space. In contrast, the Schrödinger picture uses the position or momentum representations (see also position and momentum space). The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product.
Achilles tendinitisAchilles tendinitis, also known as achilles tendinopathy, occurs when the Achilles tendon, found at the back of the ankle, becomes sore. Achilles tendinopathy is accompanied by alterations in the tendon's structure and mechanical properties. The most common symptoms are pain and swelling around the affected tendon. The pain is typically worse at the start of exercise and decreases thereafter. Stiffness of the ankle may also be present. Onset is generally gradual. It commonly occurs as a result of overuse such as running.
Territories of the United StatesTerritories of the United States are sub-national administrative divisions overseen by the federal government of the United States. The various American territories differ from the U.S. states and Indian reservations as they are not sovereign entities. In contrast, each state has a sovereignty separate from that of the federal government and each federally recognized Native American tribe possesses limited tribal sovereignty as a "dependent sovereign nation.
Sustainable developmentSustainable development is an organizing principle that aims to meet human development goals while also enabling natural systems to provide necessary natural resources and ecosystem services to humans. The desired result is a society where living conditions and resources meet human needs without undermining the planetary integrity and stability of the natural system. Sustainable development tries to find a balance between economic development, environmental protection, and social well-being.
Scientific skepticismScientific skepticism or rational skepticism (also spelled scepticism), sometimes referred to as skeptical inquiry, is a position in which one questions the veracity of claims lacking empirical evidence. In practice, the term most commonly references the examination of claims and theories that appear to be beyond mainstream science, rather than the routine discussions and challenges among scientists.
Sequence spaceIn functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.
Sustainable Development GoalsThe Sustainable Development Goals or Global Goals are a collection of seventeen interlinked objectives designed to serve as a "shared blueprint for peace and prosperity for people and the planet, now and into the future." The SDGs are no poverty; zero hunger; good health and well-being; quality education; gender equality; clean water and sanitation; affordable and clean energy; decent work and economic growth; industry, innovation and infrastructure; reduced inequalities; sustainable cities and communities; responsible consumption and production; climate action; life below water; life on land; peace, justice, and strong institutions; and partnerships for the goals.
Proposal (business)A business proposal is a written offer from a seller to a prospective sponsor. Business proposals are often a key step in the complex sales process—i.e., whenever a buyer considers more than price in a purchase. When one person signifies to another their willingness to do or to abstain from doing anything with a view to obtaining the assent of the other to such act or abstinence, they are said to make a proposal. A proposal puts the buyer's requirements in a context that favors the seller's products and services, and educates the buyer about the seller's capability to satisfy their needs.
Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
