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06A05 Total order
𝒲
0
0
0
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0
0
\alpha
0
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0
l
0
A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets
Radomír Halaš, Daniel Hort (2003)
We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.
A characterization of finite posets of the width at most three with the fixed point property
A characterization of inductive posets
Jiří Klimeš (1985)
A common approach to directoids with an antitone involution and D-quasirings
We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.
A completion for partially ordered abelian groups.
K. Rosenthal (1984)
A continuous lattice L with DID(L) incomplete.
R.E. Hoffmann (1986)
A counterexample to a Kurepa's conjecture
A counterexample to a result concerning closure operators.
Ranzato, F. (2001)
Árpád Száz (2002)
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set
S
and inequality relations on
{X}_{S}=S×ℝ
. Moreover, we also investigate a relationship between the functions of
S
{X}_{S}
A Generalization of Hanani's Theorem on Partial Order.
H. Burkill, Catherine V. Smallwood (1983)
Consuelo Martinez Lopez (1991)
A new view of relationship between atomic posets and complete (algebraic) lattices
Bin Yu, Qingguo Li, Huanrong Wu (2017)
In the context of the atomic poset, we propose several new methods of constructing the complete lattice and the algebraic lattice, and the mutual decision of relationship between atomic posets and complete lattices (algebraic lattices) is studied.
A non-associative generalization of MV-algebras
Ivan Chajda, Jan Kühr (2007)
A note on a function representation of orthomodular posets
Josef Tkadlec (1989)
A note on operators of deletion and contraction for antichains.
Matveev, Andrey O. (2002)
A note on topological
D
-posets of fuzzy sets.
Palko, V. (1995)
A partial order in the knot table.
Kitano, Teruaki, Suzuki, Masaaki (2005)
|
55P10 Homotopy equivalences
55P43 Spectra with additional structure (
{E}_{\infty }
{A}_{\infty }
, ring spectra, etc.)
H
-spaces and duals
55P48 Loop space machines, operads
55P65 Homotopy functors
55P91 Equivariant homotopy theory
{𝒞}_{p}-E
𝒞-E
Friedrich Bauer (1997)
In the S-category
P
(with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual
DX,X=\left(X,n\right)\in P
, turns out to be of the same weak homotopy type as an appropriately defined functional dual
\overline{{\left({S}^{0}\right)}^{X}}
(Corollary 4.9). Sometimes the functional object
\overline{{X}^{Y}}
is of the same weak homotopy type as the “real” function space
{X}^{Y}
(§5).
A strong shape theory with S-duality
Addendum to "Čech and Steenrod homotopy theory with applications to geometric topology"
Harold M. Hastings (1979)
Algebraic topology for proper shape theory
R. Goad (1980)
An approach to shape covering maps.
I. Pop (1999)
In this note we give an approach to shape covering maps which is comparable to that of *-fibrations (Mardesic and Rushing (1978)). The introduced notion conserves some important properties of usual covering maps.
An extension and axiomatic characterization of Borsuk's theory of shape
W. Holsztyński (1971)
Approximative expansions of maps into inverse systems
Tadashi Watanabe (1986)
Bemerkungen zur Borel-Moore-Homologie.
Michael Kernchen (1982)
Borsuk's quasi-equivalence is not transitive
Andrzej Kadlof, Nikola Koceić Bilan, Nikica Uglešić (2007)
Borsuk's quasi-equivalence relation on the class of all compacta is considered. The open problem concerning transitivity of this relation is solved in the negative. Namely, three continua X, Y and Z lying in ℝ³ are constructed such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.
Mikhail A. Batanin (1997)
|
A method of BAZLEY-FOX type for the eingenvalues of the LAPLACE operator
W. Weinelt (1974)
A note on the effect of numerical quadrature in finite element eigenvalue approximation.
Uday Banerjee (1992)
A proof of monotony of the Temple quotients in eigenvalue problems
Karel Rektorys (1984)
If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue
{\lambda }_{1}
, the sequences of the so-called Schwarz quatients (which are upper bounds for
{\lambda }_{1}
) and of the so-called Temple quotients (which are lower bounds) are constructed. While monotony of the first sequence was proved many years ago, monotony of the second one has been proved only recently by F. goerisch and J. Albrecht in their common paper “Die Monotonie der Templeschen Quotienten” (ZAMM, in print). In the present...
A remark on two dimensional periodic potentials.
E. Trubowitz, B.E.J. Dahlberg (1982)
Nicolas Ginoux, Georges Habib (2010)
We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.
Lahcène Chorfi (2010)
We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An,
n\in ℕ
, in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type
\left[\gamma ,+\infty \left[
and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.
We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators
{A}_{n}
n\in ℕ
, in a suitable Hilbert space. We show that the essential spectrum of
{A}_{n}
is an interval of type
\left[\gamma ,+\infty \left[
Qun Lin, Hehu Xie (2012)
In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic...
A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗
\delta
Bang-Yen Chen (2013)
|
f
f(-x)
2f\left(x\right)
f(x-1)
\pm f(\pm x)
f(x\pm 1),f(x)\pm 1
f(\pm x\pm 1)
\pm f(x)\pm 1
f\left(2x\right),f\left(\frac{1}{2}x\right),2f\left(x\right),\frac{1}{2}f\left(x\right)
\pm \mid f(x)\mid ,f(\pm \mid x\mid )
f(\pm {x}^{2}),\pm {f}^{2}(x)
f(\mathrm{max}/\mathrm{min}(\pm 1,x))
\mathrm{max}/\mathrm{min}(\pm 1,f(x))
\mathrm{max}/\mathrm{min}(\pm x,\pm f(x))
Description: draw a function using the graph of another, requires java. interactive exercises, online calculators and plotters, mathematical recreation and games
|
A comparison of elliptic units in certain prime power conductor cases
Ulrich Schmitt (2015)
The aim of this paper is to compare two modules of elliptic units, which arise in the study of elliptic curves E over quadratic imaginary fields K with complex multiplication by
{}_{K}
, good ordinary reduction above a split prime p and prime power conductor (over K). One of the modules is a special case of those modules of elliptic units studied by K. Rubin in his paper [Invent. Math. 103 (1991)] on the two-variable main conjecture (without p-adic L-functions), and the other module is a smaller one,...
A geometric proof of Kummer's reciprocity law for seventh powers
R. Clement Fernández, J. M. Echarri Hernández, E. J. Gómez Ayala (2011)
Rodney I. Yager (1982)
p
L
p
p
L
Annexe: Deux lettres
Approximations diophantiennes
p
Daniel Bertrand (1978)
Borne sur la torsion dans les variétés abéliennes de type CM
Nicolas Ratazzi (2007)
su\left(3\right)
M. Bauer, A. Coste, C. Itzykson, P. Ruelle (1997)
François Morain (2007)
ℰ/\overline{ℚ}
be an elliptic curve having complex multiplication by a given quadratic order of an imaginary quadratic field
𝕂
. The field of definition of
ℰ
is the ring class field
\Omega
of the order. If the prime
p
splits completely in
\Omega
, then we can reduce
ℰ
modulo one the factors of
p
and get a curve
E
{𝔽}_{p}
. The trace of the Frobenius of
E
is known up to sign and we need a fast way to find this sign, in the context of the Elliptic Curve Primality Proving algorithm (ECPP). For this purpose, we propose...
Congruences for Special Values of L-functions of Elliptic Curves with Complex Multiplication.
Corestriction of central simple algebras and families of Mumford-type
Federica Galluzzi (1999)
M
be a family of Mumford-type, that is, a family of polarized complex abelian fourfolds as introduced by Mumford in [9]. This family is defined starting from a quaternion algebra
A
over a real cubic number field and imposing a condition to the corestriction of such
A
. In this paper, under some extra conditions on the algebra
A
, we make this condition explicit and in this way we are able to describe the polarization and the complex structures of the fibers. Then, we look at the non simple
CM
-fibers...
Courbes elliptiques et formes modulaires de poids 3/2
Laure BARTHEL (1984/1985)
Courbes elliptiques, fonctions L , et tours cyclotomiques.
David E. ROHRLICH (1983/1984)
Cycles de Hodge absolus et périodes des intégrales des variétés abéliennes. (Rédigé par J. L. Brylinski)
Denominators of Igusa class polynomials
Kristin Lauter, Bianca Viray (2014)
In [22], the authors proved an explicit formula for the arithmetic intersection number
\left(CM\left(K\right).{G}_{1}\right)
on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field
K
. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus
2
curves for use in cryptography. One of the main tools in the proof was a previous result of the authors [21] generalizing the singular moduli formula of Gross...
Der Definitionskörper für den Zerfall einer abelschen Varietät mit komplexer Multiplikation.
C.-G. Schmidt (1980)
Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen.
Jürgen Wolfart, Gisbert Wüstholz (1985/1986)
|
A first order linear differential equation is a differential equation of the form
y'+p(x) y=q(x)
. The left-hand side of this equation looks almost like the result of using the product rule, so we solve the equation by multiplying through by a factor that will make the left-hand side exactly the result of a product rule, and then integrating. This factor is called an integrating factor.
An integrating factor will be a function
f(x)
such that multiplying it to both sides of the equation,
\begin{aligned} f(x) \left[ y'+p(x)y \right] &= f(x)q(x) \\ \\ f(x)y'+f(x)p(x)y &= f(x)q(x), \end{aligned}
\begin{aligned} f(x)y'+f(x)p(x)y &= f(x)y'+f'(x)y \\ \\ \int\left[ f(x)y'+f(x)p(x)y \right]\ dx &= f(x)y+C \end{aligned}
This means the function
f
should satisfy
f'(x)=f(x)p(x)
, which is a separable differential equation. This can be solved as
\begin{aligned} \frac{f'(x)}{f(x)}\, dx= p(x)\, dx &\implies \int \frac{f'(x)}{f(x)}\, dx=\int p(x)\, dx \\ \\ & \implies \ln |f(x)|=\int p(x)\, dx \\ \\ &\implies f(x)= {\large e}^{\int p(x)\, dx}. \end{aligned}
y'+e^xy=e^x
p(x)=q(x)=e^x
. Our integrating factor is
e^{\int e^x\, dx}=e^{e^x}.
Note that we omit the constant of integration, since it would just produce a shifted solution to the equation. Now we multiply both sides by
e^{e^x}
e^{e^x}y'+e^{e^x}e^xy=e^xe^{e^x}\implies \left[e^{e^x}y\right]'=e^xe^{e^x},
and now integrating both sides gives
e^{e^x}y=e^{e^x}+C\implies y=Ce^{-e^x}+1.
\dfrac{dy}{dx} - 3y = e^{2x}, \quad y(0) = 3
v(x) = e^{-3x} \Rightarrow e^{-3x} \dfrac{dy}{dx} - 3e^{-3x}y = e^{-x} \Rightarrow
\dfrac{d}{dx} \left(e^{-3x}y\right) = e^{-x} \Rightarrow
e^{-3x}y = -e^{-x} + C \Rightarrow y(x) = Ce^{3x} - e^{2x}
along the condition
y(0) = 3
C = 4
so the function is
y(x) = 4e^{3x} - e^{2x}
\begin{cases} ty' +(2t +1)y =te^{-2t},\quad t \in [1,\infty)\\ y(1) = 0 \end{cases}
y' + \frac{2t +1}{t}y = e^{-2t} \rightarrow v(t) = te^{2t} \rightarrow \dfrac{d}{dt} (te^{2t}y) = t \Rightarrow
y(t) =\frac{1}{t}e^{-2t}\left(\frac{t^2}{2} + C\right),\quad y(1) = 0 \Rightarrow C = \frac{-1}{2} \Rightarrow
y(t) = \frac{1}{2}\left(t -\frac{1}{t}\right)e^{-2t}
y
y'+y\tan x=\sec x.
y\left (\dfrac{\pi}{4}\right) = \dfrac{1}{\sqrt{2}}.
y\left (\dfrac{\pi}{2}\right)?
Suppose there is a circuit with a switch, a battery, a resistor, and an inductor in series. The battery produces a voltage of 45 volts and a current of
I(t
amperes at time
t
. The resistor is an
9
ohm resistor and the inductor has an inductance of
3
henries. If the switch is initially closed, what is the current in the circuit a long time after the switch has been opened?
Ohm's law says that the voltage drop due to the resistor is
9I(t)
volts. The voltage drop from the inductor is
3 I'(t)
. Kirchoff's laws say that the sum of the voltage drops is equal to the supplied voltage, so we find
3I'(t)+9I(t)=45\implies I'(t)+3I(t)=15.
The integrating factor is
e^{\int 3\, dt}=e^{3t}
, and multiplying through by this gives
I'(t)e^{3t}+3e^{3t}I'(t)=15e^{3t}\implies \left[I(t)e^{3t}\right]'=15e^{3t}\implies I(t)e^{3t}=5e^{3t}+C\implies I(t)=Ce^{-3t}+5.
t\to\infty
I(t)\to 5
, so the current after a long time is 5 amperes.
|
Merton jump diffusion model - MATLAB - MathWorks India
Create merton Object
The merton function creates a merton object, which derives from the gbm object.
The merton model, based on the Merton76 model, allows you to simulate sample paths of NVars state variables driven by NBrowns Brownian motion sources of risk and NJumps compound Poisson processes representing the arrivals of important events over NPeriods consecutive observation periods. The simulation approximates continuous-time merton stochastic processes.
You can simulate any vector-valued merton process of the form
d{X}_{t}=B\left(t,{X}_{t}\right){X}_{t}dt+D\left(t,{X}_{t}\right)V\left(t,{x}_{t}\right)d{W}_{t}+Y\left(t,{X}_{t},{N}_{t}\right){X}_{t}d{N}_{t}
Merton = merton(Return,Sigma,JumpFreq,JumpMean,JumpVol)
Merton = merton(___,Name,Value)
Merton = merton(Return,Sigma,JumpFreq,JumpMean,JumpVol) creates a default merton object. Specify required inputs as one of two types:
Merton = merton(___,Name,Value) sets Properties using name-value pair arguments in addition to the input arguments in the preceding syntax. Enclose each property name in quotes.
The merton object has the following Properties:
Return — Expected mean instantaneous rates of asset return
Expected mean instantaneous rates of asset return, denoted as B(t,Xt), specified as an array, a deterministic function of time, or a deterministic function of time and state.
If you specify Return as a deterministic function of time, when you call Return with a real-valued scalar time t as its only input, it must return an NVars-by-NVars matrix.
If you specify Return as a deterministic function of time and state, it must return an NVars-by-NVars matrix when you call it with two inputs:
Sigma — Instantaneous volatility rates
Instantaneous volatility rates, denoted as V(t,Xt), specified as an array, a deterministic function of time, or a deterministic function of time and state.
If you specify Sigma as an array, it must be an NVars-by-NBrowns matrix of instantaneous volatility rates or a deterministic function of time. In this case, each row of Sigma corresponds to a particular state variable. Each column corresponds to a particular Brownian source of uncertainty, and associates the magnitude of the exposure of state variables with sources of uncertainty.
If you specify Sigma as a deterministic function of time, when you call Sigma with a real-valued scalar time t as its only input, it must return an NVars-by-NBrowns matrix.
If you specify Sigma as a deterministic function of time and state, it must return an NVars-by-NBrowns matrix when you call it with two inputs:
Although merton enforces no restrictions for Sigma, volatilities are usually nonnegative.
Instantaneous jump frequencies representing the intensities (the mean number of jumps per unit time) of the Poisson processes Nt that drive the jump simulation, specified as an array, a deterministic function of time, or a deterministic function of time and state.
If you specify JumpFreq as an array, it must be an NJumps-by-1 vector.
If you specify JumpFreq as a deterministic function of time, when you call JumpFreq with a real-valued scalar time t as its only input, JumpFreq must produce an NJumps-by-1 vector.
If you specify JumpFreq as a deterministic function of time and state, it must return an NVars-by-NBrowns matrix when you call it with two inputs:
If you specify JumpMean as an array, it must be an NVars-by-NJumps matrix.
If you specify JumpMean as a deterministic function of time, when you cal JumpMean with a real-valued scalar time t as its only input, it must return an NVars-by-NJumps matrix.
If you specify JumpMean as a deterministic function of time and state, it must return an NVars-by-NJumps matrix when you call it with two inputs:
If you specify JumpVol as an array, it must be an NVars-by-NJumps matrix.
If you specify JumpVol as a deterministic function of time, when you call JumpVol with a real-valued scalar time t as its only input, it must return an NVars-by-NJumps matrix.
If you specify JumpVol as a deterministic function of time and state, it must return an NVars-by-NJumps matrix when you call it with two inputs:
If StartState is a scalar, merton applies the same initial value to all state variables on all trials.
If StartState is a column vector, merton applies a unique initial value to each state variable on all trials.
If StartState is a matrix, merton applies a unique initial value to each state variable on each trial.
Correlation between Gaussian random variates drawn to generate the Brownian motion vector (Wiener processes), specified as an NBrowns-by-NBrowns positive semidefinite matrix, or as a deterministic function Ct that accepts the current time t and returns an NBrowns-by-NBrowns positive semidefinite correlation matrix. If Correlation is not a symmetric positive semidefinite matrix, use nearcorr to create a positive semidefinite matrix for a correlation matrix.
If you specify Correlation as a deterministic function of time, you can specify a dynamic correlation structure.
F\left(t,{X}_{t}\right)=A\left(t\right)+B\left(t\right){X}_{t}
G\left(t,{X}_{t}\right)=D\left(t,{X}_{t}^{\alpha \left(t\right)}\right)V\left(t\right)
simByEuler Simulate Merton jump diffusion sample paths by Euler approximation
simBySolution Simulate approximate solution of diagonal-drift Merton jump diffusion process
Merton jump diffusion models allow you to simulate sample paths of NVARS state variables driven by NBROWNS Brownian motion sources of risk and NJumps compound Poisson processes representing the arrivals of important events over NPeriods consecutive observation periods. The simulation approximates continuous-time merton stochastic processes.
The Merton jump diffusion model (Merton 1976) is an extension of the Black-Scholes model, and models sudden asset price movements (both up and down) by adding the jump diffusion parameters with the Poisson process Pt.
\begin{array}{l}d{S}_{t}=\left(\gamma -q-{\lambda }_{p}{\mu }_{j}\right){S}_{t}dt+{\sigma }_{M}{S}_{t}d{W}_{t}+J{S}_{t}d{P}_{t}\\ \text{prob}\left(d{P}_{t}=1\right)={\lambda }_{p}dt\end{array}
\mathrm{ln}\left(1+J\right)~N\left(\text{ln(1+}{u}_{j}\right)-\frac{{\delta }^{2}}{2},{\delta }^{2}
\frac{1}{\left(1+J\right)\delta \sqrt{2\pi }}\text{exp}\left\{\frac{-{\left[\mathrm{ln}\left(1+J\right)-\left(\text{ln(1+}{\mu }_{j}\right)-\frac{{\delta }^{2}}{2}\right]}^{2}}{2{\delta }^{2}}\right\}
σM is the volatility of the asset price (σM> 0).
Under this formulation, extreme events are explicitly included in the stochastic differential equation as randomly occurring discontinuous jumps in the diffusion trajectory. Therefore, the disparity between observed tail behavior of log returns and that of Brownian motion is mitigated by the inclusion of a jump mechanism.
bates | simByEuler | simBySolution | simulate
|
Table 2.3.1 lists the essential tangent-vector facts for a curve described by the position vector
\mathbf{R}\left(p\right)
\mathbf{R}\prime \left(p\right)=\frac{d}{\mathrm{dp}}\mathbf{R}\left(p\right)
is taken componentwise.
\mathbf{R}\prime \left(p\right)
is tangent to the curve defined by
\mathbf{R}\left(p\right)
p
s
\mathbf{R}\prime \left(s\right)=\frac{d}{\mathrm{ds}}\mathbf{R}\left(s\right)
is the unit tangent vector T.
4
If T is the unit tangent vector,
\mathbf{T}·\mathbf{T}\prime =0
, that is, T is orthogonal to its derivative.
5
\mathbf{R}\prime \left(p\right)
\mathrm{ρ}=∥\mathbf{R}\prime ∥
\sqrt{{\left(\frac{\mathrm{dx}}{\mathrm{dp}}\right)}^{2}+{\left(\frac{\mathrm{dy}}{\mathrm{dp}}\right)}^{2}+{\left(\frac{\mathrm{dz}}{\mathrm{dp}}\right)}^{2}}
\frac{\mathrm{ds}}{\mathrm{sp}}
6
If the parameter
p
t
\mathbf{R}\prime \left(t\right)
is the velocity vector V; and
\mathrm{ρ}=v
, the speed.
Table 2.3.1 Essential tangent-vector facts for a curve defined by the position vector
\mathbf{R}\left(p\right)
The generic parameter along a curve defined parametrically by the position vector
\mathbf{R}\left(p\right)
p
. The derivative of R with respect to its parameter is always a tangent vector. This can be inferred from the definition of the derivative of R.
\mathbf{R}\prime \left(p\right)=\frac{d}{\mathrm{dp}}\mathbf{R}\left(p\right)
\underset{h→0}{lim}\frac{\mathbf{R}\left(p+h\right)-\mathbf{R}\left(p\right)}{h}
This definition also suggests why the derivative is taken componentwise. The difference
\mathbf{R}\left(p+h\right)-\mathbf{R}\left(p\right)
is a vector whose components are each divided by
h
h→0
, each component of the fraction
\frac{\mathbf{R}\left(p+h\right)-\mathbf{R}\left(p\right)}{h}
becomes the derivative of that component.
Figure 2.3.1 contains an animation that illustrates why this derivative results in a vector tangent to the curve described by
\mathbf{R}\left(p\right)
The blue vector is
\mathbf{R}\left(p+h\right)-\mathbf{R}\left(p\right)
and can be considered a "secant vector" that shrinks in length as
h→0
The green vector is
\frac{\mathbf{R}\left(p+h\right)-\mathbf{R}\left(p\right)}{h}
, and has the same direction as the secant vector, but does not shrink in length. In the limit as
h→0
, this green vector becomes tangent to the curve R.
Figure 2.3.1 Animation:
\mathbf{R}\prime
is a tangent vector
\mathbf{R}\left(p\right)
is the position-vector representation of the parametric curve
x={p}^{2}
y={p}^{3}
p≥0
\underset{h→0}{lim}\frac{\mathbf{R}\left(p+h\right)-\mathbf{R}\left(p\right)}{h}
\mathbf{R}\prime \left(p\right)=\frac{d\mathbf{R}}{\mathrm{dp}}
x\prime \left(p\right) \mathbf{i}+y\prime \left(p\right) \mathbf{j}
. Thus, the differentiation operator
\frac{d}{\mathrm{dp}}
is applied to R by applying it to each component of R.
\mathbf{R}\left(p\right)
is the position-vector representation of
C
, the parametric curve
x=p \mathrm{cos}\left(p\right)
y=p \mathrm{sin}\left(p\right)
p∈\left[0,3 \mathrm{π}\right]
\mathrm{ρ}=∥\mathbf{R}\prime \left(p\right)∥
and the unit tangent vector
\mathbf{T}=\mathbf{R}\prime /\mathrm{ρ}
Graph R and the vectors
\mathbf{R}\prime \left(1\right),\mathbf{R}\prime \left(5\right),\mathbf{R}\prime \left(9\right)
C
\mathbf{T}\left(1\right),\mathbf{T}\left(5\right),\mathbf{T}\left(9\right)
C
\mathbf{T}·\mathbf{T}\prime \left(p\right)=0
, thus verifying that a unit vector is necessarily orthogonal to its derivative.
To the graph in Part (c), add the vectors
\mathbf{T}\prime \left(1\right),\mathbf{T}\prime \left(5\right),\mathbf{T}\prime \left(9\right)
\mathbf{R}\left(p\right)
be the position-vector representation of the parametric curve
x={p}^{2}-p/2,y=4/3 {p}^{3/2}
p≥0
\mathbf{R}\left(s\right)=\mathbf{R}\left(p\left(s\right)\right)
be the reparametrization obtained in Example 2.2.6. (Recall that
s
is the arc length along the curve.)
\mathrm{ρ}=∥\mathbf{R}\prime \left(p\right)∥
Obtain the unit tangent vector
\mathbf{T}\left(p\right)=\mathbf{R}\prime \left(p\right)/\mathrm{ρ}
\mathbf{T}\left(p\left(s\right)\right)=\frac{d}{\mathrm{ds}}\mathbf{R}\left(s\right)
, thus verifying that
\mathbf{R}\prime \left(s\right)
is automatically a unit tangent vector.
\mathbf{R}\left(p\right)
x\left(p\right),y\left(p\right),z\left(p\right)
s≥0
\frac{d}{\mathrm{ds}}\mathbf{R}\left(p\left(s\right)\right)
\mathbf{R}\left(s\right)
C
s
\mathbf{T}\left(s\right)=\mathbf{R}\prime \left(s\right)
C
\mathbf{T}\mathbf{·}\mathbf{T}\prime =0
\mathbf{R}\left(p\right)=x\left(p\right) \mathbf{i}+y\left(p\right) \mathbf{j}+z\left(p\right) \mathbf{k}
is a position vector and
R\left(p\right)=∥\mathbf{R}\left(p\right)∥
is its length, show that
\mathbf{R}·\frac{d\mathbf{R}}{\mathrm{dp}}
R \frac{\mathrm{dR}}{\mathrm{dp}}
C
y\left(x\right)=\frac{1-{x}^{2}}{1+{x}^{2}}
\mathbf{R}\left(p\right)
x=p,y=y\left(p\right)
\mathbf{R}\prime \left(p\right),\mathrm{ρ}\left(p\right)
\mathbf{T}\left(p\right)
\mathrm{ρ}=∥\mathbf{R}\prime ∥
\mathbf{T}=\mathbf{R}\prime /\mathrm{ρ}
C
\mathbf{R}\left(1\right)
\mathbf{T}\left(1\right)
\mathrm{ρ}\left(p\right),p∈\left[0,3\right]
\left[x,y\right]
\mathrm{ρ}
\mathbf{R}\left(p\right)
is the position-vector form of the curve
C
defined parametrically by the equations
x\left(p\right)=2+3p- {p}^{2},y\left(p\right)=\mathrm{cos}\left(p\right)
p∈\left[0,\mathrm{π}\right]
\mathbf{R}\prime \left(p\right),\mathrm{ρ}\left(p\right)
\mathbf{T}\left(p\right)
\mathrm{ρ}=∥\mathbf{R}\prime ∥
\mathbf{T}=\mathbf{R}\prime /\mathrm{ρ}
C
\mathbf{T}\left(0\right),\mathbf{T}\left(1\right),\mathbf{T}\left(2\right)
On the given interval, graph
\mathrm{ρ}
and determine its absolute minimum and the point on the curve where this minimum occurs.
Given the two plane curves
f\left(x\right)={x}^{2},g\left(x\right)=8-{\left(\frac{x}{4}\right)}^{2},x\ge 0
x=1
, obtain the equation of the line tangent to
y=f\left(x\right)
Find the coordinates of the intersection of
y=g\left(x\right)
and the tangent line found in Part (a).
Construct a vector from
\left(1,f\left(1\right)\right)
to the point found in Part (b).
\mathbf{R}\prime \left(1\right)
, the natural tangent vector at
\left(1,f\left(1\right)\right)
|
{L}^{p}
A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system
Kangkang Wang (2009)
In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established....
A correction to “Some mean convergence and complete convergence theorems for sequences of
m
-linearly negative quadrant dependent random variables”
Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2017)
The authors provide a correction to “Some mean convergence and complete convergence theorems for sequences of
m
-linearly negative quadrant dependent random variables”.
Ion Grama, Michael Nussbaum (2002)
A general method to obtain the rate of convergence in the strong law of large numbers.
Tómács, Tibor (2007)
A Hájek-Rényi type inequality and its applications.
Tómács, Tibor, Líbor, Zsuzsanna (2006)
A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays.
Van Quang, Nguyen, Van Huan, Nguyen (2010)
A law of the iterated logarithm for general lacunary series
Charles N. Moore, Xiaojing Zhang (2012)
We prove a law of the iterated logarithm for sums of the form
{\sum }_{k=1}^{N}{a}_{k}f\left({n}_{k}x\right)
{n}_{k}
satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.
A law of the iterated logarithm for the sample covariance matrix.
Sepanski, Steven J. (2003)
A limit theorem for maxima of nonstationary Gaussian sequences
Deo, Chandrakant M. (1978)
A local convergence theorem for partial sums of stochastic adapted sequences
Wei Guo Yang, Zhong Xing Ye, Liu, Wen (2006)
In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.
A lower bound in the law of the iterated logarithm for general lacunary series
We prove a lower bound in a law of the iterated logarithm for sums of the form
{\sum }_{k=1}^{N}{a}_{k}f\left({n}_{k}x+{c}_{k}\right)
where f satisfies certain conditions and the
{n}_{k}
satisfy the Hadamard gap condition
{n}_{k+1}/{n}_{k}\ge q>1
A martingale proof of the Khinchin iterated logarithm law for Wiener processes
Nicolai V. Krylov (1995)
A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series
Mordechay B. Levin (2013)
We prove the central limit theorem for the multisequence
{\sum }_{1\le n₁\le N₁}\cdots {\sum }_{1\le {n}_{d}\le {N}_{d}}{a}_{n₁,...,{n}_{d}}cos\left(⟨2\pi m,A{₁}^{n₁}...{A}_{d}^{{n}_{d}}x⟩\right)
m\in {ℤ}^{s}
{a}_{n₁,...,{n}_{d}}
are reals,
A₁,...,{A}_{d}
are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in
{\left[0,1\right]}^{s}
. The main tool is the S-unit theorem.
A non-ballistic law of large numbers for random walks in i. i. d. random environment.
Zerner, Martin P.W. (2002)
A note on almost sure central limit theorem in the joint version for the maxima and sums.
Zang, Qing-Pei, Wang, Zhi-Xiang, Fu, Ke-Ang (2010)
A note on convergence of weighted sums of random variables.
Wang, Xiang Chen, Bhaskara Rao, M. (1985)
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Convert rotation angles to Euler-Rodrigues vector - Simulink - MathWorks Switzerland
Rotation Angles to Rodrigues
Convert rotation angles to Euler-Rodrigues vector
The Rotation Angles to Rodrigues block converts the rotation described by the three rotation angles R1,R2,R3 into the three-element Euler-Rodrigues vector. The rotation used in this block is a passive transformation between two coordinate systems. For more information on Euler-Rodrigues vectors, see Algorithms.
R1,R2,R3 — Rotation angles
Rotation angles, in radians, from which to determine the Euler-Rodrigues vector. Values must be double.
Euler-Rodrigues vector determined from rotation angles.
Rotation order for three wind rotation angles.
The default limitations for the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' sequences generate an R2 angle that lies between ±pi/2 radians (± 90 degrees), and R1 and R3 angles that lie between ±pi radians (±180 degrees).
The default limitations for the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' sequences generate an R2 angle that lies between 0 and pi radians (180 degrees), and R1 and R3 angles that lie between ±pi (±180 degrees).
Rodrigues transformation is not defined for rotation angles equal to ±pi radians (±180 deg).
\stackrel{⇀}{b}
\stackrel{\to }{b}=\left[\begin{array}{ccc}{b}_{x}& {b}_{y}& {b}_{z}\end{array}\right]
\begin{array}{l}{b}_{x}=\mathrm{tan}\left(\frac{1}{2}\theta \right){s}_{x},\\ {b}_{y}=\mathrm{tan}\left(\frac{1}{2}\theta \right){s}_{y},\\ {b}_{z}=\mathrm{tan}\left(\frac{1}{2}\theta \right){s}_{z}\end{array}
\stackrel{⇀}{s}
Direction Cosine Matrix to Rodrigues | Rodrigues to Direction Cosine Matrix | Rodrigues to Quaternions | Rodrigues to Rotation Angles | Quaternions to Rodrigues
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Evolution of Atomic Theory - Course Hero
General Chemistry/Atomic Theory/Evolution of Atomic Theory
Dalton's atomic theory laid important foundations in chemistry, but as time went on, parts of his theory came into question. Importantly, the assertion that atoms are indivisible seemed less likely. In 1896 French physicist Henri Becquerel discovered that some elements give off radiation similar to X-rays. Over the following two decades, Polish-born French physicist Marie Curie coined the term radioactive, which means spontaneously emitting energetic particles or radiation. She also discovered two new radioactive elements: radium and polonium.
The radioactive properties of elements led English physicist J.J. Thomson to use a cathode-ray tube to determine precisely what was happening. A cathode ray is a beam of electrons emitted from a negatively charged conducting plate in a vacuum chamber containing very little gas. Cathode rays can only be detected in a cathode-ray tube when they strike materials painted on the end of the tube called phosphors, materials that emit visible light when struck by electromagnetic radiation. A fluorescent substance is a type of phosphor that emits the visible light over a short time period.
Thomson wanted to know what exactly cathode rays were, if they were composed of anything at all. He knew that cathode rays traveled in straight lines within the tube. He conducted experiments in which he switched the gas in the tube, but he found that it had no effect on the cathode rays. Varying the metal that emitted the rays also seemed to have no effect. Thomson began to believe that the rays were composed of tiny particles that carried an electric charge. To demonstrate this idea, he placed positively and negatively charged plates alongside the beam in the tube. He found that the plates deflected the rays toward the positive side. This observation confirmed Thomson's suspicions and showed that cathode rays are negatively charged. Thomson called the negatively charged particles of cathode rays "corpuscles." We now know them as electrons. An electron is a negatively charged subatomic particle.
Cathode-Ray Tube Experiments
English physicist J.J. Thomson used a cathode ray tube to discover electrons, negatively charged subatomic particles.
Based on these experiments, Thomson proposed the plum pudding model of the atom in 1904, which shows negatively charged electrons floating in a positively charged material, similar to the way raisins are scattered throughout a British dish called plum pudding.
English physicist J.J. Thomson hypothesized the plum pudding model of the atom. The model shows negatively charged electrons floating in a positively charged material.
British physicist Ernest Rutherford was curious about Thomson's plum pudding model. Rutherford had isolated alpha particles. He had determined that an alpha particle (
\alpha
) is identical to a helium ion (He2+) that is emitted during the decay of radioactive elements. Rutherford also knew that α particles have significantly more mass than electrons. In 1909, using the plum pudding model, Rutherford hypothesized that if a beam of α particles is directed toward an atom, the particles would only be deflected if they hit an electron. This should happen rarely because electrons have very little mass and should be distributed randomly throughout the atom.
Rutherford's assistants Hans Geiger and Ernest Marsden conducted experiments to test the hypothesis. They set up a beam of alpha particles pointed directly toward a sheet of gold foil. They surrounded the gold foil with a detector that would emit light when struck by an alpha particle. Rutherford expected that most of the alpha particles would pass straight through the foil and strike the sheet behind it. Instead, Geiger and Marsden observed many alpha particles bouncing off the gold foil in multiple directions, including back toward the source emitting the beam.
Ernest Rutherford designed an experiment in which a beam of
\alpha
particles was directed toward a sheet of gold foil surrounded by a detector. The results led to his model of the nuclear atom.
From these results, Rutherford proposed the nuclear model of the atom, in which an atom is composed of a positively charged center with electrons moving around it. Today, we know that Rutherford and his assistants had discovered the nucleus, which is the positively charged center of an atom containing protons and neutrons. At the time of Rutherford's experiments, neutrons had not yet been discovered. He proposed that the nucleus was composed of positively charged particles, which he named protons. A proton is a positively charged subatomic particle in the nucleus of an atom.
Niels Bohr, a Danish physicist, was also interested in discovering the nature of the atom. Rutherford's nuclear model had clarified the physical space of the atom, but classical physics predicts that electrons lose energy as they orbit the nucleus and should quickly fall into the nucleus. Yet, clearly, electrons remain in the area surrounding the nucleus. In 1913 Bohr suggested that electrons travel along specific paths around the nucleus. He called each path a shell and proposed that only shells with a specific, discrete radius from the nucleus are possible. Electrons cannot be found outside these shells. The radius rn of each shell is represented as:
r_n=n^2\times r_1
The variable n is a positive integer representing the electron's state, its shell number,
n=1
n=2
n=3
, and so on, and r1 is the Bohr radius, which is the distance between the nucleus and the electron in a hydrogen atom. Bohr calculated r1 to be
0.529\times{10}^{-10}\;\rm{ m}
for one-electron (hydrogen-like) systems. Bohr then turned his attention to electron energies. If electrons can only occupy shells at a particular distance from the nucleus, they should gravitate toward the lowest possible energy state. Bohr calculated this energy (E) for the nth level of hydrogen. This can be calculated by using the Rydberg formula, which is a mathematical formula of an electron moving between energy levels to predict the wavelength of light. The ground state energy level for a hydrogen atom is –13.6 eV.
E=\frac{-1}{n^2}\times13.6\;\rm{eV}
Thus, the lowest possible energy level, called the ground state, for a hydrogen electron is calculated by substituting 1 for n.
\begin{aligned}E&=\frac{-1}{1^2}\times13.6\;\rm{eV}\\&=-13.6\;\rm{eV}\end{aligned}
This number is negative because it is relative to the energy of an electron that has been removed from its nucleus, which thus has an energy of 0 eV. An electron in orbit around a nucleus is more stable than an electron separated from its nucleus because it has less energy. Bohr's model only works with systems containing one electron. Bohr suggested that electrons in lower energy states (lower shells) can be excited to higher energy states (higher shells). However, electrons will always return to their lowest energy state. This return releases energy in the form of a photon, which is a packet of light. Bohr's model correctly explained and predicted absorption and emission spectra of elements. Thus, his model gained widespread acceptance and is commonly used today as an introduction to atomic theory.
Danish physicist Niels Bohr proposed a model of the atom in which electrons orbit the nucleus at defined shells. These shells have a specific radius and associated energy.
Electron Characteristics and Neutrons
The experiments of Robert Millikan, Edwin Schrödinger, and James Chadwick led to the discovery of subatomic particles and isotopes, which shaped modern-day atomic theory.
Bohr's model gave the most accurate representation of the makeup of an atom at the time. Concurrently, beginning in 1909, American physicist Robert Millikan conducted a series of experiments to determine the charge on a single electron. He set up a device that would spray charged water droplets into an electric field. He measured their charges to be multiples of a single value, but imprecision in his experimental setup drew criticism of his results. He therefore replaced charged water droplets with charged oil droplets, which evaporated much more slowly, and obtained better results. He was thus able to calculate the charge of a single electron as approximately
1.6021766208\times{10}^{-19}\;\rm{C}
American physicist Robert Millikan conducted an experiment using charged oil droplets to measure the charge on a single electron. He determined the charge on an electron to be approximately
1.6021766208\times{10}^{-19}\rm{ C}
In the years immediately after Bohr developed his atomic model, key discoveries were made that significantly changed scientists' understanding of the behavior of electrons in an atom. In 1926 Austrian physicist Erwin Schrödinger developed the quantum mechanical model of the atom in which he used mathematical equations to predict the positions of electrons. The main difference between the Bohr model and this model is the electron cloud, which is the arrangement of electrons moving around an atomic nucleus based on probabilities of their locations. Unlike the Bohr model, which describes the motion of each electron in a specific orbit, the quantum mechanical model describes an orbital, which is a region in which an electron has a high probability of being located. Orbitals are described by the quantum numbers s, p, d, and f, which differ from one another by their shapes.
Identifying the primary components of an atom was nearly complete. However, in 1932 English physicist James Chadwick began experiments to demonstrate the presence of another nuclear particle. Chadwick observed that, when struck by
\alpha
particles, beryllium released radiation of an unknown kind. This radiation, in turn, caused other elements to release protons. Chadwick showed definitively that this radiation was not gamma rays because it was much more energetic than could be accounted for by gamma rays. By measuring the velocity of the protons released by the radiation, he determined the masses of the particles involved. In so doing, he discovered the neutron, a subatomic particle that has a neutral charge in the nucleus of an atom. The mass of a neutron is about the same as the mass of a proton.
With the discovery of the neutron, the identification of an atom's primary components was complete. All three subatomic particles, the proton, the neutron, and the electron, had been experimentally observed. The positions and charges of the three particles had been determined, along with their mass in the case of the more massive particles, the proton and the neutron.
The discovery of the neutron helped scientists understand why some elements had both radioactive and nonradioactive forms. Recall that an isotope is one of two or more forms of an element that have the same number of protons but different numbers of neutrons. The word isotope is often used to refer to the radioactive form, which tends to be the form with more neutrons than protons. For example, carbon has 6 protons, but carbon isotopes can have as few as 6 or as many as 17 neutrons. The isotope carbon-14 (14C), which has eight neutrons, is commonly used to determine the age of fossils through radiometric dating.
The discovery of subatomic particles and isotopes required modification of Dalton's original atomic theory. The first two parts of Dalton's theory have been partially disproven. Scientists now know that an atom is the smallest unit that has all the properties of an element, although it can be broken down further. Additionally, all atoms of the same element have the same number of protons, but their masses can vary slightly, depending on their number of neutrons. The atomic weight listed on the periodic table is the average mass of all isotopes of an element, based on the relative abundance of each isotope. The third and fourth parts of Dalton's theory hold true: two or more elements combine to form compounds, and chemical reactions are rearrangements of atoms without destruction or creation of new atoms.
<Early Atomic Theory>Describing and Comparing Atoms
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EPDCCH search space candidates - MATLAB lteEPDCCHSpace - MathWorks India
lteEPDCCHSpace
EPDCCH Search Space
EPDCCH search space candidates
[ind,info] = lteEPDCCHSpace(enb,chs)
[ind,info] = lteEPDCCHSpace(enb,chs) returns a matrix or cell array of EPDCCH ECCE candidate indices, and related dimensional information for the given cell-wide settings structure and EPDCCH transmission configuration structure. Depending on the configuration, the function returns a matrix of candidates for a single EPDCCH set, or a cell array containing one or two matrices of candidates for one or two EPDCCH sets.
EPDCCH Search Space for DCI Format 2A and 1.
For a particular configuration, establish the sizes of DCI messages for format 2A and format 1. Note that for DCI messages conveyed on the EPDCCH, ControlChannelType should be set to 'EPDCCH'.
dcisizes = lteDCIInfo(enb,chs);
format2Asize = dcisizes.Format2A
format2Asize = uint64
format1size = dcisizes.Format1
format1size = uint64
Create the EPDCCH search space candidates for a localized EPDCCH transmission of a DCI format 2A message.
[candidates,info] = lteEPDCCHSpace(enb,chs)
candidates = 4×2
NECCEPerEPDCCH: 4
EPDCCHCase: 1
NECCE: 16
Create the candidates for a DCI format 1 message for the same configuration. The DCI format 1 message is smaller than the format 2A message, resulting in a change of case number (info.EPDCCHCase) from 1 to 3. The aggregation level (info.NECCEPerEPDCCH) changes from 4 to 2, resulting in a greater number of candidates.
chs.DCIFormat = 'Format1';
{N}_{\text{RB}}^{\text{DL}}
The following parameter applies only when chs.EPDCCHStart is absent.
EPDCCHType Required if the EPDCCH type list parameter field is absent
EPDCCHPRBSet Required if the EPDCCH Type list parameter field is absent
EPDCCHFormat Required
Number of ECCEs per EPDCCH transmission (equivalently the aggregation level L) as required by TS 36.211 Table 6.8A 1–2.
DCIFormat Optional
PRB pair indices for one or two EPDCCH sets
EPDCCHTypeList Optional
cell array of one or two arrays
EPDCCH transmission types for one or two EPDCCH sets
ind — EPDCCH ECCE candidate indices
M-by-2 matrix | cell array
EPDCCH ECCE candidate indices, returned as an M-by-2 matrix or a cell array containing 2 M-by-2 matrices. M is the number of EPDCCH candidates monitored for the configuration provided. This variable is defined in TS 36.213 Tables 9.1.4-1a to 9.1.4-5b. Each two-element row of the matrix ind (or the rows of each matrix in cell array ind) contains the inclusive indices of a single EPDCCH candidate location.
If chs.EPDCCHPRBSetList and chs.EPDCCHTypeList are present and either chs.EPDCCHPRBSet or chs.EPDCCHType are absent, one or two EPDCCH sets are returned in a cell array containing one or two matrices, one for each set.
If both chs.EPDCCHPRBSet and chs.EPDCCHType are present, only the single candidate matrix which matches the PRB set size and EPDCCH type given by chs.EPDCCHPRBSet and chs.EPDCCHType is returned. This allows the number of candidates M to be correctly calculated for TS 36.213 Tables 9.1.4-3a to 9.1.4-5b (corresponding to two EPDCCH sets) while returning a single set of candidates in matrix form. This format is consistent with the parameterization other EPDCCH-related functions that take CHS.EPDCCHPRBSet and CHS.EPDCCHType as parameters and operate on a single EPDCCH set.
If chs.EPDCCHPRBSetList is absent, then chs.EPDCCHPRBSet is required, and if chs.EPDCCHTypeList is absent then chs.EPDCCHType is required.
info — Dimensional information about the EPDCCH search space candidates
Dimensional information about the EPDCCH search space candidates, returned as a scalar structure containing:
nEPDCCH
Number of REs in a PRB pair configured for possible EPDCCH transmission. See TS 36.211. [1], Section 6.8A.1.
NECCEPerPRB
Number of ECCE per PRB pair
NEREGPerECCE
Number of EREG per ECCE
NECCEPerEPDCCH
Number of ECCES per EPDCCH transmission (equivalently the EPDCCH aggregation level L) as given by TS 36.211 [1] ,Table 6.8A.1-2
EPDCCHCase
Case number (1,2,3). See TS 36.213 [2], Section 9.1.4
One or two element vector containing the number of ECCE available for transmission of EPDCCHs in the PRB pair set
lteEPDCCH | lteEPDCCHDecode | lteEPDCCHIndices | lteEPDCCHSearch | lteEPDCCHPRBS
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Fareed wants to add
\frac { 1 } { 4 } + \frac { 5 } { 8 }
Add the fractions by using a Giant One to create a common denominator.
What do you need to multiply the first term by so that the denominator is equal to
8
Multiplying the denominator by
2
8
. Now use a Giant One to solve the problem.
\frac{1}{4} \:\cdot
=\frac{2}{8}
Now that both fractions have the same denominator, you can add the fractions together by adding the numerator and keeping the denominator.
\frac{2}{8}+\frac{5}{8}=?
\frac{7}{8}
How can factors help you find a common denominator?
Four is a factor of eight. So eight can be a common denominator.
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verify/after - Maple Help
Home : Support : Online Help : verify/after
verify after calling a function
verify(x, y, 'after'(f, verification, other, arguments))
expressions to be verified
transformer that will be applied to x and y before verification
other, arguments
(optional) arguments passed to f after x or y
The verify(x, y, after(f)) calling sequence returns true if f(x) and f(y) are equal.
The verify(x, y, after(f, ver, other, arguments)) calling sequence returns true if f(x, other, arguments) and f(y, other, arguments) compare as equal under the verification verification.
If you want to specify extra arguments to be passed to f, you must specify verification, too. The default verification is boolean, which tests for equality.
To see if two values have the same absolute value, you could use the verification after(abs).
a≔-5
\textcolor[rgb]{0,0,1}{a}\textcolor[rgb]{0,0,1}{≔}\textcolor[rgb]{0,0,1}{-5}
b≔3+4I
\textcolor[rgb]{0,0,1}{b}\textcolor[rgb]{0,0,1}{≔}\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{4}\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{I}
\mathrm{verify}\left(a,b,\mathrm{after}\left(\mathrm{abs}\right)\right)
\textcolor[rgb]{0,0,1}{\mathrm{true}}
To see if two expressions are the same, except for the arguments to the function f, you can use this verification. Note that we have to explicitly have to specify the boolean verification in order to pass extra arguments to subsindets.
a≔2+\mathrm{sin}\left(f\left(3,4\right)\right)f\left(5\right)
\textcolor[rgb]{0,0,1}{a}\textcolor[rgb]{0,0,1}{≔}\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{\mathrm{sin}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{4}\right)\right)\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{5}\right)
b≔2+\mathrm{sin}\left(f\left(1\right)\right)f\left(2,6\right)
\textcolor[rgb]{0,0,1}{b}\textcolor[rgb]{0,0,1}{≔}\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{\mathrm{sin}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{1}\right)\right)\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{6}\right)
\mathrm{verify}\left(a,b,\mathrm{after}\left(\mathrm{subsindets},\mathrm{boolean},\mathrm{specfunc}\left(f\right),\mathrm{fx}↦f\left(\right)\right)\right)
\textcolor[rgb]{0,0,1}{\mathrm{true}}
To see if two lists are the same when considered as sets, except for arguments to the function f, use a variation on the previous calling sequence that uses the as_set verification.
a≔[2+\mathrm{sin}\left(f\left(3,4\right)\right)f\left(5\right),f\left(2\right)+\mathrm{cos}\left(x\right)]
\textcolor[rgb]{0,0,1}{a}\textcolor[rgb]{0,0,1}{≔}[\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{\mathrm{sin}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{4}\right)\right)\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{5}\right)\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{2}\right)\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{\mathrm{cos}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{x}\right)]
b≔[\mathrm{cos}\left(x\right)+f\left(3,5\right),\mathrm{sin}\left(f\left(2,5\right)\right)f\left(6\right)+2]
\textcolor[rgb]{0,0,1}{b}\textcolor[rgb]{0,0,1}{≔}[\textcolor[rgb]{0,0,1}{\mathrm{cos}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{x}\right)\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{5}\right)\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{sin}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{5}\right)\right)\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{f}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{6}\right)\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{2}]
\mathrm{verify}\left(a,b,\mathrm{after}\left(\mathrm{subsindets},\mathrm{as_set},\mathrm{specfunc}\left(f\right),\mathrm{fx}↦f\left(\right)\right)\right)
\textcolor[rgb]{0,0,1}{\mathrm{true}}
The verify/after command was introduced in Maple 2021.
verify,structured
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82Dxx Applications to specific types of physical systems
82D10 Plasmas
82D15 Liquids
82D20 Solids
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
82D37 Semiconductors
82D40 Magnetic materials
82D45 Ferroelectrics
82D50 Superfluids
82D60 Polymers
82D77 Quantum wave guides, quantum wires
82D80 Nanostructures and nanoparticles
A
A
A
-\infty
Mathieu Lewin, Séverine Paul (2014)
The method of choice for describing attractive quantum systems is Hartree−Fock−Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree−Fock−Bogoliubov theory from the point of view of numerical analysis. We start by discussing its proper discretization and then analyze the convergence of the simple fixed point (Roothaan)...
José Francisco Rodrigues, Lisa Santos (2000)
C. Bolley, B. Helffer (1993)
An equation for the limit state of a superconductor with pinning sites.
Sun, Jianzhong (2005)
Zhiming Chen, Qiang Du (2000)
Bernard Helffer (2000/2001)
Bulk superconductivity in Type II superconductors near the second critical field
Soren Fournais, Bernard Helffer (2010)
We consider superconductors of Type II near the transition from the ‘bulk superconducting’ to the ‘surface superconducting’ state. We prove a new
{L}^{\infty }
estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty [AS].
Neuberger, John W., Renka, Robert J. (2003)
Critical points of the Ginzburg-Landau functional on multiply-connected domains.
Neuberger, J.W., Renka, R.J. (2000)
Decay for travelling waves in the Gross–Pitaevskii equation
Philippe Gravejat (2004)
Div-curl lemma revisited: Applications in electromagnetism
Marián Slodička, Ján Jr. Buša (2010)
Two new time-dependent versions of div-curl results in a bounded domain
\Omega \subset {ℝ}^{3}
are presented. We study a limit of the product
{v}_{k}{w}_{k}
, where the sequences
{v}_{k}
{w}_{k}
{Ł}_{2}\left(\Omega \right)
. In Theorem 2.1 we assume that
\nabla ×{v}_{k}
is bounded in the
{L}_{p}
-norm and
\nabla ·{w}_{k}
is controlled in the
{L}_{r}
-norm. In Theorem 2.2 we suppose that
\nabla ×{w}_{k}
{L}_{p}
\nabla ·{w}_{k}
{L}_{r}
-norm. The time derivative of
{w}_{k}
is bounded in both cases in the norm of
-1\left(\Omega \right)
. The convergence (in the sense of distributions) of
{v}_{k}{w}_{k}
to the product
vw
of weak limits...
Dynamical instability of symmetric vortices.
Luis Almeida, Yan Guo (2001)
Using the Maxwell-Higgs model, we prove that linearly unstable symmetric vortices in the Ginzburg-Landau theory are dynamically unstable in the H1 norm (which is the natural norm for the problem).In this work we study the dynamic instability of the radial solutions of the Ginzburg-Landau equations in R2 (...)
Evelyne Miot (2009/2010)
On considère une équation de Ginzburg-Landau complexe dans le plan. On étudie un régime asymptotique à petit paramètre dans lequel les solutions comportent des singularités ponctuelles, appelées points vortex, et on détermine un système d’équations différentielles ordinaires du premier ordre décrivant la dynamique de ces points jusqu’au premier temps de collision.
Electronic properties of superconductor-semiconductor mesoscopic device.
Awadalla, Attia.A. (2006)
Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity
Junichi Aramaki (2010)
We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space
{ℝ}^{n}
. In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is
\left(n-2\right)
-rectifiable. In this paper, we shall show that under some additive smoothness assumptions, the
\left(n-2\right)
-dimensional Hausdorff measure of singular set...
Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.
Zaouch, Fouzi (2005)
|
11E12 Quadratic forms over global rings and fields
11E10 Forms over real fields
11E41 Class numbers of quadratic and Hermitian forms
K
-theory of quadratic and Hermitian forms
p
-adic theory
A characterization of tame Hilbert-symbol equivalence
Kazimierz Szymiczek (1998)
Stephen Beale, D.K. Harrison (1989)
D.R. Heath-Brown (1996)
Jacek Bochnak, Byeong-Kweon Oh (2008)
We investigate the almost regular positive definite integral quaternary quadratic forms. In particular, we show that every such form is
p
-anisotropic for at most one prime number
p
. Moreover, for a prime
p
there is an almost regular
p
-anisotropic quaternary quadratic form if and only if
p\le 37
. We also study the genera containing some almost regular
p
-anisotropic quaternary form. We show several finiteness results concerning the families of these genera and give effective criteria for almost regularity....
An arithmetic problem on the sums of three squares
A. Arenas (1988)
An arithmetical property of quadratic forms.
Walter Ledermann (1959)
An Artin Character and Represenattions of Primes by Binary Quadratic Forms.
Pierre Kaplan, K.S. Williams (1980/1981)
Arf equivalence II
Jeonghun Kim, Robert Perlis (2012)
Arithmetical quadratic surfaces of genus 0, I.
J. Brezinski (1980)
Bounds for quadratic Waring's problem
Myung-Hwan Kim, Byeong-Kweon Oh (2002)
Arjeh M. Cohen, Gabriele Nebe, Wilhelm Plesken (1996)
Characteristic vectors of unimodular lattices which represent two
Mark Gaulter (2007)
We improve the known upper bound of the dimension
of an indecomposable unimodular lattice whose shadow has the third largest possible length,
n-16
Class number formulas for quaternary quadratic forms
Paul Ponomarev (1981)
Jih-Min Shyr (1979)
Class numbers of binary quadratic lattices over algebraic number fields
O. Körner (1981)
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Modality (philosophy) - zxc.wiki
In philosophy, modality describes the way something is, happens or is thought.
1 Concept and types of modality
1.1 Modalities in the strict sense
1.2 Modalities in the broader sense
2 Modality and Possible Worlds Theory
3 theories about actuality
Concept and types of modality
Modalities in the strict sense
In the narrower, classic sense, the term modality denotes the alethic (truth-related) modality: in ontological terms, it is the way in which a state of affairs exists or, more logically, the truth of statements .
In addition to the simple (factual) truth, a distinction is usually made between necessity , possibility and impossibility and contingency .
The concept of the (alethic) modality is already used by the commentators on Aristotle .
According to Kant , categories of modality are possibility, reality and necessity, to which the modality of judgments (problematic (possible), assertoric (real), apodictic (necessary)) should correspond.
Leibniz differentiates between four basic categories of types of statements or facts : necessary, possible, impossible and contingently true (actual).
Classical theorists as well as modern semantics , philosophy of language , logic (especially modal logic ) and ontology have proposed different theories about the nature of these statements and their truth makers .
Modalities in the broader sense
In addition to the alethic modalities mentioned, one also speaks of the modalities in the broader sense and means (among other things) the ways in which a statement can be true in relation to the knowledge of the telling, the time or the ought. This covers the doxastic (epistemic), temporal or deontic modalities.
The different modalities can be traced back to each other, are in an analogous relationship and justify different modal logics :
formula Modal logic i. e. S. Deontic logic Temporal logic Doxastic logic
{\ displaystyle \ Diamond}
p It is possible that p It is permissible that p p applies sometime in the future (past) I think it is possible that p
{\ displaystyle \ Box}
p It is necessary that p It is imperative that p p is always valid in the future (past) I consider it certain that p
Modality and Possible Worlds Theory
Following Leibniz, Rudolf Carnap ( Meaning and Necessity 1947), Saul Kripke and David Kellogg Lewis suggested that modal statements should be understood as statements about or in possible worlds . A necessary truth is true in all of these worlds, a possible truth in at least one. These worlds, according to Lewis, are real and even concrete objects, not just concepts in the mind or abstract universals. This ontologically demanding option has theoretical advantages because it enormously simplifies the semantic evaluation of modal statements . In addition, there are ontologically irreducible relationships between these possible worlds, which makes the evaluation of conditionalities (if ... then ...) and v. a. of counterfactual conditionalities (if it weren't… then…) are very elegantly simplified. Nevertheless, many ontologists are not ready to add so many additional irreducible objects to their ontological inventory. Some therefore try to maintain the theoretical elegance of many-worlds semantics, but propose anti- realistic substitute theories regarding the ontological dignity of these worlds.
Theories about actuality
Theories about actuality are a separate subject area in these debates : What is constitutive for the fact that the actual world is the actual and no other possible world? A much-discussed proposal understands "aktual" as indexical expression when: I say that a situation is aktual, then I say that he listened to the world that I (the speaker) inhabit (and I now their inventory with your finger show can ). (According to Lewis, who takes this position, there is no identity of objects across different worlds (so-called transworld identity), only counterparts; there is therefore only one speaker.) Alternatively, for example, that world can be determined as actual, in which we do the evaluation of an utterance .
Modality (linguistics) (for the linguistic expression of modality and finer distinctions)
Nicolai Hartmann: Possibility and Reality. de Gruyter, Berlin 1938.
Robert Merrihew Adams: Theories of Actuality. In: Noûs , 8/3 (1974), pp. 211-231, also in: Loux 1979.
John Divers: Possible Worlds. Routledge, 2002.
David Kellogg Lewis : On the Plurality of Worlds. Blackwell, 1986.
Michael J. Loux (Ed.): The Possible and the Actual. Cornell University Press, Ithaca NY 1979.
Uwe Meixner: Modality. Possibility, necessity, essentialism . Klostermann, Frankfurt am Main 2008, ISBN 978-3-465-04050-7 .
Alvin Plantinga : Actualism and Possible Worlds. In: Theoria 42 / 1-3 (1976), pp. 139-160, also in: ders .: Essays in the Metaphysics of Modality. Matthew Davidson (Ed.): Oxford University Press, New York NY 2003, pp. 103–121 and also in Loux 1979.
Alvin Plantinga: Two Concepts of Modality: Modal Realism and Modal Reductionism. In: James E. Tomberlin (ed.): Philosophical Perspectives , 1 (1987), Atascadero, CA: Ridgeview, pp. 189-231, also in: Plantinga 2003, 192-228.
Alexander R. Pruss: The Actual and the Possible . In: Richard M. Gale (Ed.): The Blackwell Guide to Metaphysics . Blackwell 2002.
Ted Sider : Reductive Theories of Modality (PDF; 310 kB). In: MJ Loux, DW Zimmerman (Eds.): The Oxford Handbook of Metaphysics. OUP 2003.
Robert Stalnaker : Possible Worlds. In: Noûs , 10/1 (1976), pp. 65-75 also in Loux 1979.
Peter van Inwagen : Two Concepts of Possible Worlds. In: Peter A. French, Theodore E. Uehling, Jr., Howard K. Wettstein (Eds.): Midwest Studies in Philosophy 11 (Studies in Essentialism), University of Minnesota Press, Minneapolis MN 1986, pp. 185-213; also in van Inwagen 2001, pp. 206–242.
Peter van Inwagen: Ontology, Identity, and Modality : Essays in Metaphysics. Cambridge Studies in Philosophy. Cambridge University Press, Cambridge 2001.
Boris Kment: Varieties of Modality. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
Takashi Yagisawa: possible objects. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
Christopher Menzel: actualism. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
Simo Knuuttila: Medieval Theories of Modality. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
David Kellogg Lewis: Modal Realism - Compilation of informative quotes
This page is based on the copyrighted Wikipedia article "Modalit%C3%A4t_%28Philosophie%29" (Authors); it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License. You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA.
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Physics - Tipping the Balance
January 26, 2012 • Physics 5, s15
The breaking of charge-parity symmetry at lower temperatures than expected in the initial stages of the big bang could explain the abundance of matter over antimatter in the universe.
Were physics nice and symmetric, we might not be here: a universe in which the big bang created equal parts matter and antimatter could have simply annihilated itself. Things seem to be mostly matter, however, an imbalance that requires, among other things, a breaking of CP (charge-parity) symmetry at primordial high temperatures. All the bits and pieces of a proper understanding of this asymmetry appear to be present in the standard model of particle physics, but the problem is the lack of a specific physical mechanism that yields the correct value for the abundance of matter versus antimatter.
As they explain in a paper in Physical Review Letters, Tomáš Brauner at the University of Bielefeld, Germany, and colleagues propose that an asymmetry in the number of baryons may in fact be generated at lower than expected temperatures. Previous calculations suggested that CP violation within the standard model could not be a factor at the extremely high energies found in the initial moments after the big bang and so this CP effect has conventionally been neglected. Based on their calculations of a quantity called the effective bosonic action, which captures the creation and annihilation of the building blocks of matter, the authors argue otherwise. In their calculations of the detailed temperature dependence of CP violation, Brauner et al. show that the CP symmetry breaking is much stronger at lower temperatures (below giga-electron-volt) than at temperatures where electroweak symmetry breaking occurs (around giga-electron-volts). The authors hope that this finding of a strong low-temperature effect may invite a new look at scenarios for “cold” baryon generation and a fresh approach to understanding matter/antimatter asymmetry. – David Voss
Temperature Dependence of Standard Model
CP
Violation
Tomáš Brauner, Olli Taanila, Anders Tranberg, and Aleksi Vuorinen
CP
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MIMO Robustness Analysis - MATLAB & Simulink - MathWorks í•œêµ
K\left(I+GK{\right)}^{-1}G
K\left(I+GK{\right)}^{-1}
This result tells you that the gain at the second plant output can vary by factors between about 0.07 and about 14.7, without the second loop going unstable. Similarly, the loop can tolerate phase variations at the output up to about ±82°.
This result tells you that the gain at the plant input can vary in both channels independently by factors between about 1/8 and 8 without the closed-loop system going unstable. The system can tolerate independent and concurrent phase variations up about ±76°. Because the multiloop margins take loop interactions into account, they tend to be smaller than loop-at-a-time margins.
When you consider all such variations simultaneously, the margins are somewhat smaller than those at the inputs or outputs alone. Nevertheless, these numbers indicate a generally robust closed-loop system. The system can tolerate significant simultaneous gain variations or ±30° degree simultaneous phase variations in all input and output channels of the plant.
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Design and Preliminary Validation of Grasp Assistive Device for an Industrial Environment | J. Med. Devices | ASME Digital Collection
Daniel Loewen,
e-mail: dploewen@uwaterloo.ca
1Corresponding author. e-mail: nchandra@uwaterloo.ca
Loewen, D., and Chandrashekar, N. (February 3, 2022). "Design and Preliminary Validation of Grasp Assistive Device for an Industrial Environment." ASME. J. Med. Devices. June 2022; 16(2): 021002. https://doi.org/10.1115/1.4052899
Carpal tunnel syndrome and tendonitis are two common upper extremity cumulative trauma disorders (CTD) related to repetitive and forceful activities in industrial environments. Reducing the muscular force during activities such as the operation of a pistol grip hand tool could result in lower incidence of CTDs. The objective of this research was to reduce the muscular contribution to the grip force using an active grasp assist orthosis system. A novel soft, pneumatic grasp assistive device was designed to augment the users' strength during operation of pistol grip hand tool. The optimized design was fabricated using rapid prototyping. Device effectiveness was quantified by measuring muscle activity and grip force during an in vivo study of a common industrial activity. Nine subjects experienced with power tools employed by an automobile manufacturer installed 18 fasteners using a pistol grip DC tool with and without the grasp assistive device. Surface electromyography (sEMG) was used to measure the activity of four muscles commonly associated with grasping. The grasp assist significantly reduced the mean, combined, normalized muscle activity by 18% (
p<0.05
). Muscle activation results were contextualized using the revised strain index (RSI). The grasp assistive device trial yielded a significantly lower mean RSI value than the typical trial by 13% (
p<0.05
). Using an active grasp assist orthosis could reduce the incidence of CTDs in able bodied industrial workers using DC hand tools. The device used a unique design of sinusoidal bellows oriented at 45 deg to the plane of symmetry that yielded higher force output and a lower bending ratio and lower input pressure with acceptable device rigidity and strength.
Actuators, Design, Electromyography, Fasteners, Muscle, Pressure, Bellows (Equipment), Grasping, Rapid prototyping, Orthotics
M. C. T. F. M.
Carpal Tunnel Syndrome: Prevalence in the General Population
Ergonomics Considerations in Hand and Wrist Tendinitis
Hand Wrist Cumulative Trauma Disorders in Industry
.10.1136/oem.43.11.779
,” Table 14-10-0202-01, Statistics Canada, Ottawa, ON, Canada.
,” United States Department of Labor, Washington, DC, accessed July 20, 2019, https://www.bls.gov/emp/tables/employment-by-major-industry-sector.htm
Occupational Factors and Carpal Tunnel Syndrome
.10.1002/ajim.4700110310
Carpal Tunnel Syndrome: Objective Measures and Splint Use
Björing
The Effect of Wrist Orthoses on Forearm Muscle Activity
.10.5014/ajot.53.5.434
Zoppi Filho
Electromyography of the Upper Limbs During Computer Work: A Comparison of 2 Wrist Orthoses in Healthy Adults
RoboGlove—A Robonaut Derived Multipurpose Assistive Device
Ingvast
The Soft Extra Muscle System for Improving the Grasping Capability in Neurological Rehabilitation
,” IEEE-EMBS Conference on Biomedical Engineering and Science (
), Langkawi, Malaysia, Dec. 17–19, pp.
.10.1109/IECBES.2012.6498090
Force Transmission in Joint-Less Tendon Driven Wearable Robotic Hand
, Jeju, Korea, Oct. 17–21, pp.
.https://ieeexplore.ieee.org/document/6393148?arnumber=6393148
The Excellences of Exoskeletons for Medical Equipment
Rob. Auton. Syst
Pistol Grip Power Tool Handle and Trigger Size Effects on Grip Exertions and Operator Preference
Mechanical Characterization and FE Modelling of a Hyperelastic Material
Mater. Res
Experimental Determination of Elastic and Rupture Properties of Printed Ninjaflex
Fifth. Springfield, IL
Normalization of Upper Trapezius EMG Amplitude in Ergonomic Studies
Filtering the Surface EMG Signal: Movement Artifact and Baseline Noise Contamination
Normalisation of EMG Amplitude: An Evaluation and Comparison of Old and New Methods
Kapellusch
PolygerinosWang
Elsamadisi
Scalable Manufacturing of High Force Wearable Soft Actuators
.10.3233/WOR-152146
Prediction of Handgrip Forces Using Surface EMG of Forearm Muscles
Kozupa
Hand grip-EMG Muscle Response
.10.12693/APhysPolA.125.A-7
Carpal Tunnel Syndrome and Its Relation to Occupation: A Systematic Literature Review
.10.1093/occmed/kql125
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Desaturate - Maple Help
Home : Support : Online Help : Graphics : Packages : ColorTools : Color and Color Object Manipulation Commands : Desaturate
create a new color with lower saturation
Desaturate(color)
Desaturate(color, factor)
The Desaturate command creates a new Color structure which has the same hue and lightness as the input color (in the hardward dependent HSV colorspace), but its saturation is multiplied by a factor of 0.8. In other words, the new Color structure is less colorful by a factor of 0.8, if possible within the bounds of the HSV colorspace.
If the optional parameter factor is given the output is desaturated by that factor if it is greater than 1, and the reciprocal otherwise. Use the Saturate command to increase the saturation.
\mathrm{with}\left(\mathrm{ColorTools}\right):
\mathrm{Desaturate}\left("Coral"\right)
\textcolor[rgb]{0,0,1}{〈}\colorbox[rgb]{1,0.6,0.450980392156863}{$RGB : 1 0.598 0.451$}\textcolor[rgb]{0,0,1}{〉}
\mathrm{Desaturate}\left("Coral",1.5\right)
\textcolor[rgb]{0,0,1}{〈}\colorbox[rgb]{1,0.666666666666667,0.541176470588235}{$RGB : 1 0.665 0.542$}\textcolor[rgb]{0,0,1}{〉}
\mathrm{Desaturate}\left("Coral",\frac{1}{1.5}\right)
\textcolor[rgb]{0,0,1}{〈}\colorbox[rgb]{1,0.666666666666667,0.541176470588235}{$RGB : 1 0.665 0.542$}\textcolor[rgb]{0,0,1}{〉}
\mathrm{Desaturate}\left("Black"\right)
\textcolor[rgb]{0,0,1}{〈}\colorbox[rgb]{0,0,0}{$\textcolor[rgb]{1,1,1}{RGB : 0 0 0}$}\textcolor[rgb]{0,0,1}{〉}
The ColorTools[Desaturate] command was introduced in Maple 16.
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Physics - Top Quarks Go Solo in Rare Events
Top Quarks Go Solo in Rare Events
Separate collider experiments observe the top quark without its usual antiparticle partner in unique processes that could give insight into new physics, such as additional sets of quarks.
Figure 1: These drawings (called Feynman diagrams) depict the different channels for single-top-production mechanisms. The letters refer to top quarks (
t
), bottom quarks (
b
), light quarks (
q
W
bosons (
W
), and gluons (g). In each case, the incoming particles are shown on the left and the outgoing particles on the right of the diagram. The circles indicate the
W\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}b
vertex, whose coupling strength is governed by the CKM matrix element
{V}_{t\phantom{\rule{0}{0ex}}b}
.These drawings (called Feynman diagrams) depict the different channels for single-top-production mechanisms. The letters refer to top quarks (
t
b
q
W
W
), and gluons (g). In each case, the incoming particles ... Show more
The subatomic elementary particles known as quarks are among the building blocks of the standard model (SM) of particle physics. Protons and neutrons are made of the lightest, up and down quarks, but the unstable strange, charm, bottom, and top quarks can also be produced in high-energy particle accelerators. The enigmatic top quark—which is the heaviest elementary particle, weighing as much as a gold nucleus—has only been studied at Fermilab’s Tevatron collider near Chicago and at the Large Hadron Collider at CERN, Geneva. It is most often produced with its antiparticle (antitop) through the strong interaction, but it also appears singly through the electroweak interaction, as was demonstrated in [1,2]. Two new papers in Physical Review Letters [3,4] report the first observations of single top quarks coming out of less common electroweak reactions, or “channels.” The results fall within SM predictions, but further studies of the relative frequency of these rare channels may reveal new physics, such as a hidden generation of quarks or unexpected top-quark couplings.
Although it fits into the SM as the partner of the bottom quark, the top quark appears anomalous because of its extremely large mass of giga-electron-volts ( ), about times that of the bottom quark. Its mass is also close to those of the and bosons, the force carriers of the electroweak interaction, and that of the recently discovered Higgs boson, leading to speculation that the top quark may play some role in triggering electroweak symmetry breaking, which confers mass on otherwise massless particles.
One of the ways to study the top quark is to look at how it appears in particle collision debris. Theory predicts that electroweak interactions will produce top quarks in three distinct channels (see Fig. 1). The most common channel—and the only one previously isolated—is the channel, in which a bottom quark transforms into a top quark through the exchange of a boson with another quark. In the rarer channel, a quark and antiquark convert—through an intermediate boson—into a top and an antibottom. The last single-top process is the channel, given this name because it produces a top and boson from the interaction of a bottom quark and gluon.
The rate of occurrence for these different channels is governed by elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which connects the electroweak interactions of all the quarks [5,6]. In the standard model, this is a matrix, with one row and column for each of the three doublets, or generations, of quarks. As can be seen in Fig. 1, all of the single-top channels include an interaction between a top quark, a bottom quark, and a boson. The strength of this interaction, or vertex, is given by the CKM matrix element . Current estimates—based on a global fit of all the available data within the SM framework—suggest . However, this assumes that the CKM matrix is complete; i.e., there are no other quarks. A fourth, as-yet-undiscovered generation of quarks would enlarge the CKM matrix and likely affect the value of . Observations of single top quarks can provide direct measurements of and thereby test for additional structure in the CKM matrix, or give evidence for other unexpected processes involving top quarks [7].
Single-top production is a very rare process, happening at the Tevatron about once in every proton-antiproton collisions at tera-electron-volts ( ). When the top quark is produced, it immediately decays into a bottom quark and a boson. About of the time, the decays to a high-energy electron or muon and a neutrino. The electron or muon gives a striking signature in the detector, but the neutrino escapes from the apparatus undetected and gives rise to an apparent imbalance in the total momentum transverse to the direction of the colliding beams. The bottom quark gives rise to a collimated spray or “jet” of particles in the detector, including a long-lived particle (a hadron) that typically decays a few millimeters from the initial collision point. Thanks to silicon detectors placed a few centimeters from the beam line, these “ jets” can be identified or “tagged,” distinguishing them from other, more common jets produced in the decays of light quarks and gluons. Previous work at the Tevatron was able to isolate the -channel process in their top-quark event sample [1,2]. And although the Tevatron is no longer running, scientists from its CDF and D0 experiments have now combined some of their past data in order to look for the rarer channel.
Selecting events with high-energy electrons or muons, unbalanced transverse momentum, and -tagged jets allowed the physicists of the CDF and D0 collaborations to narrow down their -channel search to a few 10,000s of events. But over of these top-producing events result from either strong interactions that give two top quarks or the already well-known -channel single-top process. No single event property provides enough discrimination power to clearly distinguish -channel single top from these backgrounds, so the collaborations employed boosted decision trees (BDT), a multivariate analysis technique based on machine learning methods to extract the most from the available information in each event. This technique relies on Monte Carlo computer simulation of high-energy particle collisions and the associated detector response to test how well certain combinations of variables—like the total energy in the event and the angles of different jets—can identify the signal from the major background sources. These simulations were extensively checked using data control samples, and their quality is a testament to the work of the many theoretical and phenomenological groups involved in modeling physics at these energies. Using a BDT analysis, each collaboration was able to demonstrate evidence for -channel single-top production [8], but only by combining their datasets did they manage to have enough sensitivity to reach the “five sigma” observation threshold, which is the gold standard in high-energy physics for establishing new phenomena beyond any reasonable doubt. The resulting rate or cross-section measurement of picobarns (pb) [3] is in good agreement with the latest theoretical calculation within the SM framework of [9].
The -channel process is initiated by the interaction of a quark and an antiquark. Since the LHC collides protons with protons (not antiprotons), it doesn’t have the same high-momentum antiquarks as the Tevatron and therefore is less likely to observe the channel. However, the much higher collision energy of the LHC ( in 2012) gives it a decisive advantage for the channel process. When the boson decays to an electron or muon, this process gives rise to events with two high-energy electrons or muons, momentum imbalance, and a jet, which unfortunately is nearly the same signature as the pair production of top quarks. Employing similar BDT-based analysis techniques, the CMS collaboration extracted a strong enough signal from part of the collision dataset recorded in 2012 to report observation of the process. The corresponding cross-section measurement is [4], in agreement with the SM theoretical prediction of [10], and giving a lower bound of at the confidence level. The ATLAS collaboration at the LHC has also reported evidence for production, but so far at a lower significance level [11].
Each of these analyses represents an experimental tour de force, extracting a very small signal from an almost overwhelming background. The Tevatron experiments developed multivariate analysis techniques, over many years, using them in their earlier -channel single-top-quark observation [1,2] and also in their searches for the Higgs boson. From the start of data taking, the LHC collaborations adopted similar techniques, which are already bearing fruit with the observation. With the closure of the Tevatron accelerator in 2011, the baton has now passed to the LHC, where we are looking forward to the first results from the upcoming run starting in 2015. This should allow a rich program of single-top-quark studies, subjecting the SM predictions to more detailed scrutiny and perhaps allowing a first glimpse of even rarer processes, such as the simultaneous production of a top quark and a or Higgs boson. Much challenging analysis will be needed, but these studies are sure to shed more light on this most mysterious elementary particle.
V. M. Abazov et al. (D0 Collaboration), “Observation of Single Top-Quark Production”, Phys. Rev. Lett. 103, 092001 (2009)
T. Aaltonen et al. (CDF Collaboration), “Observation of Electroweak Single Top-Quark Production,” Phys. Rev. Lett 103, 092002 (2009)
T. Aaltonen et al. (CDF Collaboration)†), “Observation of
s
-Channel Production of Single Top Quarks at the Tevatron,” Phys. Rev. Lett. 112, 231803 (2014)
S. Chatrchyan et al. (CMS Collaboration), “Observation of the Associated Production of a Single Top Quark -and a
W
pp
\sqrt{s}=8\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{TeV}
N. Cabibbo, “Unitary Symmetry and Leptonic Decays,” Phys. Rev. Lett. 10, 531 (1963)
M. Kobayashi and T. Maskawa, “
C\phantom{\rule{0}{0ex}}P
-Violation in the Renormalizable Theory of Weak Interaction,” Prog. Theor. Phys. 49, 652 (1973)
For a review, see T.M.P. Tait, and C.-P. Yuan, “Single Top Quark Production as a Window to Physics Beyond the Standard Model,” Phys. Rev. D 63, 014018 (2000)
T. Aaltonen et al. (CDF Collaboration), “Evidence for s-channel Single-Top-Quark Production in Events with One Charged Lepton and Two Jets at CDF,” Phys. Rev. Lett. (to be published); arXiv:1402.0484; T. Aaltonen et al. (CDF Collaboration), “Search for
s
-channel Single Top Quark Production in the Missing Energy Plus Jets Sample using the Full CDF II Data Set,” arXiv:1402.3756; V. M. Abazov et al. (D0 Collaboration), “Evidence for
s
-channel Single Top Quark Production in
p\phantom{\rule{0}{0ex}}\overline{p}
\sqrt{s}=1.96
TeV,” Phy. Lett. B 726, 656 (2013)
N. Kidonakis, “Next-to-Next-to-Leading Logarithm Resummation for
s
-channel Single Top Quark Production,” Phys. Rev. D 81, 054028 (2010)
N. Kidonakis, “NNLL Threshold Resummation for Top-Pair and Single-Top Production,” arXiv:1210.7813
G. Aad et al. (ATLAS Collaboration), “Evidence for the Associated Production of a
W
boson and a top quark in ATLAS at
\sqrt{s}=7
TeV,” Phys. Lett. B 716, 142 (2012)
Richard Hawkings has a Ph.D. in experimental particle physics from the University of Oxford, UK, and is now a senior research physicist at the CERN particle physics laboratory near Geneva, Switzerland. He has worked on the ATLAS experiment at the Large Hadron Collider since its conception in the early 1990s, and also on the OPAL experiment studying electron-positron collisions at the CERN LEP collider, and he has held physics analysis coordination roles on both experiments. His research interests focus on unraveling the mysteries of the top quark, electroweak interactions, and heavy flavor physics.
s
-Channel Production of Single Top Quarks at the Tevatron
T. Aaltonen et al. (CDF Collaboration†, D0 Collaboration‡)
Observation of the Associated Production of a Single Top Quark and a
W
pp
\sqrt{s}=8\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{TeV}
s
W
pp
\sqrt{s}=8\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{TeV}
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Estimate Time-Series Power Spectra - MATLAB & Simulink - MathWorks India
Estimate Time-Series Power Spectra at the Command Line
Estimate Time-Series Power Spectra Using the App
A frequency-response model encapsulates the frequency response of a linear system evaluated over a range of frequency values. When the data contains both input and output channels, the frequency-response model describes the steady-state response of the system to sinusoidal inputs. Time-series data contains no input channel. The frequency response of a time series model reduces to a spectral representation of the output data. This output data implicitly includes the effects of the unmeasured input noise.
For a discrete-time system sampled for both inputs and outputs with a time interval T, the transfer function G(z) relates the Z-transforms of the input U(z) and output Y(z):
Y(z) = G(z)U(z) + H(z)E(z)
H(z) represents the noise transfer functions for each output and E(z) is the Z-transform of the additive disturbance e(t) with variance Λ.
For a time-series model, this equation reduces to:
Y(z) = H(z)E(z)
In this case, E(z) represents the assumed, but unmeasured, white-noise input disturbance. The single-output noise spectrum Φ in the presence of disturbance noise with scalar variance λ is defined as:
{\Phi }_{v}\left(\omega \right)=\lambda T{|H\left(e{}^{i\omega T}\right)|}^{2}
The equivalent multi-output noise power spectrum can be given as:
{\Phi }_{v}\left(\omega \right)=TH\left({e}^{i\omega T}\right)\Lambda {H}^{\prime }\left({e}^{-i\omega T}\right)
Here, Λ is the variance vector with a length equal to the number of outputs.
You can use the etfe, spa, and spafdr commands to estimate power spectra of time series for both time-domain and frequency-domain data. These functions return estimated models that are represented by idfrd model objects, which contain the spectral data in the property SpectrumData and the spectral variance in the property NoiseCovariance. For multiple-output data, SpectrumData contains power spectra of each output and the cross-spectra between each output pair.
Commands for Estimating and Comparing Frequency Response of Time Series
Estimates a periodogram using Fourier analysis.
Estimates the power spectrum with its standard deviation using spectral analysis.
Estimates the power spectrum with its standard deviation using a variable frequency resolution.
spectrum Estimates and plots the output power spectrum of time series models.
For example, suppose y is time series data. Estimate the power spectrum g and the periodogram p using spa and etfe. Plot the models together with three standard deviation confidence intervals by using spectrum.
g = spa(y);
p = etfe(y);
spectrum(g,p);
For a more detailed example of spectral estimation, see Identify Time Series Models at the Command Line. For more information about the individual commands, see the corresponding reference pages.
You must have already imported your data into the app.
To estimate time series spectral models in the System Identification app:
Specify the frequencies at which to compute the spectral model in either of the following ways:
In the Frequency Resolution field, enter the frequency resolution, as described in Controlling Frequency Resolution of Spectral Models. To use the default value, enter default or leave the field empty.
To export the model to the MATLAB workspace, drag it to the To Workspace rectangle in the System Identification app. You can view the power spectrum and the confidence intervals of the resulting idfrd model object using the spectrum command.
idfrd | spa | spafdr | etfe
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Chapter 1 - manual
Chapter 1: Compartmental Models in Epidemiology
1. Compartmental Models in Epidemiology
1.3.1 Motivation
1.3.2 Definitions
1.3.3 Derivation
1.3.4 In Practice
1.1 Basic Disease Models
Disease modeling is quite complex. To begin with, it involves modeling entire populations in an ever-changing environment. Identifying which groups will contract a virus and how many people will have the virus at any given timestep is as much a computational challenge as it is a mathematical one.
However, at its very core, all disease modeling can be simplified to scenarios where some type of modeling is possible—and that is the beginning of infectious disease modeling.
Before starting with epispot, let's take a moment to observe simple ways to model infectious diseases—without the code and math behind compartmental models. The simplest way to do this, of course, would be through the use of simulations. For our simulations, we will need to group individuals into three categories:
Not yet infected with the virus
Infected and actively spreading the virus
Had the virus and are now immune and not spreading it or is dead (in which case they are also not spreading the virus)
The 'Removed' category is actually an abstraction created to make modeling easier. It really consists of two different categories: the Recovered and Dead categories. However, for simplicity, we merge these into one compartment in this chapter.
Now, we define a simulation in which each 'person' is a dot moving around a screen. In the beginning, everyone except one person is susceptible. The first person with the disease is often referred to as 'Patient Zero.' This patient will now go on to infect anyone they come in contact with (i.e. any dot in the same position as them). After a given amount of time, each dot will recover.
An excellent example of this can be seen in this Washington Post article by @HarryStevens. Although the simulation is small (only around 200 people), it gives a simple and intuitive feel for how a virus spreads throughout a population. Here's a sample of what it looks like:
An array of dots show susceptible, infected, and removed people in different colors; most cases are clustered around one location
Blue = Susceptible
Orange = Infected
Pink = Removed
1.2 Related Modeling Techniques
While a simulation can give us an intuitive feel for how a disease might spread, in order to actually analyze the results we're going to need data. And in order to get data we need an equation that can accurately represent the simulation above.
Before we derive this equation, though, it's important to understand the different types of models in epidemiology. Here are the main types:
1.2.1 Agent-based Modeling
Similar to the simulation we saw above, agent-based modeling is the process of using 'agents,' or some representation of people, to run a more complex simulation that will eventually give results about how a disease will spread.
Agent-based modeling, however, typically involves more complex tools than just animating dots. Most agent-based models will use population structures to model which classes of individuals will likely interact with other classes. The benefit with agent-based modeling is that it is stochastic. By stochastic, we mean that the model generates different results each time—just like a real epidemic. Because there is no guarantee that one person will be infected, real epidemics are indeed random. Additionally, agent-based models allow for more detailed analysis that other model types.
However, their largest downside is computational inefficiency. Agent-based models are not computationally efficient to implement, especially for large population sizes (imagine running the simulation above with 50,000 dots—and that's just the population of a small town).
1.2.2 Compartmental Models
Compartmental models, on the other hand, offer a nice balance between computational efficiency and mathematical precision. While they don't allow for precise per-demographic information, they can give quick and accurate estimates with some very simple (and elegant) math.
The idea behind all compartmental models is a compartment. Compartments, like we saw with our simulation, are essentially categories for grouping members of a population. Compartmental models use multiple compartments to model interactions between different compartments. For example, compartmental models will track the number of people in the susceptible compartment moving into the infected compartment because they were infected. By doing this at each timestep, compartmental models can keep track of different classes of individuals and generate estimates of the number of people in each compartment at any given timestep.
The main downside with compartmental models, aside from less detailed information, is that they are deterministic, that is to say, the opposite of stochastic. Essentially, compartmental models will give the same result every time and cannot generate a probability distribution, unlike with agent-based modeling. However, their speed and efficiency more than makes up for this.
The SIR Model, which stands for Susceptible, Infected, Recovered, is one of the most widely-used epidemiological models—it represents the simplest possible model that captures the full state of a disease outbreak through a system of ordinary differential equations.
The motivation for the SIR model may seem unclear at first since simulations, like those in 1.1, offer a much more visual and stochastic perspective than a system of ordinary differential equations. After all, in the simulation you can observe each individual dot and its contacts, as well as retain the stochastic nature of disease outbreaks.
While simulations are ideal, they lack many qualities that would be necessary for them to be used in actual modeling. Firstly, they are extremely computationally expensive (imagine running a simulation with upwards of 1 million dots for large cities). Secondly, and more importantly, they lack important constructs in epidemiology (that will be later explained in 1.3.2) that mean that the figures produced from such models are often incorrect and less precise than traditional modeling techniques (imagine how much more complex urban mobility is from the random movement in out simulations).
For these reasons, we turn to compartmental models, which not only offer more precise measurements but also strip down disease modeling to its core to achieve blazing fast modeling speeds.
In order to boil down disease modeling to its fundamental properties, we introduce the following definitions that will prove useful in 1.3.3 where we derive the actual equations for the SIR model. Later (in 1.3.4), we'll discuss how to merge the following two parameters into just one for the SIR model.
1. Beta (β)
\beta
Definition: The average number of susceptibles that one infected will infect per unit time, assuming that everyone else in the population is susceptible.
At the beginning of an outbreak, when everyone is susceptible, this parameter gives the number of susceptibles being infected by one infected per unit time. However, as people begin to get infected, beta no longer represents this quantity since an infected cannot infect another infected. At this stage in the outbreak, beta becomes a theoretical, but still important, quantity.
It is also worth pointing out that beta can and does change during the course of an outbreak. Measures like social distancing, quarantines, and improved hygiene can reduce this quantity as infecteds come into contact with less people, and festivals and large events can increase this quantity.
\gamma
Definition: The reciprocal of the average time it takes an infected to recover from the disease.
Gamma essentially tracks the inverse of the recovery time. In compartmental models, this is known as a rate—remember this, as it will come in handy later in more complex models. Higher values of gamma indicate lower recovery times and lower values of gamma indicate higher recovery times.
Armed with two important ideas—beta and gamma—we can now derive the system of equations behind the SIR model.
The first key insight is to create three different functions to represent the three different compartments, which are the building blocks of the SIR model. We let
\begin{cases} S(t) = \textrm{Susceptible}\\ I(t) = \textrm{Infected}\\ R(t) = \textrm{Removed} \end{cases}
The key here is to think about the change in each compartment rather the exact number of individuals in a compartment at a given time. To make things simpler, let's consider the base case: How many susceptibles does one infected infect per unit time? We know that:
Can be infected?
❌ (already infected)
❌ (either dead—which means reinfection not possible, or recovered—assumption is that recovered patients have already fought off the disease so reinfection is also not possible)
It is worth noting here that the SIR model makes a small assumption—deaths will not affect the population structure significantly enough to change the model dynamics. We will use this fact to simplify our derivation of the equations.
The table reveals that only susceptible patients can be infected—so we need to account for the probability that one infected will meet a susceptible to infect. We also know that if everyone was susceptible, one infected would infect
\beta
individuals. Remembering that there are
I
infecteds, we can write this as:
\frac{dS}{dt} = -\frac{\beta IS}{N}
We use the derivative to indicate the change in the susceptible compartment per unit time,
S
to represent the number of susceptibles, and
N
to represent the total population. Note the derivative is negative since these people are getting infected and leaving the susceptible compartment.
The next key insight we will use to derive this system will be to note that the population must stay constant (remember that we are assuming death does not significantly change the population structure):
S + I + R = N
In order for this to be true we must have:
\frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt} = 0
So in order to balance out the negative derivative of the susceptible compartment, either the infected or recovered compartment should have a positive derivative. Since people in the susceptible compartment cannot recover or die without first being infected, we know that the infected compartment must have the inverse derivative of the susceptible compartment.
\frac{dI}{dt} = -\frac{dS}{dt} = \frac{\beta IS}{N}
However, we also know that people move from the infected compartment into the removed compartment at the rate
\gamma
. Therefore we must also have
\frac{dI}{dt} = \frac{\beta IS}{N} - \gamma I
Lastly, since this last group of people are moving into the removed compartment, to ensure that the population is stable we must have
\frac{dR}{dt} = \gamma I
Putting all of this together yields the system of ordinary differential equations:
\begin{cases} \Delta S = -\frac{\beta IS}{N}\\ \Delta I = \frac{\beta IS}{N} - \gamma I\\ \Delta R = \gamma I \end{cases}
That's it! These equations now form the basic SIR model. However, while the base SIR model provides us with a tool for studying how many people are infected over the course of an outbreak, we can easily expand this model to include more compartments that can track hospitalizations, deaths, and other metrics.
To explore how we can expand this model, we'll consider a simple extension of the SIR model: the S-E-IR model, where the E stands for Exposed. In this model we can not only track the number of people infected but also the number of people who have the disease but cannot spread it yet. In epidemiology, the lag between exposure (having the disease) and infectiousness (spreading the disease) is known as the incubation period.
\delta
represent the incubation period in our model. Remember that, similarly to
\gamma
, it helps to use the reciprocal of the incubation period, specifically
\frac {1}{\textrm{time until infectiousness}}
We know that the derivative for the Susceptible compartment won't change because exposed individuals can't infect anyone. What does change, however, is which compartment receives the infected susceptibles. That compartment is, of course, the Exposed compartment. We can also write, similar to what we did with the Removed compartment, that the number of people leaving the Exposed compartment is equal to
\delta E
. Writing this together gives the derivative for the Exposed compartment:
\frac {dE}{dt} = \frac {\beta IS}{N} - \delta E
We also know that the portion of individuals leaving the Exposed compartment are moving to the Infected compartment. Putting this all together yields the system of equations for the SEIR model, as shown below:
\begin{cases} \Delta S = -\frac{\beta IS}{N}\\ \Delta E = \frac{\beta IS}{N} - \delta E\\ \Delta I = \delta E - \gamma I\\ \Delta R = \gamma I \end{cases}
At this point it's worth pointing out that epidemiologists don't rely on the parameter
\beta
that we have been using to simplify our models. Rather, they use a number known as R Naught, also called the effective reproductive number.
R Naught, or
R_0
, describes the number of people that one infected will infect over the duration of their infectious period assuming that the entire population is susceptible.
A very easy way to calculate
R_0
is to express it in terms of parameters we have already defined. If
\beta
yields the number of susceptibles infected per unit time, then we just need to multiply
\beta
by the infectious period to calculate
R_0
. As it happens,
\gamma
already gives us reciprocal of that number. Taking the reciprocal of
\gamma
itself will yield the time that an individual is infected. Lastly, multiplying this with
\beta
R_0 = \frac{\beta}{\gamma}
We can easily substitute this back into both our models to receive their standard forms. Both are shown below:
\begin{cases} \Delta S = -\frac{\gamma R_0 IS}{N}\\ \Delta I = \frac{\gamma R_0 IS}{N} - \gamma I\\ \Delta R = \gamma I \end{cases}
\begin{cases} \Delta S = -\frac{\gamma R_0 IS}{N}\\ \Delta E = \frac{\gamma R_0 IS}{N} - \delta E\\ \Delta I = \delta E - \gamma I\\ \Delta R = \gamma I \end{cases}
What we've just seen here is how we can compile a model from various compartments, using the SIR model as a base. We also can see the formulas that govern the laws of infectious disease dynamics. However, as you can imagine, compiling these formulas for each model you want to create and evaluating them again and again is quite tiring. That's where epispot comes in!
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13C05 Structure, classification theorems
13C10 Projective and free modules and ideals
13C11 Injective and flat modules and ideals
13C12 Torsion modules and ideals
13C60 Module categories
A characterization of Prüfer rings.
Shalom Feigelstock (1976)
A class of principal ideal rings arising from the converse of the Chinese remainder theorem.
Dobbs, David E. (2006)
A full uniform Artin-Rees theorem.
L. O'Carroll, A.J. Duncan (1989)
A General Resolution for Grade Four Gorenstein Ideals.
Andrew R. Kustin, Matthew Miller (1981)
A generalization of the finiteness problem of the local cohomology modules
Ahmad Abbasi, Hajar Roshan-Shekalgourabi (2014)
R
be a commutative Noetherian ring and
𝔞
R
. We introduce the concept of
𝔞
-weakly Laskerian
R
-modules, and we show that if
M
𝔞
R
-module and
s
is a non-negative integer such that
{\mathrm{Ext}}_{R}^{j}\left(R/𝔞,{H}_{𝔞}^{i}\left(M\right)\right)
𝔞
-weakly Laskerian for all
i<s
j
𝔞
-weakly Laskerian submodule
X
{H}_{𝔞}^{s}\left(M\right)
R
{\mathrm{Hom}}_{R}\left(R/𝔞,{H}_{𝔞}^{s}\left(M\right)/X\right)
𝔞
-weakly Laskerian. In particular, the set of associated primes of
{H}_{𝔞}^{s}\left(M\right)/X
is finite. As a consequence, it follows that if
M
R
N
𝔞
-weakly...
A note on basic free modules and the
{S}_{n}
Marcelo, Agustín, Marcelo, Félix, Rodríguez, César (2006)
A Note on Derivations of Commutative Rings.
Surender K. Gupta (1974)
A note on generalized primary rings
R. Chaudhuri (1976)
A note on indecomposable modules over valuation domains
Matt D. Lunsford (1995)
A note on indecomposable projective modules
A. G. Naoum (1989)
A Note on Projective Modules Over Polynomial Rings.
S.M. Bhatwadekar (1987)
A remark on projectively closed purities
A simple proof of uniqueness for torsion modules over principal ideal domains.
J. L. García Roig (1985)
The aim of this note is to give an alternative proof of uniqueness for the decomposition of a finitely generated torsion module over a P.I.D. (= principal ideal domain) as a direct sum of indecomposable submodules.Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces.For the sake of completeness we also include a proof of the existence theorem.
Algèbres localement polynomiales
Thierry Levasseur (1976/1977)
Groupe d'étude d'algèbre Groupe d'étude d'algèbre
Almost Artinian modules.
James Hein (1979)
Ex{t}_{R}\left(G,G\right)=0
Ext{¹}_{R}\left(G,G\right)=0
Michel Fliess, Hebertt Sira-Ramírez (2003)
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
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Up-Market Capture Ratio Definition
What Is the Up-Market Capture Ratio?
The up-market capture ratio is the statistical measure of an investment manager's overall performance in up-markets. It is used to evaluate how well an investment manager performed relative to an index during periods when that index has risen.
The up-market capture ratio can be compared with the down-market capture ratio. In practice, both measures are used in tandem.
The up-market capture ratio measures an investment manager's relative performance during bull markets.
The ratio is calculated by comparing the manager's returns in up-markets with that of a benchmark index.
Investors and analysts should consider both the up- and down-market capture ratios together to understand a manager's overall performance.
Calculating the Up-Market Capture Ratio
The up-market capture ratio is calculated by dividing the manager's returns by the returns of the index during the up-market and multiplying that factor by 100.
\begin{aligned}&\frac{\text{Up}}{\text{Down}}\ - \ \text{MCR}\ = \ \frac{\text{MR}}{\text{IR}}\ \times\ 100\\&\textbf{where:}\\&\text{MCR}=\text{market capture ratio}\\&\text{MR}=\text{manager's returns}\\&\text{IR}=\text{index returns}\end{aligned}
DownUp − MCR = IRMR × 100where:MCR=market capture ratioMR=manager’s returnsIR=index returns
Understanding the Up-Market Capture Ratio
An investment manager who has an up-market ratio greater than 100 has outperformed the index during the up-market. For example, an up-market capture ratio of 120 indicates that the manager outperformed the market by 20% during the specified period. Many analysts use this simple calculation in their broader assessments of individual investment managers.
If an investment mandate calls for an investment manager to meet or exceed a benchmark index’s rate of return, the up-market capture ratio is helpful for spotting those managers who are doing so. This is important to investors who use an active investment strategy and consider relative returns, rather than absolute returns (as hedge funds often seek).
The up-market capture ratio is just one of many indicators used by analysts to find good money managers. Because the ratio focuses on upside movements and doesn’t account for downside (losses) moves, some critics offer compelling evidence that it encourages managers to “shoot for the moon.” But when combined with complementary performance indicators, the up-market capture ratio does present valuable investment insight.
When evaluating an investment manager, it is best to consider the down-market capture ratio, too. This ratio is calculated in the same way except using down-market returns. Once both measures are known, a comparison may reveal that a manager with a large down-market ratio or poor up-market ratio still outperforms the market.
The market capture ratios of passive index funds should be very close to 100%.
Example of How to Use the Up-Market Capture Ratio
If the down-market ratio is 110 but the up-market ratio is 140, then the manager has been able to compensate for the poor down-market performance with strong up-market performance.
You can quantify this by dividing the up-market ratio by the down-market ratio to get the overall capture ratio. In our example, dividing 140 by 110 gives an overall capture ratio of 1.27, indicating the up-market performance more than offsets the down-market performance.
The same is true if the manager performs better in down-markets than up-markets. If the up-market ratio is only 90 but the down-market ratio is 70, then the overall capture ratio is 1.29, indicating that the manager is outperforming the market overall.
What Is Down-Market Capture Ratio?
The down-market capture ratio is a statistical measure of an investment manager's overall performance in down-markets.
|
Inverse incomplete gamma function - MATLAB gammaincinv - MathWorks Benelux
Plot Inverse of Lower Incomplete Gamma Function
Plot Inverse of Upper Incomplete Gamma Function
Inverse of Incomplete Gamma Function
Inverse incomplete gamma function
X = gammaincinv(Y,A)
X = gammaincinv(Y,A,type)
X = gammaincinv(Y,A) returns the inverse of the lower incomplete gamma function evaluated at the elements of Y and A, such that Y = gammainc(X,A). Both Y and A must be real. The elements of Y must be in the closed interval [0,1] and A must be nonnegative.
X = gammaincinv(Y,A,type) returns the inverse of the lower or upper incomplete gamma function. The choices for type are 'lower' (the default) and 'upper'.
Calculate the inverse of the lower incomplete gamma function for
a
= 0.5, 1, 1.5, and 2 within the interval
0\le y\le 1
. Loop over values of
a
, evaluate the inverse function at each one, and assign each result to a column of X.
Y = 0:0.005:1;
X(:,i) = gammaincinv(Y,A(i));
Plot all of the inverse functions in the same figure.
title('Lower inverse incomplete gamma function for $a = 0.5, 1, 1.5,$ and $2$','interpreter','latex')
xlabel('$y$','interpreter','latex')
ylabel('$P^{-1}(y,a)$','interpreter','latex')
Calculate the inverse of the upper incomplete gamma function for
a
0\le y\le 1
a
X(:,i) = gammaincinv(Y,A(i),'upper');
title('Upper inverse incomplete gamma function for $a = 0.5, 1, 1.5,$ and $2$','interpreter','latex')
ylabel('$Q^{-1}(y,a)$','Interpreter','latex')
Input array, specified as a scalar, vector, matrix, or multidimensional array. The elements of Y must be real and within the closed interval [0,1]. Y and A must be the same size, or else one of them must be a scalar.
Input array, specified as a scalar, vector, matrix, or multidimensional array. The elements of A must be real and nonnegative. Y and A must be the same size, or else one of them must be a scalar.
type — Type of inverse incomplete gamma function
Type of inverse incomplete gamma function, specified as 'lower' or 'upper'. If type is 'lower', then gammainc returns the inverse of the lower incomplete gamma function. If type is 'upper', then gammainc returns the inverse of the upper incomplete gamma function.
The inverse of the lower incomplete gamma function is defined as
x={P}^{-1}\left(y,a\right)
y=P\left(x,a\right)=\frac{1}{\Gamma \left(a\right)}{\int }_{0}^{x}{t}^{a-1}{e}^{-t}dt.
The inverse of the upper incomplete gamma function is defined as
x={Q}^{-1}\left(y,a\right)
y=Q\left(x,a\right)=\frac{1}{\Gamma \left(a\right)}{\int }_{x}^{\infty }{t}^{a-1}{e}^{-t}dt.
\Gamma \left(a\right)
term is the gamma function
\Gamma \left(a\right)={\int }_{0}^{\infty }{t}^{a-1}{e}^{-t}dt.
MATLAB® uses the normalized definition of the incomplete gamma function, where
P\left(x,a\right)+Q\left(x,a\right)=1
Some properties of the inverse of the lower incomplete gamma function are:
\underset{y\to 1}{\mathrm{lim}}{P}^{-1}\left(y,a\right)=\infty \text{ }\text{for}\text{\hspace{0.17em}}a>0
\underset{\begin{array}{l}y\to 1\\ a\to 0\end{array}}{\mathrm{lim}}{P}^{-1}\left(y,a\right)=0
When the upper incomplete gamma function is close to 0, specifying the 'upper' option to calculate the upper inverse function is more accurate than subtracting the lower incomplete gamma function from 1 and then taking the lower inverse function.
gamma | gammainc | gammaln | psi
|
A semilinear elliptic equation in a thin network-shaped domain
July, 2000 A semilinear elliptic equation in a thin network-shaped domain
We consider a semilinear elliptic equation in a varying thin domain of
{R}^{n}
. This thin domain degenerates into a geometric graph when a certain parameter tends to zero. We determine a limit equation on the graph and we prove that a solution of the PDE converges to a solution of the limit equation. Conversely, when a solution of the limit equation is given, we construct a solution of the PDE approaching a solution of the limit equation.
Satoshi KOSUGI. "A semilinear elliptic equation in a thin network-shaped domain." J. Math. Soc. Japan 52 (3) 673 - 697, July, 2000. https://doi.org/10.2969/jmsj/05230673
Keywords: semilinear elliptic equation , thin domain
Satoshi KOSUGI "A semilinear elliptic equation in a thin network-shaped domain," Journal of the Mathematical Society of Japan, J. Math. Soc. Japan 52(3), 673-697, (July, 2000)
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Introduction to Calculus/Quiz 1 - Wikiversity
< Introduction to Calculus
It would be better if you solve the quiz in your usename space, e.g. User:Your Username/Introduction to Calculus. After solving the quiz post the link to this quiz's talk page.
If you can pass this quiz, you are ready to take this course
{\displaystyle \tan(\theta )\!}
{\displaystyle \sin(\theta )\!}
{\displaystyle \csc(\theta )=1/x,\!}
then what does
{\displaystyle x\!}
{\displaystyle \tan ^{2}(\theta )+1=\sec ^{2}(\theta )\!}
{\displaystyle \sin ^{2}(\theta )+\cos ^{2}(\theta )=1\!}
{\displaystyle \cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\,\ }
Find the double angle idenities for the cosine function using the above rule.
Find the half angle idenities from the double angle idenities.
{\displaystyle \cos ^{2}(\theta )\!}
without exponents using the above rules.
(Challenge) Find the value of
{\displaystyle \cos ^{3}(\theta )\!}
without exponents.
Retrieved from "https://en.wikiversity.org/w/index.php?title=Introduction_to_Calculus/Quiz_1&oldid=495606"
|
18G05 Projectives and injectives
18G10 Resolutions; derived functors
18G15 Ext and Tor, generalizations, Künneth formula
18G30 Simplicial sets, simplicial objects (in a category)
18G60 Other (co)homology theories
𝒦
A Generalization of Baer's Lemma
Molly Dunkum (2009)
There is a classical result known as Baer’s Lemma that states that an
R
E
is injective if it is injective for
R
. This means that if a map from a submodule of
R
, that is, from a left ideal
L
R
E
can always be extended to
R
, then a map to
E
from a submodule
A
R
B
can be extended to
B
E
is injective. In this paper, we generalize this result to the category
{q}_{\omega }
consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...
A note on free regular and exact completions and their infinitary generalizations.
Hu, Hongde, Tholen, Walter (1996)
A Note on the Structure of Injective Diagrams.
Michael Höppner (1983)
A short proof of Eilenberg and Moore’s theorem
Maria Nogin (2007)
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
Adjoints, torsion theory and purity.
Gentle, Ron (1997)
Algebraic Vector Bundles over A3 Are Trivial.
M.Pavaman Murthy, Jacob Towber (1974)
Ex{t}_{R}\left(G,G\right)=0
Ext{¹}_{R}\left(G,G\right)=0
Bounds for the homological dimensions of pullbacks.
Kosmatov, N.V. (2002)
Characterization of injective envelopes
Hans-E. Porst (1981)
Coherent Rings and Homologically Finite Subcategories.
Svein A. Sikko, Sverre O. Smalo (1995)
Cohomología respecto a una variedad de una categoría.
A. R.-Grandjean, A. Martínez Cegarra (1980)
Comparison of abelian categories recollements.
Franjou, Vincent, Pirashvili, Teimuraz (2004)
Componentwise injective models of functors to DGAs
Marek Golasiński (1997)
The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.
Copure injective resolutions, flat resolvents and dimensions
Edgar E. Enochs, Jenda M. G. Overtoun (1993)
In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize
n
-Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring
R
has cokernels (respectively kernels), then
R
2
-Gorenstein.
Derived functors of
\underset{←}{lim}
and abelian ab3*- and Ab4*-categories with enough injectives
Piotr Ossowski (1981)
Exact completion and representations in abelian categories.
Rosický, J., Vitale, E.M. (2001)
|
47Lxx Linear spaces and algebras of operators
47L22 Ideals of polynomials and of multilinear mappings
47L40 Limit algebras, subalgebras of
{C}^{*}
47L45 Dual algebras; weakly closed singly generated operator algebras
47L75 Other nonselfadjoint operator algebras
47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
A generalization of peripherally-multiplicative surjections between standard operator algebras
Takeshi Miura, Dai Honma (2009)
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B −1 for some...
A Note on a Paper by W.J. Ricker and H.H. Schaefer.
Ben de Pagter (1990)
{d}_{\Xi }
Štefan Schwabik (1973)
Stefan Richter, Brett D. Wick (2016)
If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by [...] We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.
Thomas Tonev, Aaron Luttman (2009)
If X and Y are Banach spaces, then subalgebras ⊂ B(X) and ⊂ B(Y), not necessarily unital nor complete, are called standard operator algebras if they contain all finite rank operators on X and Y respectively. The peripheral spectrum of A ∈ is the set
{\sigma }_{\pi }\left(A\right)=\lambda \in \sigma \left(A\right):|\lambda |=ma{x}_{z\in \sigma \left(A\right)}|z|
of spectral values of A of maximum modulus, and a map φ: → is called peripherally-multiplicative if it satisfies the equation
{\sigma }_{\pi }\left(\phi \left(A\right)\circ \phi \left(B\right)\right)={\sigma }_{\pi }\left(AB\right)
for all A,B ∈ . We show that any peripherally-multiplicative and surjective map φ: → , neither assumed to be linear nor...
Algebraic and essentially algebraic composition operators on C(X).
Albrecht Böttcher, Harald Heidler (1995)
Algebraic generation of B(X) by two subalgebras with square zero
Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras
Fangyan Lu, Pengtong Li (2003)
It is shown that every algebraic isomorphism between standard subalgebras of 𝒥-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of 𝒥-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a 𝒥-subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a 𝒥-subspace lattice algebra onto an arbitrary...
An Operator Ideal in Connection with Gaussian Measures and Applications to Nuclearity of Integral Operators.
Thomas Kühn (1981)
Arens-regularity of algebras arising from tensor norms.
Daws, Matthew (2007)
Asymptotic products and enlargibility of Banach-Lie algebras.
Beltiţă, Daniel (2004)
Automorphisms of the algebra of operators in
{}^{p}
preserving conditioning
Ryszard Jajte (2010)
Let α be an isometric automorphism of the algebra
{}_{p}
of bounded linear operators in
{}^{p}\left[0,1\right]
(p ≥ 1). Then α transforms conditional expectations into conditional expectations if and only if α is induced by a measure preserving isomorphism of [0, 1].
|
Hooke's law - Simple English Wikipedia, the free encyclopedia
Hooke's law models the properties of springs for small changes in length
Hooke's experiment, shown in his own work 'de Potetia Restitutiva'
It is a law of mechanics and physics discovered by Robert Hooke.
This theory of elasticity says the extension of a spring is proportional to the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law is useful are known as linear-elastic or "Hookean" materials.
The spring equation[change | change source]
The length of a spring always changes by the same amount when it is pushed or pulled. The equation for this is:
{\displaystyle F=kx}
F is how much (push or pull) is on the spring
k is a constant, the stiffness of the spring.
x is how far the spring was pushed or pulled
When x = 0, the spring is at the equilibrium position. This equation only works on a linear spring. A linear spring is a spring that is only being pushed or pulled in one direction, such as left or right or up or down.
Examples of everyday objects that have elastic potential energy are stretched or compressed elastic bands, springs, bungee cords, car shock absorbers, etc.
Elastic potential energy is the energy saved in an object that is stretched, compressed (compression is pressing objects together), twisted or bent. For example, an arrow gets the elastic potential energy from the bow. When it leaves the bow, the potential energy turns into kinetic energy. The equation of the elastic potential energy is:
{\displaystyle U={\frac {1}{2}}kx^{2}}
U is the elastic potential energy.
x is the distance pushed or pulled.
Retrieved from "https://simple.wikipedia.org/w/index.php?title=Hooke%27s_law&oldid=7847586"
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Compact Model-Based Microfluidic Controller for Energy Efficient Thermal Management Using Single Tier and Three-Dimensional Stacked Pin-Fin Enhanced Microgap | J. Electron. Packag. | ASME Digital Collection
Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received August 1, 2013; final manuscript received September 10, 2014; published online October 15, 2014. Assoc. Editor: Gongnan Xie.
Han, X., and Joshi, Y. K. (October 15, 2014). "Compact Model-Based Microfluidic Controller for Energy Efficient Thermal Management Using Single Tier and Three-Dimensional Stacked Pin-Fin Enhanced Microgap." ASME. J. Electron. Packag. March 2015; 137(1): 011008. https://doi.org/10.1115/1.4028574
Overcooling of electronic devices and systems results in excess energy consumption, which can be reduced by closely linking cooling requirements with actual power dissipation. A thermal model-based flow rate controller for single phase liquid cooled single tier and three-dimensional (3D) stacked chips, using pin-fin enhanced microgap was studied in this paper. Thermal compact models of a planar and 3D stacked two-layer pin-fin enhanced microgap were developed, which ran
104-105
times faster than using full-field computational fluid dynamics/heat transfer (CFD/HT) method, with reasonable accuracy and spatial details. Compact model was used in conjunction with a flow rate control strategy to provide the needed amount of liquid to cool the heat sources to the desired temperature range. Example case studies show that the estimated energy savings in pump power is about 25% compared with pumping fluid at a constant flow rate.
Computational fluid dynamics, Control equipment, Flow (Dynamics), Fluids, Heat, Modeling, Temperature, Thermal management, Microfluidics
3D Heterogeneous Integrated Systems: Liquid Cooling, Power Delivery, and Implementation
), San Jose, CA, Sept. 21–24, pp.
.10.1109/CICC.2008.4672173
Optimization of Geometry and Flow Rate Distribution for Double-Layer Microchannel Heat Sink
Coupled Electrical and Thermal 3D IC Centric Microfluidic Heat Sink Design and Technology
Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities
Reduced Order Modeling of Nonlinear Transonic Aerodynamics Using a Pruned Volterra Series
Demonstration of Nonlinear Frequency Domain Methods
Computationally Fast Harmonic Balance Methods for Unsteady Aerodynamic Predictions of Helicopter Rotors
Reduced-Order Modeling and Experimental Validation of Steady Turbulent Convection in Connected Domains
Reduced-Order Modeling of Turbulent Forced Convection With Parametric Conditions
Reduced Order Modeling for Closed-Loop Control of Three-Dimensional Wakes
Forced Convective Heat Transfer Across a Pin Fin Micro Heat Sink
Heat Transfer and Fluid Flow in Shrouded Pin Fin Arrays With and Without Tip Clearance
,” 33rd International Symposium on Computer Architecture (
), Boston, MA, June 17–21, pp. 78–88.10.1109/ISCA.2006.39
), Nice, France, Apr. 20–24, pp.
.10.1109/DATE.2009.5090885
Three-Dimensional Chip-Multiprocessor Run-Time Thermal Management
.10.1109/TCAD.2008.925793
Seongmoo
), Seoul, South Korea, Aug. 25–27, pp.
.10.1109/LPE.2003.1231865
), Dresden, Germany, Mar. 8–12, pp.
Fuzzy Control for Enforcing Energy Efficiency in High-Performance 3D Systems
, Hemisphere Publishing Corp., New York.
|
Wendell also has a water balloon to launch, but he gets turned around and launches his balloon in the wrong direction! The path of his balloon is modeled by the function
y = −(x + 2)^2 + 3
x
is the horizontal distance in yards in front of the goal line and y is the height of the balloon in yards.
Make a complete graph of the function.
What is the domain of the function? What domain makes sense for this context?
For this context, a reasonable domain would be
-3.7 ≤ x ≤ -0.3
What is the maximum value of the function? What does this tell you about the path of the balloon?
y
Use your answers from parts (a) through (c) to completely describe the path of the balloon.
x
intercepts are the two places where the balloon is launched and where it lands.
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Systematic Error in the Measure of Microdamage by Modulus Degradation During Four-Point Bending Fatigue | SBC | ASME Digital Collection
Matthew D. Landrigan,
Landrigan, MD, & Roeder, RK. "Systematic Error in the Measure of Microdamage by Modulus Degradation During Four-Point Bending Fatigue." Proceedings of the ASME 2007 Summer Bioengineering Conference. ASME 2007 Summer Bioengineering Conference. Keystone, Colorado, USA. June 20–24, 2007. pp. 843-844. ASME. https://doi.org/10.1115/SBC2007-175238
The accumulation of fatigue damage in bovine and human cortical bone is conventionally measured by modulus or stiffness degradation. The initial modulus or stiffness of each specimen is typically measured in order to normalize tissue heterogeneity to a prescribed strain [1,2]. Cyclic preloading at 100 N for 20 cycles has been used for this purpose in both uniaxial tension and four-point bending tests [1–3]. In four-point bending, the specimen modulus is often calculated using linear elastic beam theory as,
E=3Fl4bh2ε
where F is the applied load, l is the outer support span, b is the specimen width, h is the specimen height, and ε is the maximum strain based on the beam deflection [2]. The maximum load and displacement data from preloading is used to determine the initial specimen modulus. The initial modulus and a prescribed maximum initial strain are then used to determine an appropriate load for fatigue testing under load control.
Biological tissues, Bone, Cycles, Deflection, Displacement, Errors, Euler-Bernoulli beam theory, Fatigue, Fatigue damage, Fatigue testing, Stiffness, Stress, Tension
|
44A05 General transforms
44A30 Multiple transforms
44A40 Calculus of Mikusiński and other operational calculi
44A55 Discrete operational calculus
A mean value inequality for positive integral transformations with application to a maximal theorem
W. Jurkat, J. Troutman (1981)
A property of L-L integral transformations.
Yu, Chuenwei (1984)
Abelian type theorems for some integral operators in
{R}^{n}
Ostrogorski, Tatjana (1984)
Abelian Type Theorems for some Integral Operators in Rn
Tatjana Ostrogorski (1984)
Convergence in evolutionary variational inequalities with hysteresis nonlinearities
Reitmann, Volker (2007)
Ein Äquikonvergenzsatz für eine Klasse von singulären Differentialoperatoren.
Gerhard Freiling (1977)
Expansions of distributions in terms of generalized heat polynomials and their Appell transforms.
Pathak, R.S., Debnath, Lokenath (1980)
Fourier transforms of Lipschitz functions on certain Lie groups.
Younis, M.S. (2001)
Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations
Xuan Thao, Nguyen, Kim Tuan, Vu, Thanh Hong, Nguyen (2008)
Mathematics Subject Classification: 44A05, 44A35With the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form.
Global behavior of integral transforms.
Vindas, Jasson, Estrada, Ricardo (2006)
Integral transformations on product spaces
J. D. Emery, P. Szeptycki (1973)
Interpolation of operations and Orlicz classes
Alberto Torchinsky (1976)
Linksdefinite singuläre kanonische Eigenwertprobleme. II.
A. Schneider (1977)
Norm-preserving L-L integral transformations.
Wei, Yu Chuen (1985)
Notes on integral transformations [Book]
Paweł Szeptycki (1984)
On a Generalized Integral Transform. II.
H.M. Srivastava (1971)
On integral transforms.
Gupta, K.C. (1982)
On Some of Professor Peter Rusev's Contributions
MSC 2010: 33-00, 33C45, 33C52, 30C15, 30D20, 32A17, 32H02, 44A05The 6th International Conference "Transform Methods and Special Functions' 2011", 20 - 23 October 2011 was dedicated to the 80th anniversary of Professor Peter Rusev, as one of the founders of this series of international meetings in Bulgaria, since 1994. It is a pleasure to congratulate the Jubiliar on behalf of the Local Organizing Committee and International Steering Committee, and to present shortly some of his life achievements...
On the integrability of a class of integral transforms
Yoshimitsu Hasegawa (1976)
|
A bound for the Milnor number of plane curve singularities
Arkadiusz Płoski (2014)
Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].
\left(𝒮,0\right)
be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor
E
and its irreducible components
{E}_{i}
i\in I
. The Nash map associates to each irreducible component
{C}_{k}
of the space of arcs through
0
𝒮
the unique component of
E
cut by the strict transform of the generic arc in
{C}_{k}
. Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if
E·{E}_{i}<0
i\in I
A contribution to the theory of tacnodal quartics
Balwant Singh (1976)
A period mapping for certain semi-universal deformations
Eduard Looijenga (1975)
ℋ=\bigcup {N}_{i}
ℋ
{N}_{i}
{N}_{j}
A regulator map for singular varieties.
Hélène Esnault (1990)
A result on the comparison principle for the log canonical threshold of plurisubharmonic functions
Hai Mau Le, Hong Xuan Nguyen, Hung Viet Vu (2014)
We prove a comparison principle for the log canonical threshold of plurisubharmonic functions under an assumption on complex Monge-Ampère measures.
Ample vector bundles on singular varieties.
Qi Zhang (1995)
H.-Ch. Graf von Bothmer, Wolfgang Ebeling, Xavier Gómez-Mont (2008)
\left(V,0\right)
be a germ of a complete intersection variety in
{ℂ}^{n+k}
n>0
, having an isolated singularity at
0
X
be the germ of a holomorphic vector field having an isolated zero at
0
V
. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of
X
is also isolated in the ambient space
{ℂ}^{n+k}
we give a formula for the homological index in terms of local linear algebra.
An example concerning a question of Zariski
An Integral Criterion for the Equivalence of Plane Curves.
Alicia Dickenstein, Carmen Sessa (1982)
|
C
{C}^{*}
{𝒞}_{p}-E
𝒞-E
A boundary set for the Hilbert cube containing no arcs
Jan van Mill (1983)
Katsuya Eda, Umed H. Karimov, Dušan Repovš (2007)
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A generalization of cohomotopy groups
Jerzy Dydak (1975)
A Lefschetz-type fixed point theorem
L. Górniewicz (1975)
{E}_{3}
A note on singularities in ANR's
W. Mitchell (1983)
A note on topological m-spaces
G. J. Michaelides (1975)
A remark on Fox's paper on shape
D. Hyman (1972)
A remark on the retracting of a ball onto a sphere in an infinite dimensional Hilbert space.
Tomasz Komorowski, Jacek Wosko (1990)
A survey of various modifications of the notions of absolute retracts and absolute neighborhood retracts
Jacek Klisowski (1982)
A theory of absolute proper retracts
R. Sher (1975)
A theory of proper shape for locally compact metric spaces
B. Ball, R. Sher (1974)
|
Engine displacement — Wikipedia Republished // WIKI 2
"Swept volume" redirects here. For the 3D display technology, see Swept-volume display.
One complete cycle of a four-cylinder, four-stroke engine. The volume displaced is marked in orange.
Engine displacement is the measure of the cylinder volume swept by all of the pistons of a piston engine, excluding the combustion chambers.[1] It is commonly used as an expression of an engine's size, and by extension as a loose indicator of the power an engine might be capable of producing and the amount of fuel it should be expected to consume. For this reason displacement is one of the measures often used in advertising, as well as regulating, motor vehicles.
It is usually expressed using the metric units of cubic centimetres (cc or cm3, equivalent to millilitres) or litres (l or L), or – particularly in the United States – cubic inches (CID, cu in, or in3).
Engine Displacement Explained Simply
What is the difference between a 1000 cc Car Engine and a 1000 cc Bike Engine ?
2 Governmental regulations
3 Automotive model names
The overall displacement for a typical reciprocating piston engine is calculated by multiplying together three values; the distance travelled by the piston (the stroke length), the circular area of the cylinder, and the number of cylinders in the whole engine.[2]
{\displaystyle {\text{Displacement}}={\text{stroke length}}\times {\pi }\times {\tfrac {1}{4}}\times {\text{bore}}^{2}\times {\text{number of cylinders}}}
Using this formula for non-typical types of engine, such as the Wankel design and the oval-piston type used in Honda NR motorcycles, can sometimes yield misleading results when attempting to compare engines. Manufacturers and regulators may develop and use specialised formulae to determine a comparative nominal displacement for variant engine types.
Main article: Road tax
Wankel engines are able to produce higher power levels for a given displacement. Therefore, they are generally taxed as 1.5 times[citation needed] their stated physical displacement (1.3 litres becomes effectively 2.0, 2.0 becomes effectively 3.0), although actual power outputs can be higher than suggested by this conversion factor.
Historically, many car model names have included their engine displacement. Examples include the 1923–1930 Cadillac Series 353 (powered by a 353 Cubic inch/5.8-litre engine), and the 1963–1968 BMW 1800 (a 1.8-litre engine) and Lexus LS 400 with a 3,968 cc engine. This was especially common in US muscle cars, like the Ford Mustang Boss 302 and 429, and later GT 5.0L, The Plymouth Roadrunner 440, and the Chevrolet Chevelle SS 396 and 454.
Active Fuel Management
Bore (engine)
Stroke (engine)
Variable displacement
^ "Piston Engine Displacement". The Engineering Toolbox. Retrieved 18 August 2021.
^ "Math for Automotives - Displacement of a Piston" (PDF). arc.edu. Antelope Valley College. Retrieved 18 August 2021.
^ Direct.gov.uk Archived 16 June 2006 at the Wayback Machine: The Cost of Vehicle Tax for Cars, Motorcycles, Light Goods Vehicles and Trade Licences.
^ SAAQ. "Additional Registration Fee for Large Cylinder Capacity Vehicles". SAAQ. Retrieved 12 March 2018.
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School and College: Software for Teaching and Learning Maths
Scientific Notebook for School and College
Software for Teaching and Learning Maths
Fractions? Maths Formulas? Physics Projects? School or College Science Courses? Problems to solve? Algebra? Geometry? Trig? Statistics? Probability? Calculus? Arithmetic? Multiplication & Division? Need to produce worksheets?
Scientific Notebook 6®
Creating attractive documents that contain text, mathematics, and graphics is seamless and easy with Scientific Notebook Version 6. Although simple to use, Scientific Notebook 6 is a powerful mathematical word processing system that facilitates teaching, learning, exploring, and communicating mathematics.
Scientific Notebook 6 gives you a choice of operating systems: Windows® or 32-bit Mac OS® up to 10.14 Mojave. With its entirely new Mozilla-based architecture, Scientific Notebook 6 provides more flexibility: you can save or export your documents in multiple formats according to your portability needs. Scientific Notebook 6 automatically saves your documents as XML files.
The Power of Computer Algebra
The embedded MuPAD 5® computer algebra engine allows the user to perform computations on the screen, and to print them out correctly formatted. There is no complex syntax to master to be able to evaluate, simplify, solve, or plot mathematical expressions. You can compute symbolically or numerically, integrate, differentiate, and solve algebraic and differential equations. With menu commands, you can compute with over 150 units of physical measure.
With Scientific Notebook 6 you can create two-dimensional and three-dimensional plots in many styles and coordinate systems, and enhance the plots with background color, grid lines, and plot labels in specified locations and orientations. You can animate these kinds of plots: 2D plots in polar coordinates; 2D and 3D plots in rectangular coordinates; 2D and 3D implicit plots; 2D and 3D vector fields; 3D tube plots; 3D plots in cylindrical coordinates; and 3D plots in spherical coordinates and vector fields.
Plots can be viewed on screen with playback toolbar controls. Use your mouse to start, stop, re-run, and loop animations. You can define an animation variable
t
for your plot and specify the animation start and end times and the rate of frames per second. With OpenGL 3D graphics, you can rotate, move, zoom in and out, and fly through 3D plots.
Scientific Notebook 6 has an updated program window with streamlined layouts for the toolbars and symbol panels. Most tools work the same way they did in earlier versions. A mouse-activated tooltip gives the name of each toolbar button and symbol.
Documents and all files related to them are automatically bundled together. In Scientific Notebook 6 you only need a single file bearing the extension .sci to share a document. In XML and Xhtml files, Version 6 represents your mathematics as MathML. This makes it easy to create xhtml web files for the representation of your mathematics on various platforms over the Internet with a browser. For Version 6 the recommended viewer is Firefox.
An important new feature of Scientific Notebook 6 is that you may Undo an unlimited number of previous editing changes from your current session within a document.
The ability to check your spelling in realtime is new. With the inline spell checking from MySpell, you can catch any misspellings. MySpell, which is open-source, includes dictionaries in over 40 languages. Misspelled words have a wavy red underline. A new visual interface is used to create tables to the exact dimensions you need. Being able to leave dialog boxes open while you make replacements and corrections saves time.
Scientific Notebook 6 supports any left-to-right or right-to-left language that is supported by your operating system.
Scientific Notebook 6 has great potential when used in an educational setting. It provides a ready laboratory where students can experiment with mathematics to develop new insights and to solve interesting problems. Scientific Notebook 6 makes it easy for students to produce clear, well-written homework.
In a classroom equipped with appropriate projection equipment, the program’s ease of use and its combination of a free-form scientific word processor and computational package make it a natural replacement for the chalkboard. You do not have to erase as you go along, so previous work can be recalled. Class notes can be edited and made available for viewing online or printed.
The manual, Doing Mathematics with Scientific WorkPlace and Scientific Notebook Version 6 by Darel W. Hardy and Carol L. Walker, describes the use of the underlying computer algebra system for doing mathematical calculations. Exercises are provided to encourage users to practise the mathematical ideas presented. This manual is available as a download.
Share Mathematics over the World Wide Web
Scientific Notebook 6 is the ideal tool for distance learning. You can send mathematical documents containing text, equations, and plots over the Internet; you can open the file at any URL address from inside the software. It is easy to build an entire website with mathematical content which can be read with any web browser that displays MathML, such as Firefox. Note the recommended browser for Version 6 is Firefox, not Scientific Viewer.
The software supports hypertext links, so your readers can easily navigate through a series of related documents.
Scientific Notebook 6 does not produce typeset output, but can use documents created in Scientific WorkPlace and Scientific Word. The addition of cross platform capability in Version 6 provides more flexibility for sharing your work.
Scientific Notebook 6.1 for Windows (162Mb)
Scientific Notebook 6.1 for Mac (60Mb)
Scientific Notebook 6.1 for Windows
Scientific Notebook 6.1 for Mac
Scientific Notebook 5.5 (43Mb)
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Modulate using differential quadrature phase shift keying method - Simulink - MathWorks Deutschland
Modulate using differential quadrature phase shift keying method
The DQPSK Modulator Baseband block modulates using the differential quadrature phase shift keying method. The output is a baseband representation of the modulated signal.
The input must be a discrete-time signal. For information about the data types each block port supports, see Supported Data Types.
When you set the Input type parameter to Integer, the valid input values are 0, 1, 2, and 3. In this case, the block accepts a scalar or column vector input signal. If the first input is m, then the modulated symbol is
where θ represents the Phase rotation parameter. If a successive input is m, then the modulated symbol is the previous modulated symbol multiplied by exp(jθ + jπm/2).
When you set the Input type parameter to Bit, the input contains pairs of binary values. In this case, the block accepts a column vector whose length is an even integer. The following figure shows the complex numbers by which the block multiples the previous symbol to compute the current symbol, depending on whether you set the Constellation ordering parameter to Binary or Gray. The following figure assumes that you set the Phase rotation parameter to
\frac{\Pi }{4}
; in other cases, the two schematics would be rotated accordingly.
The following figure shows the signal constellation for the DQPSK modulation method when you set the Phase rotation parameter to
\frac{\Pi }{4}
. The arrows indicate the four possible transitions from each symbol to the next symbol. The Binary and Gray options determine which transition is associated with each pair of input values.
More generally, if the Phase rotation parameter has the form
\frac{\Pi }{k}
for some integer k, then the signal constellation has 2k points.
Determines how the block maps each pair of input bits to a corresponding integer, using either a Binary or Gray mapping scheme.
M-DPSK Modulator Baseband | DBPSK Modulator Baseband | QPSK Modulator Baseband | DQPSK Demodulator Baseband
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Home : Support : Online Help : Mathematics : Algebra : Polynomials : RationalNormalForms : Overview
Overview of the RationalNormalForms Package
List of RationalNormalForms Package Commands
RationalNormalForms[command](arguments)
The RationalNormalForms package is used to solve the following problems:
Construct the polynomial normal form of a rational function.
Construct the rational canonical forms of a rational function.
Construct a minimal representation of a hypergeometric term.
Each command in the RationalNormalForms package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
As the underlying implementation of the RationalNormalForms package is a module, it is also possible to use the form RationalNormalForms:-command to access a command from the package. For more information, see Module Members.
To display the help page for a particular RationalNormalForms command, see Getting Help with a Command in a Package.
\mathrm{with}\left(\mathrm{RationalNormalForms}\right):
F≔\frac{\left({n}^{2}-1\right)\left(3n+1\right)!}{\left(n+3\right)!\left(2n+7\right)!}
\textcolor[rgb]{0,0,1}{F}\textcolor[rgb]{0,0,1}{≔}\frac{\left({\textcolor[rgb]{0,0,1}{n}}^{\textcolor[rgb]{0,0,1}{2}}\textcolor[rgb]{0,0,1}{-}\textcolor[rgb]{0,0,1}{1}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{1}\right)\textcolor[rgb]{0,0,1}{!}}{\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{3}\right)\textcolor[rgb]{0,0,1}{!}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{7}\right)\textcolor[rgb]{0,0,1}{!}}
\mathrm{IsHypergeometricTerm}\left(F,n,'\mathrm{certificate}'\right)
\textcolor[rgb]{0,0,1}{\mathrm{true}}
\mathrm{certificate}
\frac{\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{2}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{3}\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{4}\right)\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{2}\right)}{\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{2}\textcolor[rgb]{0,0,1}{}\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{9}\right)\textcolor[rgb]{0,0,1}{}{\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{4}\right)}^{\textcolor[rgb]{0,0,1}{2}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{-}\textcolor[rgb]{0,0,1}{1}\right)}
z,r,s,u,v≔\mathrm{RationalCanonicalForm}[1]\left(\mathrm{certificate},n\right)
\textcolor[rgb]{0,0,1}{z}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{r}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{s}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{u}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{v}\textcolor[rgb]{0,0,1}{≔}\frac{\textcolor[rgb]{0,0,1}{27}}{\textcolor[rgb]{0,0,1}{4}}\textcolor[rgb]{0,0,1}{,}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\frac{\textcolor[rgb]{0,0,1}{2}}{\textcolor[rgb]{0,0,1}{3}}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\frac{\textcolor[rgb]{0,0,1}{4}}{\textcolor[rgb]{0,0,1}{3}}\right)\textcolor[rgb]{0,0,1}{,}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\frac{\textcolor[rgb]{0,0,1}{9}}{\textcolor[rgb]{0,0,1}{2}}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{4}\right)\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{-}\textcolor[rgb]{0,0,1}{1}\textcolor[rgb]{0,0,1}{,}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{3}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{2}\right)
\mathrm{MinimalRepresentation}[1]\left(F,n,k\right)
\frac{{\left(\frac{\textcolor[rgb]{0,0,1}{27}}{\textcolor[rgb]{0,0,1}{4}}\right)}^{\textcolor[rgb]{0,0,1}{n}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{-}\textcolor[rgb]{0,0,1}{1}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0.564705882352941,0.564705882352941,0.564705882352941}{\prod }_{\textcolor[rgb]{0,0,1}{k}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{2}}^{\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{-}\textcolor[rgb]{0,0,1}{1}}\textcolor[rgb]{0,0,1}{}\frac{\left(\textcolor[rgb]{0,0,1}{k}\textcolor[rgb]{0,0,1}{+}\frac{\textcolor[rgb]{0,0,1}{2}}{\textcolor[rgb]{0,0,1}{3}}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{k}\textcolor[rgb]{0,0,1}{+}\frac{\textcolor[rgb]{0,0,1}{4}}{\textcolor[rgb]{0,0,1}{3}}\right)}{\left(\textcolor[rgb]{0,0,1}{k}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{4}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{k}\textcolor[rgb]{0,0,1}{+}\frac{\textcolor[rgb]{0,0,1}{9}}{\textcolor[rgb]{0,0,1}{2}}\right)}\right)}{\textcolor[rgb]{0,0,1}{721710}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{3}\right)\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{n}\textcolor[rgb]{0,0,1}{+}\textcolor[rgb]{0,0,1}{2}\right)}
Abramov, S., and Petkovsek, M. "Canonical Representations of Hypergeometric Terms." FPSAC. 2000.
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Sound intensity — Wikipedia Republished // WIKI 2
Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. The SI unit of intensity, which includes sound intensity, is the watt per square meter (W/m2). One application is the noise measurement of sound intensity in the air at a listener's location as a sound energy quantity.[1]
Sound intensity is not the same physical quantity as sound pressure. Human hearing is sensitive to sound pressure which is related to sound intensity. In consumer audio electronics, the level differences are called "intensity" differences, but sound intensity is a specifically defined quantity and cannot be sensed by a simple microphone.
Sound intensity level is a logarithmic expression of sound intensity relative to a reference intensity.
Sound Intensity and Decibels Distinctly Defined, Dude | Doc Physics
2 Inverse-square law
3 Sound intensity level
Sound intensity, denoted I, is defined by
{\displaystyle \mathbf {I} =p\mathbf {v} }
p is the sound pressure;
v is the particle velocity.
Both I and v are vectors, which means that both have a direction as well as a magnitude. The direction of sound intensity is the average direction in which energy is flowing.
The average sound intensity during time T is given by
{\displaystyle \langle \mathbf {I} \rangle ={\frac {1}{T}}\int _{0}^{T}p(t)\mathbf {v} (t)\,\mathrm {d} t.}
{\displaystyle \mathrm {I} =2\pi ^{2}\nu ^{2}\delta ^{2}\rho c}
{\displaystyle \nu }
is frequency of sound,
{\displaystyle \delta }
is the amplitude of the sound wave particle displacement,
{\displaystyle \rho }
is density of medium in which sound is traveling, and
{\displaystyle c}
is speed of sound.
Further information: Inverse-square law
For a spherical sound wave, the intensity in the radial direction as a function of distance r from the centre of the sphere is given by
{\displaystyle I(r)={\frac {P}{A(r)}}={\frac {P}{4\pi r^{2}}},}
P is the sound power;
A(r) is the surface area of a sphere of radius r.
Thus sound intensity decreases as 1/r2 from the centre of the sphere:
{\displaystyle I(r)\propto {\frac {1}{r^{2}}}.}
This relationship is an inverse-square law.
For other uses, see Sound level.
Sound intensity level (SIL) or acoustic intensity level is the level (a logarithmic quantity) of the intensity of a sound relative to a reference value.
It is denoted LI, expressed in nepers, bels, or decibels, and defined by[2]
{\displaystyle L_{I}={\frac {1}{2}}\ln \left({\frac {I}{I_{0}}}\right)\mathrm {Np} =\log _{10}\left({\frac {I}{I_{0}}}\right)\mathrm {B} =10\log _{10}\left({\frac {I}{I_{0}}}\right)\mathrm {dB} ,}
I is the sound intensity;
I0 is the reference sound intensity;
1 Np = 1 is the neper;
1 B = 1/2 ln(10) is the bel;
1 dB = 1/20 ln(10) is the decibel.
The commonly used reference sound intensity in air is[3]
{\displaystyle I_{0}=1~\mathrm {pW/m^{2}} .}
being approximately the lowest sound intensity hearable by an undamaged human ear under room conditions. The proper notations for sound intensity level using this reference are LI /(1 pW/m2) or LI (re 1 pW/m2), but the notations dB SIL, dB(SIL), dBSIL, or dBSIL are very common, even if they are not accepted by the SI.[4]
The reference sound intensity I0 is defined such that a progressive plane wave has the same value of sound intensity level (SIL) and sound pressure level (SPL), since
{\displaystyle I\propto p^{2}.}
The equality of SIL and SPL requires that
{\displaystyle {\frac {I}{I_{0}}}={\frac {p^{2}}{p_{0}^{2}}},}
where p0 = 20 μPa is the reference sound pressure.
For a progressive spherical wave,
{\displaystyle {\frac {p}{c}}=z_{0},}
where z0 is the characteristic specific acoustic impedance. Thus,
{\displaystyle I_{0}={\frac {p_{0}^{2}I}{p^{2}}}={\frac {p_{0}^{2}pc}{p^{2}}}={\frac {p_{0}^{2}}{z_{0}}}.}
In air at ambient temperature, z0 = 410 Pa·s/m, hence the reference value I0 = 1 pW/m2.[5]
In an anechoic chamber which approximates a free field (no reflection) with a single source, measurements in the far field in SPL can be considered to be equal to measurements in SIL. This fact is exploited to measure sound power in anechoic conditions.
Sound intensity is defined as the time averaged product of sound pressure and acoustic particle velocity.[6] Both quantities can be directly measured by using a sound intensity p-u probe comprising a microphone and a particle velocity sensor, or estimated indirectly by using a p-p probe that approximates the particle velocity by integrating the pressure gradient between two closely spaced microphones.[7]
Pressure-based measurement methods are widely used in anechoic conditions for noise quantification purposes. The bias error introduced by a p-p probe can be approximated by[8]
{\displaystyle {\widehat {I}}_{n}^{p-p}\simeq I_{n}-{\frac {\varphi _{\text{pe}}\,p_{\text{rms}}^{2}}{k\Delta r\rho c}}=I_{n}\left(1-{\frac {\varphi _{\text{pe}}}{k\Delta r}}{\frac {p_{\text{rms}}^{2}/\rho c}{I_{r}}}\right),}
{\displaystyle I_{n}}
is the “true” intensity (unaffected by calibration errors),
{\displaystyle {\hat {I}}_{n}^{p-p}}
is the biased estimate obtained using a p-p probe,
{\displaystyle p_{\text{rms}}}
is the root-mean-squared value of the sound pressure,
{\displaystyle k}
is the wave number,
{\displaystyle \rho }
{\displaystyle c}
{\displaystyle \Delta r}
is the spacing between the two microphones. This expression shows that phase calibration errors are inversely proportional to frequency and microphone spacing and directly proportional to the ratio of the mean square sound pressure to the sound intensity. If the pressure-to-intensity ratio is large then even a small phase mismatch will lead to significant bias errors. In practice, sound intensity measurements cannot be performed accurately when the pressure-intensity index is high, which limits the use of p-p intensity probes in environments with high levels of background noise or reflections.
On the other hand, the bias error introduced by a p-u probe can be approximated by[8]
{\displaystyle {\hat {I}}_{n}^{p-u}={\frac {1}{2}}\operatorname {Re} \left\{{P{\hat {V}}_{n}^{*}}\right\}={\frac {1}{2}}\operatorname {Re} \left\{{PV_{n}^{*}e^{-j\varphi _{\text{ue}}}}\right\}\simeq I_{n}+\varphi _{\text{ue}}J_{n}\,,}
{\displaystyle {\hat {I}}_{n}^{p-u}}
is the biased estimate obtained using a p-u probe,
{\displaystyle P}
{\displaystyle V_{n}}
are the Fourier transform of sound pressure and particle velocity,
{\displaystyle J_{n}}
is the reactive intensity and
{\displaystyle \varphi _{\text{ue}}}
is the p-u phase mismatch introduced by calibration errors. Therefore, the phase calibration is critical when measurements are carried out under near field conditions, but not so relevant if the measurements are performed out in the far field.[8] The “reactivity” (the ratio of the reactive to the active intensity) indicates whether this source of error is of concern or not. Compared to pressure-based probes, p-u intensity probes are unaffected by the pressure-to-intensity index, enabling the estimation of propagating acoustic energy in unfavorable testing environments provided that the distance to the sound source is sufficient.
^ "Sound Intensity". Retrieved 22 April 2015.
^ "Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units", IEC 60027-3 Ed. 3.0, International Electrotechnical Commission, 19 July 2002.
^ Ross Roeser, Michael Valente, Audiology: Diagnosis (Thieme 2007), p. 240.
^ Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel", Guide for the Use of the International System of Units (SI) 2008 Edition, NIST Special Publication 811, 2nd printing (November 2008), SP811 PDF
^ Sound Power Measurements, Hewlett Packard Application Note 1230, 1992.
^ Fahy, Frank (2017). Sound Intensity. CRC Press. ISBN 978-1138474192. OCLC 1008875245.
^ Jacobsen, Finn (2013-07-29). Fundamentals of general linear acoustics. ISBN 9781118346419. OCLC 857650768.
^ a b c Jacobsen, Finn; de Bree, Hans-Elias (2005-09-01). "A comparison of two different sound intensity measurement principles" (PDF). The Journal of the Acoustical Society of America. 118 (3): 1510–1517. Bibcode:2005ASAJ..118.1510J. doi:10.1121/1.1984860. ISSN 0001-4966.
How Many Decibels Is Twice as Loud? Sound Level Change and the Respective Factor of Sound Pressure or Sound Intensity
Acoustic Intensity
Conversion: Sound Intensity Level to Sound Intensity and Vice Versa
Ohm's Law as Acoustic Equivalent. Calculations
Relationships of Acoustic Quantities Associated with a Plane Progressive Acoustic Sound Wave
Table of Sound Levels. Corresponding Sound Intensity and Sound Pressure
What Is Sound Intensity Measurement and Analysis?
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This problem is a checkpoint for angle measures and areas of regular polygons. It will be referred to as Checkpoint 11.
20
157.5°
Calculate the area of a regular octagon with side length
5.0
If you have an eBook for Int2, login and then click the following link: Checkpoint 11: Angle Measures and Areas of Regular Polygons
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Image formation of a convex mirror and its uses — lesson. Science State Board, Class 9.
Formation of image in a convex mirror:
In the following image, the ray \(OA\) parallel to the principal axis is reflected along with \(AD\). The ray \(OB\) retraces its path. The two reflected rays diverge, but they appear to intersect at \(I\) when produced backwards. Thus
{A}_{1}{B}_{1}
is the image of the object \(AB\). It is virtual, erect and smaller than the object.
{A}_{1}{B}_{1}
is the image of the object OO’
In automobiles, convex mirrors are used as rear-view mirrors. It creates a virtual, erect, small-scale image of the object every time. The size of the image grows as the vehicles approach the driver from behind. The image size decreases as the vehicles move away from the driver. In comparison to a plane mirror, a convex mirror has a much larger field of view.
Rear-view mirror of a car
Convex mirrors are used as a traffic safety device on public roads. They are used on narrow roads with acute bends, such as hairpin bends in mountain passes, where oncoming vehicles cannot see you. It is also used in stores to cover blind spots.
Convex mirror used in a supermarket
https://www.pxfuel.com/en/free-photo-jrzpe
https://www.flickr.com/photos/centralasian/7131929699
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Cross-validate regularization of linear discriminant - MATLAB - MathWorks Switzerland
\stackrel{^}{X}
D=\text{diag}\left({\stackrel{^}{X}}^{T}*\stackrel{^}{X}\right).
\stackrel{˜}{\Sigma }
\stackrel{˜}{\Sigma }=\left(1-\gamma \right)\Sigma +\gamma D.
\stackrel{˜}{\Sigma }
\stackrel{˜}{C}
\stackrel{˜}{C}=\left(1-\gamma \right)C+\gamma I,
{\left(x-{\mu }_{0}\right)}^{T}{\stackrel{˜}{\Sigma }}^{-1}\left({\mu }_{k}-{\mu }_{0}\right)=\left[{\left(x-{\mu }_{0}\right)}^{T}{D}^{-1/2}\right]\left[{\stackrel{˜}{C}}^{-1}{D}^{-1/2}\left({\mu }_{k}-{\mu }_{0}\right)\right].
\left[{\stackrel{˜}{C}}^{-1}{D}^{-1/2}\left({\mu }_{k}-{\mu }_{0}\right)\right]
|{\stackrel{˜}{C}}^{-1}{D}^{-1/2}\left({\mu }_{k}-{\mu }_{0}\right)|\le \delta .
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GlobalOptimization - Maple Help
Home : Support : Online Help : Mathematics : Packages : GlobalOptimization
Overview of the GlobalOptimization Package
GlobalOptimization[command](arguments)
The Global Optimization Toolbox, powered by Optimus® technology from Noesis Solutions, is implemented as the GlobalOptimization package, which numerically computes global solutions to nonlinear programming (NLP) problems over a bounded region. An NLP problem is the minimization or maximization of an objective function, possibly subject to constraints.
The GlobalOptimization package contains a command for solving optimization problems, which can be specified in various forms. For information on the input forms, see the GlobalOptimization/InputForms help page. Additionally, the package offers an interactive Maplet interface that provides an easy-to-use facility for entering and solving an optimization problem, as well as plotting both the problem and its solution.
Using the many options, you can control the algorithms used by the global solver. For information on these options, see the GlobalOptimization/Options help page.
The global solver in the GlobalOptimization package calls external code that uses hardware floats, but the objective function and the constraints can be evaluated in Maple with higher precision. For more information on the global solver, the algorithms, the floating-point computation environment, and ways to achieve best performance with the solver, see the GlobalOptimization/Computation help page.
For more information and examples on the toolbox, see Introduction to the Global Optimization Toolbox and Applications of the Global Optimization Toolbox.
Each command in the GlobalOptimization package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
Because the underlying implementation of the package is a module, it is possible to use the form GlobalOptimization:-command to access a command from the package. For more information, see Module Members.
To display the help page for a particular command, see Getting Help with a Command in a Package.
The GlobalSolve help page describes the most commonly used forms of input. Use with the more advanced Matrix form of input is described in the GlobalOptimization[GlobalSolveMatrixForm] help page.
To see additional information on the progress of the solver during the solution of an optimization problem, set infolevel[GlobalOptimization] to a positive integer. More information is printed at higher infolevel settings.
\mathrm{with}\left(\mathrm{GlobalOptimization}\right):
Find the global solution to the minimization problem
\mathrm{ln}\left(x\right)\mathrm{sin}\left(x\right)
[1..20]
\mathrm{GlobalSolve}\left(\mathrm{ln}\left(x\right)\mathrm{sin}\left(x\right),x=1..20\right)
[\textcolor[rgb]{0,0,1}{-2.85006479973796}\textcolor[rgb]{0,0,1}{,}[\textcolor[rgb]{0,0,1}{x}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{17.2990352355127}]]
Find the global solution to a constrained minimization problem.
\mathrm{GlobalSolve}\left({x}^{6}-5{x}^{3}-20{x}^{2}-5,{5{x}^{2}+20x+18\le 0},x=-3..3\right)
[\textcolor[rgb]{0,0,1}{-23.0747312455205424}\textcolor[rgb]{0,0,1}{,}[\textcolor[rgb]{0,0,1}{x}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{-1.36754446796582}]]
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EUDML | Existence of infinitely many homoclinic orbits in hamiltonian systems. EuDML | Existence of infinitely many homoclinic orbits in hamiltonian systems.
Séré, Eric. "Existence of infinitely many homoclinic orbits in hamiltonian systems.." Mathematische Zeitschrift 209.1 (1992): 27-42. <http://eudml.org/doc/174347>.
@article{Séré1992,
author = {Séré, Eric},
keywords = {Hamiltonian systems; homoclinic orbits; chaos; variational problems; Palais-Smale condition; concentration-compactness},
title = {Existence of infinitely many homoclinic orbits in hamiltonian systems.},
AU - Séré, Eric
TI - Existence of infinitely many homoclinic orbits in hamiltonian systems.
KW - Hamiltonian systems; homoclinic orbits; chaos; variational problems; Palais-Smale condition; concentration-compactness
Zhaoli Liu, Zhi-Qiang Wang, Multi-bump type nodal solutions having a prescribed number of nodal domains : I
Massimiliano Berti, Heteroclinic solutions for perturbed second order systems
P. H. Rabinowitz, E. Stredulinsky, On some results of Moser and of Bangert
Enrico Serra, Massimo Tarallo, Susanna Terracini, On the existence of homoclinic solutions for almost periodic second order systems
S. V. Bolotin, P. H. Rabinowitz, A variational construction of chaotic trajectories for a Hamiltonian system on a torus
Fukun Zhao, Leiga Zhao, Yanheng Ding, Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems
Éric Séré, Looking for the Bernoulli shift
Antonio Ambrosetti, Vittorio Coti Zelati, Multiple homoclinic orbits for a class of conservative systems
Francesca Alessio, Marta Calanchi, Homoclinic-type solutions for an almost periodic semilinear elliptic equation on
{R}^{n}
Antonio Ambrosetti, Marino Badiale, Homoclinics : Poincaré-Melnikov type results via a variational approach
Hamiltonian systems, homoclinic orbits, chaos, variational problems, Palais-Smale condition, concentration-compactness
Articles by Eric Séré
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Present Value (PV) Definition .
A comparison of present value with future value (FV) best illustrates the principle of the time value of money and the need for charging or paying additional risk-based interest rates. Simply put, the money today is worth more than the same money tomorrow because of the passage of time. Future value can relate to the future cash inflows from investing today's money, or the future payment required to repay money borrowed today.
Future value (FV) is the value of a current asset at a specified date in the future based on an assumed rate of growth. The FV equation assumes a constant rate of growth and a single upfront payment left untouched for the duration of the investment. The FV calculation allows investors to predict, with varying degrees of accuracy, the amount of profit that can be generated by different investments.
Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Present value takes the future value and applies a discount rate or the interest rate that could be earned if invested. Future value tells you what an investment is worth in the future while the present value tells you how much you'd need in today's dollars to earn a specific amount in the future.
Criticism of Present Value
As stated earlier, calculating present value involves making an assumption that a rate of return could be earned on the funds over the time period. In the discussion above, we looked at one investment over the course of one year. However, if a company is deciding to go ahead with a series of projects that has a different rate of return for each year and each project, the present value becomes less certain if those expected rates of return are not realistic. It's important to consider that in any investment decision, no interest rate is guaranteed, and inflation can erode the rate of return on an investment.
Let's say you have the choice of being paid $2,000 today earning 3% annually or $2,200 one year from now. Which is the best option?
Using the present value formula, the calculation is $2,200 / (1 +. 03)1 = $2135.92
PV = $2,135.92, or the minimum amount that you would need to be paid today to have $2,200 one year from now. In other words, if you were paid $2,000 today and based on a 3% interest rate, the amount would not be enough to give you $2,200 one year from now.
Alternatively, you could calculate the future value of the $2,000 today in a year's time: 2,000 x 1.03 = $2,060.
Present value provides a basis for assessing the fairness of any future financial benefits or liabilities. For example, a future cash rebate discounted to present value may or may not be worth having a potentially higher purchase price. The same financial calculation applies to 0% financing when buying a car.
Paying some interest on a lower sticker price may work out better for the buyer than paying zero interest on a higher sticker price. Paying mortgage points now in exchange for lower mortgage payments later makes sense only if the present value of the future mortgage savings is greater than the mortgage points paid today.
Present value is calculated by taking the future cashflows expected from an investment and discounting them back to the present day. To do so, the investor needs three key data points: the expected cashflows, the number of years in which the cashflows will be paid, and their discount rate. The discount rate is a very important factor in influencing the present value, with higher discount rates leading to a lower present value, and vice-versa. Using these variables, investors can calculate present value using the formula:
\begin{aligned} &\text{Present Value} = \dfrac{\text{FV}}{(1+r)^n}\\ &\textbf{where:}\\ &\text{FV} = \text{Future Value}\\ &r = \text{Rate of return}\\ &n = \text{Number of periods}\\ \end{aligned}
Present Value=(1+r)nFVwhere:FV=Future Valuer=Rate of returnn=Number of periods
What Are Some Examples of Present Value?
To illustrate, consider a scenario where you expect to earn a $5,000 lump sum payment in five years' time. If the discount rate is 8.25%, you want to know what that payment will be worth today so you calculate the PV = $5000/(1.0825)5 = 3,363.80.
Present value is important because it allows investors to judge whether or not the price they pay for an investment is appropriate. For example, in our previous example, having a 12% discount rate would reduce the present value of the investment to only $1,802.39. In that scenario, we would be very reluctant to pay more than that amount for the investment, since our present value calculation indicates that we could find better opportunities elsewhere. Present value calculations like this play a critical role in areas such as investment analysis, risk management, and financial planning.
U.S. Securities and Exchange Commission. "Treasury Securities." Accessed Feb. 1, 2022.
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Predict response of generalized linear mixed-effects model - MATLAB - MathWorks América Latina
Predict Responses at Original Design Values
Predict Responses at Values in New Table
Predict response of generalized linear mixed-effects model
ypred = predict(glme)
ypred = predict(glme,tblnew)
ypred = predict(glme) returns the predicted conditional means of the response, ypred, using the original predictor values used to fit the generalized linear mixed-effects model glme.
ypred = predict(glme,tblnew) returns the predicted conditional means using the new predictor values specified in tblnew.
If a grouping variable in tblnew has levels that are not in the original data, then the random effects for that grouping variable do not contribute to the 'Conditional' prediction at observations where the grouping variable has new levels.
ypred = predict(___,Name,Value) returns the predicted conditional means of the response using additional options specified by one or more Name,Value pair arguments. For example, you can specify the confidence level, simultaneous confidence bounds, or contributions from only fixed effects. You can use any of the input arguments in the previous syntaxes.
[ypred,ypredCI] = predict(___) also returns 95% point-wise confidence intervals, ypredCI, for each predicted value.
[ypred,ypredCI,DF] = predict(___) also returns the degrees of freedom, DF, used to compute the confidence intervals.
New input data, which includes the response variable, predictor variables, and grouping variables, specified as a table or dataset array. The predictor variables can be continuous or grouping variables. tblnew must have the same variables as the original table or dataset array used in fitglme to fit the generalized linear mixed-effects model glme.
Offset — Model offset
zeros(m,1) (default) | m-by-1 vector of scalar values
Model offset, specified as a vector of scalar values of length m, where m is the number of rows in tblnew. The offset is used as an additional predictor and has a coefficient value fixed at 1.
Type of confidence bounds, specified as the comma-separated pair consisting of 'Simultaneous' and either false or true.
If 'Simultaneous' is false, then predict computes nonsimultaneous confidence bounds.
If 'Simultaneous' is true, predict returns simultaneous confidence bounds.
Predicted responses, returned as a vector. If the 'Conditional' name-value pair argument is specified as true, ypred contains predictions for the conditional means of the responses given the random effects. Conditional predictions include contributions from both fixed and random effects. Marginal predictions include only contributions from fixed effects.
To compute marginal predictions, predict computes conditional predictions, but substitutes a vector of zeros in place of the empirical Bayes predictors (EBPs) of the random effects.
Point-wise confidence intervals for the predicted values, returned as a two-column matrix. The first column of ypredCI contains the lower bound, and the second column contains the upper bound. By default, ypredCI contains the 95% nonsimultaneous confidence intervals for the predictions. You can change the confidence level using the Alpha name-value pair argument, and make them simultaneous using the Simultaneous name-value pair argument.
When fitting a GLME model using fitglme and one of the maximum likelihood fit methods ('Laplace' or 'ApproximateLaplace'), predict computes the confidence intervals using the conditional mean squared error of prediction (CMSEP) approach conditional on the estimated covariance parameters and the observed response. Alternatively, you can interpret the confidence intervals as approximate Bayesian credible intervals conditional on the estimated covariance parameters and the observed response.
When fitting a GLME model using fitglme and one of the pseudo likelihood fit methods ('MPL' or 'REMPL'), predict bases the computations on the fitted linear mixed-effects model from the final pseudo likelihood iteration.
If 'Simultaneous' is false, then DF is a vector.
If 'Simultaneous' is true, then DF is a scalar value.
{\text{defects}}_{ij}\sim \text{Poisson}\left({\mu }_{ij}\right)
\mathrm{log}\left({\mu }_{ij}\right)={\beta }_{0}+{\beta }_{1}{\text{newprocess}}_{ij}+{\beta }_{2}{\text{time}\text{_}\text{dev}}_{ij}+{\beta }_{3}{\text{temp}\text{_}\text{dev}}_{ij}+{\beta }_{4}{\text{supplier}\text{_}\text{C}}_{ij}+{\beta }_{5}{\text{supplier}\text{_}\text{B}}_{ij}+{b}_{i},
{\text{defects}}_{ij}
i
j
{\mu }_{ij}
i
i=1,2,...,20
j
j=1,2,...,5
{\text{newprocess}}_{ij}
{\text{time}\text{_}\text{dev}}_{ij}
{\text{temp}\text{_}\text{dev}}_{ij}
i
j
{\text{newprocess}}_{ij}
i
j
{\text{supplier}\text{_}\text{C}}_{ij}
{\text{supplier}\text{_}\text{B}}_{ij}
i
j
{b}_{i}\sim N\left(0,{\sigma }_{b}^{2}\right)
i
Predict the response values at the original design values. Display the first ten predictions along with the observed response values.
ypred = predict(glme);
[ypred(1:10),mfr.defects(1:10)]
Column 1 contains the predicted response values at the original design values. Column 2 contains the observed response values.
{\text{defects}}_{ij}\sim \text{Poisson}\left({\mu }_{ij}\right)
\mathrm{log}\left({\mu }_{ij}\right)={\beta }_{0}+{\beta }_{1}{\text{newprocess}}_{ij}+{\beta }_{2}{\text{time}\text{_}\text{dev}}_{ij}+{\beta }_{3}{\text{temp}\text{_}\text{dev}}_{ij}+{\beta }_{4}{\text{supplier}\text{_}\text{C}}_{ij}+{\beta }_{5}{\text{supplier}\text{_}\text{B}}_{ij}+{b}_{i},
{\text{defects}}_{ij}
i
j
{\mu }_{ij}
i
i=1,2,...,20
j
j=1,2,...,5
{\text{newprocess}}_{ij}
{\text{time}\text{_}\text{dev}}_{ij}
{\text{temp}\text{_}\text{dev}}_{ij}
i
j
{\text{newprocess}}_{ij}
i
j
{\text{supplier}\text{_}\text{C}}_{ij}
{\text{supplier}\text{_}\text{B}}_{ij}
i
j
{b}_{i}\sim N\left(0,{\sigma }_{b}^{2}\right)
i
Predict the response values at the original design values.
Create a new table by copying the first 10 rows of mfr into tblnew.
tblnew = mfr(1:10,:);
The first 10 rows of mfr include data collected from trials 1 through 5 for factories 1 and 2. Both factories used the old process for all of their trials during the experiment, so newprocess = 0 for all 10 observations.
Change the value of newprocess to 1 for the observations in tblnew.
tblnew.newprocess = ones(height(tblnew),1);
Compute predicted response values and nonsimultaneous 99% confidence intervals using tblnew. Display the first 10 rows of the predicted values based on tblnew, the predicted values based on mfr, and the observed response values.
[ypred_new,ypredCI] = predict(glme,tblnew,'Alpha',0.01);
[ypred_new,ypred(1:10),mfr.defects(1:10)]
Column 1 contains predicted response values based on the data in tblnew, where newprocess = 1. Column 2 contains predicted response values based on the original data in mfr, where newprocess = 0. Column 3 contains the observed response values in mfr. Based on these results, if all other predictors retain their original values, the predicted number of defects appears to be smaller when using the new process.
Display the 99% confidence intervals for rows 1 through 10 corresponding to the new predicted response values.
ypredCI(1:10,1:2)
GeneralizedLinearMixedModel | fitglme | fitted | random
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45Jxx Integro-ordinary differential equations
A Construction of Monotonically Convergent Sequences from Successive Approximations in Certain Banach Spaces.
S.G. Gal (1989/1990)
A shooting method for singular nonlinear second order Volterra integro-differential equations.
Shaw, R.E., Garey, L.E. (1997)
Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels
Maurizio Grasselli, Alfredo Lorenzi (1991)
A Cauchy problem for an abstract nonlinear Volterra integrodifferential equation is considered. Existence and uniqueness results are shown for any given time interval under weak time regularity assumptions on the kernel. Some applications to the heat flow with memory are presented.
Age of infection in epidemiology models.
Brauer, Fred (2005)
Algebraic representation of the Nakajima-Zvanzig's generalized master equation
Lubomír Skála, Oldřich Bílek (1982)
An abstract inverse problem.
Choulli, M. (1991)
An algebraic derivative associated to the operator
{D}^{\delta }
V. Almeida, N. Castro, J. Rodríguez (2000)
In this paper we get an algebraic derivative relative to the convolution
\left(f*g\right)\left(t\right)={\int }_{0}^{t}if\left(t-\psi \right)g\left(\psi \right)d\psi
associated to the operator
{D}^{\delta }
, which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation
An asymptotic expansion of the solution to a system of integrodifferential equations with exact asymptotics for the remainder.
Sgibnev, M.S. (2008)
An effective method for solving fractional integro-differential equations.
Wang, Wen--Hua (2009)
An improved exponential decay result for some semilinear integrodifferential equations
S. Mazouzi, Nasser-eddine Tatar (2003)
We prove exponential decay for the solution of an abstract integrodifferential equation. This equation involves coefficients of polynomial type, weakly singular kernels as well as different powers of the unknown in some norms.
An integral equation associated with linear homogeneous differential equations.
Bose, A.K. (1986)
An oscillation criterion for inhomogeneous Stieltjes integro-differential equations.
El-Sayed, M.A. (1994)
Xie, Xuming (2003)
Angenäherte Lösung eines Systems von Integro-Differentialgleichungen mittels der Methode von S. A. Tschaplygin
Application of a trapezoid inequality to neutral Fredholm integro-differential equations in Banach spaces.
Bica, Alexandru, Căuş, Vasile Aurel, Mureşan, Sorin (2006)
Application of Lakshmikantham's monotone-iterative technique to the solution of the initial value problem for impulsive integro-differential equations.
Bajnov, D.D., Khristova, S.G. (1993)
Application of matrix polynomials to investigation of singular equations.
Bulatov, M.V. (2005)
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f
g
t
\left(x=f\left(t\right),y=g\left(t\right)\right)
f
g
This exercise can either present the two curves of
g
\left(x=f\left(t\right),y=g\left(t\right)\right)
among others, or present the parametric curve and ask you to recognize the curves of
g
Style randomly determined by the server recognize the graphs of f and g from the parametric curve recognize the parametric curve from the graphs of
g
Description: recognize a parametric curve by the graphs of its coordinate functions. interactive exercises, online calculators and plotters, mathematical recreation and games
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A defect-correction mixed finite element method for stationary conduction-convection problems.
Si, Zhiyong, He, Yinnian (2011)
Alfredo Bermúdez, Rodolfo Rodríguez, María Luisa Seoane (2011)
This paper deals with the mathematical and numerical analysis of a simplified two-dimensional model for the interaction between the wind and a sail. The wind is modeled as a steady irrotational plane flow past the sail, satisfying the Kutta-Joukowski condition. This condition guarantees that the flow is not singular at the trailing edge of the sail. Although for the present analysis the position of the sail is taken as data, the final aim of this research is to develop tools to compute the sail...
T. Haga, H. Gao, Z. J. Wang (2011)
The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form....
A high-precision algorithm for axisymmetric flow.
Gokhman, A., Gokhman, D. (1995)
A modified Cayley transform for the discretized Navier-Stokes equations
K. A. Cliffe, T. J. Garratt, Alastair Spence (1993)
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform of the...
Jérôme Bastin, Gilbert Rogé (1999)
The fluctuation splitting schemes were introduced by Roe in the beginning of the 80's and have been then developed since then, essentially thanks to Deconinck. In this paper, the fluctuation splitting schemes formalism is recalled. Then, the hyperbolic/elliptic decomposition of the three dimensional Euler equations is presented. This decomposition leads to an acoustic subsystem and two scalar advection equations, one of them being the entropy advection. Thanks to this decomposition, the two scalar...
A network programming approach in solving Darcy's equations by mixed finite-element methods.
Arioli, M., Manzini, G. (2006)
A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations
Yun-Bo Yang, Qiong-Xiang Kong (2017)
A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations is presented. Applying the orthogonal projection technique, we introduce two local Gauss integrations as a stabilizing term in the error correction method, and derive a new error correction method. In both the coarse solution computation step and the error computation step, a locally stabilizing term based on two local Gauss integrations is introduced. The stability and convergence of the...
Oh-In Kwon, Chunjae Park (2014)
We introduce a new stable MINI-element pair for incompressible Stokes equations on quadrilateral meshes, which uses the smallest number of bubbles for the velocity. The pressure is discretized with the P1-midpoint-edge-continuous elements and each component of the velocity field is done with the standard Q1-conforming elements enriched by one bubble a quadrilateral. The superconvergence in the pressure of the proposed pair is analyzed on uniform rectangular meshes, and tested numerically on uniform...
\theta
-scheme algorithm and incompressible FEM for viscoelastic fluid flows
P. Saramito (1994)
A novel approach to modelling of flow in fractured porous medium
Jan Šembera, Jiří Maryška, Jiřina Královcová, Otto Severýn (2007)
There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article,...
A numerical approximation of non-Fickian flows with mixing length growth in porous media.
Ewing, R.E., Lin, Y., Wang, J. (2001)
-ϵ{u}^{n}+p{u}^{\text{'}}+qu=f
ϵ
\left|p\right|,q
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Poincaré's homology sphere - Manifold Atlas
Poincaré's homology sphere is a closed 3- manifold with the same homology as the 3-sphere but with a fundamental group which is non-trivial.
In his series of papers on Analysis situs (1892 - 1904) Poincaré introduced the fundamental group and studied Betti-numbers and torsion coefficients. He asked himself the question how strong these invariants are. In his last paper - the so-called fifth complement (1904) - he constructed an example of a closed manifold with vanishing first Betti-number, without torsion coefficient but with a fundamental group which he proved to be non trivial. This manifold today called Poincaré's homology sphere - or not correctly Poincaré's dodecahedron space (cf. below) - is constructed by a Heegaard splitting. Therefore Poincaré was the first author to use this idea in a sophisticated situation. Using a function which measures the "height" of the cuts through the 3-manifold (that is a sort of Morse function (in modern terms)) Poincaré described the process of attaching handles step by step, thus building up a handlebody. He arrived at a decomposition of the 3-manifold into two handle bodies; their surfaces are two homeomorphic surfaces of genus
\newcommand{\Z}{\mathbb{Z}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\N}{\mathbb{N}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\F}{\mathbb{F}} \newcommand{\bZ}{\mathbb{Z}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bC}{\mathbb{C}} \newcommand{\bH}{\mathbb{H}} \newcommand{\bQ}{\mathbb{Q}} \newcommand{\bF}{\mathbb{F}} \newcommand{\bN}{\mathbb{N}} \DeclareMathOperator\id{id} % identity map \DeclareMathOperator\Sq{Sq} % Steenrod squares \DeclareMathOperator\Homeo{Homeo} % group of homeomorphisms of a topoloical space \DeclareMathOperator\Diff{Diff} % group of diffeomorphisms of a smooth manifold \DeclareMathOperator\SDiff{SDiff} % diffeomorphism under some constraint \DeclareMathOperator\Hom{Hom} % homomrphism group \DeclareMathOperator\End{End} % endomorphism group \DeclareMathOperator\Aut{Aut} % automorphism group \DeclareMathOperator\Inn{Inn} % inner automorphisms \DeclareMathOperator\Out{Out} % outer automorphism group \DeclareMathOperator\vol{vol} % volume \newcommand{\GL}{\text{GL}} % general linear group \newcommand{\SL}{\text{SL}} % special linear group \newcommand{\SO}{\text{SO}} % special orthogonal group \newcommand{\O}{\text{O}} % orthogonal group \newcommand{\SU}{\text{SU}} % special unitary group \newcommand{\Spin}{\text{Spin}} % Spin group \newcommand{\RP}{\Rr\mathrm P} % real projective space \newcommand{\CP}{\Cc\mathrm P} % complex projective space \newcommand{\HP}{\Hh\mathrm P} % quaternionic projective space \newcommand{\Top}{\mathrm{Top}} % topological category \newcommand{\PL}{\mathrm{PL}} % piecewise linear category \newcommand{\Cat}{\mathrm{Cat}} % any category \newcommand{\KS}{\text{KS}} % Kirby-Siebenmann class \newcommand{\Hud}{\text{Hud}} % Hudson torus \newcommand{\Ker}{\text{Ker}} % Kernel \newcommand{\underbar}{\underline} %Classifying Spaces for Families of Subgroups \newcommand{\textup}{\text} \newcommand{\sp}{^}n
which are identified by an automorphism of the surface.
To obtain his example Poincaré used two surfaces of genus 2 - two ``pretzels´´. The identifying automorphism is defined by sending curves which are not null homotopic of one surface to such curves on the other. The first set of curves contains the standard generators of the fundamental group of the pretzel, the second is indicated by a diagram. By using a sort of Seifert-van Kampen argument, Poincaré was able to show that the fundamental group of the manifold is non-trivial. In order to get this result he demonstrated that the fundamental group contains a subgroup isomorphic to the icosahedron group (actually the fundamental group is isomorphic to the extended icosahedron group). He was also able to calculate the Betti-numbers of his manifold. By using the relations on the generators of the fundamental group he showed that the first Betti number is 0 - so, by duality, the second is also zero. There are no torsion coefficients.
Figure 1: Poincaré's Heegaard diagram ([Poincaré1904, 494])
This picture in Figure 1 represents a sphere with two handles, a pretzel, with the handles cut off by two closed curve represented by the four circles +
A
A
B
B
(identifying +
A
with -
A
yields the first handle, identifying +
B
to -
B
the other). The pretzel has to be identified with a second surface of this type such that the two curves indicated in the scheme are identified with those closed curves which are commonly used to dissect the handles of the pretzel (``Meridianschnitte´´, that is +
A
A
B
B
). Using this description Poincarè was able to calculate the fundamental group of the resulting closed 3-manifold. He showed that there is a homomorphism from the fundamental group onto the icosahedron group. So the first is definitely not trivial. Poincaré used the following presentation of the fundamental group.
Later on Poincaré was able to demonstrate that the fundamental group is identical to its commutator subgroup (in modern terms). Poincaré discovered this fact by using generators and relations, so to him the assertion above meant that in calculating in a commutative way homology becomes trivial - i.e. the first Betti number of the manifold vanishes. Because the manifold is orientable there is no torsion coefficient in dimension one. Using duality Poincaré got all the information he needed.
At the end of his paper Poincaré asked a question: ``Est-il possible que le groupe fondamental de V se réduise à la substitution identique, et que pourtant V ne soit pas simplement connexe?´´ In modern terms this means: ``Is it possible that a manifold with a vanishing fundamental group is not homeomorphic to the 3-sphere?´´ And he ended with the remark: ``Mais cette question nous entraînerait trop loin.´´ (``But this question leads us too far away´´). This is the starting point of the history of the so-called Poincaré conjecture.
In their joint paper Analysis situs (1907), which was a contribution to the Encyklopädie der mathematischen Wissenschaften mit Einschluß ihrer Anwendungen, P. Heegard and M. Dehn discussed Poincaré's manifold. They gave a picture representing Poincaré's identification scheme in a different way: Dehn and Heegard used a ``Doppelringfläche´´ (that is a pretzel surface) instead of Poincaré's sphere with four holes. Once again the identification was defined by curves.
Figure 2: Identification scheme of Dehn and Heegaard ([Dehn&Heegaard1907, 185])
After this paper was printed Dehn noticed that the identification scheme indicated by the picture (cf. Figure 2) is not correct. In 1907 he published a ``rectification´´ (that is an erratum) of it. In reading this carefully one becomes aware of the fact that Dehn's famous method - today called Dehn's surgery - started with the analysis of the false identification scheme. In his paper of 1910, Dehn used his method to construct another example of a closed 3-manifold with a fundamental group isomorphic to the extended or binary icosahedron group, that is the full symmetry group of the icosahedron including also reflections. The ``Gruppenbild´´, that is the graph of this group, is depicted by Dehn as a dodecahedron net; see Figure 3. His starting point in doing this was the "Kleeblattschinge" (that is the torus knot (3,2); cf. [Epple1999]). Dehn coined the name ``Poincaréscher Raum´´ (Poincaré space) in order to denote ``solche dreidimensionalen Mannigfaltigkeiten, die, ohne Torsion und mit einfachem Zusammenhang, doch nicht mit dem gewöhnlichen Raum [gemeint ist die 3-Sphäre] homöomorph sind.´´ ([Dehn1910, 138]). That is, Poincaré space is the name of three-dimensional homology spheres which are not isomorphic to the 3-sphere. The example using the torus knot is unique because it is the only Poincaré space constructed by Dehn with a finite fundamental group.
Figure 3: Graph of the icosahedron group ([Dehn1910, 145])
During the 1920s Poincaré's conjecture became a well known problem. In particular H. Kneser mentioned it in a talk he delivered to the Versammlung Deutscher Naturforscher und Ärzte (joint meeting with the DMV) in 1928; [Kneser1929]. After citing Dehn's manifold, Kneser stated that this example is also related to the 120-cell (one of the six regular polytopes of 4-space) in ordinary 4-space. The 120-cell defines a tessellation of the 3-sphere on which the icosahedron group acts transitively and without fixed points. The fundamental domain is a spheric dodecahedron, the operations define certain identifications of the faces of the fundamental domain.
The now common way in which the dodecahedron space is defined was first given by W. Threlfall and H. Seifert in their first joint paper (1931). It is characterized by the use of a dodecahedron the opposite faces of which are identified after a turn by
\pi/5
. to be more precise this is the spherical dodecahedron space. There is also an hyperbolic dodecahedron space which is a different 3-manifold. The dodecahedron is called spherical because it is bounded by spherical pentagons due to the fact that it is obtained as the intersection of 12 balls. This construction is discussed in detail in [Threlfall&Seifert1931, 64-66].
Figure 4: The dodecahedron space ([Threlfall&Seifert1931, 66])
In this scheme the decomposition of the dodecahedron space into two solid pretzels is indicated.
Another representation of a homology sphere was given by the Russian mathematician M. Kreines in 1932. Generalizing the way in which lens spaces are defined he obtained the following scheme.
Figure 5: Kreines' scheme ([Kreines1932, 277])
The identification of the sphere with itself is defined as follows:
S_1
has to identified with
S'_1
such that the points 0123498 (pictured in small print in Figure 5) are identified with the points 8076549 in the indicated order,
S_2
S'_2
, such that the points 01267 are identified with the points 32654. Using this description it is possible to get a decomposition of the manifold into cells and to calculate its fundamental group. There are two cycles
and
b
- the two edges in the decomposition - and two relations given by
S_1
S_2
which can be written in the form
This is the standard representation of the extended icosahedron group.
Around 1932 different homology spheres were known with a fundamental group isomorphic to the icosahedron group (or to an extension of it): Poincaré's original example, Dehn's manifold, Kreines' manifold and the dodecahedron space of Seifert and Threlfall. The obvious question was: Are they all homeomorphic? The positive answer was given by the theory of fibered spaces (today: Seifert fibered spaces) developed by Seifert in his paper of 1933 [Seifert1933b]; the detailed discussion of the different manifolds just cited can be found in a joint paper written by H. Seifert and C. Weber in 1933, [Weber&Seifert1933] (cf. also [Seifert&Threlfall1934, n. 38 (p. 224)]). The clue to this result is a complete list of invariants found by Seifert which solved the problem of homeomorphy for certain types of Seifert-fibered spaces.
[Dehn&Heegaard1907] M. Dehn and P. Heegaard, Analysis situs, Enzyklopädie der Mathematischen Wissenschaften III AB3: (1907) 153–200. Zbl 38.0510.14
Retrieved from "http://www.map.mpim-bonn.mpg.de/index.php?title=Poincar%C3%A9%27s_homology_sphere&oldid=10584"
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Memristor - 3D Computer
Memristor (10955 views - Computer)
A memristor (; a portmanteau of memory resistor) is a hypothetical non-linear passive two-terminal electrical component relating electric charge and magnetic flux linkage. It was envisioned, and its name coined, in 1971 by circuit theorist Leon Chua. According to the characterizing mathematical relations, the memristor would hypothetically operate in the following way: The memristor's electrical resistance is not constant but depends on the history of current that had previously flowed through the device, i.e., its present resistance depends on how much electric charge has flowed in what direction through it in the past; the device remembers its history — the so-called non-volatility property. When the electric power supply is turned off, the memristor remembers its most recent resistance until it is turned on again. In 2008, a team at HP Labs claimed to have found Chua's missing memristor based on an analysis of a thin film of titanium dioxide thus connecting the operation of RRAM devices to the memristor concept; the HP result was published in Nature. Following this claim, Leon Chua has argued that the memristor definition could be generalized to cover all forms of two-terminal non-volatile memory devices based on resistance switching effects. There are, however, some serious doubts as to whether the memristor can actually exist in physical reality. Additionally, some experimental evidence contradicts Chua's generalization since a non-passive nanobattery effect is observable in resistance switching memory. Chua also argued that the memristor is the oldest known circuit element, with its effects predating the resistor, capacitor and inductor. These devices are intended for applications in nanoelectronic memories, computer logic and neuromorphic/neuromemristive computer architectures. Commercial availability of memristor memory has been estimated as 2018. In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip.
3D CAD Models - Memristor
A memristor (/ˈmɛmrɪstər/; a portmanteau of memory resistor) is a hypothetical non-linear passive two-terminal electrical component relating electric charge and magnetic flux linkage. It was envisioned, and its name coined, in 1971 by circuit theorist Leon Chua.[1] According to the characterizing mathematical relations, the memristor would hypothetically operate in the following way: The memristor's electrical resistance is not constant but depends on the history of current that had previously flowed through the device, i.e., its present resistance depends on how much electric charge has flowed in what direction through it in the past; the device remembers its history — the so-called non-volatility property.[2] When the electric power supply is turned off, the memristor remembers its most recent resistance until it is turned on again.[3][4]
In 2008, a team at HP Labs claimed to have found Chua's missing memristor based on an analysis of a thin film of titanium dioxide thus connecting the operation of RRAM devices to the memristor concept; the HP result was published in Nature.[3] Following this claim, Leon Chua has argued that the memristor definition could be generalized to cover all forms of two-terminal non-volatile memory devices based on resistance switching effects.[2] There are, however, some serious doubts as to whether the memristor can actually exist in physical reality.[5][6][7] Additionally, some experimental evidence contradicts Chua's generalization since a non-passive nanobattery effect is observable in resistance switching memory.[8] Chua also argued that the memristor is the oldest known circuit element, with its effects predating the resistor, capacitor and inductor.[9]
These devices are intended for applications in nanoelectronic memories, computer logic and neuromorphic/neuromemristive computer architectures.[10] Commercial availability of memristor memory has been estimated as 2018.[11] In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip.[12]
5.1 Self Directed Channel Memristor
In 2011, Meuffels and Schroeder noted that one of the early memristor papers included a mistaken assumption regarding ionic conduction.[21] In 2012, Meuffels and Soni discussed some fundamental issues and problems in the realization of memristors.[5] They indicated inadequacies in the electrochemical modelling presented in the Nature paper "The missing memristor found"[3] because the impact of concentration polarization effects on the behavior of metal−TiO2−x−metal structures under voltage or current stress was not considered. This critique was referred to by Valov et al.[8] in 2013.
In a kind of thought experiment, Meuffels and Soni[5] furthermore revealed a severe inconsistency: If a current-controlled memristor with the so-called non-volatility property[2] exists in physical reality, its behavior would violate Landauer's principle of the minimum amount of energy required to change "information" states of a system. This critique was finally adopted by Di Ventra and Pershin[6] in 2013.
Within this context, Meuffels and Soni[5] pointed to a fundamental thermodynamic principle: Non-volatile information storage requires the existence of free energy barriers that separate the distinct internal memory states of a system from each other; otherwise, one would be faced with an "indifferent" situation and the system would arbitrarily fluctuate from one memory state to another just under the influence of thermal fluctuations. When unprotected against thermal fluctuations, the internal memory states exhibit some diffusive dynamics which causes state degradation.[6] The free energy barriers must therefore be high enough to ensure a low bit-error probability of bit operation.[22] Consequently, there is always a lower limit of energy requirement – depending on the required bit-error probability – for intentionally changing a bit value in any memory device.[22][23]
{\displaystyle {\begin{aligned}y(t)&=g({\textbf {x}},u,t)u(t),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u,t)\end{aligned}}}
{\displaystyle {\dot {\textbf {x}}}=f({\textbf {x}},u(t)+\xi (t),t)}
Such an analysis was performed by Di Ventra and Pershin[6] with regard to the genuine current-controlled memristor. As the proposed dynamic state equation provides no physical mechanism enabling such a memristor to cope with inevitable thermal fluctuations, a current-controlled memristor would erratically change its state in course of time just under the influence of current noise.[6][24] Di Ventra and Pershin[6] thus concluded that memristors whose resistance (memory) states depend solely on the current or voltage history would be unable to protect their memory states against unavoidable Johnson–Nyquist noise and permanently suffer from information loss, a so-called "stochastic catastrophe". A current-controlled memristor can thus not exist as a solid state device in physical reality.
The above-mentioned thermodynamic principle furthermore implies that the operation of 2-terminal, non-volatile memory devices (e.g. "resistance switching" memory devices (RRAM)) cannot be associated with the memristor concept, i.e., such devices cannot per se remember their current or voltage history. Transitions between distinct internal memory or resistance states are of probabilistic nature. The probability for a transition from state {i} to state {j} depends on the height of the free energy barrier between both states. The transition probability can thus be influenced by suitably driving the memory device, i.e., by "lowering" the free energy barrier for the transition {i} → {j} by means of, for example, an externally applied bias.
A "resistance switching" event can simply be enforced by setting the external bias to a value above a certain threshold value. This is the trivial case, i.e., the free energy barrier for the transition {i} → {j} is reduced to zero. In case one applies biases below the threshold value, there is still a finite probability that the device will switch in course of time (triggered by a random thermal fluctuation), but – as one is dealing with probabilistic processes – it is impossible to predict when the switching event will occur. That is the basic reason for the stochastic nature of all observed resistance switching (RRAM) processes. If the free energy barriers are not high enough, the memory device can even switch without having to do anything.
When a 2-terminal, non-volatile memory device is found to be in a distinct resistance state {j}, there exists therefore no physical one-to-one relationship between its present state and its foregoing voltage history. The switching behavior of individual non-volatile memory devices can thus per se not be described within the mathematical framework proposed for memristor/memristive systems.
An extra thermodynamic curiosity arises from the definition that memristors/memristive devices should energetically act like resistors. The instantaneous electrical power entering such a device is completely dissipated as Joule heat to the surrounding, viz. no extra energy remains in the system after it has been brought from one resistance state xi to another one xj. Thus, the internal energy of the memristor device in state xi, U(V, T, xi), would be the same as in state xj, U(V, T, xj), even though these different states would give rise to different device’s resistances which itself must be caused by physical alterations of the device's material.
In the article "The Missing Memristor has Not been Found", published in Scientific Reports in 2015 by Vongehr and Meng,[7] it was shown that the real memristor defined in 1971 is not possible without using magnetic induction. This was illustrated by constructing a mechanical analog of the memristor and then analytically showing that the mechanical memristor cannot be constructed without using an inertial mass. As it is well known that the mechanical equivalent of an electrical inductor is mass, it proves that memristors are not possible without using magnetic induction. Thus, it can be argued that the variable resistance devices, such as the RRAMs, and the conceptual memristors may have no equivalence at all.[7][28]
{\displaystyle f(\mathrm {\Phi } _{\mathrm {m} }(t),q(t))=0}
{\displaystyle M(q)={\frac {\mathrm {d} \Phi _{m}}{\mathrm {d} q}}}
{\displaystyle M(q(t))={\cfrac {\mathrm {d} \Phi _{m}/\mathrm {d} t}{\mathrm {d} q/\mathrm {d} t}}={\frac {V(t)}{I(t)}}}
{\displaystyle V(t)=\ M(q(t))I(t)}
{\displaystyle P(t)=\ I(t)V(t)=\ I^{2}(t)M(q(t))}
{\displaystyle M(q(t))=R_{\mathrm {OFF} }\cdot \left(1-{\frac {\mu _{v}R_{\mathrm {ON} }}{D^{2}}}q(t)\right)}
{\displaystyle E_{\mathrm {switch} }=\ V^{2}\int _{T_{\mathrm {off} }}^{T_{\mathrm {on} }}{\frac {\mathrm {d} t}{M(q(t))}}=\ V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{I(q)M(q)}}=\ V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{V(q)}}=\ V\Delta Q}
{\displaystyle {\begin{aligned}y(t)&=g({\textbf {x}},u,t)u(t),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u,t)\end{aligned}}}
{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)u(t)+g_{1}({\textbf {x}},u){\operatorname {d} ^{2}u \over \operatorname {d} t^{2}}+g_{2}({\textbf {x}},u){\operatorname {d} ^{4}u \over \operatorname {d} t^{4}}+\ldots +g_{m}({\textbf {x}},u){\operatorname {d} ^{2m}u \over \operatorname {d} t^{2m}},\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}
{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)(u(t)-a),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}
Self Directed Channel Memristor
In 2017, Campbell formally introduced the Self-Directed Channel (SDC) memristor.[36] The SDC device is the first memristive device available commercially to researchers, students and electronics enthusiast worldwide.[37] The SDC device is operational immediately after fabrication. Switching occurs in the Ge2Se3 active layer, where a key feature of the device, Ge-Ge homopolar bonds, are found. The three layers consisting of Ge2Se3/Ag/Ge2Se3, directly below the top tungsten electrode, mix together during deposition and jointly form the silver-source layer. This silver-source layer is not in direct contact with the active layer. This allows the device to have significantly higher processing and operating temperatures (above 250 °C and at least 150 °C, respectively) since silver does not migrate into the active layer at high temperatures, and the active layer maintains a high glass transition temperature (~350 °C). These processing and operating temperatures are higher than most ion-conducting chalcogenide device types, including the S-based glasses (e.g. GeS) that need to be photodoped or thermally annealed. It is a combination of these factors that allow the SDC device to operate over a wide range of temperatures, including long-term continuous operation at 150 °C.
Later it was found[57] that CNT memristive switching is observed when a nanotube has a non-uniform elastic strain ΔL0. It was shown that the memristive switching mechanism of strained СNT is based on the formation and subsequent redistribution of non-uniform elastic strain and piezoelectric field Edef in the nanotube under the influence of an external electric field E(x,t).
They can potentially be fashioned into non-volatile solid-state memory, which would allow greater data density than hard drives with access times similar to DRAM, replacing both components.[14] HP prototyped a crossbar latch memory that can fit 100 gigabits in a square centimeter,[74] and proposed a scalable 3D design (consisting of up to 1000 layers or 1 petabit per cm3).[75] In May 2008 HP reported that its device reaches currently about one-tenth the speed of DRAM.[76] The devices' resistance would be read with alternating current so that the stored value would not be affected.[77] In May 2012 it was reported that access time had been improved to 90 nanoseconds if not faster, approximately one hundred times faster than contemporaneous flash memory, while using one percent as much energy.[78]
According to Allied Market Research memristor market was worth $3.2 million in 2015 and will be worth $79.0 million by 2022.[95]
In 2009, Di Ventra, Pershin and Chua extended[96] the notion of memristive systems to capacitive and inductive elements in the form of memcapacitors and meminductors, whose properties depend on the state and history of the system, further extended in 2013 by Di Ventra and Pershin.[6]
On May 1 Strukov, Snider, Stewart and Williams published an article in Nature identifying a link between the 2-terminal resistance switching behavior found in nanoscale systems and memristors.[3]
On July 7, 2015 Knowm Inc announced Self Directed Channel (SDC) memristors commercially.[98]
Olivetti P6060Commodore 128Network-attached storageComputer engineeringDisplay deviceDepth perceptionComputer simulationSoftwareUser (computing)Computer sciencePython (programming language)Java (programming language)Microsoft WindowsData storageDigital dataFile sharingUnicodeCharacter (computing)Online and offlineOnline identitySoftware suiteApplication softwareProgramming tool
This article uses material from the Wikipedia article "Memristor", which is released under the Creative Commons Attribution-Share-Alike License 3.0. There is a list of all authors in Wikipedia
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Physics - Optimizing Topological Insulators
Optimizing Topological Insulators
October 6, 2011 • Physics 4, s147
Tweaking the bulk properties of a topological insulator reveals the behavior of its surface states.
Z. Ren et al., Phys. Rev. B (2011)
3D topological insulators comprise a class of materials that have gapless surface states on top of an insulating ground state in the bulk. Any transport measurement of these surface states is influenced by the transport properties of the bulk. We can minimize the contribution of the bulk if we can make it a better insulator. However, none of the commonly known 3D topological insulators is a good insulator.
In a paper in Physical Review B, Zhi Ren and colleagues at Osaka University, Japan, demonstrate a way to make better insulators without destroying the gapless surface states. The authors fabricated single crystals using bismuth ( ), antimony ( ), tellurium ( ), and selenium ( ) with variable concentrations of each element. They ensured that the samples preserved the crystal structure of , a prototypical 3D topological insulator. By changing the amount of each element, they managed to decrease the number of free charge carriers in the bulk, thereby making a better insulator. With this control over the property of the bulk, the authors pinpointed the contribution of the surface states in the transport measurements. The paper further suggests that the use of thinner samples may lead to easier identification of these topological surface states. – Hari Dahal
{\mathbf{Bi}}_{2\text{−}x}{\mathbf{Sb}}_{x}{\mathbf{Te}}_{3\text{−}y}{\mathbf{Se}}_{y}
solid solutions to approach the intrinsic topological insulator regime
SpintronicsStrongly Correlated Materials
{\mathbf{Bi}}_{2\text{−}x}{\mathbf{Sb}}_{x}{\mathbf{Te}}_{3\text{−}y}{\mathbf{Se}}_{y}
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Solve Stiff Transistor Differential Algebraic Equation - MATLAB & Simulink - MathWorks Switzerland
This example shows how to use ode23t to solve a stiff differential algebraic equation (DAE) that describes an electrical circuit [1]. The one-transistor amplifier problem coded in the example file amp1dae.m can be rewritten in semi-explicit form, but this example solves it in its original form
M{u}^{\prime }=\varphi \left(u\right)
. The problem includes a constant, singular mass matrix
\mathit{M}
The transistor amplifier circuit contains six resistors, three capacitors, and a transistor.
The initial voltage signal is
{U}_{e}\left(t\right)=0.4\mathrm{sin}\left(200\pi t\right)
The operating voltage is
{\mathit{U}}_{\mathit{b}}=6
The voltages at the nodes are given by
{\mathit{U}}_{\mathit{i}}\left(\mathit{t}\right)\text{\hspace{0.17em}\hspace{0.17em}}\left(\mathit{i}=1,2,3,4,5\right)
The values of the resistors
{\mathit{R}}_{\mathit{i}}\text{\hspace{0.17em}\hspace{0.17em}}\left(\mathit{i}=1,2,3,4,5,6\right)
are constant, and the current through each resistor satisfies
\mathit{I}=\mathit{U}/\mathit{R}
The values of the capacitors
{\mathit{C}}_{\mathit{i}}\text{\hspace{0.17em}\hspace{0.17em}}\left(\mathit{i}=1,2,3\right)
are constant, and the current through each capacitor satisfies
\mathit{I}=\mathit{C}\cdot \mathrm{dU}/\mathrm{dt}
The goal is to solve for the output voltage through node 5,
{\mathit{U}}_{5}\left(\mathit{t}\right)
To solve this equation in MATLAB®, you need to code the equations, code a mass matrix, and set the initial conditions and interval of integration before calling the solver ode23t. You can either include the required functions as local functions at the end of a file (as done here), or save them as separate, named files in a directory on the MATLAB path.
Using Kirchoff's law to equalize the current through each node (1 through 5), you can obtain a system of five equations describing the circuit:
\begin{array}{l}\mathrm{node}\text{\hspace{0.17em}}1:\text{\hspace{0.17em}\hspace{0.17em}}\frac{{\mathit{U}}_{\mathit{e}}\left(\mathit{t}\right)}{{\mathit{R}}_{0}}-\frac{{\mathit{U}}_{1}}{{\mathit{R}}_{0}}+{\mathit{C}}_{1}\left({{\mathit{U}}_{2}}^{\prime }-{{\mathit{U}}_{1}}^{\prime }\right)=0,\\ \mathrm{node}\text{\hspace{0.17em}}2:\text{\hspace{0.17em}\hspace{0.17em}}\frac{{\mathit{U}}_{\mathit{b}}}{{\mathit{R}}_{2}}-{\mathit{U}}_{2}\left(\frac{1}{{\mathit{R}}_{1}}+\frac{1}{{\mathit{R}}_{2}}\right)+{\mathit{C}}_{1}\left({{\mathit{U}}_{1}}^{\prime }-{{\mathit{U}}_{2}}^{\prime }\right)-0.01\mathit{f}\left({\mathit{U}}_{2}-{\mathit{U}}_{3}\right)=0,\\ \mathrm{node}\text{\hspace{0.17em}}3:\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{f}\left({\mathit{U}}_{2}-{\mathit{U}}_{3}\right)-\frac{{\mathit{U}}_{3}}{{\mathit{R}}_{3}}-{\mathit{C}}_{2}{{\mathit{U}}_{3}}^{\prime }=0,\\ \mathrm{node}\text{\hspace{0.17em}}4:\text{\hspace{0.17em}\hspace{0.17em}}\frac{{\mathit{U}}_{\mathit{b}}}{{\mathit{R}}_{4}}-\frac{{\mathit{U}}_{4}}{{\mathit{R}}_{4}}+{\mathit{C}}_{3}\left({{\mathit{U}}_{5}}^{\prime }-{{\mathit{U}}_{4}}^{\prime }\right)-0.99\mathit{f}\left({\mathit{U}}_{2}-{\mathit{U}}_{3}\right)=0,\\ \mathrm{node}\text{\hspace{0.17em}}5:\text{\hspace{0.17em}}\text{\hspace{0.17em}}-\frac{{\mathit{U}}_{5}}{{\mathit{R}}_{5}}+{\mathit{C}}_{3}\left({{\mathit{U}}_{4}}^{\prime }-{{\mathit{U}}_{5}}^{\prime }\right)=0.\end{array}
The mass matrix of this system, found by collecting the derivative terms on the left side of the equations, has the form
M=\left(\begin{array}{ccccc}-{c}_{1}& {c}_{1}& 0& 0& 0\\ {c}_{1}& -{c}_{1}& 0& 0& 0\\ 0& 0& -{c}_{2}& 0& 0\\ 0& 0& 0& -{c}_{3}& {c}_{3}\\ 0& 0& 0& {c}_{3}& -{c}_{3}\end{array}\right),
{c}_{k}=k×1{0}^{-6}
k=1,2,3
Create a mass matrix with the appropriate constants
{\mathit{c}}_{\mathit{k}}
, and then use the odeset function to specify the mass matrix. Even though it is apparent that the mass matrix is singular, leave the 'MassSingular' option at its default value of 'maybe' to test the automatic detection of a DAE problem by the solver.
c = 1e-6 * (1:3);
M(1,1) = -c(1);
M(1,2) = c(1);
opts = odeset('Mass',M);
The function transampdae contains the system of equations for this example. The function defines values for all of the voltages and constant parameters. The derivatives gathered on the left side of the equations are coded in the mass matrix, and transampdae codes the right side of the equations.
function dudt = transampdae(t,u)
% Define voltages and parameters
Ue = @(t) 0.4*sin(200*pi*t);
R15 = 9000;
Uf = 0.026;
% Define system of equations
f23 = beta*(exp((u(2) - u(3))/Uf) - 1);
dudt = [ -(Ue(t) - u(1))/R0
-(Ub/R15 - u(2)*2/R15 - (1-alpha)*f23)
-(f23 - u(3)/R15)
-((Ub - u(4))/R15 - alpha*f23)
(u(5)/R15) ];
Note: This function is included as a local function at the end of the example.
Set the initial conditions. This example uses the consistent initial conditions for the current through each node computed in [1].
u0(1) = 0;
u0(2) = Ub/2;
u0(4) = Ub;
Solve the DAE system over the time interval [0 0.05] using ode23t.
tspan = [0 0.05];
[t,u] = ode23t(@transampdae,tspan,u0,opts);
Plot the initial voltage
{U}_{e}\left(t\right)
and output voltage
{U}_{5}\left(t\right)
plot(t,Ue(t),'o',t,u(:,5),'.')
axis([0 0.05 -3 2]);
legend('Input Voltage U_e(t)','Output Voltage U_5(t)','Location','NorthWest');
title('One Transistor Amplifier DAE Problem Solved by ODE23T');
[1] Hairer, E., and Gerhard Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Berlin Heidelberg, 1991, p. 377.
Listed here is the local helper function that the ODE solver ode23t calls to calculate the solution. Alternatively, you can save this function as its own file in a directory on the MATLAB path.
ode23t | ode15s
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Ice Age - Oiler Network
The underlying of the Ice Age option is the average block time
T_a
T_a = (T_n - T_0)/n
T_n
is the current block timestamp,
T_0
is the timestamp of the block from which the option counts the average and
n
is the number of blocks since the counting started.
Each individual block can have any time between above 1 second as the PoW algorithm can generate blocks with times randomly distributed around the target block time of 15 seconds (but not shorter than 1 second). The fluctuation in the block times depend on one of the few factors:
changes in hashrate can cause temporary block times variations
miners leaving the network would cause the times to expand slightly
miners joining the network would cause the times to shrink slightly
Ice Age mechanism in Ethereum may cause the block times growth
When buying or selling an Ice Age option you are taking a view on one or all of the above. You may expect a massive shift in the hashrate or you may expect the Ice Age prevention mechanisms to fail.
Historical block time chart (see etherscan.io for the current values):
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C
{C}^{*}
A cohomological index of Fuller type for parameterized set-valued maps in normed spaces
Robert Skiba (2014)
We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.
\left(\psi ,\varphi \right)
A decomposition theorem for a class of continua for which the set function T is continuous
Sergio Macías (2007)
We prove a decomposition theorem for a class of continua for which F. B.. Jones's set function 𝓣 is continuous. This gives a partial answer to a question of D. Bellamy.
A dual of the compression-expansion fixed point theorems.
Avery, Richard, Henderson, Johnny, O'Regan, Donal (2007)
A fixed point conjecture for Borsuk continuous set-valued mappings
Dariusz Miklaszewski (2002)
The main result of this paper is that for n = 3,4,5 and k = n-2, every Borsuk continuous set-valued map of the closed ball in the n-dimensional Euclidean space with values which are one-point sets or sets homeomorphic to the k-sphere has a fixed point. Our approach fails for (k,n) = (1,4). A relevant counterexample (for the homological method, not for the fixed point conjecture) is indicated.
A fixed point index for bimaps
Helga Schirmer (1990)
A fixed point principle for locally expansive multifunctions
Solomon Leader (1980)
A fixed point result of Seghal-Smithson type
A fixed point theorem for multivalued maps in symmetric spaces.
El Moutawakil, Driss (2004)
A Fixed Point Theorem in Reflexive Banach Spaces
G
G
A general coincidence theory for set-valued maps.
O'Regan, D. (1999)
A generalized Amman's fixed point theorem and its application to Nash equlibrium.
Stouti, Abdelkader (2005)
A Hahn-Banach type generalization of the Hyers-Ulam theorem.
Glavosits, Tamás, Száz, Árpád (2011)
A Nielsen number for fixed points and near points of small multifunctions
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Understanding Quadrilaterals, Popular Questions: CBSE Class 8 ENGLISH, English Grammar - Meritnation
Bhawna Saini & 1 other asked a question
What is CPCT in geometry?
Prasanna S asked a question
Shivangi Gupta asked a question
ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then angle A and angle B are respectively ____ & ____.
(pls answer with explanation)
Anusha Iyer asked a question
the measures of two adjacent angles of a quadrilateral are 122 and 38.if the other two aqngles are equaql,find them
Bhargavi Rao asked a question
how to draw a decagon ? its too hard....
Mohamed Naeem asked a question
The five angles of a pentagon are in the ratio 5:6:7:8:10.find the angles.
1) x and y are respectively the mid points of sides AB and BC of a parallelogram ABCD.DX and DY intersect AC at M and N respectively .If AC = 4.5 ,find MN.
2) The angle between two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 60 degree .Find the angles of the parallelogram.
plzzz answer this question sir.
Sai Vamsi Thanneru asked a question
Playing fields, much sports equipment, and play in general involve the use of
quadrilaterals. List as many sporting events as you can that use quadrilaterals. Also, list
the types of quadrilaterals involved in each sport.
how many radii does a circle have, tell me the exact number of radii in a circle.
Gurisha Khera asked a question
n.c.e.r.t book of maths for class 8th..page no. 43 try these(pink box )...ques no.3...pls ans..!
Prove that vertically opposite angles are equal .
Amrita Sinha asked a question
Q. (i) A quadrilateral has three acute angles each measuring 85
°
. Find the measure of the fourth angle.
(ii) The four angles of quadrilateral are 2(x-10)
°
, (x+30)
°
°
and 2x
°
. Find all the four angles.
What is the difference between intersect and bisect?
ncert class 8 maths chapter 3 solve all try these pink box
Bably asked a question
In PQRS and LMNQ are parallelogram . If Angle Q=60 degree ,Find angle L, angle M ,angle P, angle Snd angle R
Mohd Iqbal asked a question
what are 3 example of trapezium in real life
Ishan Saini asked a question
PQRS is a rectangle and its diagonal PR and QS intersect at O.if angle POQ=110 find the measure of
angle PQO
angle PSQ
angle ORS
Samkit Jain asked a question
One of the diagonals of the rhombus is equal to one of its sides. Find the angles of the rhombus.
Answer in detail with steps.
Draw two line segments 8 cm 6 cm Long such that they bisect each other at right angle . Join the end points . what type the figure will you get .
Manthan Hiremath asked a question
ABCD is a rhombus if angle ACB=40 then angle ADB?????
If the three angles of a quadrilateral are 120°,130°,10° then what is the fourth angle?
What Is Apollonius Theorem?
Shreya Raawat asked a question
Q1. In a quadrilateral, angle A=63*, angle B=54* , angle C=136* and angle D=117* are these the measures of a trapezium.
Sushanth Reddy & 4 others asked a question
MINT is a parallelogram. OM =5x+2 and OI = 17, find MN
ABCD is an isosceles trapezium with AB parallel to DC and AD=BC.If Angle A is 130 degree,find angle B, angle C and angle D.
V.lakshmi Narayanan asked a question
The angle between two altitude of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 60degree . Find the angles of the parallelogram.
Prakhar Bhatnagar asked a question
1) The diagonals of a rectangle ABCD intersect at O .If angles BOC = 68 degree , find angle ODA.
2) ABCD is a rhombus in which the altitude from D to side AB bisects AB . Find the angles of the rhombus.
( here what is altitude explain in 2 ques. and defination of altitude.)
answer it fast plzzz
The sum of two opposite angles of a parallelogram is 150 Degree. Find all the angles of the parallelogram.
Meraj & 1 other asked a question
Tick the correct option in the following multiple choice questions.
i) The angles of a quadrilateral are in ratio 2:3:5:8. The smallest angle is:
ii) Which of the following rational number is in standard form:
a)-14/30 b) 6/-7 c) -39/125 d) -21/78
iii) When a certain number is added to the numerator of 9/17. the new
fraction is 5/7. The number is :
a)10 b) 9 c) 11 d) (-1)
iv) A boy gets 3 marks for each correct sum and loses 2 marks for each
incorrect sum. He does 24 sums and obtained 37 marks. The number of
correct sums were :
Draw two lines of length 6cm and 4cm which bisects at each other at right angles. Join the end points. What figure do you get? Write all the properties of that figure.
The measure of an angle of a parallelogram is 80 degree.Find its remaining angles.
4. These quadrilaterals were convex. What would happen if the
quadrilateral is not convex? Consider quadrilateral ABCD. Split it
into two triangles and find the sum of the interior angles (Fig 3.7).*
* (Fig 3.7).in ncert text 8th pg no 41.
Anusha Hariharan asked a question
WHAT DO U MEAN BY : RATE COMPOUNDED ANNUALLY OR HALF YEARLY ( SEMI ANNUALLY)
Keshav Sharma asked a question
ABCD is a kite and angle a=anglec.If angle cad=70 degree, angle cbd=65 degree,find:[a]angle bcd [b] angle adc
Rihana Ritz asked a question
A closed figure made up of only line segments is called _____________
2] A line segment connecting two consecutive vertices of a polygon is called a_________
3} The diagonal of a convex polygon lie in the ___________ of the polygon.
4) A ___________polygon is equiangular and quadilateral.
5) The sum of the int. angle of a three sided regular polygon is __________
6) The sum of the measures of the external angles of any polygon is___________
in a quadrilateral line RT is drawn parallel to SQ .If angle QPS = 100 , angle PQS = 40 , angle PSR = 85 AND angle QRS = 70 , then angle QRT IS
safahasan97... asked a question
In figure 16.1 4 determine angle p + angle q + angle r + angle s + angle t
Kaashvi Dubey asked a question
the parallel side of a trapezium are 20 cm and 10 cm and its non parallel side are equal each being 13 cm .find area of the trapezium
The diogonals AC and BD of a parallelogram ABCD bisect each other at O. A line segment XY through O has its end-points on the pposite sides AB and CD. Is XY also bisected at O.
pls help :-
1)a quadrilateral is in the form of a kite whose perimeter is 32 cm. if one of the sides is 6 cm,find the length of the other sides .
2)if the diagonals of a rhombus are 10 cm and 24 cm , find the length of the side of a rhombus .
Three angles of a quadrilateral are in the ratio 3:4:5. The difference of the least and the greatest of these angles is 45. Find all the four angles of the quadrilateral
PQRS is a rectangle. QM and SN are perpendiculars from Q and S on PR.
a) is triangle QMR concurrent to triangle SNP?
b) state the pairs of matching parts needed to answer this.
c) is it true that QM= SN ?
By selling a bouquet or rs 322, aflorist gains 15percent at what price should he sell it to gain 25percent
PQRS is a kite and angle P = angle R.If angle RPS=70 DEGREE and angle RQS= 65 DEGREE, Find angle QRS and angle PSR.
Ncert ?? of class 8 chapter 3 of try these mathst
Stefna S asked a question
The perimeter of a parallelogram is 60 cm. If one of it's sides is 12 cm, find it's other three sides.
In the adjoining figure, ABC is a triangle. Through A, B and C lines are drawn parallel to BC, CA and AB respectively, which forms a triangle PQR. Show that
2(AB + BC + CA) = PQ + QR + RP
Two angles, of a parallelogram, which have no common arm are called the opposite angles. Is it false ?
If atleast one angle of a polygon is more than 180 degree, then the polygon is called a concave polygon. Is it true ?
If a convex polygon has n sides, then the sum of its interior angles is equal to the product of_______ and 180 degree.
THe sum of the interior angles of a convex polygon with 12 sides is what ?
how is square prism and pentagonal prism. also shoe net.
Nnnn asked a question
In a triangleABC, if the circle drawn on BC as diameter passes through A, the triangleABC is a)an acute angled triangle b) an equilateral triangle c)an obtuse angled triangle
Pritish Gupta asked a question
PQRSTU is a regular hexagon . Determine each angle of triangle PQT
Is there a triangle that is equilateral but not equiangular?
Shubham Sherki asked a question
how will u prove that the sum of all interior angles of a quadrilateral is 360 degree?
Can I get the list of the 'types of angles'
Sasha Suhel asked a question
Is it possible to construct a rhombus ABCD where AC=6cm and BD=7cm, justify your answer
Richa Vatsa asked a question
Wts the difference between concave nd convex qadrilaterals?
Vrisha asked a question
Q.14.In the trapezium ABCD(fig 2),BE is drawn ti cut DC at E such that AD=BE. Prove that angle ADE=angle EBC + angle BCE.
ABCDE is a regular pentagon.the bisector of angle A of the pentagon meets the side CD in M.Show that angle AMC =360
Alena Reji asked a question
find the number of diagonals in an octagon?
Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5 : 7 . Find
the original numbers. i need it with prper steps.for my exam
Vineet Joshi asked a question
Arunit Dewangan asked a question
In a quadrilateral abcd linesegments bisecting angle c & d meet at E . prove that angle A + angle B = 2? angle ced
Ankita Mukherjee asked a question
Q.1 Three horse are standing in triangular field , which is exactly 100 yards on each side . One horse stands at each corner , and simultaneously all three set off running . Each horse runs after the horse in the adjacent corner on his left , Thus following a curved course , Which terminates in the middle of the field , all three horses arriving there together . If the horses ran at the same speed , How far did they run ? Q.2 Two adjacent angles of a parallelogram are in the ratio of 4:5 . Find all the angles of the parallelogram
Q8. Show that the four triangles as shown in the adjoining figure, formed by diagonals and sides of a rhombus are congruent.
HOW MANY SIDES DOES A REGULAR POLYGON HAVE IF EACH OF ITS INTERIOR ANGLES IS 165 ?
Q.17. RENT is a trapezium in which
TN\parallel RE
. What is the value of x.
Aman Makkar asked a question
Tushaar Vsl asked a question
In the given parallelogram AO=OD=OC and reflex angle AOC= 230?. Find value of x
Does a polygon usually have more sides or more angles? Explain.
X and Y are respectively the mid-pointsof sides AB and BC of the parallelogram ABCD . DX and DY intersect AC at M and N respectively . If AC =4.5cm, find MN
Aarunish Sinha asked a question
How many will a regular polygon have if the measure of each angle is 165 degree?
Govardhana Kishore V asked a question
PQRS is a parallelogram,T is the midpoint of PQ ,ST bisects angle S
a) QR = QT
b) RT bisects Angle R
c)angle STR = 90o
find the number of sides of a regular polygon if each INTERIOR angle is 24 degrees. Experts please solve this one and show because i tried to solve it many times the same sum, i am not getting the answer. Wednesday is my exam please help me as soon as possible....
how are different quadrilaterals helpful 2 us in our daily life???
Udisha Pandey asked a question
What are convex and concave polygons? I was told by my teacher that in concave polygon one of the angle reflex angle. Is that true?
prove the angle sum property of a quadrilateral by cutting and pasting
Vidhu Kota asked a question
Match the following: Column A Column B 1. Parallelogram a) One pair of opposite sides is parallel 2. Rhombus b) Both pairs of opposite sides are equal with each angle 90 degree 3. Square c) Opposite sides are equal 4. Rectangle d) Diagonals bisects each other at 90 degrees but not equal 5. Trapezium e) Diagonal are equal and bisect each other at right angle
Three angles of a quadrilateral are in the ratio 1:2:3.The sum of the least and the greatest of these angles is equal to 180 degree.Find all the angles of the quadrilateral.
in the rectangle ABCD , Diagonals AC and BD meet at O . If OA= 2X+ 7 and OD =3X-5, Find the value of x
Joel George & 1 other asked a question
What is the difference between trapezium and kite
Megha - asked a question
Find out the answer of the following question
Reena & 1 other asked a question
a comparative study of the scores of various teams of IPL, and represent it in the form of bar graph. Do it from quarter finals to finals.
the adjacent side of a parallelogram are in the ratio 3:7 and its perimeter is 100 cm . find the side of the parallogram .
Vitasta Gehlawat asked a question
Take a cut-out of a parallelogram, say,ABCD. Let its diagonals AC and DB meet at O.Find the mid point of AC by a fold, placing C on A. Is themid-point same as O?Does this show that diagonal DB bisects the diagonal AC at the point O? Discuss itwith your experts. Repeat the activity to find where the mid point of DB could lie.please explain with figure...!!
Construct a parallogram ABCD in which AB=7cm,AC=10cm,and BD=8cm{remember that the diagonals bisect each other.}
please answer me fast....................
If the diagonals of a quadrilateral bisect each other at right angle, then it is a .....
(A) Kite (B) Parallelogram (C) Rhombus (D) Rectangle
Abhisu Poddar asked a question
Can anyone out there help me ?
Q1. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively.Find the length of each of its sides.
Q2. The sum of two opposite angles of a 11gm is 130 degrees. Find the measure of each of its angles.
Consider the following parallelogram find the value of unknown x y z.
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{\beta }_{X}
A Multiplication Of M-Relations
M. Miličić (1978)
A multiplication of m-relations.
M. Milicic (1978)
A note on general relations
Josef Šlapal (1995)
A note on metrics and tolerances
Prem N. Bajaj (1981)
A Note On Reproductive Solutions
Milan Božić (1975)
A note on reproductive solutions.
M. Bozic (1975)
A note on tolerance lattices of finite chains
A note on tolerance lattices of products of lattices
A propos des quasi-ordres - Note
O. Cogis (1980)
A revision of Bandler-Kohout compositions of relations.
De Baets, B., Kerre, E. (1993)
A semigroup in function algebra.
Algebraicity of endomorphisms of some relational structures
All reproductive solutions of finite equations.
Prešić, Slaviša B. (1988)
Almost every function is independent
An algorithm of calculation of lower solutions of fuzzy relational equations.
Antonio Di Nola (1984)
This paper deals with the problem of the determination of lower solutions of fuzzy relational equations. An algorithm of calculation of such a solution is presented.
An ordering of the set of natural numbers based on Peano axioms
Vladimir Devidé (1967)
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15A80 Max-plus and related algebras
15A83 Matrix completion problems
A basis of the set of sequences satisfying a given m-th order linear recurrence.
Claude Levesque (1987)
A duality based proof of the combinatorial nullstellensatz.
Kouba, Omran (2009)
Gunawan, Hendra, Neswan, Oki, Setya-Budhi, Wono (2005)
Matsuura, Masaya (2003)
A graph-theoretic method for choosing a spanning set for a finite-dimensional vector space, with applications to the Grossman-Larson-Wright module and the Jacobian conjecture.
Singer, Dan (2009)
A new characterization of generalized complementary basic matrices
Miroslav Fiedler, Frank J. Hall (2014)
In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases.
In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases
A new equivalent condition of the reverse order law for
G
-inverses of multiple matrix products.
Zheng, Bing, Xiong, Zhiping (2008)
A new rank formula for idempotent matrices with applications
Yong Ge Tian, George P. H. Styan (2002)
\text{rank}\left({P}^{*}AQ\right)=\text{rank}\left({P}^{*}A\right)+\text{rank}\left(AQ\right)-\text{rank}\left(A\right),
A
is idempotent,
\left[P,Q\right]
has full row rank and
{P}^{*}Q=0
. Some applications of the rank formula to generalized inverses of matrices are also presented.
A new simple approach to linear dependence
Ladislav Beran (2004)
A new solvable condition for a pair of generalized Sylvester equations.
Wang, Qing-Wen, Zhang, Hua-Sheng, Song, Guang-Jing (2009)
A note on hypervector spaces
Sanjay Roy, Tapas K. Samanta (2011)
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.
A note on preserving the spark of a matrix
Marcin Skrzyński (2015)
Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F).
A note on the cp-rank of matrices generated by Soules matrices.
Shaked-Monderer, Naomi (2005)
A note on the ranks of set-inclusion matrices.
de Caen, D. (2001)
A remark on spaces over a special local ring
Marek Jukl (1998)
This paper deals with A-spaces in the sense of McDonald over linear algebras A of a certain type. Necessary and sufficient conditions for a submodule to be an A-space are derived.
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Brownian interpolation of stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, or SDEMRD models - MATLAB interpolate - MathWorks India
\begin{array}{l}d{X}_{1t}=0.3dt+0.2d{W}_{1t}-0.1d{W}_{2t}\\ d{X}_{2t}=0.4dt+0.1d{W}_{1t}-0.2d{W}_{2t}\\ E\left[d{W}_{1t}d{W}_{2t}\right]=\rho dt=0.5dt\end{array}
{X}_{t}=P\left(t,{X}_{t}\right)
d{X}_{t}=F\left(t,{X}_{t}\right)dt+G\left(t,{X}_{t}\right)d{W}_{t}
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A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics.
Baudouin, Lucie (2006)
A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations
Hitoshi Ishii (1989)
A Canonical Formalism for Multiple Integral Problems in the Calculus of Variation. (Short Communication).
Hanno Rund (1968)
C. Lederman (1996)
A Method of Solving Nonlinear Variational Problems by Nonlinear Transformation of the Objective Functional. Part I.
A moving mesh fictitious domain approach for shape optimization problems
Raino A. E. Mäkinen, Tuomo Rossi, Jari Toivanen (2000)
Raino A.E. Mäkinen, Tuomo Rossi, Jari Toivanen (2010)
A new numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation is proposed. The basic idea is to combine the boundary variation technique, in which the mesh is moving during the optimization, and efficient fictitious domain preconditioning in the solution of the (adjoint) state equations. Neumann boundary value problems are solved using an algebraic fictitious domain method. A mixed formulation based on boundary Lagrange multipliers is...
Kenan Yildirim, Ismail Kucuk (2017)
In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as...
Y
Galina C. García, Axel Osses, Jean Pierre Puel (2011)
Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim. 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...
A null controllability data assimilation methodology applied to a large scale ocean circulation model*
Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...
Patrick Penzler, Martin Rumpf, Benedikt Wirth (2012)
Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...
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Detect Lines Using the Radon Transform - MATLAB & Simulink - MathWorks Benelux
Compute the Radon Transform of an Image
Interpreting the Peaks of the Radon Transform
This example shows how to use the Radon transform to detect lines in an image. The Radon transform is closely related to a common computer vision operation known as the Hough transform. You can use the radon function to implement a form of the Hough transform used to detect straight lines.
Read an image into the workspace. Convert it into a grayscale image.
Compute a binary edge image using the edge function. Display the binary image returned by the edge function.
title('Edges of Original Image')
Calculate the radon transform of the image, using the radon function, and display the transform. The locations of peaks in the transform correspond to the locations of straight lines in the original image.
[R,xp] = radon(BW,theta);
Display the result of the radon transform.
imagesc(theta, xp, R); colormap(hot);
ylabel('x^{\prime} (pixels from center)');
title('R_{\theta} (x^{\prime})');
The strongest peak in R corresponds to
\theta =1
degree and x' = -80 pixels from center.
To visualize this peak in the original figure, find the center of the image, indicated by the blue cross overlaid on the image below. The red dashed line is the radial line that passes through the center at an angle
\theta =1
degree. If you travel along this line -80 pixels from center (towards the left), the radial line perpendicularly intersects the solid red line. This solid red line is the straight line with the strongest signal in the Radon transform.
To interpret the Radon transform further, examine the next four strongest peaks in R.
Two strong peaks in R are found at
\theta =1
degree, at offsets of -84 and -87 pixels from center. These peaks correspond to the two red lines to the left of the strongest line, overlaid on the image below.
Two other strong peaks are found near the center of R. These peaks are located at
\theta =91
degrees, with offsets of -8 and -44 pixels from center. The green dashed line in the image below is the radial line passing through the center at an angle of 91 degrees. If you travel along the radial line a distance of -8 and -44 pixels from center, then the radial line perpendicularly intersects the solid green lines. These solid green lines correspond to the strong peaks in R.
The fainter lines in the image relate to the weaker peaks in R.
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Quantum K-theory of Grassmannians
15 February 2011 Quantum
K
-theory of Grassmannians
Anders S. Buch, Leonardo C. Mihalcea
Anders S. Buch,1 Leonardo C. Mihalcea2
2Department of Mathematics, Baylor University
We show that (equivariant)
K
-theoretic
3
-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the (equivariant)
K
-theory of a two-step flag manifold, thus generalizing an earlier result of Buch, Kresch, and Tamvakis. In the process we show that the Gromov-Witten variety of curves passing through three general points is irreducible and rational. Our applications include Pieri and Giambelli formulas for the quantum
K
-theory ring of a Grassmannian, which determine the multiplication in this ring. We also compute the dual Schubert basis for this ring and show that its structure constants satisfy
{S}_{3}
-symmetry. Our formula for Gromov-Witten invariants can be partially generalized to cominuscule homogeneous spaces by using a construction of Chaput, Manivel, and Perrin.
Anders S. Buch. Leonardo C. Mihalcea. "Quantum
K
-theory of Grassmannians." Duke Math. J. 156 (3) 501 - 538, 15 February 2011. https://doi.org/10.1215/00127094-2010-218
Secondary: 14E08 , 14M15 , 14N15 , 19E08
Anders S. Buch, Leonardo C. Mihalcea "Quantum
K
-theory of Grassmannians," Duke Mathematical Journal, Duke Math. J. 156(3), 501-538, (15 February 2011)
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p
A blow up condition for a nonautonomous semilinear system.
Perez-Perez, Aroldo (2006)
A boundary control problem with a nonlinear reaction term.
Cannon, John R., Salman, Mohamed (2009)
{u}_{t}-\Delta u={u}^{p}\phantom{\rule{4pt}{0ex}}\text{with}\phantom{\rule{4pt}{0ex}}0<p<1
Olaf Klein (2010)
In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.
A class of time discrete schemes for a phase-field system of Penrose-Fife type
A combustion model with unbounded thermal conductivity and reactant diffusivity in non-smooth domains.
Sanni, Sikiru Adigun (2009)
A comment on the Jäger-Kačur's linearization scheme for strongly nonlinear parabolic equations
Jiří Vala (1999)
The aim of this paper is to demonstrate how the variational equations from can be formulated and solved in some abstract Banach spaces without any a priori construction of special linearization schemes. This should be useful e.g. in the analysis of heat conduction problems and modelling of flow in porous media.
Matteo Novaga, Emanuele Paolini (1999)
A Construction of Stable Subharmonic Orbits in Monotone Time-periodic Dynamical Systems.
Takác, Peter (1993)
A coupled Cahn-Hilliard particle system.
Shardlow, Tony (2002)
Vladimir Shelukhin (2007)
A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.
A description of blow-up for the solid fuel ignition model
Bebernes, Jerrold W. (1986)
n\ge 3
J. Bebernes, D. Eberly (1988)
A dual mesh method for a nonlocal thermistor problem.
El Hachimi, Abderrahmane, Sidi Ammi, Moulay Rchid, Torres, Delfim F.M. (2006)
A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition
Lucjan Sapa (2008)
We deal with a finite difference method for a wide class of nonlinear, in particular strongly nonlinear or quasi-linear, second-order partial differential functional equations of parabolic type with Dirichlet's condition. The functional dependence is of the Volterra type and the right-hand sides of the equations satisfy nonlinear estimates of the generalized Perron type with respect to the functional variable. Under the assumptions adopted, quasi-linear equations are a special case of nonlinear...
Sören Bartels, Georg Dolzmann, Ricardo H. Nochetto (2010)
We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in [J.B. Fournier and P. Galatoa, J. Phys. II7 (1997) 1509–1520; N. Uchida, Phys. Rev. E66 (2002) 040902] which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We introduce...
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The field of electronics offers a powerful set of tools for obtaining accurate numerical data. Instead of just saying that there is a difference between two things (color, brightness, charge, etc.), electronic devices allow you to measure precisely how big the difference is.
The word electronics is derived from "electron." Electrons are sub-atomic particles with a negative charge. The unit for electric charge is the coulomb. One coulomb equals the charges of 6.24 billion billion (1018) electrons. A single electron has a charge that is too small to measure in most electronic devices, so scientists use coulombs as a more useful way to describe charge.
The basic outputs for electronic devices are voltage, current, and resistance. Inexpensive and sensitive devices, called multimeters, can measure each of these. If you can devise a way for the output of your experiment to be in the form of voltage, for example, you can use a multimeter to get precise numerical data. For more information about using a multimeter, see the Science Buddies reference How to Use a Multimeter.
The definition of voltage is: the measurement of the potential for an electric field to cause a current in a conductor. An electric field "pushes and pulls" electric charges, so if you put an electron in an electric field, it will move. The movement of charged particles is a current (more about current below). The essential point is that the voltage is a measure of how strongly charged particles are being pushed and pulled by an electric field. The symbol for voltage is V.
Consider a simple flashlight with two D batteries. Each D battery has a voltage of 1.5 V. By putting two 1.5-V batteries together, the total voltage equals 3 V. This voltage is high enough to power a lightbulb. When you turn the flashlight on, the voltage difference causes electrons to flow through the lightbulb, making it shine. The electric field provides the energy to move charged particles through wires (electrical conductors) and through the lightbulb.
Voltage can be direct (DC) or alternating (AC). In DC voltage, the voltage does not alternate. If you graph the voltage of a 9-V battery vs. time, for example, you will have a straight line at a value of 9 V. Alternating current flips back and forth between positive and negative. If you make a graph of AC current vs. time, it will alternate from positive to negative, often in the form of a sine wave. Voltage is supplied to a circuit by a battery or other power supply.
Current is a measurement of how much charge moves through a circuit in a given period of time. In the case of the flashlight, the current through the lightbulb is a measurement of the amount of electric charge flowing through the lightbulb in a given time.
The symbol for current is I. The symbol for the unit of current, the ampere, is A. The precise definition of an ampere is: the current produced by the flow of one coulomb per second. Use "I" when referring to current (as in Ohm's law, discussed below) and "A" when referring to the amount of current.
DC current is produced by DC voltage and AC current is produced by AC voltage.
Electrons flow through materials in response to a voltage, creating a current. Some materials, such as copper, have very low resistance, so the electrons flow freely—they are good conductors. Some materials have intermediate resistance, such as the semiconductors used to make transistors. Semiconductors might have a threshold value for the voltage that will cause a current to flow, for example. And some materials, such as rubber, have high resistance and are used as insulators to separate charges.
The symbol for resistance is R. The unit for resistance is the ohm, which has the symbol Ω, and is the capital letter "W" in Greek.
Ohm's law relates voltage, current, and resistance, mathematically. Ohm's law can be written as:
V = IR
. In words, Ohm's law states that the voltage in a component in a circuit equals the current through the component, times the resistance of the component.
An electronic circuit is a closed path formed by the interconnection of electronic components through which an electric current can flow. You might find it helpful to compare an electronic circuit to a circuit in which water flows.
Voltage in the electronic circuit is like the pump in the water circuit—it provides the push to make things go.
Current in the electronic circuit is like the rate (in liters per second, for example) that water flows in the water circle.
And resistance in an electronic circuit is like a constriction in a hose in the water circuit. An electronic resistor impedes the flow of electrons, just as a constriction in a hose impedes the flow of water.
AC - Abbreviation for alternating current, which is voltage that flips back and forth between positive and negative.
Ampere - Unit of current (symbol: A).
Breadboard - A board used to make temporary circuits. The breadboard has metal-lined sockets for connecting electronic components in a test circuit.
Capacitor - An electronic component consisting of two conducting surfaces, separated by an insulator. It is used to store and release energy and to control high-frequency signals.
Circuit - A collection of electronic parts connected together, usually designed to perform some kind of function.
Circuit diagram - A diagram that depicts a circuit, using symbols for electronic components. Used to design and communicate circuits with other people, like a blueprint or a plan.
Closed circuit - A circuit in which current can flow through electronic components, from a point of high voltage to a point of low voltage.
Conductance - The opposite of resistance. Materials with high conductance (e.g. metals) have low resistance. The unit of conductance is siemens (S).
Current - The flow of electric charge. The unit for current is amperes (A).
DC - Abbreviation for direct current voltage, which is voltage that does not alternate.
Diode - An electronic component that allows current to flow freely in only one direction.
I - Symbol for current. The unit for current is the ampere (A).
Integrated circuit (IC) - An electronic component that contains several simpler electronic components. An IC is a miniaturized electronic circuit.
Jumper - A short length of wire used to temporarily complete a circuit or to bypass a break in a circuit.
Kilo - A prefix meaning "thousand." A 10-kΩ resistor is 10,000 ohms.
Lead - Length of wire used to make connections between components in a circuit.
Light-emitting diode (LED) - A solid-state device that has two key features: it allows current to flow in only one direction (that is the "diode" part), and it emits light when current flows through it in the "allowed" direction. LEDs are described by several specifications, some of the more important of which are:
Angle of light beam (for example, an LED with an angle of 15 degrees produces a more focused beam than one with a beam of 45 degrees); and
Size, usually 5 mm.
Figure 1. Light-emitting diodes come in a variety of sizes, shapes, and colors. (Wikipedia, 2008.)
Mega - A prefix meaning "million" (symbol: M). A 1-MΩ (megaohm) resistor has a resistance of 1 million ohms.
Multimeter - An instrument with several different kinds of meters. Multimeters are used to measure voltage, current, and resistance, among other things.
Ohm - Unit of resistance. The symbol for the ohm is Ω. You can make this symbol in Microsoft Word by changing the font of a capital "W" into the font called "Symbol," using the "Format" menu.
Ohm's law - V = IR, or "Voltage equals current times resistance." Example: Say a 1,000-Ω resistor has a voltage drop of 9 V. What is the amount of current that is flowing through the resistor? Plugging the numbers in yields 9 V = I amps x 1,000 Ω, so I = 9/1,000 amps (A), or 9 milliamps (mA).
Open circuit - A circuit with a gap in it that prevents current from flowing. When you turn of a light with a light switch, you open up the circuit connecting the lightbulb to the source of electricity.
Parallel connection - Current flows through two or more components at the same time. As an analogy, imagine a river splitting into two or more parallel streams, which then merge together again. The amount of current flowing through the various "streams" depends on their resistance.
Figure 2. This diagram shows two resistors in a parallel connection.
R - Symbol for resistance. The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. Metals have very low resistance, whereas substances such as rubber and plastic have high resistance. The unit of resistance is the ohm, with the symbol Ω.
Resistor - An electronic component used to "resist" the flow of current. Resistors are used to control current in an electric circuit. The unit of resistance is the ohm (Ω). The value for the resistance of a resistor is coded by colored lines on the resistor. When they are in a circuit with a voltage supply, a "voltage drop" occurs across the resistor.
Resistors have three key features: their level of resistance, their power rating, and their tolerance. Say a resistor has a resistance of 220 ohms (Ω), a power rating of 1/4 watt (W), and a tolerance of 5 percent. The power rating tells you the limit of the power (power = current x voltage through the resistor) that the resistor can withstand without overheating. Tolerance is a measure of the resistance range. A 220-ohm resistor with a 5 percent tolerance will have a resistance in the range of 220 ohms ± 11 ohms. An electrical specification might call for a resistor with a value of 100 Ω (ohms), but will also state a tolerance, such as "±1%". This means that any resistor with a value in the range 99 Ω–101 Ω is acceptable.
Short circuit - A low-resistance connection established between two points in an electric circuit that are designed to be at different voltages. For example, connecting the positive and negative poles of a battery with a wire causes a short circuit. Because of the low resistance of the connection, the level of current can be very high, leading to excessive heat and damage to the circuit. Short circuits can cause fires and explosions if the current is large enough.
Serial connections - In a serial connection, the current flows through each component one at a time, like a river passing through several dams. The amount of current flowing through the components is equal, since they are connected "end-to-end." Compare to parallel connection.
Figure 3. In this diagram, two resistors are shown in a serial connection.
Tolerance - The range of variation permitted in an electrical component.
V - Symbol for voltage. The unit for voltage is the volt.
Voltage - A measure of the difference in electric potential between two points. A voltage difference causes electrons to flow, much like a difference in height can make water flow. The unit for voltage is the volt (V).
Winscope - A free program that lets you use your computer as an oscilloscope. It is very useful for measuring voltage vs. time data for beginner electronics projects.
The following videos present helpful "how-to" information about working with breadboards.
User: Amanshad. (2007, October 20). How breadboards work. Retrieved April 16, 2009, from http://www.youtube.com/watch?v=lqw6ask5HK0&feature=related
User: Electroinstructor. (2007, September 10.) Introduction to Breadboard (Protoboards), Part 1 of 2. Retrieved April 16, 2009, from http://www.youtube.com/watch?v=oiqNaSPTI7w
Safronoff, R. (n.d.). How to Build Electronic Circuits: How to Use a Breadboard to Prototype a Circuit Board. Retrieved on April 17, 2009, from http://www.expertvillage.com/video/4923_electronic-circuit-breadboard.htm
User: Makemagazine. (2007, August 24). Intro to Breadboard Electronics. Retrieved April 17, 2009, from http://www.youtube.com/watch?v=HteDBfSJ9zo&feature=related
These websites and documents provide more information about working with breadboards.
University of Alabama, Department of Mechanical Engineering. (n.d.). Breadboard Circuit Techniques. Retrieved April 17, 2009, from http://www.me.ua.edu/me360/PDF/Beadboard_Circuit_Techniques.pdf
The Electronics Club. (2009). Breadboard: Connections on Breadboard. Retrieved April 16, 2009, from http://www.kpsec.freeuk.com/breadb.htm
Igoe, T. (n.d.). Making prototype circuits using a solderless breadboard. Retrieved April 15, 2009, from http://www.tigoe.com/pcomp/code/?s=prototype+circuits
Wikipedia Contributors. (2009, April 3). Breadboard. Wikipedia: The Free Encyclopedia. Retrieved April 17, 2009 from http://en.wikipedia.org/w/index.php?title=Breadboard&oldid=281548350
For additional electronics information, visit these Science Buddies pages:
You can find this page online at: https://www.sciencebuddies.org/science-fair-projects/references/electronics-primer-introduction
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Import Knowpia
An import is the receiving country in an export from the sending country. Importation and exportation are the defining financial transactions of international trade.[3]
Geigercars, which imports cars from North America to Europe, is called an importer.[1][2]
Imports consist of transactions in goods and services to a resident of a jurisdiction (such as a nation) from non-residents.[4] The exact definition of imports in national accounts includes and excludes specific "borderline" cases.[5] Importation is the action of buying or acquiring products or services from another country or another market other than own. Imports are important for the economy because they allow a country to supply nonexistent, scarce, high cost, or low-quality certain products or services, to its market with products from other countries.
A general delimitation of imports in national accounts is given below:
An import of a good occurs when there is a change of ownership from a non-resident to a resident; this does not necessarily imply that the good in question physically crosses the frontier. However, in specific cases, national accounts impute changes of ownership even though in legal terms no change of ownership takes place (e.g. cross border financial leasing, cross border deliveries between affiliates of the same enterprise, goods crossing the border for significant processing to order or repair). Also, smuggled goods must be included in the import measurement.
Imports of services consist of all services rendered by non-residents to residents. In national accounts any direct purchases by residents outside the economic territory[6] of a country are recorded as imports of services; therefore all expenditure by tourists in the economic territory of another country are considered part of the imports of services. Also, international flows of illegal services must be included.
Data on international trade in goods are mostly obtained through declarations to custom services. If a country applies the general trade system, all goods entering the country are recorded as imports. If the special trade system (e.g. extra-EU trade statistics) is applied goods that are received into customs warehouses are not recorded in external trade statistics unless they subsequently go into free circulation of the importing country.
A special case is the intra-EU trade statistics. Since goods move freely between the member states of the EU without customs controls, statistics on trade in goods between the member states must be obtained through surveys. To reduce the statistical burden on the respondent's small-scale traders are excluded from the reporting obligation.
Balance of tradeEdit
A country has demand for an import when the price of the good (or service) on the world market is less than the price on the domestic market.
The balance of trade, usually denoted
{\displaystyle NX}
, is the difference between the value of all the goods (and services) a country exports and the value of the goods the country imports. A trade deficit occurs when imports are larger than exports. Imports are impacted principally by a country's income and its productive resources. For example, the US imports oil from Canada even though the US has oil and Canada uses oil. However, consumers in the US are willing to pay more for the marginal barrel of oil than Canadian consumers are, because there is more oil demanded in the US than there is oil produced.
In macroeconomic theory, the value of imports can be modeled as a function of domestic absorption (spending on everything, regardless of source) and the real exchange rate. These are the two most important factors affecting imports and they both affect imports positively.[7]
Types of importEdit
Those looking for any product around the world to import and sell
Those looking for foreign sourcing to get their products at the cheapest price
Those who using foreign sourcing as part of their global supply chain
Direct-import refers to a type of business importation involving a major retailer (e.g. Wal-Mart) and an overseas manufacturer. A retailer typically purchases products designed by local companies that can be manufactured overseas. In a direct-import program, the retailer bypasses the local supplier (colloquial: "middle-man") and buys the final product directly from the manufacturer, possibly saving in added cost data on the value of imports and their quantities often broken down by detailed lists of products are available in statistical collections on international trade published by the statistical services of intergovernmental organisations (e.g. UNSD,[8] FAOSTAT, OECD), supranational statistical institutes (e.g. Eurostat) and national statistical institutes.
Import of goodsEdit
Importation and declaration and payment of customs duties is done by the importer of record, which may be the owner of the goods, the purchaser, or a licensed customs broker.
^ Singh, Rakesh Mohan, (2009) International Business, Oxford University Press, New Delhi and New York ISBN 0-19-568909-7
^ O'Sullivan, Arthur; Shjsnsbeffrin, Steven M. (2003). Economics: Principles in Action. Upper Saddle River: Pearson Prentice Hall. p. 552. ISBN 0-13-063085-3.
^ ICC Export/Import Certification
^ Lequiller, F; Blades, D.: Understanding National Accounts, Paris: OECD 2006, pp. 139-143
^ for example, see Eurostat: European System of Accounts - ESA 1995, §§ 3.128-3.146, Office for Official Publications of the European Communities, Luxembourg, 1996
^ economic territory
^ Burda, Wyplosz (2005): Macroeconomics: A European Text, Fourth Edition, Oxford University Press
^ "United Nations Statistics Division". Unstats.un.org. Retrieved 2013-03-25.
General Procedure of Import Trade
World imports by country, in World Bank's World Integrated Trade Solution
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Squares And Square Roots, Popular Questions: CBSE Class 8 ENGLISH, English Grammar - Meritnation
Anu & 1 other asked a question
how to find square root of 35 step by step
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find square root by long division method.
FIND THE PGT TRIPLET-
WHOSE GREATEST MEMBER IS 101.(METHOD)
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give the answer for the exact number! experts plssanswer the question it's imprortant
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are 330550are perfect square yes or not
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(i) 6 (ii) 14
(iii) 16 (iv) 18
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2 real life applications of squares and square roots
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Munstor & 5 others asked a question
find the least sqare number which is exactly divisible by 6,9,15,and20
8,108,24,36,72,?,216
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i want some sample papers for guru sishya examination council bursary.
Find the square root of the following decimal numbers (correct to 2 decimal places). a) 262.44 b) 326.88 c) 30.25 d) 400.80 e) 62.41
Priya Dua asked a question
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the smallest numberby which 11045 should be multiplied to get a perfect square
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(i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100
Question) The diagram illustrates a staircase with 14 steps and a total height of 252 cm. What si the height of each of the 14 steps.
there are 2401 students in a school.p.t.teacher wants to stand them in such a manner that number of rows and columns are the same.find the number of rows
Aakriti Bhatia asked a question
\sqrt{9216}
and from this value calculate
\sqrt{92.16}
+ 9.216.
Waleed & 2 others asked a question
find the least square number exactly divisible by 8,12,15.
Q) Find the smallest number by which the following numbers can be multiplied or divided to get perfect squares. : a) 128 b) 6480 c) 2156 d) 3468 e) 1458
Mann Shah & 2 others asked a question
FIND THE SQUARE ROOT OF 100 BY REPEATED SUBTRACTION METHOD
Estimate the square root of each of the following numbers by looking at unit digits and the pair of numbers which form the hundreds and thousands place .a)2916 b)3844 c)9025 d)144
find the square root of 5 correct upto 3 decimal places
How to find the least no. which must be added to 9225 to get a perfect square..
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give 3 uses of "square and square root" in daily life
Dhairaya Joshi asked a question
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Sonal Jain asked a question
(i) 1 + 3 + 5 + 7 + 9
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Dimple Sharma asked a question
Find the square root of 0.025 and 13 (upto two places of decimals)
Find the square root of 256 by repeated subtraction method.
Find ?37.22 correct up two places of decimal Using Long Division Method
Akshat Rawat asked a question
Try These of class 8 chapter 6 page 90
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Brahmvir Gill asked a question
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Square roots of 1 to 100
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find the perfect squares between 100 and 150.
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1) Write the pythagorean triplet whose one member is 16.
2) Find the cube root of 8000
3) Find the smallest square number that is divisible by each of the numbers 8,15,20
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5) Find the square root of
Isaac Jesby asked a question
the number of non square numbers between 10000 and 10201
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Athiya Rahman asked a question
1156 plants are to be planted in such a way that each row contains as many as the number of rows.Find the number of rows and the number of plants in each row.
[i know that we have to find the square root,but while doing it i am having problem]
Karthik D asked a question
IN A PYTHAGOREAN TRIPLET ONE OF ITS MEMBER IS 13 ,FIND THE OTHERS
Is (root x ) a polynomial ? Why?
Khaled Ansari asked a question
find the smallest number by which 2940 must be multiplied so that it becomes a perfect square
Study the statements and choose the correct answer.
Statement 1 : the square root of certain decimals are obtained by first changing the decimals into fractions with perfect square as their numerators and denominators.
Statement 2 ; (26.1)2 liesbetween 400 and 900.
A. Statement 1 is true and 2 is false
B.Statement 1 is false and 2 is true
C. Both statement 1 and 2 is false
D. Both statement 1 and 2 is false
a man purchased some eggs at 3 for rs 5 and sold them at 5 for rs12 thus , he gained rs 143 in all how many eggs did he purchased.
a person wants to plant 2704 medicinal plants with boards depicting the diseases they can cure. He planted these in rows. if each row contains as many plants as the number of rows, then find the number of rows. why should we grow medicinal plants? what values are being promoted?
Koninika Pandit asked a question
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sqrt 0f 12 69/121 (mixed fraction)
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(i) 525 (ii) 1750
Anushka Rai asked a question
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Adithyaa asked a question
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Evalute: √6 115/289
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Gayathri Maniraj asked a question
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(iii) 3250 (iv) 825
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World3 - Wikipedia
System dynamics simulation model
The World3 model is a system dynamics model for computer simulation of interactions between population, industrial growth, food production and limits in the ecosystems of the earth. It was originally produced and used by a Club of Rome study that produced the model and the book The Limits to Growth (1972). The creators of the model were Dennis Meadows, project manager, and a team of 16 researchers.[1]: 8
World3 is one of several global models that have been generated throughout the world (Mesarovic/Pestel Model, Bariloche Model, MOIRA Model, SARU Model, FUGI Model) and is probably the model that generated the spark for all later models[citation needed].
1.1 Agricultural system
1.2 Nonrenewable resources system
1.3 Reference run predictions
2 Criticism of the model
5.1 Model implementations
Agricultural system[edit]
Nonrenewable resources system[edit]
Reference run predictions[edit]
The Dynamics of Growth in a Finite World provides several different scenarios. The "reference run" is the one that "represent the most likely behavior mode of the system if the process of industrialization in the future proceeds in a way very similar to its progress in the past, and if technologies and value changes that have already been institutionalized continue to evolve."[3]: 502 In this scenario, in 2000, the world population reaches six billion, and then goes on to peak at seven billion in 2030. After that population declines because of an increased death rate. In 2015, both industrial output per capita and food per capita peak at US$375 per person (1970s dollars, about $2,430 today) and 500 vegetable-equivalent kilograms/person. Persistent pollution peaks in the year 2035 at 11 times 1970s levels.[3]: 500
World Model Standard Run as shown in The Limits to Growth
Criticism of the model[edit]
There has been criticism of the World3 model. Some has come from the model creators themselves, some has come from economists and some has come from other places.
In the book Groping in the Dark: The First Decade of Global Modelling,[4]: 129 Donella Meadows (a Limits author) writes:
A detailed criticism of the model is in the book Models of Doom: A Critique of the Limits to Growth.[5]: 905–908
Czech-Canadian scientist and policy analyst Vaclav Smil disagreed with the combination of physically different processes into simplified equations:
But those of us who knew the DYNAMO language in which the simulation was written and those who took the model apart line-by-line quickly realized that we had to deal with an exercise in misinformation and obfustication rather than with a model delivering valuable insights. I was particularly astonished by the variables labelled Nonrenewable Resources and Pollution. Lumping together (to cite just a few scores of possible examples) highly substitutable but relatively limited resources of liquid oil with unsubstitutable but immense deposits of sedimentary phosphate rocks, or short-lived atmospheric gases with long-lived radioactive wastes, struck me as extraordinarily meaningless.[6]: 168
Only the widespread scientific illiteracy and innumeracy—all you need to know in this case is how to execute the equation
{\displaystyle y=x*e^{rt}}
—prevents most of the people from dismissing the idea of sustainable growth at healthy rates as an oxymoronic stupidity whose pursuit is, unfortunately, infinitely more tragic than comic. After all, even cancerous cells stop growing once they have destroyed the invaded tissues.[6]: 338–339
Others have put forth criticisms, such as Henshaw, King, and Zarnikau who in a 2011 paper, Systems Energy Assessment[7] point out that the methodology of such models may be valid empirically as a world model, but might not then also be useful for decision making. The impact data being used is generally collected according to where the impacts are recorded as occurring, following standard I/O material processes accounting methods. It is not reorganized according to who pays for or profits from the impacts, so who is actually responsible for economic impacts is never determined. In their view
The authors of the book Surviving 1,000 Centuries consider some of the predictions too pessimistic, but some of the overall message correct.[8]: 4–5
At least one study disagrees with the criticism. Writing in the journal Global Environmental Change, Turner notes that "30 years of historical data compare favorably with key features of the 'business-as-usual' scenario called the 'standard run' produced by the World3 model".[9]
A number of researchers have attempted to test the predictions of the World3 model against observed data, with varying conclusions. One of the more recent of these, published in Yale's Journal of Industrial Ecology,[10] found that current empirical data is broadly consistent with the 1972 projections, and that if major changes to the consumption of resources are not undertaken, economic growth will peak and then rapidly decline by around 2040.[11][12]
^ Meadows, Donella H; Meadows, Dennis L; Randers, Jørgen; Behrens III, William W (1972). The Limits to Growth; A Report for the Club of Rome's Project on the Predicament of Mankind. New York: Universe Books. ISBN 0876631650. Retrieved 26 November 2017.
^ Meadows, Donella; Randers, Jorgen; Meadows, Dennis. "A Synopsis: Limits to Growth: The 30-Year Update". Donella Meadows Project. Retrieved 28 November 2017.
^ a b Meadows, Dennis L.; et al. (1974). Dynamics of Growth in a Finite World. Cambridge: MIT Press. ISBN 0262131420. Retrieved 28 November 2017.
^ Meadows, Donella H. (1982). Groping in the dark: the first decade of global modelling. New York: Wiley. ISBN 0471100277. Retrieved 28 November 2017.
^ Cole, H. S. D.; Freeman, Christopher (1973). Models of Doom: A Critique of the Limits to Growth. Vhps Rizzoli. ISBN 0876639058.
^ a b Smil, Vaclav (2005). Energy at the Crossroads; Global Perspectives and Uncertainties. Cambridge: MIT Press. ISBN 9780262693240. Retrieved 28 November 2017.
^ Henshaw, King, Zarnikau, 2011 Systems Energy Assessment. Sustainability, 3(10), 1908-1943; doi:10.3390/su3101908
^ Bonnet, Roger-Maurice; Woltjer, Lodewijk (2008). Surviving 1,000 Centuries; Can we do it?. Berlin: Springer. ISBN 9780387746333. Retrieved 28 November 2017.
^ Turner, G. (2008). "A comparison of the Limits to Growth with 30 years of reality". Global Environmental Change. 18 (3): 397–411. doi:10.1016/j.gloenvcha.2008.05.001.
^ Herrington, Gaya (2020). "Update to limits to growth: Comparing the World3 model with empirical data". Journal of Industrial Ecology. Wiley. 25 (3): 614–626. doi:10.1111/jiec.13084. S2CID 226019712.
^ Ahmed, Nafeez (14 July 2021). "MIT Predicted in 1972 That Society Will Collapse This Century. New Research Shows We're on Schedule". Vice.com. Study also available here
^ Rosane, Olivia (26 July 2021). "1972 Warning of Civilizational Collapse Was on Point, New Study Finds". Ecowatch. Retrieved 29 August 2021.
"Basic Literature" : selected bibliography on limits to growth with short summary on each publication - published by All-Party Parliamentary Group (APPG)
Model implementations[edit]
pyworld3 on GitHub - Python version of World3
Retrieved from "https://en.wikipedia.org/w/index.php?title=World3&oldid=1062334184"
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\left(2,n\right)
2-recognizability by prime graph of
\text{PSL}\left(2,{p}^{2}\right)
A characterization of alternating groups by the set of orders of maximal Abelian subgroups.
Chen, Guiyun (2006)
{C}_{2}\left(q\right)
q>5
Ali Iranmanesh, Behrooz Khosravi (2002)
The order of every finite group
G
can be expressed as a product of coprime positive integers
{m}_{1},\cdots ,{m}_{t}
\pi \left({m}_{i}\right)
is a connected component of the prime graph of
G
{m}_{1},\cdots ,{m}_{t}
are called the order components of
G
. Some non-abelian simple groups are known to be uniquely determined by their order components. As the main result of this paper, we show that the projective symplectic groups
{C}_{2}\left(q\right)
q>5
are also uniquely determined by their order components. As corollaries of this result, the validities of a...
A class of Cayley graphs induced by right solvable ward groupoids
Anil V. Kumar (2013)
A classification of tetravalent one-regular graphs of order 3p²
Mohsen Ghasemi (2012)
A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, tetravalent one-regular graphs of order 3p², where p is a prime, are classified.
A combinatorial property and power graphs of semigroups
Andrei V. Kelarev, Stephen J. Quinn (2004)
Research on combinatorial properties of sequences in groups and semigroups originates from Bernhard Neumann's theorem answering a question of Paul Erd"{o}s. For results on related combinatorial properties of sequences in semigroups we refer to the book [3]. In 2000 the authors introduced a new combinatorial property and described all groups satisfying it. The present paper extends this result to all semigroups.
A Geometric Construction of Janko's Group J... .
Richard Weiss (1982)
A graph associated to proper non-small ideals of a commutative ring
S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel (2017)
In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring
R
G\left(R\right)
, is a graph with all non-small proper ideals of
R
as vertices and two distinct vertices
I
J
I\cap J
is not small in
R
. In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter,...
A note on another construction of graphs with
4n+6
vertices and cyclic automorphism group of order
4n
Peteris Daugulis (2017)
The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having
4n+6
vertices and automorphism group cyclic of order
4n
n\ge 1
. As a special case we get graphs with
{2}^{k}+6
vertices and cyclic automorphism groups of order
{2}^{k}
. It can revive interest in related problems.
A note on commuting graphs for symmetric groups.
Bates, C., Bundy, D., Hart, S., Rowley, P. (2009)
A note on constructing large Cayley graphs of given degree and diameter by voltage assignments.
Branković, Ljiljana, Miller, Mirka, Plesník, Ján, Ryan, Joe, Širáň, Jozef (1998)
A note on cycle double covers in Cayley graphs.
Hoffman, F., Locke, S.C., Meyerowitz, A.D. (1991)
Jana Tomanová (1989)
A note on solvable vertex stabilizers of
s
-transitive graphs of prime valency
Song-Tao Guo, Hailong Hou, Yong Xu (2015)
X
, with a group
G
of automorphisms of
X
, is said to be
\left(G,s\right)
-transitive, for some
s\ge 1
G
is transitive on
s
-arcs but not on
\left(s+1\right)
-arcs. Let
X
be a connected
\left(G,s\right)
-transitive graph of prime valency
p\ge 5
{G}_{v}
the vertex stabilizer of a vertex
v\in V\left(X\right)
{G}_{v}
is solvable. Weiss (1974) proved that
|{G}_{v}{|\mid p\left(p-1\right)}^{2}
. In this paper, we prove that
{G}_{v}\cong \left({ℤ}_{p}⋊{ℤ}_{m}\right)×{ℤ}_{n}
m
n
ndivm
m\mid p-1
|
Home : Support : Online Help : Education : Student Packages : Statistics : Hypothesis Tests : TwoSampleTTest
TwoSampleTTest(X1, X2, beta, confidence_option, output_option)
The TwoSampleTTest function computes the two sample t-test upon datasets X1 and X2. This tests whether the population mean of X1 minus the population mean of X2 is equal to beta, under the assumption that both populations are normally distributed. No assumptions are made on the standard deviation.
\mathrm{with}\left(\mathrm{Student}[\mathrm{Statistics}]\right):
X≔[9,10,8,4,8,3,0,10,15,9]:
Y≔[6,3,10,11,9,8,13,4,4,4]:
\mathrm{Mean}\left(X\right)-\mathrm{Mean}\left(Y\right)
\frac{\textcolor[rgb]{0,0,1}{2}}{\textcolor[rgb]{0,0,1}{5}}
Calculate the two sample t-test on a list of values.
\mathrm{TwoSampleTTest}\left(X,Y,0,\mathrm{confidence}=0.95\right)
[\textcolor[rgb]{0,0,1}{\mathrm{hypothesis}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{\mathrm{true}}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{confidenceinterval}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{-3.26224630470081}\textcolor[rgb]{0,0,1}{..}\textcolor[rgb]{0,0,1}{4.06224630470081}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{distribution}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{\mathrm{StudentT}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{17.3463603321218}\right)\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{pvalue}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{0.820713744505649}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{statistic}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{0.230089496654211}]
\mathrm{TwoSampleTTest}\left(X,Y,0,\mathrm{confidence}=0.95,\mathrm{output}=\mathrm{plot}\right)
\mathrm{report},\mathrm{graph}≔\mathrm{TwoSampleTTest}\left(X,Y,0,\mathrm{confidence}=0.95,\mathrm{output}=\mathrm{both}\right):
\mathrm{report}
[\textcolor[rgb]{0,0,1}{\mathrm{hypothesis}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{\mathrm{true}}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{confidenceinterval}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{-3.26224630470081}\textcolor[rgb]{0,0,1}{..}\textcolor[rgb]{0,0,1}{4.06224630470081}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{distribution}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{\mathrm{StudentT}}\textcolor[rgb]{0,0,1}{}\left(\textcolor[rgb]{0,0,1}{17.3463603321218}\right)\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{pvalue}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{0.820713744505649}\textcolor[rgb]{0,0,1}{,}\textcolor[rgb]{0,0,1}{\mathrm{statistic}}\textcolor[rgb]{0,0,1}{=}\textcolor[rgb]{0,0,1}{0.230089496654211}]
\mathrm{graph}
The Student[Statistics][TwoSampleTTest] command was introduced in Maple 18.
Student/Statistics/TwoSampleTTest/overview
|
Markdown Reference | Revolt
Revolt uses a simple, plain-text based, and super easy text formatting system called Markdown.
Use it to make your text stand out!
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bold **bold** or __bold__
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bold italics ***bold italics*** or ___bold italics___
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Single-line Code Block
This is a single-line code block! `This is a single-line code block!`
This is how it looks on Revolt:
Multi-line Code Block
This is a multi-line code block!
let x = "This is a multi-line code block, with the language set to JS"
The language display, shown above as a purple button, also acts as a copy button - if you click on it, the entire contents of the code block get pasted into your clipboard! This is especially useful for code blocks that contain a lot of text.
Block Quotes
You can use Block Quotes to signify a quote. The block quote can be multiple levels deep.
trash can sus
> > If you change the way you look at things, the things you look at change.
> — Wayne Dyer
Three Block Quotes on a single line will not quote the whole message - it will make the first line a triple-quote.
You need to put an empty line after every Block Quote to signify the end of the Block Quote.
You can hide spoilers using spoiler tags.
Simply wrap your spoiler in two exclamation marks before and after, and the text will only be revealed after an additional click.
The impostor is !!jan!!
You can embed links in regular text.
Revolt [Revolt](https://revolt.chat)
You can add headings to your messages. The lower the heading number, the larger the text. The smallest heading is 6.
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You can use KaTeX to render math and some other advanced markup in your messages.
x^2
\sin(x)
$\sin(x)$
\frac{x}{y}
$\frac{x}{y}$
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$\sqrt{x^2}$
\sum_{i=1}^n a_i
$\sum_{i=1}^n a_i$
\lim_{x \to \infty}
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\color{red}\textsf{Red Text}
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See KaTeX's documentation for more information.
You can display timestamps in your messages. The format requires you to get the time as a Unix timestamp. You can do this with online services like unixtimestamp.com.
01:37 <t:1663846662:t>
01:37:42 <t:1663846662:T>
22 September 2022 <t:1663846662:D>
22 September 2022 01:37 <t:1663846662:f>
Thursday, 22 September 2022 01:37 <t:1663846662:F>
in 9 months (f.e.) <t:1663846662:R>
Emoji
You can use emoji in your messages. This allows you to express yourself in a more human way.
:smiling_face_with_three_hearts:
You can see the full list of emoji shortcodes using auto-completion - simply start typing with a :.
Single-line Code Block
|
Pierre Fatou - Wikipedia
Fatou–Bieberbach domain
Pierre Joseph Louis Fatou (28 February 1878 – 9 August 1929[1]) was a French mathematician and astronomer. He is known for major contributions to several branches of analysis. The Fatou lemma and the Fatou set are named after him.
2 Mathematical work of Fatou
Pierre Fatou's parents were Prosper Ernest Fatou (1832-1891) and Louise Eulalie Courbet (1844-1911), both of whom were in the military.[1] Pierre's family would have liked for him to enter the military as well, but his health was not sufficiently good for him to pursue a military career.[1]
Fatou entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an intern (stagiaire) in the Paris Observatory. Fatou was promoted to assistant astronomer in 1904 and to astronomer (astronome titulaire) in 1928. He worked in this observatory until his death.
Fatou was awarded the Becquerel prize in 1918; he was a knight of the Legion of Honour (1923).[2] He was the president of the French mathematical society in 1927.[3]
He was in friendly relations with several contemporary French mathematicians, especially, Maurice René Fréchet and Paul Montel.[4]
In the summer of 1929 Fatou went on holiday to Pornichet, a seaside town to the west of Nantes. He was staying in Le Brise-Lames Villa near the port and it was there at 8 p.m. on Friday 9 August that he died in his room.[1] No cause of death was given on the death certificate but Audin argues that he died as a result of a stomach ulcer that burst. Fatou's nephew Robert Fatou wrote:
Having never thought it useful during his life to consult a doctor, my dear uncle died suddenly in a hotel room in Pornichet.
— Pierre Joseph Louis Fatou, [1]
Fatou's funeral was held on 14 August in the church of Saint-Louis, and he was buried in the Carnel Cemetery in Lorient.[1]
Mathematical work of Fatou[edit]
Fatou's work had very large influence on the development of analysis in the 20th century.
Fatou's PhD thesis Séries trigonométriques et séries de Taylor (Fatou 1906) was the first application of the Lebesgue integral to concrete problems of analysis, mainly to the study of analytic and harmonic functions in the unit disc. In this work, Fatou studied for the first time the Poisson integral of an arbitrary measure on the unit circle. This work of Fatou is influenced by Henri Lebesgue who invented his integral in 1901.
The Fatou theorem, which says that a bounded analytic function in the unit disc has radial limits almost everywhere on the unit circle was published in 1906 (Fatou 1906). This theorem was at the origin of a large body of research in 20th-century mathematics under the name of bounded analytic functions.[5] See also the Wikipedia article on functions of bounded type.
A number of fundamental results on the analytic continuation of a Taylor series belong to Fatou.[6]
Julia set of
{\displaystyle {\tfrac {1}{2}}(z+z^{2})}
investigated by Fatou in 1906. This picture is made with a modern computer.
Julia set of z+1+e−z investigated by Fatou in 1926.
Julia set of a sine function studied by Fatou in 1926
In 1917–1920 Fatou created the area of mathematics which is called holomorphic dynamics (Fatou 1919, 1920, 1920b). It deals with a global study of iteration of analytic functions. He was the first to introduce and study the set which is called now the Julia set.[citation needed] (The complement of this set is sometimes called the Fatou set). Some of the basic results of holomorphic dynamics were also independently obtained by Gaston Julia and Samuel Lattes in 1918.[7] Holomorphic dynamics has experienced a strong revival since 1982 because of the new discoveries of Dennis Sullivan, Adrian Douady, John Hubbard and others. In 1926, Fatou pioneered the study of dynamics of transcendental entire functions (Fatou 1926), a subject which is intensively developing at this time.
As a byproduct of his studies in holomorphic dynamics, Fatou discovered what are now called Fatou–Bieberbach domains (Fatou 1922). These are proper subregions of the complex space of dimension n, which are biholomorphically equivalent to the whole space. (Such regions cannot exist for n=1.)
Fatou did important work in celestial mechanics. He was the first to prove rigorously[8] a theorem (conjectured by Gauss) on the averaging of a perturbation produced by a periodic force of short period (Fatou 1928). This work was continued by Leonid Mandelstam and Nikolay Bogolyubov and his students and developed into a large area of modern applied mathematics. Fatou's other research in celestial mechanics includes a study of the movement of a planet in a resisting medium.[citation needed]
Fatou, P. (1906). "Séries trigonométriques et séries de Taylor". Acta Mathematica. 30: 335–400. doi:10.1007/BF02418579. JFM 37.0283.01.
Fatou, P. (1919). "Sur les équations fonctionnelles, I". Bulletin de la Société Mathématique de France. 47: 161–271. doi:10.24033/bsmf.998. JFM 47.0921.02. ; Fatou, P. (1920). "Sur les équations fonctionnelles, II". Bulletin de la Société Mathématique de France. 48: 33–94. doi:10.24033/bsmf.1003. JFM 47.0921.02. ; Fatou, P. (1920b). "Sur les équations fonctionnelles, III". Bulletin de la Société Mathématique de France. 48: 208–314. doi:10.24033/bsmf.1008. JFM 47.0921.02.
Fatou, P. (1922). "Sur les fonctions méromorphes de deux variables". Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. 175: 862–865. JFM 48.0391.03.
Fatou, P. (1923). "Sur les fonctions holomorphes et bornées à l'intérieur d'un cercle". Bulletin de la Société Mathématique de France. 51: 191–202. doi:10.24033/bsmf.1033.
Fatou, P. (1926). "Sur l'itération des fonctions transcendantes entières". Acta Mathematica. 47 (4): 337–370. doi:10.1007/BF02559517.
Fatou, P. (1928). "Sur le mouvement d'un système soumis à des forces à courte période". Bulletin de la Société Mathématique de France. 56: 98–139. doi:10.24033/bsmf.1131. JFM 54.0834.01.
Fatou conjecture
Fatou–Lebesgue theorem (same as Fatou's lemma)
^ a b c d e f "Fatou biography". www-history.mcs.st-andrews.ac.uk. Retrieved 8 November 2017.
^ Audin 2009, p. 138.
^ "Anciens Présidents" (in French). French mathematical society. Archived from the original on 29 November 2014. Retrieved 24 January 2012.
^ Garnett, John B. (1981). Bounded analytic functions. Academic Press.
^ Bieberbach, Ludwig (1955). Analytische Fortsetzung. Berlin: Springer Verlag.
^ Julia, Gaston (1918). "Mémoire sur l'itération des fonctions rationnelles" (PDF). Journal de Mathématiques Pures et Appliquées (in French). 1: 47–245.
^ Mitropolsky, Iu. A. (1967). "Averaging method in non-linear mechanics". Intl. J. Non-Lin. Mech. 2 (1): 69–95. Bibcode:1967IJNLM...2...69M. doi:10.1016/0020-7462(67)90020-0.
Audin, Michèle (2009). Fatou, Julia, Montel, le Grand prix des sciences mathématiques de 1918, et après... Heidelberg: Springer. doi:10.1007/978-3-642-00446-9. ISBN 978-3-642-00445-2.
"Notice sur les travaux scientifique de Pierre Fatou (pdf)" (PDF). Paris. 1929.
Chazy, Jean (1933). "Pierre Fatou". Bulletin Astronomique. 8: 389–384.
Daniel Alexander, Felice Iavernaro, Alessandro Rosa: Early days in complex dynamics: a history of complex dynamics in one variable during 1906-1942, History of Mathematics 38, American Mathematical Society 2012
O'Connor, John J.; Robertson, Edmund F., "Pierre Fatou", MacTutor History of Mathematics archive, University of St Andrews
Pierre Fatou, mathématicien et astronome by Michèle Audin, on the site Images des Mathématiques.
List of publications of Pierre Fatou on zbMATH.
"Pierre Fatou". Dictionary of Scientific Biography. New York: Charles Scribner's Sons. 1970–1980. ISBN 978-0-684-10114-9.
Pierre Fatou at the Mathematics Genealogy Project
Retrieved from "https://en.wikipedia.org/w/index.php?title=Pierre_Fatou&oldid=1079955255"
|
p
\mathrm{GL}\left(2\right)
L
L
p
A basis for the space of modular forms
Shinji Fukuhara (2012)
Andrea Mori, Lea Terracini (1999)
D
un corpo di quaternioni indefinito su
\mathbf{Q}
di discriminante
\mathrm{\Delta }
\mathrm{\Gamma }
il gruppo moltiplicativo degli elementi di norma 1 in un ordine di Eichler di
D
di livello primo con
\mathrm{\Delta }
. Consideriamo lo spazio
{S}_{k}\left(\mathrm{\Gamma }\right)
delle forme cuspidali di peso
k
\mathrm{\Gamma }
e la corrispondente algebra di Hecke
{\mathbf{H}}^{D}
. Utilizzando una versione della corrispondenza di Jacquet-Langlands tra rappresentazioni automorfe di
{D}^{×}
G{L}_{2}
, realizziamo
{\mathbf{H}}^{D}
come quoziente dell'algebra di Hecke classica di livello
N\mathrm{\Delta }
. Questo risultato permette di...
Adriaan Herremans (2003)
We state a conjecture concerning modular absolutely irreducible odd 2-dimensional representations of the absolute Galois group over finite fields which is purely combinatorial (without using modular forms) and proof that it is equivalent to Serre’s strong conjecture. The main idea is to replace modular forms with coefficients in a finite field of characteristic
p
, by their counterparts in the theory of modular symbols.
A condition for the rationality of certain elliptic modular forms over primes dividing the level
f
be a weight
k
holomorphic automorphic form with respect to
{\mathrm{\Gamma }}_{0}\left(N\right)
. We prove a sufficient condition for the integrality of
over primes dividing
N
. This condition is expressed in terms of the values at particular
CM
curves of the forms obtained by iterated application of the weight
k
Maaß operator to
f
and extends previous results of the Author.
A decomposition of the space of higher order modular cusp forms
Karen Taylor (2012)
A larger GL 2 large sieve in the level aspect
Goran Djanković (2012)
In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.
A local large sieve inequality for cusp forms
Jonathan Wing Chung Lam (2014)
We prove a large sieve type inequality for Maass forms and holomorphic cusp forms with level greater or equal to one and of integral or half-integral weight in short interval.
A negative result on the representation of modular forms by theta series.
Walter R. Parry (1979)
A new multiple Dirichlet series induced by a higher-order form
Anton Deitmar, Nikolaos Diamantis (2010)
A relation between Fourier coefficients of holomorphic cusp forms and exponential sums
Anne-Maria Ernvall-Hytönen (2009)
Andrew Knightly, Charles Li (2006)
Action of Hecke Operator T(p) on Theta Series.
Anatolii N. Andrianov (1980)
All Congruent Numbers Less than 2000.
Gerhard Kramarz (1985/1986)
An analog of crank for a certain kind of partition function arising from the cubic continued fraction
An analytic function and iterated integrals
Bruno Harris (1988)
An application of the projections of
{C}^{\infty }
automorphic forms
Takumi Noda (1995)
An infinite ferm in the universal deformation space of Galois representations.
B. Mazur (1997)
I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks to some...
|
A new modeling and solution approach for the number partitioning problem.
Alidaee, Bahram, Glover, Fred, Kochenberger, Gary A., Rego, Cesar (2005)
Jérôme Monnot (2008)
In this note, we strengthen the inapproximation bound of O(logn) for the labeled perfect matching problem established in J. Monnot, The Labeled perfect matching in bipartite graphs, Information Processing Letters96 (2005) 81–88, using a self improving operation in some hard instances. It is interesting to note that this self improving operation does not work for all instances. Moreover, based on this approach we deduce that the problem does not admit constant approximation algorithms for connected...
A space lower bound for acceptance by one-way
{\Pi }_{2}
-alternating machines
Viliam Geffert, Norbert Popély (2000)
We show that one-way Π2-alternating Turing machines cannot accept unary nonregular languages in o(log n) space. This holds for an accept mode of space complexity measure, defined as the worst cost of any accepting computation. This lower bound should be compared with the corresponding bound for one-way Σ2-alternating machines, that are able to accept unary nonregular languages in space O(log log n). Thus, Σ2-alternation is more powerful than Π2-alternation for space bounded one-way machines with...
Nicolas Boria, Vangelis T. Paschos (2011)
This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The...
An Oriented Version of the 1-2-3 Conjecture
Olivier Baudon, Julien Bensmail, Éric Sopena (2015)
The well-known 1-2-3 Conjecture addressed by Karoński, Luczak and Thomason asks whether the edges of every undirected graph G with no isolated edge can be assigned weights from {1, 2, 3} so that the sum of incident weights at each vertex yields a proper vertex-colouring of G. In this work, we consider a similar problem for oriented graphs. We show that the arcs of every oriented graph −G⃗ can be assigned weights from {1, 2, 3} so that every two adjacent vertices of −G⃗ receive distinct sums of outgoing...
Automated proofs of upper bounds on the running time of splitting algorithms.
Kulikov, A.S., Fedin, S.S. (2004)
Marc Demange, Vangelis Paschos (2010)
This paper is the continuation of the paper “Autour de nouvelles notions pour l'analyse des algorithmes d'approximation: Formalisme unifié et classes d'approximation” where a new formalism for polynomial approximation and its basic tools allowing an “absolute” (individual) evaluation the approximability properties of NP-hard problems have been presented and discussed. In order to be used for exhibiting a structure for the class NPO (the optimization problems of NP), these tools must be enriched...
Autour de nouvelles notions pour l'analyse des algorithmes d'approximation : formalisme unifié et classes d'approximation
Cet article est le premier d'une série de deux articles où nous présentons les principales caractéristiques d'un nouveau formalisme pour l'approximation polynomiale (algorithmique polynomiale à garanties de performances pour les problèmes NP-difficiles). Ce travail est l'occasion d'un regard critique sur ce domaine et de discussions sur la pertinence des notions usuelles. Il est aussi l'occasion de se familiariser avec l'approximation polynomiale, de comprendre ses enjeux et ses méthodes. Ces deux...
Autour de nouvelles notions pour l’analyse des algorithmes d’approximation : formalisme unifié et classes d’approximation
The main objective of the polynomial approximation is the development of polynomial time algorithms for NP-hard problems, these algorithms guaranteeing feasible solutions lying “as near as possible” to the optimal ones. This work is the fist part of a couple of papers where we introduce the key-concepts of the polynomial approximation and present the main lines of a new formalism. Our purposes are, on the one hand, to present this theory and its objectives and, on the other hand, to discuss the...
Autour de nouvelles notions pour l’analyse des algorithmes d’approximation : de la structure de NPO à la structure des instances
Cet article est la suite de l’article «Autour de nouvelles notions pour l’analyse des algorithmes d’approximation : formalisme unifié et classes d’approximation» où nous avons présenté et discuté, dans le cadre d’un nouveau formalisme pour l’approximation polynomiale (algorithmique polynomiale à garanties de performances pour des problèmes NP-difficiles), des outils permettant d’évaluer, dans l’absolu, les proporiétés d’approximation de problèmes difficiles. Afin de répondre pleinement à l’objectif...
Balanced problems on graphs with categorization of edges
Štefan Berežný, Vladimír Lacko (2003)
Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function:
L₅\left(D\right)=ma{x}_{1\le i\le p}\left(ma{x}_{e\in {S}_{i}\cap D}w\left(e\right)-mi{n}_{e\in {S}_{i}\cap D}w\left(e\right)\right)
For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary...
Tınaz Ekim, Aysel Erey (2014)
In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (g-extension problem) can be efficiently solved. Our method allows us to derive linear time algorithms for the minimum geodetic set problem in (a proper superclass of) block-cacti and monopolar chordal graphs....
Comparing numerical integration schemes for a car-following model with real-world data
Přikryl, Jan, Vaniš, Miroslav (2017)
A key element of microscopic traffic flow simulation is the so-called car-following model, describing the way in which a typical driver interacts with other vehicles on the road. This model is typically continuous and traffic micro-simulator updates its vehicle positions by a numerical integration scheme. While increasing the order of the scheme should lead to more accurate results, most micro-simulators employ the simplest Euler rule. In our contribution, inspired by [1], we will provide some additional...
Martin Grohe, Nicole Schweikardt (2004)
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog.
Succinctness...
Xiaoguang Yang (2001)
For a given partial solution, the partial inverse problem is to modify the coefficients such that there is a full solution containing the partial solution, while the full solution becomes optimal under new coefficients, and the total modification is minimum. In this paper, we show that the partial inverse assignment problem and the partial inverse minimum cut problem are NP-hard if there are bound constraints on the changes of coefficients.
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As Shannon peels her orange for lunch, she realizes that it is very close to being a sphere. If her orange has a diameter of
8
centimeters, what is its approximate surface area (the area of the orange peel)? What is the approximate volume of the orange? Show all work.
\text{ SA}=4\pi(r)^{2}
\text{ V}=\frac{4}{3}\pi(r)^{3}
\text{ SA}=4\pi(4)^{2}=64\pi\approx201\;\text{cm}^{2}
\text{V}=\frac{4}{3}\pi(4)^3=\frac{256}{3}\pi\approx268\text{ cm}^2
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Binomial Theorem, Popular Questions: CBSE Class 11-science ENGLISH, English Grammar - Meritnation
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please prove binomial theorem
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prove that nCr +nCr-1 = n+1Cr
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(Summation) of r.r!
r=1 to n
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iam not able to view the ncert solutions of alll subjects
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Mining - Old School Bot
You can train Mining using +mine [quantity] <ore>, for example +mine 10 coal.
See Mining Training and Volcanic Mine
The bot uses XP rates based off rune pickaxe as standard; however, you can get one of the following boosts to mining output from owning these items:
50% (on gem rocks only)
Golden nugget cost
Golden Nuggets & Unidentified Minerals
Some ores reward you with golden nuggets or unidentified minerals. You can use nuggets to buy the prospector outfit and minerals to buy the three mining gloves, this is done via the +buy command.
The amount of golden nuggets or unidentified minerals rewarded is based in the total trip time. The amount received is a randomly selected number between 0 and the total trip time divided by 4, floored/rounded down.
⌊\frac{tripTime}{4}⌋=maxAmount
For example, a trip of 30 minutes will award between 0 and 7 golden nuggets or unidentified minerals.
XP/Hr @ 99
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Abstract Algebra/Composition series - Wikibooks, open books for an open world
Abstract Algebra/Composition series
{\displaystyle G}
be a group. A normal series of
{\displaystyle G}
are finitely many subgroups
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle G}
{\displaystyle \{e\}=N_{n}\triangleleft N_{n-1}\triangleleft \cdots \triangleleft N_{1}=G}
Two normal series
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle M_{1},\ldots ,M_{k}}
{\displaystyle G}
{\displaystyle n=k}
and there exists a bijective function
{\displaystyle \sigma :\{1,\ldots ,n\}\to \{1,\ldots ,n\}}
{\displaystyle j\in \{1,\ldots ,n-1\}}
{\displaystyle N_{j}/N_{j+1}\cong M_{\sigma (j)}/M_{\sigma (j)+1}}
A normal series
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle G}
is a composition series of
{\displaystyle G}
if and only if for each
{\displaystyle j\in \{1,\ldots ,n-1\}}
{\displaystyle N_{j}/N_{j+1}}
{\displaystyle G}
be a finite group. Then there exists a composition series of
{\displaystyle G}
We prove the theorem by induction over
{\displaystyle |G|}
{\displaystyle |G|=1}
{\displaystyle G}
is the trivial group, and
{\displaystyle M_{1}}
{\displaystyle M_{1}=G}
{\displaystyle G}
2. Assume the theorem is true for all
{\displaystyle n\in \mathbb {N} }
{\displaystyle n<|G|}
Since the trivial subgroup
{\displaystyle \{e\}\subset G}
{\displaystyle G}
, the set of proper normal subgroups of
{\displaystyle G}
is not empty. Therefore, we may choose a proper normal subgroup
{\displaystyle N}
of maximum cardinality. This must also be a maximal proper normal subgroup, since any group in which it is contained must have at least equal cardinality, and thus, if
{\displaystyle M}
is normal such that
{\displaystyle N\subsetneq M\subsetneq G}
{\displaystyle |M|>|N|}
, which is why
{\displaystyle N}
is not a proper normal subgroup of maximal cardinality.
{\displaystyle G/N}
is simple. Further, since
{\displaystyle |N|<|G|}
, the induction hypothesis implies that there exists a composition series of
{\displaystyle N}
{\displaystyle N_{2},\ldots ,N_{n}}
{\displaystyle \{e\}=N_{n}\triangleleft N_{n-1}\triangleleft \cdots \triangleleft N_{2}=N}
{\displaystyle \{e\}=N_{n}\triangleleft \cdots \triangleleft N_{2}=N\triangleleft N_{1}:=G}
, and further for each
{\displaystyle m\in \{1,\ldots ,n-1\}}
{\displaystyle N_{m}/N_{m+1}}
{\displaystyle N_{1},\ldots ,N_{n}}
is a composition sequence of
{\displaystyle G}
{\displaystyle \Box }
Our next goal is to prove that given two normal sequences of a group, we can find two 'refinements' of these normal sequences which are equivalent. Let us first define what we mean by a refinement of a normal sequence.
{\displaystyle G}
{\displaystyle N_{1},\ldots ,N_{n}}
be a normal sequence of
{\displaystyle G}
. A refinement of
{\displaystyle N_{1},\ldots ,N_{n}}
is a normal sequence
{\displaystyle N_{1}',\ldots ,N_{k}'}
{\displaystyle \{N_{1},\ldots ,N_{n}\}\subseteq \{N_{1}',\ldots ,N_{k}'\}}
Theorem 2.7.4 (Schreier):
{\displaystyle G}
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle M_{1},\ldots ,M_{k}}
be two normal series of
{\displaystyle G}
. Then there exist refinements
{\displaystyle N_{1}',\ldots ,N_{m}'}
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle M_{1}',\ldots ,M_{l}'}
{\displaystyle M_{1},\ldots ,M_{k}}
{\displaystyle N_{1}',\ldots ,N_{m}'}
{\displaystyle M_{1}',\ldots ,M_{l}'}
Theorem 2.7.5 (Jordan-Hölder):
{\displaystyle G}
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle M_{1},\ldots ,M_{k}}
be two composition series of
{\displaystyle G}
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle M_{1},\ldots ,M_{k}}
Due to theorem 2.6.?, all the elements of
{\displaystyle \{N_{1},\ldots ,N_{n}\}}
must be pairwise different, and the same holds for the elements of
{\displaystyle \{M_{1},\ldots ,M_{k}\}}
Due to theorem 2.7.4, there exist refinements
{\displaystyle N_{1}',\ldots ,N_{m}'}
{\displaystyle N_{1},\ldots ,N_{n}}
{\displaystyle M_{1}',\ldots ,M_{l}'}
{\displaystyle M_{1},\ldots ,M_{k}}
{\displaystyle N_{1}',\ldots ,N_{m}'}
{\displaystyle M_{1}',\ldots ,M_{l}'}
But these refinements satisfy
{\displaystyle \{N_{1}',\ldots ,N_{m}'\}=\{N_{1},\ldots ,N_{n}\}}
{\displaystyle \{M_{1}',\ldots ,M_{l}'\}=\{M_{1},\ldots ,M_{k}\}}
, since if this were not the case, we would obtain a contradiction to theorem 2.6.?.
We now choose a bijection
{\displaystyle \sigma :\{1,\ldots ,m\}\to \{1,\ldots ,m\}}
{\displaystyle j\in \{1,\ldots ,m-1\}}
{\displaystyle N_{j}/N_{j+1}\cong M_{\sigma (j)}/M_{\sigma (j)+1}}
Retrieved from "https://en.wikibooks.org/w/index.php?title=Abstract_Algebra/Composition_series&oldid=3249848"
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Machine Learning for Statistical Arbitrage II: Feature Engineering and Model Development - MATLAB & Simulink - MathWorks 日本
To create a Markov model of the dynamics, collect the smoothed imbalance index sI into bins, discretizing it into a finite collection of states rho (
\mathrm{Ï}
). The number of bins numBins is a hyperparameter.
The setting corresponds to an interval of 20 ticks, or about 0.8 seconds on average. Discretize price movements into three states DS (
\mathrm{Î}\mathit{S}
) given by the sign of the forward price change.
Together, the state of the LOB imbalance index rho (
\mathrm{Ï}
) and the state of the forward price movement DS (
\mathrm{Î}\mathit{S}
) describe a two-dimensional continuous-time Markov chain (CTMC). The chain is modulated by the Poisson process of order arrivals, which signals any transition among the states.
To simplify the description, give the two-dimensional CTMC a one-dimensional encoding into states phi (
\mathrm{Ï}=\left(\mathrm{Ï},\mathrm{Î}\mathit{S}\right)
Successive states of
\mathrm{Ï}
, and the component states
\mathrm{Ï}
\mathrm{Î}\mathit{S},
proceed as follows.
Hyperparameters dI (
\mathrm{Î}{\mathit{t}}_{\mathit{I}}
) and dS (
\mathrm{Î}{\mathit{t}}_{\mathit{S}}
) determine the size of a rolling state characterizing the dynamics. At time
\mathit{t}
, the process transitions from
\mathrm{Ï}=\left({\mathrm{Ï}}_{\mathit{previous}},\mathrm{Î}{\mathit{S}}_{\mathit{current}}\right)=\mathit{i}
\mathrm{Ï}=\left({\mathrm{Ï}}_{\mathit{current}},\mathrm{Î}{\mathit{S}}_{\mathit{future}}\right)=\mathit{j}
(or holds in the same state if
\mathit{i}=\mathit{j}
Execution of the trading strategy at any time
\mathit{t}
is based on the probability of
\mathrm{Î}{\mathit{S}}_{\mathit{future}}
being in a particular state, conditional on the current and previous values of the other states. Following [3] and [4], determine empirical transition probabilities, and then assess them for predictive power.
To obtain a trading matrix Q containing
\mathrm{Prob}\left(\mathrm{Î}{\mathit{S}}_{\mathit{future}}|{\mathrm{Ï}}_{\mathit{previous}},{\mathrm{Ï}}_{\mathit{current}},\mathrm{Î}{\mathit{S}}_{\mathit{current}}\right)
as in [4], apply Bayes’ rule,
\mathrm{Prob}\left(\mathrm{Î}{\mathit{S}}_{\mathit{future}}|{\mathrm{Ï}}_{\mathit{previous}},{\mathrm{Ï}}_{\mathit{current}},\mathrm{Î}{\mathit{S}}_{\mathit{current}}\right)=\frac{\mathrm{Prob}\left({\mathrm{Ï}}_{\mathit{current}},\mathrm{Î}{\mathit{S}}_{\mathit{future}}|{\mathrm{Ï}}_{\mathit{previous}},\mathrm{Î}{\mathit{S}}_{\mathit{current}}\right)}{\mathrm{Prob}\left({\mathrm{Ï}}_{\mathit{current}}|{\mathrm{Ï}}_{\mathit{previous}},\mathrm{Î}{\mathit{S}}_{\mathit{current}}\right)}
Display Q in a table. Label the rows and columns with composite states
\mathrm{Ï}=\left(\mathrm{Ï},\mathrm{Î}\mathit{S}\right)
QTable=9×9 table
Rows are indexed by (
{\mathrm{Ï}}_{\mathit{previous}},\mathrm{Î}{\mathit{S}}_{\mathit{current}}
). Conditional probabilities for each of the three possible states of
\mathrm{Î}{\mathit{S}}_{\mathit{future}}
are read from the corresponding column, conditional on
{\mathrm{Ï}}_{\mathit{current}}
The bright, central 3 x 3 square shows that in most transitions, tick to tick, no price change is expected (
\mathrm{Î}{\mathit{S}}_{\mathit{future}}=0
). Bright areas in the upper-left 3 x 3 square (downward price movements
\mathrm{Î}{\mathit{S}}_{\mathit{future}}=-1
) and lower-right 3 x 3 square (upward price movements
\mathrm{Î}{\mathit{S}}_{\mathit{future}}=+1
) show evidence of momentum, which can be leveraged in a trading strategy.
The entry in the (1,1) position shows a chance of more than 50% that a downward price movement (
\mathrm{Î}{\mathit{S}}_{\mathit{current}}=-1
) will be followed by another downward price movement (
\mathrm{Î}{\mathit{S}}_{\mathit{future}}=-1
), provided that the previous and current imbalance states
\mathrm{Ï}
are both 1.
[1] Cartea, Ãlvaro, Sebastian Jaimungal, and Jason Ricci. "Buy Low, Sell High: A High-Frequency Trading Perspective." SIAM Journal on Financial Mathematics 5, no. 1 (January 2014): 415–44. https://doi.org/10.1137/130911196.
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Temporal resistance variation of the second generation HTS tape during superconducting-to-normal state transition | SpringerPlus | Full Text
Vladimir A Malginov1,
Andrey V Malginov1 &
The quench process in high-temperature superconducting (HTS) wires plays an important role in superconducting power devices, such as fault current limiters, magnets, cables, etc. The superconducting device should survive after the overheating due to quench.
We studied the evolution of the resistance of the YBCO tape wire during the quench process with 1 ms time resolution for various excitation voltages.
The resistive normal zone was found to be located in a domain of about 1-4 cm long. The normal state nucleation begins in 40-60 ms after voltage is applied across the HTS tape. In subsequent 200-300 ms other normal state regions appear. The normal domain heating continues in the following 5-10s that results in a factor of 2–3 increase of its resistance.
Formation of the normal domain during the quench process follows the same stages for different excitation voltages. Characteristic domain sizes, lifetimes and temperatures are determined for all stages.
The quench process in high-temperature superconducting (HTS) wires plays an important role in superconducting fault current limiter operation. It occurs when current in a wire exceeds the critical value and as a result, the wire resistance becomes nonzero. The problem of quench stability is related to the heat transfer and is especially crucial for the Second Generation HTS wires on highly resistive substrates. We present here the results of studies of the normal zone generation.
We studied the process of quench in HTS tapes using the experimental procedure described in (Fleishman et al., 2010). The sample was 12 mm wide and 100 mm long SuperPower YBCO tape SF12100 (Super-power). Both nominal and measured critical currents at 77 K are about 300A. It consists of 100 mu of Hastelloy substrate, 1 mu YBCO (critical temperature Tc = 91 K) and 1.5mu Ag layers. Measurements were performed with the tape immersed in liquid nitrogen. The AC (50 Hz) voltage step with the amplitude V0 was applied to the sample at the time t0. After that, during the subsequent 40s, we registered the current I and sample AC resistance Z with 1 ms time resolution.
Figures 1 and 2 show the resistance Z as a function of time t for V0 = 379 mV. Time dependence of Z observed in all measurements may be divided into three stages. At the first stage the normal zone forms in a “weak” segment due to exceeding of the local critical current, and Z increases up to Z1 at the moment t1. At the second stage from t1 to t2, the normal region grows due to heat generation inside the initial normal zone, and Z increases up to Z2. At the third stage, t > t2, the resistance increases to the equilibrium value Z3 as a result of temperature growth in the newly formed normal domain and decrease of current.
The sample resistance versus time dependence. AC voltage step of V0 = 379 mV was applied at the moment t0
The expanded view of the sample resistance vs. time dependence for the initial period (t < 5 s). AC voltage step V0 = 379 mV was applied at the moment t0.
The sample resistances Z1, Z2, and Z3 as functions of voltage step magnitude V0 are shown in Figure 3. These resistances grow monotonically with V0. Up to V0 = 300 mV heating processes are weak and all the three stages merge. At V0 = 1 V the initial stage resistance Z1 is about 30% of the final value Z3.
Resistances Z 1 , Z 2, and Z 3 as the functions of the voltage V 0 .
The normal domain size can be estimated using the voltage dependence of the domain temperature and temperature dependence of the wire resistance. Maximal temperature TM(K) is expressed the following way (Mal’ginov et al., 2013):
{T}_{M}=0.623*\left({V}_{0}-300\right)+90
Equation (1) is experimentally proven to be valid in the range 0.5 V < V_0 < 0.8 V. In order to estimate the length of the normal zone we do assume that this formula is applicable also outside the specified range. The resistance Z (mOhm) of the zone where the YBCO layer is in the normal state (T(K) > Tc) is given by the following expression:
Z=L/\left(0.96+1.2/\left(0.29+0.0061*\left(T-77\right)\right)\right)
here L (mm) is the length of the zone where T > Tc for t > t1, V0 (mV) is the applied voltage magnitude.
Using (1) and (2) and assuming that Z1 is the domain resistance at liquid nitrogen temperature and Z3 is the resistance at the maximum temperature, one can obtain the domain size (L1) and the size of zone with TM (L3) as function of V0:
{L}_{1}={Z}_{1}/0.2
{L}_{3}={Z}_{3}*\left(0.96+1.2/\left(0.37+0.0038*\left({V}_{0}-300\right)\right)\right)
Figure 4 shows L1 and L3 values versus V0 calculated from (3) and (4).
The normal domain size (L 1 ) and the size of zone with maximum temperature (L 3 ) as a function of the voltage V 0 .
From the above results we conclude that during the superconducting-to-normal state transition in HTS tape the normal phase is limited to a single domain. The domain nucleates in 40-60 ms after the voltage is applied. In the subsequent 5-10s the domain heats up; it results in 2–3 times increase of the resistance. Central part of the domain is about 20-30 mm long. Inside the both of the 3-5 mm long edges of the domain the temperature falls from the maximal temperature TM to 90 K.
Fleishman LS, Mal’ginov VA, Mal’ginov AV: Ways for increasing the rated capacity of a superconducting current-limiting device. Thermal Engineering 2010, 57(14):1216-1221. 10.1134/S0040601510140077
Mal’ginov AV, Yu Kuntsevich A, Mal’ginov VA, Fleishman LS: Normal domain temperature profile in second generation HTS tape wire. SpringerPlus 2013, 2: 535. 10.1186/2193-1801-2-535
Super-power http://www.superpower-inc.com/
Lebedev Physical Institute RAS, Moscow, 119991, Russia
Vladimir A Malginov & Andrey V Malginov
Krzhizhanovsky Power Engineering Institute, Moscow, 119991, Russia
Malginov, V.A., Malginov, A.V. & Fleishman, L.S. Temporal resistance variation of the second generation HTS tape during superconducting-to-normal state transition. SpringerPlus 2, 599 (2013). https://doi.org/10.1186/2193-1801-2-599
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Markup language - Simple English Wikipedia, the free encyclopedia
A markup language is a computer language. It is made up of a set of instructions, and of data. It is not the same as a programming language, as only programming languages can have if statements and other conditional statements.[1] The first markup languages were used for printing; there was the text, and there were instructions how the text should be printed. The source code is generally done in ASCII. Then there are tags. That way, LaTeX (and with that, Wikipedia), uses the instruction \mu to get the symbol
{\displaystyle \mu }
, the Greek letter "Mu". HTML uses µ to get the same symbol.
↑ "Why HTML is Not a Programming Language". Syracuse University. Archived from the original on 8 July 2016. Retrieved 27 June 2016.
Retrieved from "https://simple.wikipedia.org/w/index.php?title=Markup_language&oldid=7590899"
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A new universal equation using planet magnetic pole strength is presented and given reasoning for its assemblage. Coulomb’s Constant, normally used in calculating electrostatic force is utilized in a new magnetic dipole equation for the first time, along with specific orbital energy. Results were generated for five planets that give insight into specific orbital energy as an energy constant for differing planets based on gravitational potential at the surface of a planet. Specific energy can be evaluated as both energy per unit volume (J/kg) and/or specific orbital energy (m2/s2). Due to a multitude of terms that lead to confusion it is recommended that the IEEE standards committee review specific orbital energy SI units for m2/s2. The magic number for cyclonic “lift off”, or anti-gravity, is calculated to be ∈ = 148 m2/s2 the value at which a classical law of magnetism appears as F = ke × H.
Coulomb’s Constant, Magnetic Moment, Magnetic Pole Strength, Specific Orbital Energy, Storm Relative Helicity
Poole, G. (2018) Law of Universal Magnetism, F = ke × H. Journal of High Energy Physics, Gravitation and Cosmology, 4, 471-484. doi: 10.4236/jhepgc.2018.43025.
F=\frac{G{m}_{1}{m}_{2}}{{r}_{2}}
F=\frac{{k}_{e}{H}_{1}{H}_{2}}{{r}^{2}ϵ}
ϵ=\frac{\mu }{2{a}^{2}}
\mu =G{m}_{1}+G{m}_{2}
a
\sqrt{2}
\sqrt{2}
\sqrt{2}
g=3.72\text{\hspace{0.17em}}\text{m}/{\text{s}}^{\text{2}}
{G}_{PE}=g\times h
{k}_{e}=9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}
{H}_{1}=\frac{7.644\times {10}^{22}\text{A}\cdot {\text{m}}^{2}}{12.74\times {10}^{6}\text{m}}=6.0\times {10}^{15}\text{A}\cdot \text{m}
{H}_{2}=\frac{4\times {10}^{19}\text{A}\cdot {\text{m}}^{2}}{4.88\times {10}^{6}\text{m}}=8.2\times {10}^{12}\text{A}\cdot \text{m}
r=77\times {10}^{6}\text{m}
ϵ=1.85\text{\hspace{0.17em}}{\text{m}}^{2}/{\text{s}}^{2}
F=\frac{9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}\times 6.0\times {10}^{15}\text{A}\cdot \text{m}\times 8.2\times {10}^{12}\text{A}\cdot \text{m}}{{\left(77\times {10}^{9}\right)}^{2}\times 1.85\text{\hspace{0.17em}}{\text{m}}^{2}/{\text{s}}^{2}}
F=4\times {10}^{16}\text{N}
F=2.2\times {10}^{16}\text{N}
{k}_{e}=9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}
{H}_{1}=\frac{\left(7.644\times {10}^{22}\text{A}\cdot {\text{m}}^{2}\right)}{12.74\times {10}^{6}\text{m}}=6.0\times {10}^{15}\text{A}\cdot \text{m}
{H}_{2}=\frac{\left(1.55\times {10}^{27}\text{A}\cdot {\text{m}}^{2}\right)}{1.38\times {10}^{8}\text{m}}=1.12\times {10}^{19}\text{A}\cdot \text{m}
r=588\times {10}^{9}\text{m}
ϵ=12.4\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}
F=\frac{\left(9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}\times 6.0\times {10}^{15}\text{A}\cdot \text{m}\times 1.12\times {10}^{19}\text{A}\cdot \text{m}\right)}{{\left(588\times {10}^{9}\text{m}\right)}^{2}\times 12.4\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}}
F=1.4\times {10}^{20}\text{N}
F=2.18\times {10}^{18}\text{N}
{k}_{e}=9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}
{H}_{1}=\frac{\left(7.644\times {10}^{22}\text{A}\cdot {\text{m}}^{2}\right)}{12.74\times {10}^{6}\text{m}}=6.0\times {10}^{15}\text{A}\cdot \text{m}
{H}_{2}=\frac{\left(4.6\times {10}^{25}\text{A}\cdot {\text{m}}^{2}\right)}{1.2\times {10}^{8}\text{m}}=3.8\times {10}^{17}\text{A}\cdot \text{m}
r=1.2\times {10}^{12}\text{m}
ϵ=5.25\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}
F=\frac{\left(9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}\times 6.0\times {10}^{15}\text{A}\cdot \text{m}\times 3.8\times {10}^{17}\text{A}\cdot \text{m}\right)}{{\left(1.2\times {10}^{12}\text{m}\right)}^{2}\times 5.25\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}}
F=2.7\times {10}^{18}\text{N}
F=1.57\times {10}^{17}\text{N}
{k}_{e}=9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}
{H}_{1}=\frac{\left(7.644\times {10}^{22}\text{A}\cdot {\text{m}}^{2}\right)}{12.74\times {10}^{6}\text{m}}=6.0\times {10}^{15}\text{A}\cdot \text{m}
{H}_{2}=\frac{\left(3.9\times {10}^{24}\text{A}\cdot {\text{m}}^{2}\right)}{5.0\times {10}^{7}\text{m}}=7.8\times {10}^{16}\text{A}\cdot \text{m}
r=2.6\times {10}^{12}\text{m}
ϵ=4.3\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}
F=\frac{\left(9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}\times 6.0\times {10}^{15}\text{A}\cdot \text{m}\times 7.8\times {10}^{16}\text{A}\cdot \text{m}\right)}{{\left(2.6\times {10}^{12}\text{m}\right)}^{2}\times 4.3\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}}
F=1.4\times {10}^{17}\text{N}
F=5.11\times {10}^{15}\text{N}
{k}_{e}=9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}
{H}_{1}=\frac{\left(7.644\times {10}^{22}\text{A}\cdot {\text{m}}^{2}\right)}{12.74\times {10}^{6}\text{m}}=6.0\times {10}^{15}\text{A}\cdot \text{m}
{H}_{2}=\frac{\left(2.2\times {10}^{24}\text{A}\cdot {\text{m}}^{2}\right)}{4.9\times {10}^{7}\text{m}}=4.5\times {10}^{16}\text{A}\cdot \text{m}
r=4.3\times {10}^{12}\text{m}
ϵ=5.6\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}
F=\frac{\left(9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}\times 6.0\times {10}^{15}\text{A}\cdot \text{m}\times 4.5\times {10}^{16}\text{A}\cdot \text{m}\right)}{{\left(4.3\times {10}^{12}\text{m}\right)}^{2}\times 5.6\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}}
F=2.4\times {10}^{16}\text{N}
F=2.15\times {10}^{15}\text{N}
{k}_{e}=9\times {10}^{9}\text{N}\cdot {\text{m}}^{2}/{\text{A}}^{\text{2}}\cdot {\text{s}}^{2}
{H}_{1}=\frac{\left(7.644\times {10}^{22}\text{A}\cdot {\text{m}}^{2}\right)}{12.74\times {10}^{6}\text{m}}=6.0\times {10}^{15}\text{A}\cdot \text{m}
{H}_{2}=\frac{\left(\text{MagneticMoment}\text{\hspace{0.17em}}\text{A}\cdot {\text{m}}^{2}\right)}{\text{Lengthm}}
r=6.371\times {10}^{6}
ϵ=148\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}
F=\frac{{k}_{e}{H}_{1}{H}_{2}}{{r}^{2}ϵ}
F=\frac{{k}_{e}\times 6.0\times {10}^{15}\times {H}_{2}}{{\left(6.371\times {10}^{6}\right)}^{2}\times 148}\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}
F={k}_{e}\times H
ϵ=148\text{\hspace{0.17em}}{\text{m}}^{\text{2}}/{\text{s}}^{\text{2}}
F=k\times H
F=k\times H
F=ma
ϵ=\frac{{v}^{2}}{2}-\frac{G{m}_{1}+G{m}_{2}}{r}
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Jonald P. Fenecios, Emmanuel A. Cabral, "Left Baire-1 Compositors and Continuous Functions", International Journal of Mathematics and Mathematical Sciences, vol. 2013, Article ID 878253, 3 pages, 2013. https://doi.org/10.1155/2013/878253
Jonald P. Fenecios1 and Emmanuel A. Cabral2
1Department of Mathematics, Ateneo de Davao University, E. Jacinto Street, 8000 Davao City, Philippines
2Department of Mathematics, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, Philippines
Academic Editor: Hernando Quevedo
We showed that the class of left Baire-1 compositors is precisely the class of continuous functions. This answers a characterization problem posed in the work by Zhao (2007, page 550) and settles in the affirmative the conjecture in the work by Fenecios and Cabral (2012, page 43). Moreover, based on the above result we provide a new proof that the class of functions where is the class of all positive continuous functions and is the class of all positive constants as defined in the work by Bakowska and Pawlak (2010) is exactly the class of all continuous functions.
Let be a complete separable metric space. In the classical sense a function where is the real line is Baire-1 if, for every open set , is an set in . Equivalently, a function is Baire-1 if, for every closed set in , the restriction has a point of continuity in . In fact, the set of points of continuity of is a residual subset of .
Recently, Lee et al. [1] discovered a new equivalent definition of Baire-1 functions. A function is Baire-1 if and only if for each there is a positive function such that for any Various investigations have been done on the class of Baire-1 functions as well as on its subclasses using the - characterization. See, for instance, [2–4].
Let us recall in [4] that the notion of the left Baire-1 compositors was introduced as a natural counterpart of the notion of right Baire-1 compositors. A function is a left Baire-1 compositor if for every Baire-1 function the composition of functions is Baire-1. Unlike the right Baire-1 compositors there is no known characterization for the left Baire-1 functions. It was shown in [3] that there exists a function with finite set of discontinuity which is not a left Baire-1 compositor. This observation leads to the conjecture that left Baire-1 functions must have very nice properties. We proved that this is indeed the case: the class of the left Baire-1 compositors is precisely the class of all continuous functions defined on . Moreover, we use this fact to reestablish that where is the class of all positive continuous functions, is the class of all positive real constants, and is the class of all continuous functions on as defined in [2].
Let us denote the by . For easy reference, we present the following useful results.
In [4, Proposition 1], it was shown that is Baire-1 if and only if for every positive continuous function there is a corresponding positive function such that for any On the other hand, following [2] a function belongs to if for every there exists a function such that for any where and are families of positive functions defined on .
The following theorem was proved in [2].
Theorem 1. The following holds: where , , and are the families of all positive lower semicontinuous, functions all positive constant functions, and all continuous functions, respectively, defined on .
Another important result is due to Alinayat in [5]. We will state it as a theorem.
Theorem 2. If is continuous, then for each there exists a positive continuous function such that for any
We are now ready to prove our main result. To make the result as general as possible we consider real-valued Baire-1 functions defined in the Euclidean space for with the standard Euclidean norm.
Theorem 3. The following statements are equivalent.(1) is continuous.(2)For every Baire-1 function , is Baire-1.That is, is a left Baire-1 compositor.
Proof. It is easy to see that if is continuous, then is a left Baire-1 compositor. Suppose is a left Baire-1 compositor. If, on the contrary, we suppose has a discontinuity point , we may assume without loss of generality that is the only point of discontinuity of . Then may take one of the following forms:(I) with or ,(II) (III)Note that the functions and are continuous functions on their own domain. We will tackle Case I. Let be an enumeration of the cross product . Let such that First, we need to show that is Baire-1. We will adapt a well-known technique in showing that is continuous on the complement of . If , then is discontinuous at . Let and be an arbitrary element of . We can find a natural number such that . For such , choose such that for each . Suppose . Then either or for some . If , then clearly . If for some , then . Hence, is continuous on the complement of . If is any nonempty perfect set in , then is uncountable. Hence, has at least a point of continuity in . Consequently, is Baire-1. Next, we show that is not Baire-1 so that is not a left Baire-1 compositor, a contradiction to our hypothesis. Now, It is straightforward to show that is discontinuous everywhere in some set of the second category in . Case II may be dealt with similarly with given by Following the same line of reasoning in Case I, one can show that is discontinuous everywhere in some set of the second category in . The remaining case can be proved similarly. All these arguments show that is not Baire-1. Therefore, must be a continuous function.
A part of the statement of the next result is contained in [2]. This inclusion is in Theorem 1. With our main result, Theorem 1 (Theorem 11 in [2]) admits a very straightforward proof.
Corollary 4. Let be the family of all positive continuous functions, the family of all positive constant functions, the family of all positive lower semicontinuous functions, and the family of all continuous functions defined on . Then
Proof. The inclusion is immediate from Theorem 2. Let . We will show that is a left Baire-1 compositor so that by Theorem 3 is continuous. Let be any Baire-1 function and let . Then there is a positive continuous function such that for any Since is Baire-1, there is a positive function such that for any It follows that for any Thus, . Since , then it follows that The proof is complete.
The authors are thankful to the referee for the helpful suggestions that led to the improvement of the current paper. Moreover, the first author wishes to thank the Department of Science and Technology through the Science Education Institute for the financial support while this research was ongoing.
P.-Y. Lee, W.-K. Tang, and D. Zhao, “An equivalent definition of functions of the first Baire class,” Proceedings of the American Mathematical Society, vol. 129, no. 8, pp. 2273–2275, 2001. View at: Publisher Site | Google Scholar | MathSciNet
A. Bakowska and R. J. Pawlak, “On some characterizations of Baire class one functions and Baire class one like functions,” Tatra Mountains Mathematical Publications, vol. 46, pp. 91–106, 2010. View at: Google Scholar | MathSciNet
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{B}_{1}
compositors,” Journal of the Indonesian Mathematical Society, vol. 18, no. 1, pp. 37–44, 2012. View at: Google Scholar | MathSciNet
D. Zhao, “Functions whose composition with Baire class one functions are Baire class one,” Soochow Journal of Mathematics, vol. 33, no. 4, pp. 543–551, 2007. View at: Google Scholar | MathSciNet
A. Alinayat, “δ as a continuous function of x and ε,” The American Mathematical Monthly, vol. 107, no. 2, pp. 151–155, 2000. View at: Publisher Site | Google Scholar | MathSciNet
Copyright © 2013 Jonald P. Fenecios and Emmanuel A. Cabral. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Gameplay - MetaFish
How To Play MetaFish? Go Fishing and Earn!
Fishing isn't as simple as you may imagine so let's take some time to educate ourselves before heading out to the water.
👩🏻🌾 Select a Character
1️⃣ Select a character you would like to become
2️⃣ After selecting, you may see your character profile including character name, wallet address and in-game reward
🧰 Unbox Fishing Starter Kits
1️⃣ Purchase a fishing starter kit for specific amount of 1,000 $FISH
Mainnet price of a fishing box: 1,000 $FISH
2️⃣ Unbox a fishing box using a key worth the amount of 50 $FISH
Unbox any boxes in your Box Collection
Got Arweavezao ⭐⭐ from Shikibox
You may see the list of fishing rods you own in the tab "Rod" in your Collection
🎣 Go Fishing
Fishing is the primary method for obtaining $FISH by using your NFT fishing rods. Fishing entails the players selecting their fishing rod and a lake from a random group based on your rod power calculation system.
1️⃣ Select your fishing rod to use & select a lake you would like to go fishing
2️⃣ Let's begin our fishing expedition with the easiest lake. The contract calculates your chances of success in fishing after the fisherman has chosen the lake with the simple formula is:
SuccessRate = FishingRod[Lucky]+Lake[Lucky]
E.g: Arweavezao's luckiness is 5 and Trench's luckiness is 60, then the fishing success rate is 65%.
Alice is using her Arweavezao to go fishing at trench Yanagawa
A success turn grants you $FISH reward into your in-game wallet.
A failed turn fishing results in a loss of gas fee (your bait).
The lower the success, the higher the reward. A success or failure in fishing both reduces the durability of your fishing rod.
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Transition Metals and Coordination Chemistry - Vocabulary - Course Hero
General Chemistry/Transition Metals and Coordination Chemistry/Vocabulary
f-block elements in period 7 of the periodic table, which consists of elements actinium (Ac) through lawrencium (Lr)
ligand in a coordination complex that donates two pairs of electrons to the central metal atom or ion
coordination complex formed between a central metal atom or ion and chelating ligands, which are ions or molecules that bond to it with more than one atom
geometric arrangement in which two identical substituents are on the same side of the central part of a molecule or an ion
central metal atom or ion surrounded by ligands, as well as bonded ions if the central part has an overall charge
number of atoms bound to the single central metal center in a coordination complex
part of a coordination complex consisting of the central metal atom or ion and all ligands surrounding it
energy difference between the higher energy
e_g
{d_{{z^2}}}
{d_{{x^2}-{y^2}}}
) and lower energy
t_{2g}
{d_{xy}}
{d_{yz}}
{d_{xz}}
) symmetric orbitals
electrostatic model that is used to describe and predict energy differences between nd orbital sets in transition metal complexes
element with one or more valence electrons in a d orbital
element with 4f or 5f electrons in its valence shell
one of two or more molecules that have the same molecular formula and bond structure but differ in the positions of substituents around a rigid part of the molecule
high-spin complexes
complex in which electrons fill higher orbitals singly and the pairing energy is large relative to the crystal field splitting energy
one of two forms of a coordination complex that differ only in which of two species is a ligand and which is outside the coordination sphere
one of two or more molecules that share the same chemical formula but have different arrangements of atoms
f-block elements in period 6 of the periodic table, which consists of elements lanthanum (La) to lutetium (Lu)
ion or molecule that bonds to a central metal atom or ion as part of a coordination complex
one of two or more coordination complexes that differ in how a ligand is bonded to the central metal atom or ion
low-spin complexes
complex in which electrons preferentially pair in lower-energy orbitals and the pairing energy is small relative to the crystal field splitting energy
ligand in a coordination complex that donates a single pair of electrons to the central metal atom or ion
one of a pair of mirror-image molecules that are not identical and cannot be superimposed
energy required for two electrons to occupy a single orbital
ligand in a coordination complex that donates three or more pairs of electrons to the central metal atom or ion
one of 15 lanthanides and 2 transition metals that have similar chemical properties and are commonly found together in nature
technique by which an elemental metal is extracted from its ore through heating and melting
list of ligands ordered according to their ability to induce crystal field splitting for a common metal center
material that can conduct electric current with almost zero resistance when cooled to appropriate temperatures
geometric arrangement in which two identical substituents are on opposite sides of the central part of a molecule or an ion
<Overview>What Are Transition Metals?
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81V15 Weak interaction
81V22 Unified theories
81V25 Other elementary particle theory
81V65 Quantum dots
{\left(QED\right)}_{2}
A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor. I: The Boltzmann-Poisson-Schrödinger solver.
Khoie, R. (1996)
A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor. II: The full quantum transport.
A single scale infinite volume expansion for three dimensional many Fermion Green's functions.
Magnen, Jacques, Rivasseau, Vincent (1995)
Gian Michele Graf (1996)
O. Steinmann (1995)
Born-Infeld electrodynamics: Clifford number and spinor representations.
Chernitskii, Alexander A. (2002)
G. Morchio (1996)
Charges in gauge theories.
McMullan, David (2007)
Complex scaling technique in non-relativistic massive QED
T. Okamoto, K. Yajima (1985)
Contact transformations in Wheeler-Feynman electrodynamics
Yurij Yaremko (1997)
W. Hunziker (1986)
Electroweak interaction model with an undegenerate double symmetry.
Slad, Leonid M. (2006)
Form perturbations of the second quantized Dirac field.
Helffer, Bernard, Siedentop, Heinz (1998)
Heavy molecules in the strong magnetic field
Victor Ivrii (1997)
Mary Beth Ruskai (1994)
T. Kawai, H. P. Stapp (1993)
On higher order estimates in quantum electrodynamics.
Matte, Oliver (2010)
On the infrared problem in a model of scalar electrons and massless, scalar bosons
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Portfolio Optimization with Semicontinuous and Cardinality Constraints - MATLAB & Simulink Example - MathWorks India
{x}_{i}
{\mathit{v}}_{\mathit{i}}
{v}_{i}
{\mathit{v}}_{\mathit{i}}
{\text{\hspace{0.17em}}\mathrm{lb}*{\mathit{v}}_{\mathit{i}}\le \mathit{x}}_{\mathit{i}}\le \mathrm{ub}*{\mathit{v}}_{\mathit{i}}
{\mathit{v}}_{\mathit{i}}
{v}_{i}
{\mathit{v}}_{\mathit{i}}
\mathrm{MinNumAssets}\le {\sum }_{1}^{\mathrm{NumAssets}}{\mathit{v}}_{\mathit{i}}\le \mathrm{MaxNumAssets}
{\mathit{v}}_{\mathit{i}}
{\mathit{x}}_{\mathit{i}}\ge 0\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}}\mathrm{sum}\left({\mathit{x}}_{\mathit{i}}\right)=1
{\mathit{x}}_{\mathit{i}}=0\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}{\mathit{x}}_{\mathit{i}}\ge 0.05
\mathrm{lb}\le {\mathit{x}}_{\mathit{i}}\le \mathrm{ub}\text{\hspace{0.17em}}
{\mathit{x}}_{\mathit{i}}=0\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}{\text{\hspace{0.17em}}\mathrm{lb}\le \mathit{x}}_{\mathit{i}}\le \mathrm{ub}
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Create symbolic scalar variables and functions, and matrix variables and functions - MATLAB syms - MathWorks Switzerland
x
y
{a}_{1},\dots ,{a}_{4}
\left(\begin{array}{cccc}{a}_{1}& {a}_{2}& {a}_{3}& {a}_{4}\end{array}\right)
\left(\begin{array}{cccc}{p}_{\mathrm{a1}}& {p}_{\mathrm{a2}}& {p}_{\mathrm{a3}}& {p}_{\mathrm{a4}}\end{array}\right)
\left(\begin{array}{cccc}{p}_{\mathrm{b1}}& {p}_{\mathrm{b2}}& {p}_{\mathrm{b3}}& {p}_{\mathrm{b4}}\end{array}\right)
{A}_{i,j}
{A}_{1,1},\dots ,{A}_{3,4}
\left(\begin{array}{cccc}{A}_{1,1}& {A}_{1,2}& {A}_{1,3}& {A}_{1,4}\\ {A}_{2,1}& {A}_{2,2}& {A}_{2,3}& {A}_{2,4}\\ {A}_{3,1}& {A}_{3,2}& {A}_{3,3}& {A}_{3,4}\end{array}\right)
\left(\begin{array}{cccc}x\in \mathbb{Z}& y\in \mathbb{Z}& z\in \mathbb{Q}& 0<z\end{array}\right)
x\in \mathbb{Z}
\left(\begin{array}{ccc}{a}_{1}\in \mathbb{R}& {a}_{2}\in \mathbb{R}& {a}_{3}\in \mathbb{R}\end{array}\right)
x+2 y
5
\left(\begin{array}{cc}x& {x}^{3}\\ {x}^{2}& {x}^{4}\end{array}\right)
\left(\begin{array}{cc}2& 8\\ 4& 16\end{array}\right)
\left(\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right)
\left(\begin{array}{cc}{f}_{1,1}\left(x,y\right)& {f}_{1,2}\left(x,y\right)\\ {f}_{2,1}\left(x,y\right)& {f}_{2,2}\left(x,y\right)\end{array}\right)
{f}_{1,1}\left(x,y\right)
{f}_{2,2}\left(x,y\right)
\left(\begin{array}{cc}{f}_{1,1}\left(x,y\right)& {f}_{1,2}\left(x,y\right)\\ {f}_{2,1}\left(x,y\right)& {f}_{2,2}\left(x,y\right)\end{array}\right)
\left(\begin{array}{cc}2 x& {f}_{1,2}\left(x,y\right)\\ {f}_{2,1}\left(x,y\right)& x-y\end{array}\right)
\left(\begin{array}{cc}4& {f}_{1,2}\left(2,3\right)\\ {f}_{2,1}\left(2,3\right)& -1\end{array}\right)
A
B
\text{A}+\text{B}
A+B
\left(\begin{array}{ccc}{A}_{1,1}+{B}_{1,1}& {A}_{1,2}+{B}_{1,2}& {A}_{1,3}+{B}_{1,3}\\ {A}_{2,1}+{B}_{2,1}& {A}_{2,2}+{B}_{2,2}& {A}_{2,3}+{B}_{2,3}\end{array}\right)
\left(\begin{array}{ccc}{A}_{1,1}+{B}_{1,1}& {A}_{1,2}+{B}_{1,2}& {A}_{1,3}+{B}_{1,3}\\ {A}_{2,1}+{B}_{2,1}& {A}_{2,2}+{B}_{2,2}& {A}_{2,3}+{B}_{2,3}\end{array}\right)
A B-B A
{\text{X}}^{T}\text{A}\text{X}
{X}^{\mathrm{T}} A X
{A}^{\mathrm{T}}+A
\mathit{v}\left(\mathbit{r},\mathit{t}\right)=\frac{‖\mathit{r}‖}{\mathit{t}}
\mathbit{r}
\mathit{t}
\mathbit{r}
\mathit{t}
\mathit{v}\left(\mathbit{r},\mathit{t}\right)
\mathbit{r}
\mathit{t}
\mathit{v}\left(\mathbit{r},\mathit{t}\right)
{‖r‖}_{2} {t}^{-1}
\mathbit{r}=\left(1,2,2\right)
\mathit{t}=3
\begin{array}{l}\frac{1}{3} {‖{\Sigma }_{1}‖}_{2}\\ \\ \mathrm{where}\\ \\ \mathrm{ }{\Sigma }_{1}=\left(\begin{array}{ccc}1& 2& 2\end{array}\right)\end{array}
1
\mathit{f}\left(\mathbit{A}\right)={\mathbit{A}}^{2}-3\mathbit{A}+2\mathbit{I}
\mathbit{A}
\mathbit{I}
\mathbit{A}
\mathit{f}\left(\mathbit{A}\right)
\mathbit{A}
\mathit{f}\left(\mathbit{A}\right)
2 {\mathrm{I}}_{2}-3 A+{A}^{2}
\mathbit{A}=\left[\begin{array}{cc}1& 2\\ -2& -1\end{array}\right]
\begin{array}{l}-3 {\Sigma }_{1}+{{\Sigma }_{1}}^{2}+2 {\mathrm{I}}_{2}\\ \\ \mathrm{where}\\ \\ \mathrm{ }{\Sigma }_{1}=\left(\begin{array}{cc}1& 2\\ -2& -1\end{array}\right)\end{array}
\left(\begin{array}{cc}-4& -6\\ 6& 2\end{array}\right)
k
|
p
\mathrm{GL}\left(2\right)
L
L
p
p
A stationary phase formula for exponential sums over
ℤ/{p}^{m}ℤ
and applications to GL(3)-Kloosterman sums
Romuald Dąbrowski, Benji Fisher (1997)
A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums.
Booker, Andrew R. (2000)
{C}^{\infty }
Analytic continuation of representations and estimates of automorphic forms.
Bernstein, Joseph, Reznikov, Andre (1999)
Asymptotic formulae for partition ranks
Jehanne Dousse, Michael H. Mertens (2015)
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.
Asymptotic formulas for the coefficients of certain automorphic functions
Jaban Meher, Karam Deo Shankhadhar (2015)
We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index 1 and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions
{\theta }^{k}/{\eta }^{l}
for all integers k,l...
Automorphic forms, hyperfunction cohomology, and period functions.
Roelof W. Bruggeman (1997)
Binary quadratic forms and the Fourier coefficients of elliptic and Jacobi modular forms.
Nils-Peter Skoruppa (1990)
Bounding hyperbolic and spherical coefficients of Maass forms
Valentin Blomer, Farrell Brumley, Alex Kontorovich, Nicolas Templier (2014)
We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.
Bounds for automorphic L-functions.
H. Iwaniec, W. Duke, J. Frielander (1993)
Bounds for automorphic L-functions. II.
H. Iwaniec, W. Duke, J.B. Firedlander (1994)
Coefficient bounds for level 2 cusp forms
Paul Jenkins, Kyle Pratt (2015)
We give explicit upper bounds for the coefficients of arbitrary weight k, level 2 cusp forms, making Deligne’s well-known
O\left({n}^{\left(k-1\right)/2+ϵ}\right)
bound precise. We also derive asymptotic formulas and explicit upper bounds for the coefficients of certain level 2 modular functions.
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Worst-case norm of uncertain matrix - MATLAB wcnorm - MathWorks India
wcnorm
Basic syntax with third output argument
Worst-Case Norm and Condition Number of an Uncertain Matrix
Worst-case norm of uncertain matrix
maxnorm = wcnorm(m)
[maxnorm,wcu] = wcnorm(m)
[maxnorm,wcu] = wcnorm(m,opts)
[maxnorm,wcu,info] = wcnorm(m)
[maxnorm,wcu,info] = wcnorm(m,opts)
The norm of an uncertain matrix generally depends on the values of its uncertain elements. Determining the maximum norm over all allowable values of the uncertain elements is referred to as a worst-case norm analysis. The maximum norm is called the worst-case norm.
As with other uncertain-system analysis tools, only bounds on the worst-case norm are computed. The exact value of the worst-case norm is guaranteed to lie between these upper and lower bounds.
Suppose mat is a umat or a uss with M uncertain elements. The results of
[maxnorm,maxnormunc] = wcnorm(mat)
maxnorm is a structure with the following fields.
Lower bound on worst-case norm, positive scalar.
Upper bound on worst-case norm, positive scalar.
maxnormunc is a structure that includes values of uncertain elements and maximizes the matrix norm. There are M field names, which are the names of uncertain elements of mat. The value of each field is the corresponding value of the uncertain element, such that when jointly combined, lead to the norm value in maxnorm.LowerBound. The following command shows the norm:
norm(usubs(mat,maxnormunc))
A third output argument provides information about sensitivities of the worst-case norm to the uncertain elements ranges.
[maxnorm,maxnormunc,info] = wcnorm(mat)
The third output argument info is a structure with the following fields:
Index of model with largest gain (when mat is an array of uncertain matrices)
Structure of worst-case uncertainty values. The fields of info.WorstPerturbation are the names of the uncertain elements in mat, and each field contains the worst-case value of the corresponding element.
A struct with M fields. Fieldnames are names of uncertain elements of sys. Field values are positive numbers, each entry indicating the local sensitivity of the worst-case norm in maxnorm.LowerBound to all of the individual uncertain elements’ uncertainty ranges. For instance, a value of 25 indicates that if the uncertainty range is increased by 8%, then the worst-case norm should increase by about 2%. If the Sensitivity property of the wcOptions object is 'off', the values are NaN.
ArrayIndex Same as Model. Included for compatibility with R2016a and earlier.
Construct an uncertain matrix and compute the worst-case norm of the matrix and of its inverse. These computations let you accurately estimate the worst-case, or the largest, value of the condition number of the matrix.
b = ureal('b',3,'Range',[2 10]);
c = ureal('c',9,'Range',[8 11]);
d = ureal('d',1,'Range',[0 2]);
Mi = inv(M);
maxnormM = wcnorm(M)
maxnormM = struct with fields:
maxnormMi = wcnorm(Mi)
maxnormMi = struct with fields:
The condition number of M must be less than the product of the two upper bounds for all values of the uncertain elements of M. Conversely, the condition number of the largest value of M must be at least equal to the condition number of the nominal value of M. Compute these bounds on the worst-case value of the condition number.
condUpperBound = maxnormM.UpperBound*maxnormMi.UpperBound;
condLowerBound = cond(M.NominalValue);
[condLowerBound condUpperBound]
The range between these lower and upper bounds is fairly large. You can get a more accurate estimate. Recall that the condition number of an n-by-m matrix M can be expressed as an optimization, where a free norm-bounded matrix
\Delta
tries to align the gains of M and inv(M):
\begin{array}{c}\kappa \left(M\right)=\underset{\Delta \in {C}^{m×m}}{\mathrm{max}}\left({\sigma }_{\mathrm{max}}\left(M\Delta {M}^{-1}\right)\right)\\ {\sigma }_{\mathrm{max}}\left(\Delta \right)\le 1\end{array}
If M is uncertain, then the worst-case condition number involves further maximization over the possible values of M. Therefore, you can compute the worst-case condition number of an uncertain matrix by using a ucomplexm uncertain element and using wcnorm to carry out the maximization.
Create a 2-by-2 ucomplexm element with nominal value 0.
Delta = ucomplexm('Delta',zeros(2,2));
The range of values represented by Delta includes 2-by-2 matrices with the maximum singular value less than or equal to 1.
Create the expression involving M, Delta, and inv(M).
H = M*Delta*Mi;
[maxKappa,wcu,info] = wcnorm(H,opt);
maxKappa = struct with fields:
Verify that the values in wcu make the condition number as large as maxKappa.LowerBound.
cond(usubs(M,wcu))
See wcgain.
norm | wcgain | wcOptions
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Spectral centroid for audio signals and auditory spectrograms - MATLAB spectralCentroid - MathWorks Switzerland
Spectral Centroid of Time-Domain Audio
Spectral Centroid of Frequency-Domain Audio Data
Calculate Spectral Centroid of Streaming Audio
Spectral centroid for audio signals and auditory spectrograms
centroid = spectralCentroid(x,f)
centroid = spectralCentroid(x,f,Name=Value)
spectralCentroid(___)
centroid = spectralCentroid(x,f) returns the spectral centroid of the signal, x, over time. How the function interprets x depends on the shape of f.
centroid = spectralCentroid(x,f,Name=Value) specifies options using one or more name-value arguments.
spectralCentroid(___) with no output arguments plots the spectral centroid. You can specify an input combination from any of the previous syntaxes.
If the input is in the time domain, the spectral centroid is plotted against time.
If the input is in the frequency domain, the spectral centroid is plotted against frame number.
Read in an audio file and calculate the centroid using default parameters.
centroid = spectralCentroid(audioIn,fs);
Plot the centroid against time.
spectralCentroid(audioIn,fs);
Read in an audio file and then buffer the signal into 30 ms frames with 20 ms overlap. Calculate the octave power spectrum using the poctave function.
audioBuffered = buffer(audioIn,round(fs*0.03),round(fs*0.02),"nodelay");
[p,cf] = poctave(audioBuffered,fs);
Calculate the centroid of the octave power spectrum over time.
centroid = spectralCentroid(p,cf);
Plot the centroid against the frame number.
spectralCentroid(p,cf)
Calculate the centroid of the power spectrum over time. Calculate the centroid for 50 ms Hamming windows of data with 25 ms overlap. Use the range from 62.5 Hz to fs/2 for the centroid calculation.
centroid = spectralCentroid(audioIn,fs, ...
spectralCentroid(audioIn,fs, ...
Create a dsp.AudioFileReader object to read in audio data frame-by-frame. Create a dsp.SignalSink to log the spectral centroid calculation.
Calculate the spectral centroid for the frame of audio.
Log the spectral centroid for later plotting.
To calculate the spectral centroid for only a given input frame, specify a window with the same number of samples as the input, and set the overlap length to zero.
centroid = spectralCentroid(audioIn,fileReader.SampleRate, ...
logger(centroid)
If the input to your audio stream loop has a variable samples-per-frame, an inconsistent samples-per-frame with the analysis window size of spectralCentroid, or if you want to calculate the spectral centroid for overlapped data, use dsp.AsyncBuffer.
Specify that the spectral centroid is calculated for 50 ms frames with a 25 ms overlap.
centroid = spectralCentroid(audioBuffered,fs, ...
"power" –– The spectral centroid is calculated for the one-sided power spectrum.
"magnitude" –– The spectral centroid is calculated for the one-sided magnitude spectrum.
The spectral centroid is calculated as described in [1]:
\text{centroid}=\frac{\sum _{k={b}_{1}}^{{b}_{2}}{f}_{k}{s}_{k}}{\sum _{k={b}_{1}}^{{b}_{2}}{s}_{k}}
spectralSkewness | spectralKurtosis | spectralSpread
|
62E20 Asymptotic distribution theory
62E10 Characterization and structure theory
62E15 Exact distribution theory
62E17 Approximations to distributions (nonasymptotic)
62E86 Fuzziness in connection with the topics on distributions in this section
\left(h,\Phi \right)
-entropy differential metric
María Luisa Menéndez, Domingo Morales, Leandro Pardo, Miquel Salicrú (1997)
Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on
\left(h,\Phi \right)
-entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic...
N. Henze, L Baringhaus (1988)
A contribution to bootstrapping autoregressive processes
Zuzana Prášková (1995)
A general class of entropy statistics
María Dolores Esteban (1997)
To study the asymptotic properties of entropy estimates, we use a unified expression, called the
{H}_{h,v}^{{\varphi }_{1},{\varphi }_{2}}
-entropy. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators are considered, so they can be used to construct confidence intervals and to test statistical hypotheses based on one or more samples. These results can also be applied to multinomial populations.
A Lower Bound for the Normal Approximation of U-Statistics.
Y. Maesono (1988)
Fraga Alves, M.I., Gomes, M.Ivette, de Haan, Laurens (2003)
A new family of compound lifetime distributions
A. Asgharzadeh, Hassan S. Bakouch, Saralees Nadarajah, L. Esmaeili (2014)
In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual...
A new semigroup technique in Poisson approximation.
M.L. Puri, D. Pfeifer, P. Deheuvels (1989)
A Note Invariance Principles for v. Mises'-Statistics.
M. Denker, C. Grillenberger, G. Keller (1985)
A Note on Generalized Wald's Method.
M.T. Wells, A.S. Hadi (1990)
A Note on Hájek's Theory of Rejective Sampling.
H. Milbrodt (1987)
A note on the continuity of projection matrices with application to the asymptotic distribution of quadratic forms
G. Forchini (2005)
This paper investigates the continuity of projection matrices and illustrates an important application of this property to the derivation of the asymptotic distribution of quadratic forms. We give a new proof and an extension of a result of Stewart (1977).
A note on the distribution of angles associated to indefinite integral binary quadratic forms
Dragan Đokić (2019)
To each indefinite integral binary quadratic form
Q
, we may associate the geodesic in
ℍ
through the roots of quadratic equation
Q\left(x,1\right)
. In this paper we study the asymptotic distribution (as discriminant tends to infinity) of the angles between these geodesics and one fixed vertical geodesic which intersects all of them.
Ole E. Barndorff-Nielsen, Claudia Klüppelberg (1992)
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Synthetic position - Wikipedia
Find sources: "Synthetic position" – news · newspapers · books · scholar · JSTOR (December 2010) (Learn how and when to remove this template message)
A synthetic short position in the underlying, created using a short call and a long put
A synthetic long position in the underlying, created using a long call and a short put
In finance, a synthetic position is a way to create the payoff of a financial instrument using other financial instruments.
A synthetic position can be created by buying or selling the underlying financial instruments and/or derivatives.
If several instruments which have the same payoff as investing in a share are bought, there is a synthetic underlying position. In a similar way, a synthetic option position can be created.
For example, a position which is long a 60-strike call and short a 60-strike put will always result in purchasing the underlying asset for 60 at exercise or expiration. If the underlying asset is above 60, the call is in the money and will be exercised; if the underlying asset is below 60 then the short put position will be assigned, resulting in a (forced) purchase of the underlying at 60.
One advantage of a synthetic position over buying or shorting the underlying stock is that there is no need to borrow the stock if selling it short. Another advantage is that one need not worry about dividend payments on the shorted stock (if any, declared by the underlying security).
When the underlying asset is a stock, a synthetic underlying position is sometimes called a synthetic stock.
Synthetic long put[edit]
The synthetic long put position consists of three elements: shorting one stock, holding one European call option and holding
{\displaystyle Ke^{-rT}}
dollars in a bank account.
{\displaystyle K}
is the strike price of the option, and
{\displaystyle r}
is the continuously compounded interest rate,
{\displaystyle T}
is the time to expiration and
{\displaystyle S}
is the spot price of the stock at option expiration.)
At expiry the stock has to be paid for, which gives a cashflow
{\displaystyle -S}
. The bank account will give a cashflow of
{\displaystyle K}
dollars. Moreover, the European call gives a cashflow of
{\displaystyle \max(0,S-K)}
. The total cashflow is
{\displaystyle K-S+\max(0,S-K)=\max(0,K-S)}
. The total cashflow at expiry is exactly the cashflow of a European put option.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Synthetic_position&oldid=1063944211"
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a(x-{x}_{0}{)}^{2}+b(y-{y}_{0}{)}^{2}=c
a{x}^{2}+b{y}^{2}+cx+dy+e=0
\left({x}_{0},{y}_{0}\right)
and
b
Description: recognize an ellipse according to its equation, or vice versa. interactive exercises, online calculators and plotters, mathematical recreation and games
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Development of the Damage State Variable for a Unified Creep Plasticity Damage Constitutive Model of the 95.5Sn–3.9Ag–0.6Cu Lead-Free Solder | J. Electron. Packag. | ASME Digital Collection
Arlo F. Fossum,
Arlo F. Fossum
Mike K. Neilsen
Pierce, D. M., Sheppard, S. D., Fossum, A. F., Vianco, P. T., and Neilsen, M. K. (January 31, 2008). "Development of the Damage State Variable for a Unified Creep Plasticity Damage Constitutive Model of the 95.5Sn–3.9Ag–0.6Cu Lead-Free Solder." ASME. J. Electron. Packag. March 2008; 130(1): 011002. https://doi.org/10.1115/1.2837513
A unified creep plasticity damage (UCPD) constitutive model was developed to predict the fatigue of 95.5Sn–3.9Ag–0.6Cu solder joints. Compression, stress-strain and creep properties were generated in previous studies of this solder. Crack damage was reflected in a single state variable,
Dω
, in the model. Isothermal fatigue tests were performed at
25°C
100°C
160°C
using a double-lap shear test specimen. A new approach to fitting the revised damage model is proposed based on finite element analysis (FEA) simulation of the load decay of the fatigued solder material. Accurate predictions required that those parameters be temperature dependent. The UCPD constitutive model was successfully implemented as a subroutine in the commercial finite element code ANSYS®. Consistent predictions were obtained as demonstrated by a comparison of results generated from FEA simulation of the test assembly against analogous experimental results.
copper alloys, creep, fatigue, finite element analysis, plasticity, silver alloys, stress-strain relations, tin alloys
Constitutive equations, Creep, Damage, Finite element analysis, Plasticity, Simulation, Solders, Temperature, Stress, Fatigue, Shear (Mechanics), Dynamic light scattering, Solder joints, Testing
Saphores
Lead-Free Solders: Issues of Toxicity, Availability and Impacts of Extraction
53rd Electronic Components and Technology Conference (ECTC)
Reduced Environmental Impacts by Lead Free Electronic Assemblies
IPCWorks’99
, IPC.
Reliability and Au Embrittlement of Lead Free Solders for BGA Applications
Rethinking the Importance of Reflow Atmospheres in the Lead-Free Era
Analysis of the Current Status of European Lead-Free Soldering 2004
,” European Lead-Free Soldering Network, Report No. D5.1, pp.
A Microstructural Study of the Thermal Fatigue Failures of 60Sn–40Pb Solder Joints
Life Prediction Modeling of Solder Interconnects for Electronic Systems
ASME InterPack’97
, Kohula, HI.
Microstructurally Based Finite Element Simulation of Solder Joint Behaviour
Computational Continuum Modeling of Solder Interconnects
Coarsening of the Sn–Pb Solder Microstructure in Constitutive Model-Based Predictions of Solder Joint Thermal Mechanical Fatigue
Computational Methodologies for Predicting Thermal Mechanical Fatigue in Soldered Interconnects
, 2005, unpublished data, Sandia National Laboratories, Albuquerque, NM and SUNY Binghamton, NY.
Meilunas
Microstructural Evolution and Damage Mechanisms in Pb-Free Solder Joints During Extended −40°Cto125°C Thermal Cycles
The Compression Stress-Strain Behavior Of Sn–Ag–Cu Solder
Time-Independent Mechanical and Physical Properties of the Ternary 95.5Sn–3.9Ag–0.6Cu Solder
Creep Behavior of the Ternary 95.5Sn–3.9Ag–0.6Cu Solder. Part I. As-Cast Condition
Creep Behavior of the Ternary 95.5Sn–3.9Ag–0.6Cu Solder. Part II. Aged Condition
A Viscoplastic Theory for Braze Alloys
,” Sandia Report No. SAND96-0984, pp.
Constitutive Relations for the Nonelastic Deformation of Metals
Micromechanical Basis for Constitutive Equations With Internal State Variables
Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation. Part 1. Equations Development and Analytical Procedures
Modeling the Temperature and Strain Rate Dependent Large Deformation of Metals
Viscoplasticity With Creep and Plasticity Bounds
Evolution Equations for Anisotropic Hardening and Damage of Elastic-Viscoplastic Materials
Plasticity Today: Modeling, Methods and Applications
Modeling of Continuum Damage for Application in Elastic-Viscoplastic Constitutive Equations
Creep Rupture Under Multi-Axial States of Stress
IPC-9701 Performance Test Methods and Qualification Requirements for Surface Mount Solder Attachments
, 2003–2006, private communication.
Mechanical Behavior of the 98Ag–2Zr and 97Ag–1Cu–2Zr Active Braze Alloys
Continuum Damage Mechanics Based Failure Prediction Methodology for 95.5Sn–3.9Ag–0.6Cu Solder Alloy Interconnects in Electronic Packaging
,” Mechanical Engineering, Stanford University, p.
Development and Applications of a Rosenbrock Integrator
,” Lewis Research Center, National Aeronautics and Space Administration, NASA Technical Memorandum No. 4709, pp.
,” Lewis Research Center, National Aeronautics and Space Administration, NASA Technical Memorandum No. 107313. pp.
Unified Creep Plasticity Damage (UCPD) Model for SAC396 Solder
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{H}^{p}
A discrete integral representation for polynomials of fixed maximal degree and their universal Korovkin closure.
Michael Pannenberg (1986)
A general description of the Bergman projection
Maciej Skwarczyński (1985)
A generalization of Pick's theorem and its applications to intrinsic metrics
Jacob Burbea (1981)
A generalized area integral estimate and applications
S. Chang (1981)
A Geometrie Characterization of the Ball and the Bochner-Martinelli Kernel.
Harold P. Boas (1980)
A new invariant Kähler metric on relatively compact domains in a complex manifold
Bo-Yong Chen (2007)
We introduce a new invariant Kähler metric on relatively compact domains in a complex manifold, which is the Bergman metric of the L² space of holomorphic sections of the pluricanonical bundle equipped with the Hermitian metric introduced by Narasimhan-Simha.
A New Proof of the Newlander-Nirenberg Theorem.
A note on the Cauchy-Bochner formula for a class of Beurling ultradistributions
Pilipovic, Stevan (1989)
About the derivatives of Cauchy type integrals in the polydisc.
Harutyunyan, A.V., Petrosyan, A.I (2005)
An integral formula on submanifolds of domains of Cn..
Telemachos Hatziafratis (1991)
A Bochner-Martinelli-Koppelman type integral formula on submanifolds of pseudoconvex domains in Cn is derived; the result gives, in particular, integral formulas on Stein manifolds.
An integral represantation formula for holomorphic functions on analytic varieties
Telemachos E. Hatziafaris (1986)
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Formula and Calculation for EPS
Example of EPS
EPS and Price-to-Earnings (P/E)
EPS can be arrived at in several forms, such as excluding extraordinary items or discontinued operations, or on a diluted basis.
Like other financial metrics, earnings per share is most valuable when compared against competitor metrics, companies of the same industry, or across a period of time.
Earnings per share value is calculated as net income (also known as profits or earnings) divided by available shares. A more refined calculation adjusts the numerator and denominator for shares that could be created through options, convertible debt, or warrants. The numerator of the equation is also more relevant if it is adjusted for continuing operations.
\text{Earnings per Share}=\frac{\text{Net Income }-\text{ Preferred Dividends}}{\text{End-of-Period Common Shares Outstanding}}
Earnings per Share=End-of-Period Common Shares OutstandingNet Income − Preferred Dividends
To calculate a company's EPS, the balance sheet and income statement are used to find the period-end number of common shares, dividends paid on preferred stock (if any), and the net income or earnings. It is more accurate to use a weighted average number of common shares over the reporting term because the number of shares can change over time.
Any stock dividends or splits that occur must be reflected in the calculation of the weighted average number of shares outstanding. Some data sources simplify the calculation by using the number of shares outstanding at the end of a period.
EPS for FAANG Stocks
Say that the calculation of EPS for three companies at the end of the fiscal year was as follows:
Earnings per share is one of the most important metrics employed when determining a firm's profitability on an absolute basis. It is also a major component of calculating the price-to-earnings (P/E) ratio, where the E in P/E refers to EPS. By dividing a company's share price by its earnings per share, an investor can see the value of a stock in terms of how much the market is willing to pay for each dollar of earnings.
For example, the total number of shares that could be created and issued from NVIDIA's convertible instruments for the fiscal year that ended in 2017 was 23 million. If this number is added to its total shares outstanding, its diluted weighted average shares outstanding will be 541 million + 23 million = 564 million shares. The company's diluted EPS is, therefore, $1.67 billion /.564 million = $2.96.
Earnings per share can be distorted, both intentionally and unintentionally, by several factors. Analysts use variations of the basic EPS formula to avoid the most common ways that EPS may be inflated.
\text{EPS}=\frac{\text{Net Income }-\text{ Pref.Div. }\left(+or-\right)\text{ Extraordinary Items}}{\text{Weighted Average Common Shares}}
EPS=Weighted Average Common SharesNet Income − Pref.Div. (+or−) Extraordinary Items
In this example, that could increase the EPS because the 100 closed stores were perhaps operating at a loss. By evaluating EPS from continuing operations, an analyst is better able to compare prior performance to current performance
An important aspect of EPS that is often ignored is the capital that is required to generate the earnings (net income) in the calculation. Two companies could generate the same EPS, but one could do so with fewer net assets; that company would be more efficient at using its capital to generate income and, all other things being equal, would be a "better" company in terms of efficiency. A metric that can be used to identify more efficient companies is the return on equity (ROE).
Analysts will sometimes distinguish between basic and diluted EPS. Basic EPS consists of the company’s net income divided by its outstanding shares. It is the figure most commonly reported in the financial media and is also the simplest definition of EPS.
When looking at EPS to make an investment or trading decision, be aware of some possible drawbacks. For instance, a company can game its EPS by buying back stock, reducing the number of shares outstanding, and inflating the EPS number given the same level of earnings. Changes to accounting policy for reporting earnings can also change EPS. EPS also does not take into account the price of the share, so it has little to say about whether a company's stock is over or undervalued.
After collecting the necessary data, input the net income, preferred dividends, and number of common shares outstanding into three adjacent cells, say B3 through B5. In cell B6, input the formula "=B3-B4" to subtract preferred dividends from net income. In cell B7, input the formula "=B6/B5" to render the EPS ratio.
FINRA. "Six Financial Performance Metrics Every Investor Should Know."
FINRA. "Evaluating Stocks."
NVIDIA. "2017 NVIDIA Corporation Annual Report," Pages 25 and 27.
U.S. Securities and Exchange Commission. "Beginners Guide to Financial Statements."
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