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• ###### displaystyle
• In mathematics, an initial algebra is an initial object in the category of F {\displaystyle F} -algebras for a given endofunctor F {\displaystyle F} . This initiality provides a general framework for induction and recursion. (wikipedia.org)
• An algebra for this endofunctor is a set X {\displaystyle X} (called the carrier of the algebra) together with a point x ∈ X {\displaystyle x\in X} and a function X → X {\displaystyle X\to X} . The set of natural numbers is the carrier of the initial such algebra: the point is zero and the function is the successor map. (wikipedia.org)
• end{aligned}}} Then the set N {\displaystyle \mathbf {N} } of natural numbers together with the function [ zero , succ ] : 1 + N → N {\displaystyle [\operatorname {zero} ,\operatorname {succ} ]\colon 1+\mathbf {N} \to \mathbf {N} } is an initial F {\displaystyle F} -algebra. (wikipedia.org)
• The constant A {\displaystyle A} denotes the initial attractiveness of the node. (wikipedia.org)
• Here m {\displaystyle m} denotes the initial number of links in the network. (wikipedia.org)
• As γ {\displaystyle \gamma } is higher than 3 it follows that the network is in the random network regime and as the number of initial nodes is higher it converges to the scale-free regime. (wikipedia.org)
• The same holds for the value of the initial attractiveness as A {\displaystyle A} is higher the more the network is into the random network regime. (wikipedia.org)
• In general topology and related areas of mathematics, the initial topology (or weak topology or limit topology or projective topology) on a set X {\displaystyle X} , with respect to a family of functions on X {\displaystyle X} , is the coarsest topology on X that makes those functions continuous. (wikipedia.org)
• Given a set X and an indexed family (Yi)i∈I of topological spaces with functions f i : X → Y i {\displaystyle f_{i}:X\to Y_{i}} the initial topology τ {\displaystyle \tau } on X {\displaystyle X} is the coarsest topology on X such that each f i : ( X , τ ) → Y i {\displaystyle f_{i}:(X,\tau )\to Y_{i}} is continuous. (wikipedia.org)
• The initial topology on X can be characterized by the following characteristic property: A function g {\displaystyle g} from some space Z {\displaystyle Z} to X {\displaystyle X} is continuous if and only if f i ∘ g {\displaystyle f_{i}\circ g} is continuous for each i∈I. Note that, despite looking quite similar, this is not a universal property. (wikipedia.org)
• X 0 {\displaystyle X_{0}} is called the vector of initial conditions or simply the initial condition, and contains nk pieces of information, n being the dimension of the vector X and k = 1 being the number of time lags in the system. (wikipedia.org)
• Here the constants c 1 , … , c k {\displaystyle c_{1},\dots ,c_{k}} are found by solving a system of k different equations based on this equation, each using one of k different values of t for which the specific initial condition x t {\displaystyle x_{t}} Is known. (wikipedia.org)
• ###### typically
• In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0). (wikipedia.org)
• In this case the k initial pieces of information will typically not be different values of the variable x at different points in time, but rather the values of x and its first k - 1 derivatives, all at some point in time such as time zero. (wikipedia.org)
• ###### specific
• All applicants to the Initial Teaching Credential Programs must meet specific admission requirements. (csusm.edu)
• All applicants to Initial Teaching Credential Programs must meet the Subject Matter Competence requirement specific to the program option and submit proof of completion in order to be considered for admission. (csusm.edu)
• In surveying, an initial point is a datum (a specific point on the surface of the earth) that marks the beginning point for a cadastral survey. (wikipedia.org)
• Various finite data structures used in programming, such as lists and trees, can be obtained as initial algebras of specific endofunctors. (wikipedia.org)
• ###### syllable
• Initial dropping is caused by the nature of stress in Australian languages: although stress is usually on the first syllable, the pitch peak of stress occurs late in the syllable, so that stress applies to the vowel and the following consonant, but not the preceding consonant. (wikipedia.org)
• ###### known
• In 2007, Rentokil sold the Initial Fire, Electronic Security and manned guarding businesses - previously known as Shorrock - to United Technologies Corporation. (wikipedia.org)
• Initial Rock, also known as Name Rock, in the Medora Ranger District of the Little Missouri National Grassland, near Medora, North Dakota, was listed on the National Register of Historic Places (NRHP) in 1976. (wikipedia.org)
• Initial was well known for releasing genre defining records from Falling Forward, Boysetsfire and Ink & Dagger, and creating the annual weekend long music festival, Krazy Fest. (wikipedia.org)
• Over the next few years Initial would blossom into one of independent music's most well known labels. (wikipedia.org)
• ###### Decisions
• Administrative Law Judges issued the following Initial Decisions pursuant to 5 U.S.C § 557 and 17 C.F.R. § 201.360(a). (sec.gov)
• ###### decorative
• Besides its most common meaning as the first letter of any word or name, an initial is a letter at the beginning of a written work, a chapter or a paragraph that is larger than the rest of the text and often decorative. (wikipedia.org)
• ###### Rule
• In the U.S. federal court system, initial conferences are governed by Rule 26 of the Federal Rules of Civil Procedure. (wikipedia.org)
• Unless all parties agree otherwise, the parties should submit to each other the Initial Disclosures under Rule 26(a) within 14 days after the conference. (wikipedia.org)
• ###### common
• In the Late Antique period both came into common use in Italy, the initials usually were set in the left margin (as in the third example below), as though to cut them off from the rest of the text, and about twice as tall as the other letters. (wikipedia.org)
• ###### however
• However, in line with suggestions from some of the others, I'm going to call it an INITIAL bioburden, not just bioburden on its own. (proz.com)
• However, evidence for the existence of an initial singularity, and the Big Bang theory itself, comes in the form of the cosmic microwave background and the continued expansion of the Universe. (wikipedia.org)
• ###### often
• After this period, in Gothic art large paintings of scenes tended to go in rectangular framed spaces, and the initial, although often still historiated, tended to become smaller again. (wikipedia.org)
• A principal meridian and base line are usually established based on a preselected initial point, often some distinct geographical feature. (wikipedia.org)
• ###### value
• Why not use a routine like this to calculate the initial value directly from windows settings? (iconico.com)
• The Joint Initial Condition Actuator block supplies the prismatic and revolute joint primitives of a Joint block with initial value data. (mathworks.com)
• Enter a value for the initial position of the primitive, either prismatic or revolute. (mathworks.com)
• In both differential equations in continuous time and difference equations in discrete time, initial conditions affect the value of the dynamic variables (state variables) at any future time. (wikipedia.org)
• In continuous time, the problem of finding a closed form solution for the state variables as a function of time and of the initial conditions is called the initial value problem. (wikipedia.org)
• ###### seen
• The difference between this and a true drop cap may be seen when the text extends below the initial. (wikipedia.org)
• ###### Example
• For example: With a drop cap, the initial sits within the margins and runs several lines deep into the paragraph, indenting some normal-sized text in these lines. (wikipedia.org)
• As an example, the first established initial point in California was the Mount Diablo meridian. (wikipedia.org)
• In Mbabaram for example, initial dropping doesn't occur if it results in a cluster other than nasal + stop. (wikipedia.org)
• ###### Several
• Several initial tests were undertaken in order to find the best way to remove corrosion and deposits from the surface. (kunsthaus.ch)
• While there may be several initial algebras for a given end functor, they are unique up to isomorphism, which informally means that the "observable" properties of a data structure can be adequately captured by defining it as an initial algebra. (wikipedia.org)
• Longtime Initial Records label chief Andy Rich now resides in Las Vegas where he works for Caesars Entertainment running several of their poker rooms. (wikipedia.org)
• Several topological constructions can be regarded as special cases of the initial topology. (wikipedia.org)
• ###### generally
• The converse fails, since generally the cylinder sets will only form a subbase (and not a base) for the initial topology. (wikipedia.org)
• For a system of order k (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension n (that is, with n different evolving variables, which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace the system's variables forward through time. (wikipedia.org)
• ###### necessary
• In the very early history of printing the typesetters would leave blank the necessary space, so that the initials could be added later by a scribe or miniature painter. (wikipedia.org)
• Here the dimension is n = 1 and the order is k, so the necessary number of initial conditions to trace the system through time, either iteratively or via closed form solution, is nk = k. (wikipedia.org)
• Here the number of initial conditions necessary for obtaining a closed form solution is the dimension n = 1 times the order k, or simply k. (wikipedia.org)
• ###### space
• To avoid having to hardcode handling for so many special cases into the kernel, an initial boot stage with a temporary root file-system - now dubbed early user space - is used. (wikipedia.org)
• The weak topology on a locally convex space is the initial topology with respect to the continuous linear forms of its dual space. (wikipedia.org)
• A topological space is completely regular if and only if it has the initial topology with respect to its family of (bounded) real-valued continuous functions. (wikipedia.org)
• Every topological space X has the initial topology with respect to the family of continuous functions from X to the Sierpiński space. (wikipedia.org)
• The initial singularity was a singularity of infinite density thought to have contained all of the mass and space-time of the Universe before quantum fluctuations caused it to rapidly expand in the Big Bang and subsequent inflation, creating the present-day Universe. (wikipedia.org)
• ###### Process
• To become accredited, a facility becomes an AABB Accredited Institutional member (AI) and completes ALL of the steps in the Initial Accreditation Process followed by a formal accreditation assessment. (aabb.org)
• An initial conference is one of the first steps of the discovery process in a civil case. (wikipedia.org)
• Only after the initial disclosures have been sent, the main discovery process begins, which includes: depositions, interrogatories, request for admissions (RFA) and request for production of documents(RFP). (wikipedia.org)
• In computing, initrd (initial ramdisk) is a scheme for loading a temporary root file system into memory, which may be used as part of the Linux startup process. (wikipedia.org)
• On February 4, the band announced Initial was in the process of being mixed. (wikipedia.org)
• ###### continuous
• The inverse limit of any inverse system of spaces and continuous maps is the set-theoretic inverse limit together with the initial topology determined by the canonical morphisms. (wikipedia.org)
• ###### list
• At minimum, the Initial Disclosures should list: People that may have discoverable information, their addresses and the subjects of information (including names of the opposite party). (wikipedia.org)
• ###### conditions
• The output is the connector port you connect to the Joint block whose initial conditions you want to set. (mathworks.com)
• Suppose you actuate a Joint with initial conditions, and that Joint has other Joints in a sequence connected to it through intermediate Bodies. (mathworks.com)
• Then the initial conditions applied to the first Joint change the absolute positions and velocities of the other Joints (as measured in World ) because the initial conditions of the other Joints are defined relative to the first. (mathworks.com)
• The initial conditions applied to a Joint indirectly affect the initial conditions of the other connected Joints only up to (but not including) the cut Joint. (mathworks.com)
• Select this check box if you want to actuate the primitive with initial conditions. (mathworks.com)
• that behavior is stable or unstable based on the eigenvalues of the matrix A but not based on the initial conditions. (wikipedia.org)
• Again the initial conditions do not affect the qualitative nature of the variable's long-term evolution. (wikipedia.org)
• The initial conditions do not affect the qualitative behavior (stable or unstable) of the system. (wikipedia.org)
• The initial conditions do not affect the qualitative nature of the system's behavior. (wikipedia.org)
• ###### little
• Very narrow mono-hull boats such as canoes and kayaks have little initial stability, but twin-hull W-kayaks are considerably more stable due to the fact that their buoyancy is distributed at a greater distance from their center line and therefore acts more effectively to reduce tilting. (wikipedia.org)
• ###### border
• The initial point for the Gila and Salt River meridian was established based on an existing marker that had been set up in 1851 to mark a point on the Mexico-United States border before the Gadsden Purchase. (wikipedia.org)
• ###### point
• The initial point establishes a local geographic coordinate system for the surveys that refer to that point. (wikipedia.org)
• An initial point is defined by the intersection of a principal meridian and a base line. (wikipedia.org)
• The initial point would be established where the meridian and the base line crossed, which turned out to be in the middle of a swamp in eastern Arkansas. (wikipedia.org)
• ###### period
• The initial singularity is part of the Planck epoch, the earliest period of time in the history of the universe. (wikipedia.org)
• ###### Connect
• You must add an Actuator port (connector port) to the Joint block to connect the Joint Initial Condition Actuator to it. (mathworks.com)
• ###### text
• In a written or published work, an initial or drop cap is a letter at the beginning of a word, a chapter, or a paragraph that is larger than the rest of the text. (wikipedia.org)
• The initial may sit on the same baseline as the first line of text, at the same margin, as it does here. (wikipedia.org)
• Alternatively, the initial may be in the left margin, with the text indented, as shown here. (wikipedia.org)
• In word processors and HTML, this may be implemented using a table with two cells, one for the initial and one for the rest of the text. (wikipedia.org)
• ###### small
• Initial stability is the resistance of a boat to small changes in the difference between the vertical forces applied on its two sides. (wikipedia.org)
• Wide mono-hull small boats such as the jonsboat have a great deal of initial stability and allow the occupants to stand upright to engage in fishing activities, and so do narrower small boats such as W-kayaks that feature a twin hull. (wikipedia.org)
• ###### Records
• Initial Records was an iconic Louisville based independent record label during the Nineties and early part of the new millennium. (wikipedia.org)
• Initial released records from hardcore punk to indie rock over its 12-year span. (wikipedia.org)
• The April 1998 issue of Playboy magazine declared Initial one of the country's ten hottest record labels alongside other notable labels such as P-Diddy owned Bad Boy Entertainment, DE based Jade Tree Records and legendary CA punk label Epitaph Records. (wikipedia.org)
• Krazy Fest was the brain child of Initial Records President Andy Rich. (wikipedia.org)
• Initial t. is an EP by the Japanese noise rock band Melt Banana, released in 2009 on Init Records. (wikipedia.org)
• ###### Configuration
• When you build your model, the geometric configuration of the Bodies (the home configuration ) implicitly specifies the initial positions/angles of bodies relative to one another and to World. (mathworks.com)
• ###### State
• All applicants to Initial Teaching Credential Programs must complete a graduate application to California State University San Marcos in order to be considered for admission. (csusm.edu)
• The initial values are the positions and velocities of the joint primitives and fully specify the initial state of motion (initial kinematic state ) of those primitives. (mathworks.com)
• The Joint Initial Condition Actuator applies the initial state along/about the joint axis in the reference coordinate system (CS) specified for that joint primitive in the Joint's dialog. (mathworks.com)
• Starting a simulation in this state sets all initial velocities to zero. (mathworks.com)
• ###### either
• The actual copies of the documents can be either attached with the Initial Disclosures, or more frequently provided later on the opposite party's request. (wikipedia.org)
• ###### name
• The "Initial" name originated as every towel was marked with the customer's initials, which ensured that customers only received their own towels. (wikipedia.org)
• National Register of Historic Places Registration: Initial Rock / Name Rock" (PDF). (wikipedia.org)
• ###### allow
• Other languages allow initial dropping, dropping additional consonants if needed to simplify the cluster. (wikipedia.org)
• ###### Press
• The May 1998 issue of Alternative Press Magazine named Initial as one of "Ten independent labels that have helped to change not only the way hardcore sounds, but the way it does business. (wikipedia.org)
• ###### load
• If it is not sterilised, then it is the initial load of bacteria on the packing before it is sent out. (proz.com)
• The bootloader will load the kernel and initial root file system image into memory and then start the kernel, passing in the memory address of the image. (wikipedia.org)
• ###### linear
• You set the initial linear and/or angular positions and velocities in the block's dialog, so there is no input signal. (mathworks.com)
• ###### similar
• I'd use initial or something similar instead of residual (see my answer). (proz.com)
• ###### category
• In the language of category theory, the initial topology construction can be described as follows. (wikipedia.org)
• ###### Guide
• Our School of Education Initial Teaching Credential Programs Admission Application Companion Guide provides complete details related to requesting and submitting CSET scores. (csusm.edu)
• ###### points
• Some initial points were chosen based on existing markers. (wikipedia.org)
• Many of the initial points in the United States have been listed on the National Register of Historic Places. (wikipedia.org)
• ###### sets
• All applicants to Initial Teaching Credential Programs must submit two sets of official transcripts in order to be considered for admission. (csusm.edu)
• ###### time
• Parties must supplement their Initial Disclosures each time when they discover new witnesses or documents that they want to use in court to support their claims or defenses. (wikipedia.org)
• ###### model
• The initial attractiveness is a possible extension of the Barabási-Albert model (preferential attachment model). (wikipedia.org)