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Topics referred to by the same term
Look up separable in Wiktionary, the free dictionary. Separability may refer to: Separable algebra, a generalization to associative algebras of the notion
Separability
Geometric property of a pair of sets of points in Euclidean geometry
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane)
Linear_separability
A} , we call A {\displaystyle A} a separable algebra over K {\displaystyle K} . It is useful to describe separability in terms of the element p := σ ( 1
Separable_algebra
Topological space with a dense countable subset
on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset. Contrast separability with
Separable_space
Quantum states that are not entangled
The separability problem is a subject of current research. A separability criterion is a necessary condition a state must satisfy to be separable. In
Separable_state
Type of algebraic field extension
field is separable. It follows that most extensions that are considered in mathematics are separable. Nevertheless, the concept of separability is important
Separable_extension
The separability problem is a concept from the field of social choice theory that describes the situation where two or more issues up for vote on a ballot
Separability_problem
In mathematics in complex analysis, the concept of holomorphic separability is a measure of the richness of the set of holomorphic functions on a complex
Holomorphic_separability
Type of vector space in math
separable Hilbert spaces are therefore isometrically isomorphic to the square-summable sequence space, ℓ 2 . {\displaystyle \ell ^{2}.} Separability was
Hilbert_space
Algebraic field extension
a separable closure of K {\displaystyle K} . Since a separable extension of a separable extension is again separable, there are no finite separable extensions
Algebraic_closure
About polynomials in several variables
false in one dimension, so the separable Jacobian conjecture, also called Adjamagbo's Jacobian conjecture, adds a separability premise to make the conjecture
Jacobian_conjecture
Verb with a prefix which separates from the core verb in certain positions in a sentence
A separable verb is a verb that is composed of a lexical core and a separable particle. In some sentence positions, the core verb and the particle appear
Separable_verb
Legal concept regulating rights of a creative work
A copyright is a type of intellectual property that gives its owner the exclusive legal right to copy, distribute, adapt, display, and perform a creative
Copyright
Polynomial coprime with its derivative
was considered separable if each of its irreducible factors in K[X] is separable in the modern definition. In this definition, separability depended on the
Separable_polynomial
mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations
Separable_permutation
Image-processing filter decomposable into two 1D filters
A separable filter in image processing can be written as the product of two or more simple filters. Typically a 2-dimensional convolution operation is
Separable_filter
School of thought of philosophy of law and jurisprudence
In legal philosophy, legal positivism is the theory that the existence of the law and its content depend on social facts, such as acts of legislation,
Legal_positivism
Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space
Non-separable_wavelet
Algebraic structure of set algebra
) . {\displaystyle (X,\,{\mathfrak {F}}).} A separable σ {\displaystyle \sigma } -algebra (or separable σ {\displaystyle \sigma } -field) is a σ {\displaystyle
Σ-algebra
Thought experiment by Ibn Sina
prove the separability of consciousness from the physical body. This initial version focuses on the principle of existential separability, which concerns
Floating_man
Type of logical matrix
mathematics, a logical matrix may be described as d-disjunct and/or d-separable. These concepts play a pivotal role in the mathematical area of non-adaptive
Disjunct_matrix
Technique for solving differential equations
differential equation for the unknown f ( x ) {\displaystyle f(x)} is separable if it can be written in the form d d x f ( x ) = g ( x ) h ( f ( x ) )
Separation_of_variables
Concept in computability theory
In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated"
Computably_inseparable
Quantum entanglement of more than 2 qubits
However, many separability criteria used in the bipartite setting can be generalized to the multipartite case. The characterization of separability in terms
Multipartite_entanglement
Algorithm for supervised learning of binary classifiers
converge regardless of (prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if desired
Perceptron
Physics phenomenon
criterion is merely a necessary one for separability, as the problem becomes NP-hard when generalized. Other separability criteria include (but not limited
Quantum_entanglement
Basic concept of graph theory
A graph G which is connected but not 2-connected is sometimes called separable. Analogous concepts can be defined for edges. In the simple case in which
Connectivity_(graph_theory)
Ability of certain terms in a contract to be voided without voiding the remainder
In law, severability (sometimes known as salvatorius, from Latin) refers to a provision in a contract or piece of legislation which states that if some
Severability
Upper bound in coding theory
achieve equality in the Singleton bound are called MDS (maximum distance separable) codes. Examples of such codes include codes that have only q {\displaystyle
Singleton_bound
Topological space whose topology has a countable base
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base. More explicitly
Second-countable_space
dual space is a measurable function in the usual (strong) sense. For separable spaces, the notions of weak and strong measurability agree. If ( X , Σ
Weakly_measurable_function
Field extension that is not algebraic
transcendence basis S such that L is a separable algebraic extension over K(S). A field extension L / K is said to be separably generated if it admits a separating
Transcendental_extension
Morpheme that is attached to a word stem to form a new word
them are bound morphemes by definition; prefixes and suffixes may be separable affixes. Adding a morpheme at the beginning of a word is called prefixation
Affix
state must satisfy in order for it to be separable. In other words, the reduction criterion is a separability criterion. It was first proved and independently
Reduction_criterion
cosmic space is any topological space that is a continuous image of some separable metric space. Equivalently (for regular T1 spaces but not in general)
Cosmic_space
Techniques to train attention and awareness
meditation do not exist as solitary practices but are only artificially separable from an entire system of practice and belief." For instance, while monks
Meditation
Collection of random variables
space. The concept of separability of a stochastic process was introduced by Joseph Doob. The underlying idea of separability is to make a countable
Stochastic_process
Concept in topology
In mathematics, a Polish space is a separable, completely metrizable topological space; i.e., a space homeomorphic to a complete metric space that has
Polish_space
Represents a function with diffusion properties useful in cryptography
An MDS matrix (maximum distance separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography
MDS_matrix
Class of economic models
the assumption of weak separability, under which groups of goods or inputs can be treated as composite aggregates. Separability allows a high-dimensional
Computable general equilibrium
Computable_general_equilibrium
Galois group of the separable closure
{\displaystyle K} , where K sep {\displaystyle K^{\textrm {sep}}} is a separable closure of K {\displaystyle K} . Alternatively, it is the group of all
Absolute_Galois_group
Study of demons or beliefs about demons
it concerns the study of a hierarchy of demons. Demons may be nonhuman separable souls,[clarification needed] or discarnate spirits which have never inhabited
Demonology
A separable partial differential equation can be broken into a set of equations of lower dimensionality (fewer independent variables) by a method of separation
Separable partial differential equation
Separable_partial_differential_equation
Field of knowledge
physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart. In the 19th century
Mathematics
Image edge detection algorithm
Sobel–Feldman operator is based on convolving the image with a small, separable, and integer-valued filter in the horizontal and vertical directions and
Sobel_operator
Normed vector space that is complete
a separable Banach space need not be separable, but: Theorem—Let X be a normed space. If X′ is separable, then X is separable. When X′ is separable, the
Banach_space
West Germanic language
fahren (to drive), erfahren (to experience). Many German verbs have a separable prefix, often with an adverbial function. In finite verb forms, it is
German_language
brief summary of some of the most frequently used methods. Using the separability property of the Gaussian kernel g N ( x 1 , … , x N , t ) = G ( x 1
Scale_space_implementation
Thought experiment in quantum mechanics
point of contact. The EPR paper concludes with a claim that this lack of separability meant that quantum mechanics as a theory of reality was incomplete. Schrödinger
Schrödinger's_cat
to a finite product of finite separable field extensions. An étale algebra is a special sort of commutative separable algebra. Let K be a field. Let
Étale_algebra
(USDA) 1963, 2002 "Beef, roasted, cooked, select, trimmed to 0" fat, separable lean and fat, boneless, tenderloin roast, loin nutrition facts and analysis"
Table_of_food_nutrients
1954 United States Supreme Court case
Copyright Act of 1976 as the concept of separability. For many years, there was confusion over how to determine separability, so tests proliferated and competed
Mazer_v._Stein
2017 United States Supreme Court case
articles" can be restricted by copyright law. The Court created a two-prong "separability" test, granting copyrightability based on separate identification and
Star Athletica, LLC v. Varsity Brands, Inc.
Star_Athletica,_LLC_v._Varsity_Brands,_Inc.
Question in functional analysis
(not necessarily separable) Hilbert space. The problem has been solved in the affirmative for special cases (specifically for separable and Type-I C*-algebras)
Naimark's_problem
Neural network technology
Depthwise separable convolution separates the standard convolution into two steps: depthwise convolution and pointwise convolution. The depthwise separable convolution
Convolutional_layer
Mathematical theorem
essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space. It was proved in the 1970s by Kallianpur–Satô–Stefan and
Structure theorem for Gaussian measures
Structure_theorem_for_Gaussian_measures
Theorem in quantum information science
state of another, as cloning specifically refers to the creation of a separable state with identical factors. For example, one might use the controlled
No-cloning_theorem
Type of feedforward neural network
layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks are trained using backpropagation and are colloquially
Multilayer_perceptron
Polish physicist
to the field of quantum informatics. In his most widely cited paper, 'Separability of Mixed States: Necessary and Sufficient Conditions' written together
Ryszard_Horodecki
Measure of nonclassical correlations between two subsystems of a quantum system
quantum correlations can be present in certain mixed separable states; In other words, separability alone does not imply the absence of quantum correlations
Quantum_discord
All infinite-dimensional, separable Banach spaces are homeomorphic
the Anderson–Kadec theorem states that any two infinite-dimensional, separable Banach spaces, or, more generally, Fréchet spaces, are homeomorphic as
Anderson–Kadec_theorem
Nonparametric spectral estimation method
separable as N → ∞ {\displaystyle N\rightarrow \infty } . In practice N {\displaystyle N} is fixed and one is interested in approximate separability between
Singular_spectrum_analysis
Theoretical study of law
merits. The separability thesis states that law is conceptually distinct from morality. While law might contain morality, the separability thesis states
Jurisprudence
United States law
a ballot, and having that ballot counted. Title VII established the separability of the act, affirming that the rest of the act shall go unaffected if
Civil_Rights_Act_of_1960
Result in Fourier analysis
holds for arbitrary Hilbert spaces, not necessarily separable. When the Hilbert space is not separable any orthonormal basis is uncountable and we need to
Parseval's_identity
Frequently-cited counterexample in topology
space, and this is a non-separable subset of the separable space S {\displaystyle \mathbb {S} } . It shows that separability does not inherit to closed
Sorgenfrey_plane
Criterion in quantum information theory
dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states, where the Schmidt decomposition does not apply. The
Peres–Horodecki_criterion
State or quality of being bodiless
not made out of matter. In the problem of universals, universals are separable from any particular embodiment in one sense, while in another, they seem
Incorporeality
Construction of a larger algebraic field by "adding elements" to a smaller field
L / K {\displaystyle L/K} is called separable if the minimal polynomial of every element of L over K is separable, i.e., has no repeated roots in an algebraic
Field_extension
Condition in order theory and topology
Suslin's Problem. Every separable topological space has the ccc. Furthermore, a product space of an arbitrary number of separable spaces has the ccc. A
Countable_chain_condition
Process of allocating investable wealth in assets over time
Intertemporal portfolio choice is the process of allocating one's investable wealth to various assets, especially financial assets, repeatedly over time
Intertemporal portfolio choice
Intertemporal_portfolio_choice
Theorem in measure theory
Vasilyevich Prokhorov, who considered probability measures on complete separable metric spaces. The term "Prokhorov’s theorem" is also applied to later
Prokhorov's_theorem
sacred in Tonga and is often considered the physical manifestation of a separable soul. In the Zapotec civilization of Mesoamerica, the bat god presided
List_of_fictional_bats
Block cipher
a Feistel structure like DES. Twofish also employs a Maximum Distance Separable matrix. When it was introduced in 1998, Twofish was slightly slower than
Twofish
Description of physical properties at the atomic and subatomic scale
1007/s10701-009-9347-0. S2CID 32755624. Howard, D. (1985). "Einstein on locality and separability". Studies in History and Philosophy of Science Part A. 16 (3): 171–201
Quantum_mechanics
American bible scholar (1934–2022)
article in Pneuma in 1985, "Baptism in the Holy Spirit: The Issue of Separability and Subsequence", he argued that there is little biblical evidence for
Gordon_Fee
Pronoun that is associated with a particular grammatical person
Phrasal Predicative Preterite-present Pure Reflexive Regular / Irregular Separable Stative Stretched Transitive Unaccusative Unergative Adjective Anti-intersective
Personal_pronoun
Word or expression used to express an emotion or sentiment
Phrasal Predicative Preterite-present Pure Reflexive Regular / Irregular Separable Stative Stretched Transitive Unaccusative Unergative Adjective Anti-intersective
Interjection
Act providing national standards for cigarette packaging in the US
The Federal Cigarette Labeling and Advertising Act (also known as the Cigarette Act) is a comprehensive act designed to provide a set of national standards
Cigarette Labeling and Advertising Act
Cigarette_Labeling_and_Advertising_Act
1967 U.S. Supreme Court case on arbitration
processes and separability fosters cynicism and distrust in the rule of law, undermining its legitimacy." Defenders of the decision and separability have said
Prima Paint Corp. v. Flood & Conklin Manufacturing Co.
Prima_Paint_Corp._v._Flood_&_Conklin_Manufacturing_Co.
Word or phrase separable from adjacent syntax
and both are in respectable use. Absolute construction – Word or phrase separable from adjacent syntax Conjunct – Semantic or grammatical clustering of
Disjunct_(linguistics)
Construct in quantum information theory
{\displaystyle H_{A}} . Terhal, Barbara M. (2000). "Bell inequalities and the separability criterion". Physics Letters A. 271 (5–6): 319–326. arXiv:quant-ph/9911057
Entanglement_witness
Rules in probabilistic logic
S2CID 19791149. M. Horodecki and P. Horodecki (1999). "Reduction criterion of separability and limits for a class of distillation protocols". Phys. Rev. A. 59 (6):
Fréchet_inequalities
Art style
Decorative panel showing the two separable elements of Grotesque: the elaborate acanthus leaf and candelabra type design and the hideous mask or face
Grotesque
Grammar of the German language
The grammar of the German language is quite similar to that of the other Germanic languages. Although some features of German grammar, such as the formation
German_grammar
Unique von Neumann algebra
In mathematics, there are up to isomorphism exactly two separably acting hyperfinite type II factors; one infinite and one finite. Murray and von Neumann
Hyperfinite_type_II_factor
French software engineer, artificial intelligence (born 1989)
(ICLR). Chollet is the author of Xception: Deep Learning with Depthwise Separable Convolutions, which is among the top ten most cited papers in CVPR proceedings
François_Chollet
Generalization of the concept of a direct sum in mathematics
reduce the classification of (what are now called) von Neumann algebras on separable Hilbert spaces to the classification of so-called factors. Factors are
Direct_integral
Soviet/Russian multiple launch rocket system
243 kg 646 × 0.25 kg (up to 120 mm RHA armor-piercing) 260 sec 9M55F Separable HE-Fragmentation 258 kg 9M55C Thermobaric 243 kg 9M528 HE-Fragmentation
BM-30_Smerch
the Urysohn universal space is a certain metric space that contains all separable metric spaces in a particularly nice manner. This concept is due to Pavel
Urysohn_universal_space
Indo-European language
Greek." Woodhouse 2009, p. 171: "This question is of course only just separable from the question of which languages within Indo-European are most closely
Greek_language
Area of mathematics
infinite-dimensional separable Hilbert spaces are isomorphic to ℓ 2 ( ℵ 0 ) {\displaystyle \ell ^{\,2}(\aleph _{0})\,} . Separability being important for
Functional_analysis
*-algebra of bounded operators on a Hilbert space
Neumann algebra that acts on a separable Hilbert space is called separable. Note that such algebras are rarely separable in the norm topology. The von
Von_Neumann_algebra
Generalization of games used in game theory
Nash equilibria of separable games are easier to compute than non-separable games as implied by the following theorem: For any separable game there exists
Continuous_game
American industrial company
lamp holders, key sockets, soon followed the same path Later, Hubbell's "separable plug" design took shape on the drawing board back in Bridgeport, and then
Hubbell_Incorporated
Invariant of polynomial roots
separable, which means that, if they have a multiple root, then the polynomial p is not irreducible. It is not known if there is an always separable resolvent
Resolvent_(Galois_theory)
Jesus' death as described in the gospels
4:25) based on the plan of God. For Paul the "power of the cross" is not separable from the resurrection of Jesus. Furthermore, Paul highlighted the idea
Crucifixion_of_Jesus
Ring that is also a vector space or a module
of A, sometimes called the bidimension of A, measures the failure of separability. Let A be a finite-dimensional algebra over a field k. Then A is an Artinian
Associative_algebra
Iterative method for finding a linear decision boundary
non-separability. The convergence rate depends on the choice of the learning rate parameter ρ {\displaystyle \rho } and the degree of linear separability
Ho–Kashyap_algorithm
Statement in computational learning theory
as counting function theorem. Let the number of homogeneously linearly separable sets of N {\displaystyle N} points in d {\displaystyle d} dimensions be
Cover's_theorem
travel, tourism, insurance
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travel, tourism, insurance