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Mathematical modeling language
A vector addition system (VAS) is one of several mathematical modeling languages for the description of distributed systems. Vector addition systems were
Vector_addition_system
Geometric object that has length and direction
physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude
Euclidean_vector
Problem in math and computer science
for Ackermann function time complexity. In 2022 reachability in vector addition systems was shown to be Ackermann-complete and therefore a nonelementary
Reachability_problem
Broad concept generalizing scalars in mathematics and physics
added and scaled, and these vector operations led to the concept of a vector space, which is a set equipped with a vector addition and a scalar multiplication
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Algebraic structure in linear algebra
operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces
Vector_space
Model to describe distributed systems
levels. See for an informal introduction to object Petri nets. A vector addition system with states (VASS) is an equivalent formalism to Petri nets. However
Petri_net
Submachine gun
seeing limited production since 2009, the KRISS Vector uses an unconventional delayed blowback system combined with in-line design to reduce perceived
KRISS_Vector
American mathematician
search algorithm Karp–Lipton theorem Karp's 21 NP-complete problems Vector addition system Awards Fulkerson Prize (1979) Turing Award (1985) John von Neumann
Richard_M._Karp
Mathematical operation on vectors in 3D space
product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional
Cross_product
Proving or disproving the correctness of certain intended algorithms
machines, labelled transition systems, Horn clauses, Petri nets, vector addition systems, timed automata, hybrid automata, process algebra, formal semantics
Formal_verification
Set of decision problems
EXPSPACE-complete to decide whether the reachability of a given vector addition system is finite. Game complexity Meyer, A.R. and L. Stockmeyer. The equivalence
EXPSPACE
Computational problem with high complexity
ACK-complete problems: reachability in vector addition systems (VAS). reachability in labeled vector addition system with states (VASS) reachability in Petri
Nonelementary_problem
Use of coordinates for representing vectors
Vector notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more
Vector_notation
One of the seven crystal systems
crystal is described by vectors of unequal length, as in the orthorhombic system. In addition, the angles between these vectors must all be different and
Triclinic_crystal_system
Assignment of a vector to each point in a subset of Euclidean space
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle
Vector_field
Arithmetic operation
also be performed on abstract objects such as vectors, matrices, and elements of additive groups. Addition has several important properties. It is commutative
Addition
Branch of mathematics
called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v +
Linear_algebra
In mathematics, vector space of linear forms
the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces
Dual_space
Vector representing the position of a point with respect to a fixed origin
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.
Position_(geometry)
Concepts from linear algebra
algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear
Eigenvalues_and_eigenvectors
Calculus of vector-valued functions
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional
Vector_calculus
Quickly growing function
function appears in the time complexity of some algorithms, such as vector addition systems and Petri net reachability, thus showing they are computationally
Ackermann_function
True when either but not both inputs are true
disjunction of two n-bit strings is identical to the standard vector of addition in the vector space ( Z / 2 Z ) n {\displaystyle (\mathbb {Z} /2\mathbb {Z}
Exclusive_or
Vector space with a notion of nearness
topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar
Topological_vector_space
Standard for assessing computer system vulnerabilities
exploited and then used to attack other parts of a system or network. These new metrics allow the Base vector to more clearly express the type of vulnerability
Common Vulnerability Scoring System
Common_Vulnerability_Scoring_System
Euclidean space without distance and angles
or sometimes free vectors. Explicitly, the definition above means that the action is a mapping, generally denoted as an addition, A × A → → A ( a , v
Affine_space
Topics referred to by the same term
supplementation Value-added service, a telecommunications industry term Vector addition system, a mathematical modeling language Vehicle-activated sign Virtual
VAS
Abstract machine used in a formal logic and theoretical computer science
Post–Turing machine Random-access machine Register machine Wang B-machine Vector addition system Hopcroft, Motwani & Ullman 2003, p. 352. Schönhage 1973. Schönhage
Counter_machine
Set of methods for supervised statistical learning
In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms
Support_vector_machine
Facet of ballistics and aeronautics
Thrust vectoring, also known as thrust vector control (TVC), is the ability of an aircraft, rocket or other vehicle to manipulate the direction of the
Thrust_vectoring
Vector sum of all forces acting upon a particle or body
basis of vector addition. This concept has been central to physics since the times of Galileo and Newton, forming the cornerstone of Vector calculus,
Net_force
Two-dimensional vector image file format
Scalable Vector Graphics (SVG) is an XML-based vector graphics format for defining two-dimensional graphics, having support for interactivity and animation
SVG
Mathematical operation in linear algebra
distributive with respect to the addition. In particular, the entries may be matrices themselves (see block matrix). A vector x {\displaystyle \mathbf {x}
Matrix_multiplication
Set of vectors used to define coordinates
In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite
Basis_(linear_algebra)
Array of numbers
is an m × 1 column vector, then the matrix equation A x = b {\displaystyle \mathbf {Ax} =\mathbf {b} } is equivalent to the system of linear equations
Matrix_(mathematics)
Function valued in a vector space; typically a real or complex one
of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension
Vector-valued_function
Computational approach
learning process conducted by fruit flies olfactory system. The input is a roughly 50-dimensional vector corresponding to odor receptor neuron types. The
Hyperdimensional_computing
Vector satisfying some of the criteria of an eigenvector
eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria which are more relaxed than those for an
Generalized_eigenvector
Directional planes
plane regions, vectors, directions, etc. A surface is horizontal if its tangent planes are everywhere perpendicular to the gravity vector at the tangent
Vertical_and_horizontal
Topics referred to by the same term
Vass, North Carolina, a town Vass of Lochslin, Scottish family Vector addition system with states, a mathematical modeling language Volleyball All-Star
Vass
Equation used in relativistic physics
relative to A (ship's velocity away from the shore). The addition here is the vector addition of vector algebra and the resulting velocity is usually represented
Velocity-addition_formula
Vector in relativity
In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components
Four-vector
Mathematical function, in linear algebra
is a particular kind of function between vector spaces, which respects the basic operations of vector addition and scalar multiplication. A standard example
Linear_map
Vector space on which a distance is defined
In mathematics, a normed vector space or normed space is a vector space, typically over the real or complex numbers, on which a norm is defined. A norm
Normed_vector_space
Mathematical operation on vector spaces
{\displaystyle V\otimes W} of two vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field) is a vector space to which is associated
Tensor_product
Computer processor which works on arrays of several numbers at once
one-dimensional arrays of data called vectors. When integrated as a hardware component the vector processor is often called a vector processing unit (VPU). This
Vector_processor
Instructions for the x86 microprocessors
has a book on the topic of: X86 Assembly/AVX, AVX2, FMA3, FMA4 Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge
Advanced_Vector_Extensions
Algebra associated to any vector space
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
Exterior_algebra
Linear map from a vector space to its field of scalars
the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is
Linear_form
Algebraic object with geometric applications
of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There
Tensor
Agent that carries and transmits pathogens
In epidemiology, a disease vector is any living agent that carries and transmits an infectious pathogen such as a parasite or microbe, to another living
Disease_vector
Four-dimensional number system
the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition, subtraction, multiplication,
Quaternion
Supercomputer manufactured by Cray Research
and the cooling system. The Cray-1 was the first supercomputer to successfully implement the vector processor design. These systems improve the performance
Cray-1
Hypotenuse of right triangle from its sides
In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its
Pythagorean_addition
Similarity measure for number sequences
between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot
Cosine_similarity
Software tool by Vector Informatik
Ethernet systems as well as CAN-based protocols such as J1939, CANopen, ARINC 825, ISOBUS and many more. In 1996 the first CANoe license was sold by Vector. Since
CANoe
Mathematical operation with two operands
examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. A binary function
Binary_operation
Real number that is strictly less than zero
and positive numbers as in −2 + −5 gives −7. Addition of two negative numbers is very similar to addition of two positive numbers. For example, (−3) +
Negative_number
Standardized means of organizing and storing digital images
800 bits = 921,600 bytes = 900 KiB With vector images, the file size increases only with the addition of more vectors. There are two types of image file compression
Image_file_format
SQL relational database management system
Actian Vector (formerly known as VectorWise) is an SQL relational database management system designed for high performance in analytical database applications
Actian_Vector
Curve traced by a string as it is unwrapped from another curve
the catenary ( t , cosh t ) {\displaystyle (t,\cosh t)} , the tangent vector is c → ′ ( t ) = ( 1 , sinh t ) {\displaystyle {\vec {c}}'(t)=(1,\sinh
Involute
Type of application software
to convert from vector graphics to raster graphics, but going the other way is harder. Some software attempts to do this. In addition to static graphics
Graphics_software
Physical quantity that changes sign with improper rotation
physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations
Pseudovector
Direction and rate of rotation
letter omega), also known as the angular frequency vector, is a three-dimensional Euclidean vector that uniquely identifies the plane, direction and angular
Angular_velocity
Set with operations obeying given axioms
elements of the field (called scalars), and elements of the vector space (called vectors). Abstract algebra is the name that is commonly given to the
Algebraic_structure
Military light utility vehicle
The VECTOR (Versatile Expeditionary Commando Tactial Off Road) is a Dutch light all-terrain tactical vehicle, designed and developed by defence contractor
Versatile Expeditionary Commando Tactial Off Road
Versatile_Expeditionary_Commando_Tactial_Off_Road
Linux distribution
VectorLinux, abbreviated VL, was a Linux distribution for the x86 platform based on the Slackware Linux distribution, originally developed by Canadian
VectorLinux
Coordinate system using perpendicular axes
the plane was later generalized into the concept of vector spaces. Many other coordinate systems have been developed since Descartes, such as the polar
Cartesian_coordinate_system
1980s supercomputer
The ETA10 is a vector supercomputer designed, manufactured, and marketed by ETA Systems, a spin-off division of Control Data Corporation (CDC). The ETA10
ETA10
Biotechnology for gene delivery
non-integrative vectors are also commonly used. In addition to agriculture and laboratory research, viral vectors are widely applied in gene therapy: as of 2022
Viral_vector
Type of vector space in math
spaces of any finite or infinite dimension. A Hilbert space is an abstract vector space, and it has the additional structure of an inner product that allows
Hilbert_space
Navigation service provided to aircraft by air traffic control
FAA. Vectoring is the provision of navigational guidance to aircraft in the form of specific headings, based on the use of an ATS surveillance system. Aircraft
Aircraft_vectoring
Property of space that quantifies the magnetic influence at a given location
mathematically by assigning a vector to each point of space, making it a vector field. There are two different, but closely related, vector fields which are called
Magnetic_field
Defunct launch vehicle designer and launch service provider
Vector Launch, Inc. (formerly Vector Space Systems) was an American space technology company which aims to launch suborbital and orbital payloads. Vector
Vector_Launch
Algebraic structure with addition and multiplication
dimension n2 as a real vector space. A ring R is a topological ring if its set of elements R is given a topology which makes the addition map ( + : R × R →
Ring_(mathematics)
Influence that can change motion of an object
a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that graphical vector addition can
Force
Quickly accessible working storage available as part of a digital processor
Operation (PDF) (Seventh ed.). IBM. 2008. "IBM Enterprise Systems Architecture/370 and System/370 - Vector Operations" (PDF). IBM. SA22-7125-3. Retrieved May
Processor_register
4D relativistic energy and momentum
four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum
Four-momentum
Experimental thrust-vectoring version of the Su-35 fighter aircraft
Association before having thrust-vectoring nozzles installed. It also had updated flight- and weapons-control systems. The aircraft made its maiden flight
Sukhoi_Su-37
Statistical model to calculate the value of multiple quantities as they change over time
Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type
Vector_autoregression
Series of high-end 1980s IBM mainframe computers
2021-10-13. "VECTOR FACILITY (VF) FOR IBM 3090 PROCESSOR UNITS". Announcement Letters. IBM. October 1, 1985. 185-121. IBM System/370 Vector Operations (PDF)
IBM_3090
Set of values that describe the polarization state of electromagnetic radiation
ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying
Stokes_parameters
Sub-brand by Audi that designed for its all-wheel-drive cars
Nissan S-AWC - a torque vectoring all-wheel drive system from Mitsubishi Motors SH-AWD - a torque vectoring all-wheel drive system from Honda BMW xDrive
Quattro (four-wheel-drive system)
Quattro_(four-wheel-drive_system)
Method of data analysis
space are a sequence of p {\displaystyle p} unit vectors, where the i {\displaystyle i} -th vector is the direction of a line that best fits the data
Principal_component_analysis
Space formed by the ''n''-tuples of real numbers
component-wise addition and scalar multiplication, it is a real vector space. The coordinates over any basis of the elements of a real vector space form a
Real_coordinate_space
American multinational software company
a wide range of programs from web design tools, photo manipulation, and vector creation to video and audio editing, mobile app development, print layout
Adobe_Inc.
One-dimensional physical quantity
of the real number field. Since a field is a vector space with addition defined based on vector addition and multiplication defined as scalar multiplication
Scalar_(physics)
Conserved physical quantity; rotational analogue of linear momentum
Solar System because angular momentum is exchanged to a small but important extent among the planets and the Sun. The orbital angular momentum vector of
Angular_momentum
Computer company
case. The Vector Graphic 4 was a transitional 8-bit and 16-bit hybrid model. Although primarily used with the CP/M operating system, the Vector 3 ran several
Vector_Graphic
Complex number representing a particular sine wave
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude A and initial
Phasor
Infection spread in hospitals or health care facilities
direct-contact transmission and indirect-contact transmission. Alongside reducing vectors for transmission, patient susceptibility to hospital-acquired infections
Hospital-acquired_infection
Speed web pages are downloaded and displayed
the replacement of raster graphics with resolution-independent vector graphics. Vector substitution is best suited for simple geometric images.[citation
Web_performance
Single force representing the combination of all forces acting on a physical body
associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force
Resultant_force
64-bit extension of the ARM architecture
Doubling Multiply Subtract, Returning High Half. The instructions are added in vector and scalar forms. A set of AArch64 load and store instructions that can
AArch64
Property of a mass in motion
object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then
Momentum
Type of memory addressing
input/output systems, allowing large data sets to be transferred to main memory more rapidly. The concept is somewhat similar to vectored I/O, which is
Gather/scatter (vector addressing)
Gather/scatter_(vector_addressing)
Inclination of road or surface other than flat
Serway, p. 143 Beer, Ferdinand P.; Johnston, E. Russell (July 11, 2003). Vector Mechanics for Engineers: Dynamics. Science/Engineering/Math (7 ed.). McGraw-Hill
Banked_turn
Correspondence between quaternions and 3D rotations
3 × (3 multiplications + 2 additions) = 9 multiplications and 6 additions, the most efficient method for rotating a vector. A rotation can be represented
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Motion problem in classical mechanics
always in the plane perpendicular to the constant vector L. If the force F(r) is conservative then the system has a potential energy U(r), so the total energy
Two-body_problem
Results from a system of equations in econometrics
vector of explanatory (exogeneous) variables. In addition let ε {\displaystyle \varepsilon } be a vector of error terms. Then the general expression of
Reduced_form
VECTOR ADDITION-SYSTEM
VECTOR ADDITION-SYSTEM
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Surname or Lastname
Scottish
Scottish : Anglicized form of the Gaelic personal name Eachann (earlier Eachdonn, already confused with Norse Haakon), composed of the elements each ‘horse’ + donn ‘brown’.English : found in Yorkshire and Scotland, where it may derive directly from the medieval personal name. According to medieval legend, Britain derived its name from being founded by Brutus, a Trojan exile, and Hector was occasionally chosen as a personal name, as it was the name of the Trojan king’s eldest son. The classical Greek name, HektÅr, is probably an agent derivative of Greek ekhein ‘to hold back’, ‘hold in check’, hence ‘protector of the city’.German, French, and Dutch : from the personal name (see 2 above). In medieval Germany, this was a fairly popular personal name among the nobility, derived from classical literature. It is a comparatively rare surname in France.
Male
Russian
(Cyrillic Виктор): Slavic form of Roman Latin Victor, VIKTOR means "conqueror." In use by the Bulgarians, Russians and Serbians. Compare with another form of Viktor.
Female
Swiss
, addition.
Male
English
Roman Latin name VICTOR means "conqueror."Â
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Female
Swiss
, addition.
Boy/Male
English American
Doctor; teacher.
Male
Swiss
, addition.
Male
English
Old English surname transferred to unisex forename use, ADDISON means "son of Adam."Â
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Romanian, Slovenia, Spanish, Swedish, Swiss, Tamil, Ukrainian
Victorious; Conqueror; Winner; Champion; One who Conquers; Victory
Boy/Male
Spanish
Victor.
Male
Swiss
, addition.
Male
Arthurian
, sir Hector de Maris; (defender).
Boy/Male
Latin American Spanish
Conqueror.
VECTOR ADDITION-SYSTEM
VECTOR ADDITION-SYSTEM
Boy/Male
Muslim
Wise
Boy/Male
Indian, Sanskrit
With Grey Horses
Boy/Male
Bengali, Indian
Lord of Courage
Girl/Female
Gujarati, Hindu, Indian
Cute
Girl/Female
Arabic, Muslim
Smell
Girl/Female
Greek
Named for the Sirens.
Boy/Male
Arabic, Australian
One who Saves
Boy/Male
Arabic, Muslim
Slave of the Manifest
Female
Norwegian
Norwegian feminine form of Scandinavian Benedikt, BENEDIKTE means "blessed."
Girl/Female
Hindu, Indian
Luck
VECTOR ADDITION-SYSTEM
VECTOR ADDITION-SYSTEM
VECTOR ADDITION-SYSTEM
VECTOR ADDITION-SYSTEM
VECTOR ADDITION-SYSTEM
n.
A literary work edited and published, as by a certain editor or in a certain manner; as, a good edition of Chaucer; Chalmers' edition of Shakespeare.
n.
The turning factor of a quaternion.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
a.
Added; supplemental; in the way of an addition.
n.
A pregnant woman; a mother; as, A has a son B by one venter, and a daughter C by another venter; children by different venters.
n.
The choosing and making that to be one's own which originally was not so; acceptance; as, the adoption of opinions.
n.
Anything added; increase; augmentation; as, a piazza is an addition to a building.
v. t.
To confer a doctorate upon; to make a doctor.
n.
An African weaver bird (Textor alector).
n.
The province of a rector; a parish church, parsonage, or spiritual living, with all its rights, tithes, and glebes.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
v. t.
To tamper with and arrange for one's own purposes; to falsify; to adulterate; as, to doctor election returns; to doctor whisky.
n.
A woman who wins a victory; a female victor.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
a.
Pertaining to a rector or a rectory; rectoral.
n.
The chief elective officer of some universities, as in France and Scotland; sometimes, the head of a college; as, the Rector of Exeter College, or of Lincoln College, at Oxford.
n.
A contrivance for removing superfluous ink or coloring matter from a roller. See Doctor, 4.
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
n.
Same as Radius vector.
a.
Of or pertaining to victory, or a victor' being a victor; bringing or causing a victory; conquering; winning; triumphant; as, a victorious general; victorious troops; a victorious day.