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when making an ensemble weather forecast: initial condition uncertainty and model uncertainty. Initial condition uncertainty arises due to errors in the

process at a given time in the future depend continuously on the initial condition of the process. The concept is named after Croatian-American mathematician

{sgn}(X_{t})\,\mathrm {d} B_{t},} driven by canonical Brownian motion B, with initial condition X0 = 0, where sgn denotes the sign function sgn ⁡ ( x ) = { + 1 ,

equation: d P d t = r P {\displaystyle {\frac {dP}{dt}}=rP} with initial condition: P(0)= P0 This model is often referred to as the exponential law.

hyperbolic equation. The solution to the equation and along with the initial condition ∂ u ∂ t + u ∂ u ∂ x = 0 , u ( x , 0 ) = f ( x ) {\displaystyle {\frac

number of generations it takes before the pattern returns to its initial condition is called the period of the oscillator. An oscillator with a period

carbon cycle, atmospheric chemistry, land use etc. can be perturbed. Initial condition ensembles involve the same model in terms of the same atmospheric

liveness properties. For example, CTL can specify that when some initial condition is satisfied (e.g., all program variables are positive or no cars

with its Borel σ {\displaystyle \sigma } -algebra, such that: 1. (Initial Condition) The process starts at ξ {\displaystyle \xi } at time τ {\displaystyle

this minimum number of steps will be at most N (depending on the initial condition), provided that the system is null controllable (that it can be brought

fluctuations of the asymmetric simple exclusion process (ASEP) with step initial condition, and in simplified mathematical models of the behavior of the longest

mapping from the truncated initial condition has deviated exponentially from the mapping from the true initial condition. And since our simulation has

matrix functions, and x 0 {\displaystyle \mathbf {x} _{0}} is the initial condition at t 0 {\displaystyle t_{0}} . Using the state-transition matrix Φ

bodies, except such as at the close of the processes are left in their initial condition. The initial state of the body, according to Gibbs, is supposed to

Executive Order 10450 of 1953. Executive Order 12968 required as an initial condition of access to classified information the filing of financial disclosure

solutions to the dispersion relation may be complex-valued. Now, an initial condition y ( x , 0 ) {\displaystyle y(x,0)} can be written as a superposition

{\displaystyle \partial _{q}\Omega } , η o {\displaystyle \eta _{o}} is the initial condition, and m {\displaystyle m} is the outward normal to ∂ Ω {\displaystyle

systems, a direct cause-and-effect relationship exists between the initial condition and the final state of the system: When a computer's 'on' switch is

patterns form in any sufficiently sparse and sufficiently large random initial condition for Life. This result leads to standard collision sequences for many

y(t)={\frac {k}{c}}+f(y_{0})e^{-ct}} where y 0 {\displaystyle y_{0}} is any initial condition for the initial value problem. However, the above model assumes that

}^{-1}(t_{0})} . The solution of the linear differential equation with the initial condition x ( 0 ) = x 0 {\displaystyle x(0)=x_{0}} is x ( t ) = ϕ ( t ) ϕ −

property of being trace-preserving and completely positive for any initial condition. The Schrödinger equation or, actually, the von Neumann equation,

widely used to make circuit analysis simpler and to study a circuit's initial-condition and steady-state response. Thévenin's theorem can be used to convert

is determined by the initial condition N(0). The solution can also be written as a weighted harmonic mean of the initial condition and the carrying capacity

c , 0 ≤ t ≤ d {\displaystyle b\leq x\leq c,\;0\leq t\leq d} with initial condition u ( x , 0 ) = u 0 ( x ) {\displaystyle u(x,0)=u_{0}(x)\,} and the

storage of the diving spread, and where relevant, restoring the site to initial condition. Mobilization is the converse process. Demobilisation of the British

This also shows that given λ i {\textstyle \lambda _{i}} and the initial condition c i ( 0 ) {\textstyle c_{i}(0)} , the solution at any time t can be

failing to reach thermal equilibrium, and retaining a memory of its initial condition in local observables for infinite times. Textbook quantum statistical

be reached from an initial condition. Because of energy conservation, only the states with the same energy as the initial condition are accessible. The

{\displaystyle dX_{t}=\Phi (X_{t-})dL_{t}} exists for each deterministic initial condition x ∈ R d {\displaystyle x\in \mathbb {R} ^{d}} and yields a Feller

initial state x (e.g., all voltage–current trajectories for a given initial condition of the system). A system is considered passive if EA is finite for

conditions, a floating node in a circuit represents an error because its initial condition is unknown unless it is somehow fixed. This generates two problems:

by the capillary length. The solution of the equation requires an initial condition for position, and the gradient of the surface at the start point.

ergodic properties so that after initially flowing away from its initial condition it would generate samples from the posterior probability model. Jump

the deducible statement Q {\displaystyle Q} can be broken into an initial condition and a prediction as in C ⇒ P {\displaystyle C\Rightarrow P} in which

solution to a stochastic differential equation) if, whenever the initial condition Z 0 {\displaystyle Z_{0}} is distributed according to μ , {\displaystyle

the time evolution of the system, one only needs to determine the initial condition of the state function |Ψ(t) and its first derivative with respect

( x ) Initial condition {\displaystyle {\begin{cases}u_{t}=ku_{xx}&(x,t)\in \mathbb {R} \times (0,\infty )\\u(x,0)=g(x)&{\text{Initial condition}}\end{cases}}}

)=0} , which may be solved using the method of images. Based on the initial condition, the fundamental solution to the Fokker-Planck equation, denoted by

climbing. It iteratively does hill-climbing, each time with a random initial condition x 0 {\displaystyle x_{0}} . The best x m {\displaystyle x_{m}} is

{\displaystyle z_{x}} sequence; however, the initial condition is the same for encryption. The initial condition of the LFSR for decryption varies on the

\left\langle {n-1 \atop k}\right\rangle \!\!\right\rangle ,} with initial condition for n = 0, expressed in Iverson bracket notation: ⟨ ⟨ 0 k ⟩ ⟩ = [

formulas as illustrated below on the examples given above. Setting the initial condition w 0 {\displaystyle w_{0}} equal to zero and denoting Laplace transforms

{\displaystyle \sigma \in {\mathcal {K_{\infty }}}} so that for any initial condition x 0 ∈ R n {\displaystyle x_{0}\in {\mathbb {R} }^{n}} and for any

_{k+1}p_{k+1}(t)-(\lambda _{k}+\mu _{k})p_{k}(t),k=1,2,\ldots ,\,} and the initial condition ∑ k = 0 ∞ p k ( t ) = 1. {\displaystyle \sum _{k=0}^{\infty }p_{k}(t)=1

for this random dynamical system would be to require that for any initial condition x 0 ∈ X {\displaystyle x_{0}\in X} , φ ( t , ω ) x 0 → A {\displaystyle

starts to define "I" and separate him or herself from an adult is the initial condition for and the result of role play. There are also experiments that found

q_{2}} represent the envelope of the electromagnetic field as an initial condition. For theoretical purposes, the integral equation version is often

{\displaystyle y(t)} over time depends on the initial condition y ( 0 ) {\displaystyle y(0)} . If the initial condition is positive ( y ( 0 ) > 0 {\displaystyle

{\displaystyle {\frac {dy}{dt}}=-y^{2},\ t\in [0,a]\quad \quad (2)} with the initial condition y ( 0 ) = 1. {\displaystyle y(0)=1.} Consider a grid t k = a k n {\displaystyle

{\displaystyle f(x+1)=\left(1+{\frac {i}{\sqrt {x+1}}}\right)\cdot f(x),} the initial condition f ( 0 ) = 1 , {\displaystyle f(0)=1,} and monotonicity in both argument

Since Q-learning is an iterative algorithm, it implicitly assumes an initial condition before the first update occurs. High initial values, also known as

"inferior condition", referring both to his physical height and to his initial condition as a slave. He could do, however, what was not allowed to anyone else:

Lorentz-invariant, but the Gibbs probability density is not a Lorentz-invariant initial condition). A classical continuous random field can be constructed that has

Since SARSA is an iterative algorithm, it implicitly assumes an initial condition before the first update occurs. A high (infinite) initial value, also

severe contact dermatitis which is often hard to distinguish from the initial condition. As a consequence, the European Medicines Agency recommended to withdraw

any process to one which includes the complete history from a given initial condition and it would be made to be Markovian. But the state space would be

the solution y by the polynomial p of degree n which satisfies the initial condition p ( t 0 ) = y 0 {\displaystyle p(t_{0})=y_{0}} , and the differential

Schrödinger equation (with 2Δx, m, and ħ set equal to one) satisfying the initial condition ψ ( x , 0 ) = 2 / π 4 exp ⁡ ( − x 2 + i k 0 x ) , {\displaystyle \psi

c 0 {\displaystyle c_{0}} is an arbitrary shift dependent on the initial condition x ( 0 ) {\displaystyle x(0)} (specifically by the formula c 0 = arctan

The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a

{\displaystyle b,a} and σ {\displaystyle \sigma } , together with the initial condition r 0 {\displaystyle r_{0}} , completely characterize the dynamics,

problem for the wave equation with the time-asymmetric homogeneous initial condition [ ∂ τ 2 − ρ − 1 ∂ ρ ( ρ ∂ ρ ) − ∂ z 2 ] ψ ( τ , ρ , z ) = s ( τ ,

and one might say that the variable x depends on the time t and the initial condition x = x0. Examples are given below. In the case of a flow of a vector

studies, which either aim to reproduce a possible evolution of a given initial condition over time or a statistical (quasi) steady-state of a given system

point, then the value of M from the subsonic equation is used as the initial condition for fixed point iteration of the supersonic equation, which usually

transition rate matrix. The formal solution is constructed from the initial condition P ( 0 ) {\displaystyle \mathbf {P} (0)} (that defines that at t =

date. Observations of superclusters can give information about the initial condition of the universe, when these superclusters were created. The directions

}{\partial q_{1}}}L_{d}\left(t_{1},t_{2},q_{1},q_{2}\right).} Given an initial condition ( q 0 , q 1 ) {\displaystyle (q_{0},q_{1})} , and a sequence of times

x^{2}}},} which is the simplest form of a diffusion equation. If the initial condition is p ( x , 0 ) = δ ( x ) {\displaystyle p(x,0)=\delta (x)} , the solution

variables are the shadow prices. The state equation is subject to an initial condition and is solved forwards in time. The costate equation must satisfy

analytic, found by Jaap Fabius (1966). This function satisfies the initial condition f ( 0 ) = 0 {\displaystyle f(0)=0} , the symmetry condition f ( 1

produces no unique solution, but an aggregate of many solutions. At initial condition, the nodes carry a label that denotes the community they belong to

t_{1}} taking the current state x ( t ) {\displaystyle x(t)} as "new" initial condition must be optimal for the remaining problem. If the value function happens

and is then added back to the control to create the new perturbed initial condition. After a short transient period, this "breeding" process creates bred

destroyed much of the social fabric of the valley and perhaps were the initial condition for the emergence of terrible epidemics (typhus, smallpox, etc.) which

t+\sigma {\frac {\sqrt {\Delta t}}{2}}\,(R_{t}+R_{t+\Delta t}),} with initial condition X 0 := X ( 0 ) {\displaystyle X_{0}:=X(0)} , and where X t ≈ X ( t

hopes the station would 'open up' access to the area, and on the initial condition that the cost of the station would be refunded when profits over three

probability distribution. The outcomes may diverge largely although the initial condition of threshold may only differ very slightly. This threshold model of

was hovering over the face of the waters. Genesis 1:2 presents an initial condition of creation - namely, that it is tohu wa-bohu, formless and void.

methods → it is more accurate than the Euler method. In this method, an initial condition is required: y = y0 at x = x0. The problem is to find the value of

prophylactic antibiotics are sometimes used after resolution of the initial condition. The disease prognosis includes: Spread of infection to other areas

that even though the initial condition of the (2,3) Turing machine is not repetitive, the construction of that initial condition is not universal. Hence

needed] The butterfly effect theory proposes: "Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the

Pittsburgh. April 9, 1920. p. 1. "The Unexpected Hero of Light," Initial Condition podcast, Episode 9 Works by or about John Brashear at the Internet

the first N elements of the array are valid values. The Default_Initial_Condition of the Stack type, by specifying an empty stack, ensures the initial

the motion of the plate, there is no imposed pressure gradient. The initial condition is not required because of periodicity. Since both the equation and

the initial value problem defined by Hamilton's equations and the initial condition r ( t = 0 ) = r 0 ∈ R 2 N {\displaystyle {\boldsymbol {r}}(t=0)={\boldsymbol

X_{t}=b(X_{t})\,\mathrm {d} t+\mathrm {d} B_{t}} with square-integrable initial condition, i.e. X0 ∈ L2(Ω, Σ, P; Rd). Then the following are equivalent: The

Thus, the cocycle property can be read as saying that evolving the initial condition x 0 {\displaystyle x_{0}} with some noise ω {\displaystyle \omega

because jumps usually cause a pipeline stall. Additionally, if the initial condition is known at compile-time and is known to be side-effect-free, the

called Amoeba that evolved self-replication from a randomly seeded initial condition. More recently REvoSim - a software package based around binary digital

magnetic flux inside a perfect conductor will vanish depends on the initial condition (whether it's zero-field cooled or not). It is also possible to justify

{\displaystyle {\frac {\partial \psi }{\partial t}}(t,x)=P\psi (t,x)} with initial condition ψ ( 0 , x ) . {\displaystyle \psi (0,x).} Knowing ψ {\displaystyle

(GEM) Daily Frequency 0000 UTC and 1200 UTC Forecast Length 16 days Initial Condition Uncertainty Ensemble Kalman Filter (EnKF) Control 1 NWS + 1 MSC Ensemble

differential equation together with a specified value, called the initial condition Intravenous pyelogram, a radiological procedure used to visualize

differential equations. Such linear PDE's have a unique solution for a given initial condition. In quantum field theory, an operator valued distribution is a free

standard r-dimensional Brownian motion, independent of B and the initial condition Y0, and c : [0, +∞) × Rn → Rn and γ : [0, +∞) × Rn → Rn×r satisfy

{\displaystyle m} and v > 0 {\displaystyle v>0} are real constants and for an initial condition X 0 {\displaystyle X_{0}} , is called an Arithmetic Brownian Motion

x(t)=ke^{-At}+{\frac {C}{A}}} where k {\displaystyle k} is a constant encoding the initial condition. Eliasmith, Anderson, Chris, Charles (2003). Neural Engineering. Cambridge

integrated with the original signal x n {\displaystyle x_{n}} as initial condition. This was the original approach. Alternatively, since this is a convex

sensitive to initial conditions. It suggests that a small change in an initial condition can completely alter the progression of a system. This phenomenon

symptoms of his disease as beginning in October 2013. Williams's initial condition included a sudden and prolonged spike in fear, anxiety, stress, and

t}}=D{\frac {\partial ^{2}p(x,t\mid x_{0})}{\partial x^{2}}},} given the initial condition p ( x , t = 0 ∣ x 0 ) = δ ( x − x 0 ) {\displaystyle p(x,t={0}\mid

larger than N {\displaystyle N} and computes a trial solution taking initial condition a M {\displaystyle a_{M}} to an arbitrary non-zero value (such as

{\displaystyle h(t)={\frac {f(t)}{R(t)}}=-{\frac {R'(t)}{R(t)}}} with initial condition R ( 0 ) = 1 {\displaystyle R(0)=1} , which yields F ( t ) = 1 − exp

understood, it is natural to ask next whether a small change in the initial condition will lead to similar behavior. Stability theory addresses the following

θ π ) {\displaystyle x_{n}=\sin ^{2}(2^{n}\theta \pi )} where the initial condition parameter θ {\displaystyle \theta } is given by θ = 1 π sin − 1 ⁡

\alpha _{1}} and β 1 {\displaystyle \beta _{1}} . Now given some initial condition ( G 0 , σ 0 2 ) {\displaystyle (G_{0},\sigma _{0}^{2})} , the system

Example of iterating the initial condition x0 = 0.4 over the tent map with μ = 1.9.

description of the history of the component starting from the sound initial condition of a homogeneous, isotropic and stress free melt resp. gas phase and

{ S − K , 0 } {\displaystyle C(S,T)=\max\{S-K,0\}} now becomes an initial condition u ( x , 0 ) = u 0 ( x ) := K ( e max { x , 0 } − 1 ) = K ( e x − 1

states?", or "Does the long-term behavior of the system depend on its initial condition?" An important goal is to describe the fixed points, or steady states

The solution of this differential equation, by integration from the initial condition, is Δ T ( t ) = Δ T ( 0 ) e − t / τ . {\displaystyle \Delta T(t)=\Delta

expansion of the universe can be understood as resulting from an initial condition in which the contents of the universe are flying apart. The mutual

Essays on Buddhism and Psychology (Curzon 1997) "The Complexity of the Initial Condition." In The International Journal of Transpersonal Studies, vol. 16,

imply both conditions in characterization 4. Indeed, one gets the initial condition f(0) = 1 by dividing both sides of the equation f ( 0 ) = f ( 0 +

flow is reduced to the initial condition which forms the coordinates encoding the diffeomorphism. From the initial condition v 0 {\displaystyle v_{0}}

mamba that was part of his personal collection of exotic animals. His initial condition was very serious, but he recovered after extensive treatment involving

temperature, degree of compaction, moisture content, etc. Depending on the initial condition of the snow, grooming may achieve an increase in density for new-fallen

mapping between an initial state and a final state. Starting from an initial condition and moving forward in time, a deterministic process always generates

x t + 1 = A x t {\displaystyle x_{t+1}=Ax_{t}} starting from the initial condition x 0 = c {\displaystyle x_{0}=c} is solved by x t = A t c {\displaystyle

differential equation x ′ ( t ) = x 2 {\textstyle x'(t)=x^{2}} , with initial condition x ( 0 ) = x 0 {\displaystyle x(0)=x_{0}} , has as its unique solution

suffers from a structural defect, often related to its cartilage. This initial condition, known as a "primary lesion", causes an abnormal level of wear and

solution to the differential equation ⁠dfx/dt⁠(t) = x fx(t), with initial condition fx(0) = 1; it follows that fx(t) = etx for every t in R. Given a Lie

}(t)=\alpha \left(1-\left({\frac {Y}{K}}\right)^{\nu }\right)Y} with initial condition Y ( t 0 ) = Y 0 {\displaystyle Y(t_{0})=Y_{0}} where Q = − 1 + ( K

solution is then a linear combination of these; when fitted to the initial condition φ ( x , 0 ) {\displaystyle \varphi (x,0)} , the general solution reduces

^{ij}} , this equation, subjected to the integral condition and the initial condition w + ( x , t 0 ) = w 0 ( x ) {\displaystyle w_{+}(x,t_{0})=w_{0}(x)}

t}}={\frac {1}{2}}{\frac {\partial ^{2}w}{\partial x^{2}}}-uV(x)w} with initial condition w(x, 0) = f(x). In practical applications, the Feynman–Kac formula

{\displaystyle {\frac {dy}{dx}}=-{\frac {\sqrt {a^{2}-x^{2}}}{x}}} with the initial condition y(a) = 0. Its solution is y = ∫ x a a 2 − t 2 t d t = a ln ⁡ a + a

localisation (MBL), quantum many-body systems retaining memory of their initial condition in local observables for arbitrary amounts of time. Other systems

Mandelbrot set is the set of values of the parameter c for which the initial condition z0 = 0 does not cause the iterates to diverge to infinity. A critical

where they showed that mathematical singularities were an inevitable initial condition of relativistic models of the Big Bang. Then, from the 1970s to the

straightforward to design economic models susceptible to butterfly effects of initial-condition sensitivity. However, the econometric research program to identify

  initial condition of EL geodesic φ ˙ 0 = v 0 , φ 0 = i d , φ 1 = φ   . {\displaystyle \log _{\rm {id}}(\varphi )=v_{0}\ {\text{initial condition of

v)+V(t,x).\,} The differential equations are to be solved with the initial condition x ( t 0 ) = x 0 , v ( t 0 ) = v 0 . {\displaystyle x(t_{0})=x_{0}

via the equation Y ˙ = J Y {\displaystyle {\dot {Y}}=JY} with the initial condition Y i j ( 0 ) = δ i j {\displaystyle Y_{ij}(0)=\delta _{ij}} . The matrix

{aw_{t}+b}{cw_{t}+d}}.} When a , b , c , d {\displaystyle a,b,c,d} and the initial condition w 0 {\displaystyle w_{0}} are real numbers, this difference equation

w ) {\displaystyle \displaystyle {{dw \over dt}=-wp_{t}(w)}} with initial condition w ( s ) = z {\displaystyle w(s)=z} . To obtain the differential equation

of these differences will be magnified or minimized based on the initial condition of the fruit after harvest (with moldy, damaged, sun-burnt or botryized

program, and infinitely repeating, the patterns of 0s and 1s at the initial condition can be represented by an infinitely repeating string. Each production

produce very different operations for tetration and beyond. Another initial condition that has been used is A ( 0 , b ) = 2 b + 1 {\displaystyle A(0,b)=2b+1}

parameter of 10 ms (.tran 10mS), 2) a SPICE directive to set the initial condition of RC "out" net to zero volts (.ic v(OUT)=0V), and 3) a text comment

, {\displaystyle n!=n(n-1)!\quad {\text{for}}\quad n>0,} and the initial condition 0 ! = 1. {\displaystyle 0!=1.} A graph is commonly used to give an

universality class - the PNG droplet - converges under suitable scaling and initial condition to the Airy2 process and that it is a stationary process with almost

the fine-scale simulator estimate local time derivatives. Given an initial condition for the coarse variables U ( t k ) {\displaystyle U(t_{k})} at time

perturbed physics ensembles (PPE), multi-model ensembles (MME), or initial condition ensembles (ICE). As the spatial resolution of the underlying GCMs

within. It is convenient to identify a reference configuration or initial condition which all subsequent configurations are referenced from. The reference

can be multiple distinct self-consistent extensions for the same initial condition—indeed, Echeverria et al. found an infinite number of consistent extensions

starts like Free style (crawl), breaststroke and butterfly. But at initial condition, while start and going into the water hands are moved up straight

Pentaradiality as a plesiomorphy Supporters of pentaradiality as an initial condition of the phylum note that radial forms are the first uncontested echinoderms

nuclear magnetization in the rotating frame at time t = 0. This is the initial condition for the differential equation. Note that when the rotating frame of

every case, X always has exactly two Jewish grandparents. Unless this initial condition applies, there is no point in applying these tests, as the categorization

is p t = p t − 1 r − A {\displaystyle \;p_{t}=p_{t-1}r-A} And the initial condition is p 0 = P {\displaystyle \;p_{0}=P} The principal immediately after

for Γ k {\displaystyle \Gamma _{k}} must be supplemented with the initial condition Γ k → Λ = S {\displaystyle \Gamma _{k\to \Lambda }=S} , where the

S2CID 6691714. Tracy, C. A.; Widom, H. (2009), "Asymptotics in ASEP with step initial condition", Communications in Mathematical Physics, 290 (1): 129–154, arXiv:0807

{\displaystyle v_{in}(t)=v_{L}(t)+v_{R}(t)=L{\frac {di}{dt}}+Ri} With initial condition: i ( 0 ) = i 0 {\displaystyle i(0)=i_{0}} Which can be solved by Laplace

x + 2 x F = 1 {\displaystyle {\frac {dF}{dx}}+2xF=1\,\!} with the initial condition F ( 0 ) = 0. {\displaystyle F(0)=0.} Consequently, it has extrema

(X_{t})\,\mathrm {d} B_{t}.} Let Px denote the law of X given the initial condition X0 = x, and let Ex denote expectation with respect to Px. Let LX be

equation) P ′ ( t ) = P ( t ) Q {\displaystyle P'(t)=P(t)Q} with initial condition P(0) is the identity matrix. If the state space is finite, the transition

limit ( X ¯ {\displaystyle {\bar {X}}} ) must be independent of the initial condition at t 0 {\displaystyle t_{0}} . In the case of a chaotic dynamical

meaning the iterates do not converge. For example, if one uses a real initial condition to seek a root of x2 + 1, all subsequent iterates will be real numbers

{OUT}}(t)\right)\,\mathrm {d} t.} The general solution is obtained by fixing the initial condition time t 0 {\displaystyle t_{0}} , leading to the integral equation:

stochastic or random process there is some indeterminacy: even if the initial condition (or starting point) is known, there are several (often infinitely

control mode v ∈ V {\displaystyle v\in V} three predicates. Each initial condition init ( v ) {\displaystyle (v)} is a predicate whose free variables

}^{\text{S}}(t)+\sum _{\nu }c_{\nu }(t)\psi _{\nu }^{\text{T}}(t)} with the initial condition c ν ( 0 ) = 0 {\displaystyle c_{\nu }(0)=0} . When the new wave function

f:[t_{0},\infty )\times \mathbb {R} ^{d}\to \mathbb {R} ^{d}} , and the initial condition y 0 ∈ R d {\displaystyle y_{0}\in \mathbb {R} ^{d}} is a given vector

because jumps usually cause a pipeline stall. Additionally, if the initial condition is known at compile-time and is known to be side-effect-free, the

t\mid x',t')} is the solution of the Fokker–Planck equation with initial condition P ( x , t ′ ) = δ ( x − x ′ ) {\displaystyle P(x,t')=\delta (x-x')}

along ACD. So the remaining analysis is the same, accommodating the initial condition that the maximal r {\displaystyle r} is R cos ⁡ θ = A O {\displaystyle

x ≥ 0 {\displaystyle u'(t)=2tu(t),\,\,\,\,\,\,\,x\geq 0} and the initial condition: u ( 0 ) = 1 {\displaystyle u(0)=1} If we integrate both sides of

continuous Kinematic wave equation when the density specified in the initial condition changes gradually. However, CTM replicates discontinuities and shock

for the parameter r and performing calculations starting from an initial condition x 0 {\displaystyle x_{0}} , we obtain the sequence x 0 {\displaystyle

demonstrated that, to create an imbalance in matter and antimatter from an initial condition of balance, the Sakharov conditions must be satisfied, one of which

{\mathcal {O}}(\varepsilon ^{2})} terms. Uniformity with respect to the initial condition x 0 {\displaystyle x_{0}} : if we vary x 0 {\displaystyle x_{0}} this

{c}}_{3}={\frac {i}{2}}(\Omega _{p}c_{1}+\Omega _{c}c_{2}).} Using the initial condition | ψ ( 0 ) ⟩ = c 1 ( 0 ) | 1 ⟩ + c 2 ( 0 ) | 2 ⟩ + c 3 ( 0 ) | 3 ⟩

acknowledged that any useful model must not only account for the initial condition of the material but also the constantly changing relationship between

semimartingale X can be defined as the solution to the SDE dY = Y dX with initial condition Y0 = 1. It is sometimes denoted by Ɛ(X). Applying Itô's lemma with

polynomial vector field p such that for any f and ε there exists some initial condition of the differential equation y' = p(y) that yields a unique and analytic

differential equation for ⁠ φ {\displaystyle \varphi } ⁠, with the initial condition ⁠ φ ( x 0 ) = y 0 {\displaystyle \varphi (x_{0})=y_{0}} ⁠. Since ∂

t) → 0 as |r| → ∞. For the 1D free-space problem with point-source initial condition, f (x, p, 0) = δ(x - x')δ(p - p'), the solution which is a bivariate

owned by a few entrepreneurs eventually approaches 100%. Given an initial condition in which wealth is unevenly distributed (i.e., a "wealth gap"), several

F[ρ(t, ·)] still makes sense for each time t ≥ 0, provided that the initial condition has F[ρ(0, ·)] < +∞. The free energy functional F is, in fact, a Lyapunov

differential equation for Ψ ( x , t ) {\displaystyle {\Psi }(x,t)} with initial condition Ψ ( x , 0 ) = x i {\displaystyle \Psi (x,0)=x^{i}} . After some manipulations

generator, Logic analyzer, Logic probe, Logic Pulser Simulation Controls Initial Condition and Nodeset devices Miscellaneous Optoisolators, Photodiodes, Voltage

{M}}} as a material surface (see Fig. 1). Since any choice of the initial condition set M ( t 0 ) {\displaystyle {\mathcal {M}}(t_{0})} yields an invariant

heqats in one day". In other words, the daily rate of consumption (and initial condition) i {\displaystyle i} is equal to 2 + 1/2. Determine the number of

required. The syntax of the JavaScript for loop is as follows: for (initial; condition; loop statement) { /* statements will be executed every time the for{}

satisfies a sort of recurrence relation. This recurrence relation has the initial condition v ( ε ) = 0 {\displaystyle v\left(\varepsilon \right)=0} where ε {\displaystyle

part of growing relations between the two countries at the time. The initial condition of the vessels was unclear and they subsequently went through various

the system taking states at time t′ to states at time t. Note the initial condition enforced by lim t → t ′ K ( x , t ; x ′ , t ′ ) = δ ( x − x ′ ) .

take account of the irreversibility by restoring the system to its initial condition by running a cycle, for example a Carnot cycle, that includes the

solution of the KdV equation ut + uux + δ2uxxx = 0 (δ = 0.022) with an initial condition u(x, 0) = cos(πx). Time evolution was done by the Zabusky–Kruskal

a property of the dynamical law and does not require any special initial condition. Mercati, Flavio (2014). "A Shape Dynamics Tutorial". arXiv:1409.0105

a spatially periodic pattern even from a random or almost uniform initial condition. Prior to the discovery of this instability mechanism arising due

is to say, the shock wave has travelled enough to forget about the initial condition. Since the shock wave in the self-similar region is strong, the pressure

matrix ρ that is trace-preserving and completely positive for any initial condition is the Gorini–Kossakowski–Sudarshan–Lindblad equation or GKSL equation:

Initial condition Reconstruction for which old photographs were utilized

the squared mass of those particles is positive. Now consider an initial condition where at time t=0, all the pendulums are pointing straight up. Clearly

A forward equation for | ψ ⟩ {\displaystyle |\psi \rangle } with initial condition | ψ ( 0 ) ⟩ = | ϕ i ⟩ {\displaystyle |\psi (0)\rangle =|\phi _{i}\rangle

represent the level set of the underlying Hamiltonian. Note that the same initial condition used for this quantum propagation as well as for the KvN propagation

In two dimensions, the mean squared displacement corresponding to initial condition f (r, ŝ, 0) = δ(r)/(2π) is ⟨ r 2 ⟩ = 2 v 0 2 α 2 ( 1 − σ 1 ) [ α t

controls the positioning and composition of squads on both sides, their initial condition and supply levels, the location of flags, the default opponent, and

}(z)-\alpha _{n}z\Phi _{n}(z)} for n ≥ 0 {\displaystyle n\geq 0} and initial condition Φ 0 = 1 {\displaystyle \Phi _{0}=1} , with Φ n ∗ ( z ) = z n Φ n (

that had been calling for the return of Lebanon's borders to their initial condition – prior to the Protocol of 1861 – as per the map laid down by the

ordinary differential equations, which has a unique solution for any initial condition given by the second condition (for instance, by the Picard–Lindelöf

jointly conducted by CarTrade engineers and sellers who inspect the initial condition of cars at different levels, and a detailed condition report is presented

through the cold vessel where it cools the rock while warming to its initial condition. The energy is recovered as electricity by reversing the cycle. The

equation d y d x = − κ y {\displaystyle {\frac {dy}{dx}}=-\kappa y} with initial condition y ( 0 ) = y 0 {\displaystyle y(0)=y_{0}} . We can approximate a solution

t}}=D{\frac {\partial ^{2}p(x,t\mid x_{0})}{\partial x^{2}}},} given the initial condition p ( x , t = 0 ∣ x 0 ) = δ ( x − x 0 ) {\displaystyle p(x,t=0\mid x_{0})=\delta

{\displaystyle f'\!(x)\!=\!-\!\,{\frac {x-\mu }{\sigma ^{2}}}f(x)} with an initial condition set by the probability axiom ∫ − ∞ ∞ f ( x ) d x = 1 {\displaystyle

communication components, it has been shown that even with an approximate initial condition (in the case of this work, an initial sinusoidal beating), a profile

) = 0 {\displaystyle \sigma (\mathbf {x} )=\mathbf {0} } from any initial condition Having reached σ ( x ) = 0 {\displaystyle \sigma (\mathbf {x} )=\mathbf

identify all possible new stationary states, and also the case where the initial condition was just the spontaneous state, to identify when the spontaneous state

t}}=\nu {\frac {\partial ^{2}u}{\partial y^{2}}}} subject to the initial condition u ( y , 0 ) = 0 , 0 < y < h , {\displaystyle u(y,0)=0,\quad 0<y<h

describes the ability of an external input to move the output from any initial condition to any final condition in a finite time interval. It is not necessary

expression above) and so has a unique solution for each possible initial condition. That is, for each vector v {\displaystyle v} in E x {\displaystyle

equation Y ′ − A   Y = F ( t ) {\displaystyle Y'-A\ Y=F(t)} with the initial condition Y(t0) = Y0, where A is an n by n complex matrix, F is a continuous

switch to its default position after pressing twice, changing the initial condition of the electrical circuit or restaurant, connecting or blocking the

and momentum p ′ {\displaystyle \mathbf {p} '} , corresponding to initial condition f ( r , p , 0 ) = δ ( r − r ′ ) δ ( p − p ′ ) {\displaystyle f(\mathbf

that can be warped, twisted, pulled or stretched as desired. The initial condition of the fields is recorded on a Cartesian mesh. As the elastic medium

is seen, for a four cell neighborhood and a square grid, when the initial condition consists of a half line of excited cells (1's) going off to infinity

which an ordinary differential equation is given together with an initial condition, plays a central role in all natural and engineering sciences and

the test equation y ′ = k y {\displaystyle y'=ky} subject to the initial condition y ( 0 ) = 1 {\displaystyle y(0)=1} with k ∈ C {\displaystyle k\in

\Sigma (C)} , then the solution of this differential equation with initial condition f ( 0 ) = 0 {\displaystyle f(0)=0} exists as a mapping [0,∞) → Σ(B)

(1)} . The numerical solution of a one-step method depends on the initial condition y 0 {\displaystyle y_{0}} , but the numerical solution of an s-step

t − L {\displaystyle \partial _{t}-L} for the Cauchy problem with initial condition f ( x , s ) {\displaystyle f(x,s)} .) Duhamel's principle also holds

is crucial for accurately describing the system dynamics from an initial condition. I ^ ( t ) = i ℏ Tr n { L e − i Q τ / ℏ Q ρ ^ n ( 0 ) } {\displaystyle

is the inverse hyperbolic sine function. If one desires to use the initial condition P ( x 0 ) = P 0 {\displaystyle P\left(x_{0}\right)=P_{0}} , then α

filtering equation is stable (in the sense that it corrects any erroneous initial condition), the bias and the variance of the particle particle estimates I k

{\displaystyle \partial _{t}L={\frac {1}{2}}\nabla ^{2}L,} with initial condition L ( x , y ; 0 ) = f ( x , y ) {\displaystyle L(x,y;0)=f(x,y)} . This

Their position change when we change equation parameters and the initial condition θ ( 0 ) {\displaystyle \theta (0)} , and therefore, they are called

SBMLsimulator, are then able to simulate the system dynamics given an initial condition. Often these rate laws contain kinetic parameters with uncertain values

_{i}^{2}\\L^{2}=\sum _{i}I_{i}^{2}\omega _{i}^{2}\end{cases}}} and so for any initial condition ω ( 0 ) {\displaystyle \omega (0)} , the trajectory of ω ( t ) {\displaystyle

orthogonal to the pulse direction. Thus, the idea is to produce an initial condition for the mixing period τm. During the NOE mixing time, magnetization

human action is neither random nor mystical, and this sets up the initial condition necessary for an inquiry into the motivating principles that give

g t g − 1 = F t F / 2 {\displaystyle g_{t}g^{-1}=F_{t}F/2} , with initial condition g ( 0 ) = I {\displaystyle g(0)=I} , has a unique C1 solution g(t)

value of d m , ± ( 0 ) {\displaystyle d_{m,\pm }(0)} depends on the initial condition of the system. An exact solution of spin-1/2 system in an oscillating

values of parameters. In order to visualize the spirals, we set the initial condition in a specific configuration x i j = i ∗ 0.0033 {\displaystyle x^{ij}=i*0

or C is applied repeatedly from any Pythagorean triple used as an initial condition, then the dynamics of any of a, b, and c can be expressed as the dynamics

{\displaystyle {\dot {u}}=g(u)} must have a unique solution for each initial condition. Under these conditions and a few others, u k {\displaystyle u_{k}}

exact equation without any perturbative approximations. Given an initial condition it determines Γ k {\displaystyle \Gamma _{k}} for all scales uniquely

x = ( 0 , x ′ ) {\displaystyle x=(0,x')} can be thought of as the initial condition, by thinking of x 1 {\displaystyle x_{1}} as t . {\displaystyle t

range(res): DummyList.append(1) DensityField.append(DummyList[:]) # Set initial condition DensityField[50][50] = 2 DensityField[40][50] = 2 # Maximum solving

t}}{\hat {U}}(t,t_{0})={\hat {H}}(t){\hat {U}}(t,t_{0}),} along with the initial condition U ^ ( t 0 , t 0 ) = 1 {\displaystyle {\hat {U}}(t_{0},t_{0})=1} .

from the reference point. Any point of the time can be used as the initial condition to predict the future after it using this numerical model with assumption

M + ρ M = 0 {\displaystyle D_{0}\nabla M+\rho M=0} on S with the initial condition t = 0 {\displaystyle t=0} and M = M 0 {\displaystyle M=M_{0}} where

the height function to the KPZ fixed point and only depend on the initial condition. Matetski-Quastel-Remenik constructed the KPZ fixed point for the

)_{tt'}\right|_{t=t'}={\text{Id}}_{X},} such that the solution of the ODE with initial condition x ( t ′ ) = x ′ {\displaystyle x(t')=x'} can be expressed as x ( t

t − 1 {\displaystyle \mathbf {A} \mathbf {\alpha } _{t-1}} . The initial condition is set in accordance to the prior probability over x 0 {\displaystyle

to thermal circuit. After all a thermal moment marching (TMM) with initial condition and DC input is required to be implemented. The TMM model is as follows:

features. The examples of predictive features used in the literature are initial condition, traffic, climatic features, pavement type and road class. Melchers

t 2 {\displaystyle \sigma _{t}^{2}} . The following is a possible initial condition (assuming that initially every pixel is background): μ 0 = I 0 {\displaystyle

to Mataram City Indonesia Based on North Lombok Earthquake as The Initial Condition". The International Conference on Disaster Management 2018. Retrieved

as starting conditions, final goal, and a program that links the initial condition to the final state, are not taken into account. The degree of conditionality

Lane–Emden equation with polytropic index 3 / 2 {\displaystyle 3/2} , the initial condition is not that of the Lane–Emden equation. When the central density becomes

individual trierarch, the duration of the military campaign and the initial condition of the vessel entrusted to him. The trierarchy cost a minimum of 2

integral in the above equation is a Cauchy principal value integral. The initial condition for a flat vortex sheet with constant strength is z ( Γ , 0 ) = Γ

} Obviously, P 1 ( 0 ) = 1 {\displaystyle P_{1}(0)=1} due to the initial condition. The frequency Ω = | r | ℏ = 1 ℏ β 2 + γ 2 + δ 2 = | Ω R | 2 + Δ 2

v) is smooth then the differential equation ⁠dv/dt⁠ = f(t, v) with initial condition v(0) = v0 has a unique solution for |t| sufficiently small and the

of electron, N, which together determine a Hamiltonian Hv, and an initial condition on the wavefunction Ψ(t = t0) = Ψ0, the evolution of the wavefunction

are strongly associated, as they use the relationship between the initial condition and actual outcomes; however, they are not isomorphic. They differ

above ordinary differential equation can be solved for e0 with the initial condition e0 = 0 when V = V0 (χ = 0). The exact solution is e 0 = ρ C 0 2 V

(\mathbf {0} ,0)} after the system is started from some arbitrary initial condition. First, by assumption, the subsystem x ˙ = F ( x ) where F ( x ) ≜

by constructing a heat equation, and showing that for any map as initial condition, solution that exists for all time, and the solution uniformly subconverges

}(x,t)-{\frac {1}{\gamma }}\nabla (p_{\varepsilon }(x,t)F(x))} with initial condition p ε ( x , 0 ) = ρ 0 ( x ) {\displaystyle p_{\varepsilon }(x,0)=\rho

vortex. If Γ = 0 {\displaystyle \Gamma =0} , say in the case where the initial condition is composed of two equal and opposite vortices, then the first term

{\displaystyle \varphi (x_{0},t)} is the solution of the system for the initial condition x ( 0 ) = x 0 {\displaystyle x(0)=x_{0}} . This system of differential

such that Newton's method converges Newton fractal — indicates which initial condition converges to which root under Newton iteration Quasi-Newton method

k\leq n-1}(1+{\text{Cuts}}(k+1)+{\text{Cuts}}(n-k+1))} . Adding the initial condition Cuts ( 2 ) = 2 {\displaystyle {\text{Cuts}}(2)=2} yields the claimed

State transition signal-flow graph. Each initial condition is considered as a source (shown in blue).

on the sculpture in February 2001. After documenting the statue's initial condition, the paint was stripped away using a combination of pressure washers

By varying the convolutional kernel, the growth mapping and the initial condition, over 400 "species" of "life" have been discovered in Lenia, displaying

problem consists in finding a solution of the equation, satisfying the initial condition u ( 0 ) = u 0 ∈ D ( A ) ∩ D ( B ) {\displaystyle u(0)=u_{0}\in D(A)\cap

{\displaystyle {\frac {d\mathbf {x} }{dt}}=\mathbf {v} (\mathbf {x} )} with initial condition x ( t n ) = x p n {\displaystyle \mathbf {x} (t_{n})=\mathbf {x} _{p}^{n}}

problems which include initial conditions problems. An example of initial condition problem for an ordinary differential equation is the following: y

PMID 32786977. Barbatti M, Sen K (May 2016). "Effects of different initial condition samplings on photodynamics and spectrum of pyrrole" (PDF). International

Dirichlet's problem is looking for a solution which is a linear function of initial condition X ( 0 ) = x ( 0 ) {\displaystyle \mathbf {X} (0)=\mathbf {x} (0)}

t\in \left[t_{0},T\right],\qquad \qquad \qquad \qquad (4.1)} with initial condition x ( t 0 ) = x 0 {\displaystyle \mathbf {x} (t_{0})=\mathbf {x} _{0}}

that obeys the following nonlinear differential equation with zero initial condition ( z ( 0 ) = 0 {\displaystyle \textstyle z(0)=0} ), and that has dimensions

the wall, in rooms, which Daniel and Geo Fuchs still found in their initial condition. In compliance with the status-quo, the artists photographed solely

for driving state to setpoint by user-prescribed time regardless of initial condition (with Song) PT observers for state estimate convergence in arbitrary

initial conditions of the flow structure. Hence, documentation of the initial condition is essential for capturing the evolution and interactions of coherent

subsystem under the OSR evolution. This is true for any possible initial condition of the environment. To understand the difference between a decoherence-free

different local environments and the entire system lose memory of the initial condition. This effect is called Spectral Diffusion. The temporal evolution

(parabolic) u t t + L u = f {\displaystyle u_{tt}+Lu=f} (hyperbolic) Initial Condition u ( 0 ) ∈ H x 2 m + 1 {\displaystyle u(0)\in H_{x}^{2m+1}} u ( 0 )

while attempting to take the .45 caliber firearm from him. Dado's initial condition was listed as "critical" and emergency surgery was required to remove

\left[t_{0};\alpha \right]} , α > t 0 {\displaystyle \alpha >t_{0}} with an initial condition y ( t 0 ) = y 0 {\displaystyle y\left(t_{0}\right)=y_{0}} . For the

complex, least well documented, and most difficult to reconstruct. The initial condition was so bad that many professionals opposed any attempt to restore

n} define the market portfolio μ {\displaystyle \mu } . With the initial condition Z μ ( 0 ) = X ( 0 ) , {\displaystyle Z_{\mu }(0)=X(0),} the associated

{Ad} (E))\times \Gamma ^{\infty }(B,\operatorname {Ad} (E))} with initial condition in it fulfills: A = lim t → ∞ α ( t ) , {\displaystyle A=\lim _{t\rightarrow

[0,\infty )\rightarrow \Omega ^{1}(B,\operatorname {Ad} (E))} with initial condition in it fulfills: A = lim t → ∞ α ( t ) . {\displaystyle A=\lim _{t\rightarrow

The quantities x0 and p0 are (roughly) string position from the initial condition and string momentum. If all the αμ n are zero, the solution represents

unique maximal solution to every SDE on M {\displaystyle M} with initial condition X 0 = x {\displaystyle X_{0}=x} . If we have identified the maximal

2qth-order differential operator on u intrinsic to surface S, and the initial condition for the equation will be u ( y , t ) = f {\displaystyle u(y,t)=f}

equations as identifying a map between function spaces, such as from an initial condition to a time-evolved state. In other PDEs this map takes an input coefficient

(}P_{1}^{n},\ldots ,P_{N_{Q}}^{n}{\Big )}^{T}.} Problem is completed by an initial condition on the velocity U ( 0 ) = U 0 {\displaystyle \mathbf {U} (0)=\mathbf

Sisyphus effect after the mythological Greek character. Note that this initial condition for velocity requires the atom to be cooled already, for example through

\theta _{t})}{\partial \theta _{j}}}\;dx\right]\circ dY_{k}} with initial condition a chosen θ 0 {\displaystyle \theta _{0}} . By substituting the definition

selective effects are assumed to be present in the population as an initial condition ... The second major type of models does allow mutations to occur